Higgs found?
Aaron Bergman
<http://lephiggs.web.cern.ch/LEPHIGGS/talks/tully_talk.pdf>
<http://l3www.cern.ch/scan_program/2000/higgs.html>
<http://alephwww.cern.ch/ALPUB/seminar/lepc_sep00/lepc_0509.pdf>
<http://physicsweb.org/article/news/04/9/2> (find the misspelling)
<http://www.nytimes.com/2000/09/06/science/06PART.html>
My own editorial comment is that it would be very depressing if it was
just the SM Higgs that was found.
Aaron
--
Aaron Bergman
<http://www.princeton.edu/~abergman/>
Douglas A. Singleton
Aaron Bergman <aber...@Princeton.EDU> wrote:
>Some links:
>
><http://lephiggs.web.cern.ch/LEPHIGGS/talks/tully_talk.pdf>
><http://l3www.cern.ch/scan_program/2000/higgs.html>
><http://alephwww.cern.ch/ALPUB/seminar/lepc_sep00/lepc_0509.pdf>
><http://physicsweb.org/article/news/04/9/2> (find the misspelling)
><http://www.nytimes.com/2000/09/06/science/06PART.html>
>
>My own editorial comment is that it would be very depressing if it was
>just the SM Higgs that was found.
If this is already the Higgs particle that LEP is seeing
then it should be fairly light, right ? Although the
plain, minimal SM seems to work fine with either a lighter
or heavier Higgs, doesn't the minimal SUSY version of
the SM favor (require ?) a light Higgs (for example I
think I remember reading somewhere that at tree level the
lightest Higgs in the minimal SUSY SM was supposed to be
lighter than the Z; with radiative corrections it was
less than 125 GeV for m_top =175 GeV and the stop<1 TeV).
So it seems if you're a believer in SUSY/string theory
finding a lighter Higgs could appear as marginally good
news.
Doug
Kwok Man Hui
> Some links:
>
> <http://lephiggs.web.cern.ch/LEPHIGGS/talks/tully_talk.pdf>
> <http://l3www.cern.ch/scan_program/2000/higgs.html>
> <http://alephwww.cern.ch/ALPUB/seminar/lepc_sep00/lepc_0509.pdf>
> <http://physicsweb.org/article/news/04/9/2> (find the misspelling)
> <http://www.nytimes.com/2000/09/06/science/06PART.html>
>
> My own editorial comment is that it would be very depressing if it was
> just the SM Higgs that was found.
Hi, Aaron,
Afraid of lacking evidence support for string theory statements beyond SM
is your origin of your depression?
In my opinion, just can find the SM Higgs is very good enough. Based on
what John Baez recently posted about the ad hoc-ness of breaking SUSY in
superstring theory and the background independence problems plagued with
string theory, we really should be skeptical to the ideas proposed by
string theorists until they have a complete sound theory from
relativists point of view. This doesn't mean that their theory is
incorrect, but instead we should be open to new and compatible ideas.
Besides, I'm one of the adherent of "dynamical symmetry breaking" , if
such a term is well-defined yet, for a true unified theory which
encompasses quantum gravity. I expect that this sort of mechanism must
appear in a kind of unified with gravity gauge field theory which can
explain why our current physical constants are constants and can sovle
the mass gap problem, i.e., how particle mass naturally appears as bound
states for some gauge field theories. It can tell how to pick up a
unique set of physical laws for our universe and those entropy-like
asymmetries can have an essential role in our physical laws. I've this
anticipation because I've attended seminars about mirror symmetry,
mathematically speaking their theory has emergence of some combinatorial
and discrete structure which plays an ANALOGOUS role as picking up a set
of consistent physical laws. In addition, I've got "dynamical"
combinatorial and discrete ideas from John. The mixture of those
commensurable ideas lead me to such an anticipation. If superstring
theory can be incorporated with these sorts of "dynamical" ideas, that
will only makes it better indeed.
Regards,
Charles K. M. Hui
Jeff Berryhill
Aaron Bergman <aber...@Princeton.EDU> writes:
> Some links:
>
> <http://lephiggs.web.cern.ch/LEPHIGGS/talks/tully_talk.pdf>
> <http://l3www.cern.ch/scan_program/2000/higgs.html>
> <http://alephwww.cern.ch/ALPUB/seminar/lepc_sep00/lepc_0509.pdf>
> <http://physicsweb.org/article/news/04/9/2> (find the misspelling)
> <http://www.nytimes.com/2000/09/06/science/06PART.html>
>
> My own editorial comment is that it would be very depressing
> if it was just the SM Higgs that was found.
>
> Aaron
The actual results, if anything, are a rumor of a hint of a glimpse of
a possible Higgs boson. They're looking for a signal near the kinematic
limit of the accelerator, so only a handful of events
are Higgs candidates. Only one of the four LEP experiments
(ALEPH) sees anything significant, and among the ALEPH data only
one of the decay channels has an excess (HZ, H to bbar, Z to 2 jets),
leading to a total excess of 2.6 sigma when combined with all LEP data.
Statistical fluctuations of this magnitude are observed in HEP
experiments quite often, due to the large numbers of cross sections
and distributions analyzed by experimenters.
Every year at least one of the LEP experiments has reported
a similar excess in some measurement somewhere, and every following
year the excess goes away upon accumulation of more data.
Last winter there was a Higgs discovery rumor running rampant at
a lower mass than is claimed here; it turned out to be a <2 sigma
excess that went away eventually. Without a lot more data,
skepticism is very much in order.
In fact, because 3-4 sigma false positives have occurred so frequently
in the past, the commonly agreed-upon industry standard for
"official discovery" is a 5 sigma excess, which LEP is a long ways from
demonstrating. It is unclear whether the proposed extension of LEP
running can accomplish this for a SM Higgs of 115 GeV, so even if the signal
is for real it will be left to the Tevatron or the LHC to conclusively
measure it.
Aaron Bergman
wrote:
> Hi, Aaron,
>
> Afraid of lacking evidence support for string theory statements beyond SM
> is your origin of your depression?
Nah. The Higgs is an ugly kludge. It has no reason to be there. It would
also be quite neat if supersymmetry wasn't found and something entirely
new was. I'm not emotionally attached to string theory.
Mark William Hopkins
>Nah. The Higgs is an ugly kludge. It has no reason to be there.
One could fall under that impression if the concept is presented wrong.
The way it is usually presented is wrong: it shows the historical
development of the idea (in other words, the choreography of the stumbling
motions that led people to fall into the idea), but not how it derives
naturally and logically from basic requirements.
The basic problem is that the term
psi' m^2 psi
(where I'm using psi' as the adjoint multiplied by gamma0: psi+ gamma0),
creates all sorts of havoc in the basic theory because it directly
couples left-handed and right-handed components of the field:
psi' m^2 psi = L' m^2 R + R' m^2 L.
This ruins the symmetry of the theory, and the symmetry is a necessary
condition to give finite consistent results.
As such, this strongly suggests that the coupling is (in reality) NOT
direct and that m^2 is, itself, actually a field! The "Mass Field".
The term m^2, itself, is then the 'frozen' value of the field, and you
then have to explain why the field remains frozen around this value.
More precisely, the matter field psi has a coupling to the M-field
of strength V (proportional to the mass m), and the field itself would
be represented as H frozen around the value H_0. So the interaction
term looks like this:
V^2 (L' H^2 R + R' H^2 L)
So you have to explain why H is 'frozen' around the value H_0.
The most natural way to do this is to FORCE the setting by assuming that
it is the one energetically favored. So then there is an extra term
corresponding to the potential energy:
a (H^2 - H_0^2)^2
whose minimum occurs where H^2 = H_0^2.
This is the Higgs field with a Yukawa coupling to the fermion fields.
So the Higgs field is nothing more and nothing less than the
representation of a Universal Inertia Field, which is responsible for
giving all matter the property of inertia and is the quantum field
[Moderator's note: Hopkins' post ends mysteriously at this point.
Yet another victim of those who would keep us from learning the real
truth about nature? - jb]
Aaron Bergman
William Hopkins) wrote:
> In article <abergman-986548...@cnn.princeton.edu> Aaron
> Bergman <aber...@Princeton.EDU> writes:
>
> >Nah. The Higgs is an ugly kludge. It has no reason to be there.
>
> One could fall under that impression if the concept is presented wrong.
[snip what is apparently a presentation of the necessity of the Higgs in
obtaining SU(2) invariant mass terms in the standard model]
You need something that's Higgs-like, but it doesn't have to be the
Higgs. I think technicolor is a much prettier idea, but unfortunately,
it's apparently ruled out by precision electroweak measurements.
squ...@my-deja.com
Aaron Bergman <aber...@Princeton.EDU> wrote:
> Nah. The Higgs is an ugly kludge. It has no reason to be there.
Actually Connes managed to interpret the Higgs as a gauge boson using
an extension of usual space-time to new, non-commutative dimensions. I
also thought the Higgs is just an artificially inserted scalar matter
(while all the other non-gauge-particles are fermionic) until I saw
this. I think it sheds new light on the matter - especially anticpating
a GUT on extended, non-commutative space-time.
Best regards, squark.
Sent via Deja.com http://www.deja.com/
Before you buy.
Gordon D. Pusch
> In article <abergman-986548...@cnn.princeton.edu> Aaron
> Bergman <aber...@Princeton.EDU> writes:
>> Nah. The Higgs is an ugly kludge. It has no reason to be there.
> One could fall under that impression if the concept is presented wrong.
<interesting argument not relevent to my point elided -- /gdp>
> So the Higgs field is nothing more and nothing less than the
> representation of a Universal Inertia Field, which is responsible for
> giving all matter the property of inertia and is the quantum field
One possible problem with this claim is that, about a decade or so ago,
Hawking wrote a paper that claimed that *elementary* scalar particles
(i.e., non-composite scalars) could never be observed (or at least, could
never appear as asymptotic plane-wave states in a quantized spacetime),
because interactions with gravitational instantons would turn them into
Planck-mass tachyons.
The gist of the argument was that an elementary scalar particle could
``feel'' a class of gravitational instantons that a spin-nonzero particle
could not, because spin-nonzero particles were prevented from reaching
the cores of these instantons by a sort of ``angular momentum barrier.''
However, an elementary scalar _could_ penetrate all the way to the cores
of these instantons, and interact very strongly with them, with disastrous
consequences --- they would thereby acquire an imaginary effective rest-mass
on the order of the Planck mass, i.e., become a tachyon. Hawking therefore
argued that the Higgs mechanism could _not_ be a fundamental feature of
particle physics, but could only be a temporary stopgap measure.
Does anyone know what (if anything) came of this work, and whether it is
currently considered valid ???
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Aaron Bergman
> In article <abergman-986548...@cnn.princeton.edu>,
> Aaron Bergman <aber...@Princeton.EDU> wrote:
> > Nah. The Higgs is an ugly kludge. It has no reason to be there.
> Actually Connes managed to interpret the Higgs as a gauge boson using
> an extension of usual space-time to new, non-commutative dimensions.
IIRC, it's actually just a noncommutative Z_2. Unfortunately, the model
has trouble with mass relations or something like that, I think. It's
too bad, really, especially as the model actually gives almost exactly
the standard model gauge group.
Nathan Urban
> One possible problem with this claim is that, about a decade or so ago,
> Hawking wrote a paper that claimed that *elementary* scalar particles
> (i.e., non-composite scalars) could never be observed (or at least, could
> never appear as asymptotic plane-wave states in a quantized spacetime),
> because interactions with gravitational instantons would turn them into
> Planck-mass tachyons.
Are you talking about his "Virtual Black Holes" paper of half a decade
ago (hep-th/9510029)?
Aaron Bergman
ba...@galaxy.ucr.edu (John Baez) wrote:
>Aaron Bergman wrote:
> >Unfortunately, the model has trouble with mass relations or something
> >like that, I think.
> Really? There are a bunch of versions of this model, which give
> different relations between masses of particles. The first ones
> were obviously "wrong", and only meant to illustrate the general
> idea; he has been working to improve them, and I didn't think the
> newest ones were experimentally ruled out. They are, however,
> becoming more and more complicated.
I read it in hep-th/9701078. I haven't actually seen it myself. It also
talks about a "disturbing Fermion doubling".
> >It's too bad, really, especially as the model actually gives almost
> >exactly the standard model gauge group.
> I'm not sure what you mean here.
You're right. Looking back at the paper, I misread it -- it went from
the two point model to the Standard Model so fast that I missed the
transition.
John Baez
Aaron Bergman <aber...@Princeton.EDU> wrote:
>In article <8pl406$4q3$1...@nnrp1.deja.com>, squ...@my-deja.com wrote:
>> Actually Connes managed to interpret the Higgs as a gauge boson using
>> an extension of usual space-time to new, non-commutative dimensions.
>IIRC, it's actually just a noncommutative Z_2.
A noncommutative Z_2 - now *that's* something mathematicians would
like to hear about! :-)
Seriously, if all you want is the Higgs, Connes doesn't need full-fledged
noncommutative geometry: he just needs a "two-sheeted" spacetime of the
form R^4 x Z_2. I.e.: two copies of ordinary Minkowski spacetime, about
10^{-16} centimeters apart from other. The algebra of functions on this
spacetime is still commutative! It's just his generalized definition of
"connection" that allows the two sheets to talk to each other, with the
Higgs as the part of the connection that lets you compare the value of a
field on one sheet to its value on the other sheet.
He got the Higgs this way in his very simplest model, "Model I" of his
"Essay on Physics and Non-Commutative Geometry". When you want the
whole standard model, that's when you need some noncommutative geometry:
you have to take the algebra of functions on R^4 and tensor it with a
finite-dimensional noncommutative algebra.
>Unfortunately, the model has trouble with mass relations or something
>like that, I think.
Really? There are a bunch of versions of this model, which give different
relations between masses of particles. The first ones were obviously
"wrong", and only meant to illustrate the general idea; he has been working
to improve them, and I didn't think the newest ones were experimentally
ruled out. They are, however, becoming more and more complicated.
>It's too bad, really, especially as the model actually gives almost exactly
>the standard model gauge group.
I'm not sure what you mean here. The simplest models (the 3 presented
in his old "Essay on Physics and Noncommutative Geometry") have gauge
group either U(1) x U(2) or U(1) x SU(2), and it's exciting how this
pops out so naturally. The more sophisticated models include the SU(3)
for the strong force, but the problem (to my mind) is that this is put in
more or less "by hand", namely by cleverly choosing the finite-dimensional
algebra mentioned above. In other words, it seems to me that at this
stage, his model no longer puts out more than he puts in.
A nice description of one of Connes' more recent particle physics models
can be found in Daniel Kastler's essay "Noncommutative Geometry and
Basic Physics", which appears in the book _Geometry and Quantum Phyics_.
Here he tensors the algebra of functions on R^4 by the noncommutative
algebra
C + H + C[3]
where C is the complex numbers, H is the quaternions, and C[3] is the
3x3 complex matrices. These three summands correspond to the three factors
in the Standard Model gauge group U(1) x SU(2) x SU(3). The stuff about
Z_2 is gone in this model. Moreover, in this model one needs to input a
bunch of numbers to describe the quark masses and weak mixing of the
quarks - just as in the Standard Model.
Kastler also mentions an interesting attempt to simplify things by
taking the noncommutative algebra to be the semisimple quotient of
U_q(sl(2)) where q is a third root of unity. This algebra turns out
to be
C + C[2] + C[3]
Whether this is profound or a coincidence remains to be seen.
Gordon D. Pusch
I don't *think* so, although it appears to contain a similar claim that
elementary scalars can't propagate on a ``spacetime foam'' background
(pp. 17--19), although the mechanism seems to be different than what
I recall (generation of a huge effective \phi^4 coupling, rather than
a huge tachyonic effective mass)...
However, I'm _fairly_ sure the paper I'm thinking of appeared in
Nucl. Phys. B in the mid to late 1980's, not Phys. Rev D. in 1996
(although if that were the case, I would have expected it to be cited
in the paper you mention, so probably my wetware is glitching... :-(
At any rate, how reliable is the sort of semiclassical approximation to
``spacetime foam'' Hawking is using here currently considered to be?
Has anyone else made claims that elementary scalars can't propagate
on a spacetime foam background ???
Mark William Hopkins
William Hopkins) writes:
>So the Higgs field is nothing more and nothing less than the
>representation of a Universal Inertia Field, which is responsible for
>giving all matter the property of inertia and is the quantum field
>
>[Moderator's note: Hopkins' post ends mysteriously at this point.
>Yet another victim of those who would keep us from learning the real
>truth about nature? - jb]
... um ... that dominates the matter-energy content of the Universe?
F.S. Guzm\'am, L.A. Ure\~na-L\'opez
"Scalar field as dark matter in spiral galaxies"
Classical and Quantum Gravity, 17, Jan 2000 pp L9-16
T. Matos, F.S. Guzm\'an, L.A. Ure\~na-L\'opez
"Scalar field as dark matter in the universe"
Classical and Quantum Gravity, 17 (7), Apr 2000, pp 1707-1712
both provide good arguments (including results of numerical simulations)
to show that the Dark Energy is a universal scalar field -- namely the
one which appears in the 4-dimension effective field theory reduction
of the 5-dimensional vacuum to (Gravity + Electromagnetism + Scalar
Field).
This could very well be the Higgs field, itself.
There is also a recent article in either the Foundations of Physics or
the International Journal of Physics which provides an equivalent
representation of the Higgs field as a conformal scale breaking field
very similar both to the scalar field in the Brans-Dicke formalism, as
well as the scalar field mentioned above.
Cl.Massé
> So the Higgs field is nothing more and nothing less than the
> representation of a Universal Inertia Field, which is
> responsible for giving all matter the property of inertia and is
> the quantum field
It is really amazing the heap of hidden assumptions you make.
Only some examples : why should psi be a field? Why should the
gauge symmetry be an exact symmetry (before being broken)? Why
should an electron be pointlike? Why should even be a term
psi' m^2 psi?..
It was formerly certainly not less logically proven that Nature
loath vacuum.
A last question : What gives its property of inertia to a photon?
--
~~~~ %20cl...@free.fr%20 LPF
God says : "Do what I say. Do not what I do."
Jim Graber
what are the implications for supersymmetry versus the
nonsupersymmetric standard model? (My understanding is
that a light Higgs favors supersymmetry. How strong is
this implication?)
Second, if we assume the 115 GEV Higgs exists -and- is a
part of or related to a supersymmetric constellation of
sparticles, what is the implication for things like the
mass of the lightest supersymmetric particle, and the
neutralino, etc.?
Can some particle expert or at least someone who can accurately
decode what the particle experts are saying give us
a reading on this? (Crosspost to sci.physics.particle added.)
Thanks Jim Graber
In article <abergman-DD88DE...@cnn.princeton.edu>,
Hendrik van Hees
> Can some particle expert or at least someone who can accurately
> decode what the particle experts are saying give us
> a reading on this? (Crosspost to sci.physics.particle added.)
I do not know which level of information you are looking for, but as a
textbook for phycisists I'd recommend to read
As an introduction:
Peskin/Schroeder An Introduction to Quantum field Theory, Addison Wesley
S. Weinberg, The Quantum Theory of Fields, (Vol. I-III), Cambridge
University Press.
Vol. III is an introduction to supersymmetric QFT.
--
Hendrik van Hees Phone: ++49 6159 71-2751
c/o GSI-Darmstadt SB3 3.183 Fax: ++49 6159 71-2990
Planckstr. 1 mailto:h.va...@gsi.de
D-64291 Darmstadt http://theory.gsi.de/~vanhees/index.html
[Moderator's note: Graber was asking what implications a ~115 GeV Higgs
boson would have for supersymmetric extensions of the Standard Model,
e.g. the mass of the lightest superparticle. I doubt reading these books
is an efficient way for him to get that information. Someone should just
tell him. - jb]
Peter
John Baez stated supersymmetry theories have yet to recover the standard
model in a convincing way.
What about the Z* boson which decays into the Higgs & Z?
At 206.6GeV this would be very interesting for my theory.
Peter
Jim Graber wrote:
> Assuming that a 115 GEV Higgs has or soon will be found,
> what are the implications for supersymmetry versus the
> nonsupersymmetric standard model? (My understanding is
> that a light Higgs favors supersymmetry. How strong is
> this implication?)
>
> Second, if we assume the 115 GEV Higgs exists -and- is a
> part of or related to a supersymmetric constellation of
> sparticles, what is the implication for things like the
> mass of the lightest supersymmetric particle, and the
> neutralino, etc.?
>
John Baez
Peter <peter.h...@ntlworld.com> wrote:
>Jim Graber wrote:
>> Assuming that a 115 GEV Higgs has or soon will be found,
>> what are the implications for supersymmetry versus the
>> nonsupersymmetric standard model?
>Not a lot as I gather from postings in sci.physics.research.
>John Baez stated supersymmetry theories have yet to recover the standard
>model in a convincing way.
I was referring to the fact that to break supersymmetry in theories such
as the minimal supersymmetric extension of the Standard Model, about 50
extra terms are added by hand to the Lagrangian of the theory -
basically, all possible terms which break supersymmetry without
destroying renormalizability. This is ad hoc, and it introduces a large
number of undetermined parameters into the theory.
This has not stopped people from studying the resulting theory and
deriving predictions from it. A lot of work has been done on this.
For more information, try this webpage:
http://fnth37.fnal.gov/higgs/higgs.html
This contains the June 25th 2000 version of the "Higgs Working Group
Report", together with links to Postscript files of lots of papers and
transparencies of talks. The summary says:
"This working group is studying Higgs searches at Run-II of the
Tevatron. The Higgs discovery potential for an upgraded higher
luminosity Tevatron (with an total integraded luminosity from 10 to 30
fb-1) is also under investigation. Our work focuses on the Standard
Model Higgs boson, the Higgs bosons of the minimal supersymmetric
extension of the Standard Model (MSSM), and possible extensions
thereof. The MSSM Higgs sector is of particular interest to the Tevatron
search, since the mass of the lightest Higgs boson is predicted to lie
below 130 GeV. In the future, we also plan to examine the phenomenology
of the next-to-minimal supersymmetric (NMSSM) Higgs sector in which an
additional Higgs singlet is added and exotic weakly-coupled non-minimal
Higgs sectors with or without supersymmetry."
Check out the graph and the charts!
I'm not an expert on this stuff, so I'm still hoping someone who is
will answer Jim Graber's questions.
Dale Woodside
>
> Assuming that a 115 GEV Higgs has or soon will be found,
> what are the implications for supersymmetry versus the
> that a light Higgs favors supersymmetry.
I was under the impression that a light Higgs favors the
SM (standard model) and not the supersymmetric model.
> How strong is
> this implication?)
>
Dale Woodside
Mark William Hopkins
>Mark William Hopkins wrote :
>> So the Higgs field is nothing more and nothing less than the
>It is really amazing the heap of hidden assumptions you make.
Oh?
>Only some examples : why should psi be a field?
Because we're discussing Quantum Field Theory? I mean, if you want to
consider alternative theories (like Bohm's interpretation of Quantum
Mechanics, or a pre-quantized theory like classical electromagnetism
augmented with a stochastic zero-point field) that's fine. But none
of these have, as of yet, met the same standard of explanatory power
of Quantum Field Theory.
> Why should the gauge symmetry be an exact symmetry (before being broken)?
That was explained in the description, not assumed. Self-consistency
and finiteness would be ruined without it.
>Why should an electron be pointlike?
That wasn't assumed or even mentioned. But it is true that the electron
is pointlike within current powers of resolution.
>Why should even be a term psi' m^2 psi?
Actually psi' m psi is what it should have said.
There CAN'T be a psi' m psi term, since that would violate gauge
symmetry. But that's what's already present in QED (for instance).
>A last question : What gives its property of inertia to a photon?
A photon has no rest mass. Inertia in the sense of following a
geodesic is already explained perfectly well both in General Relativity
and Quantum Field Theory (except in the latter, the geodesics are on a
flat spacetime).
As far as rest mass goes, the simple explanation provided in the case of
(other) bosons would have to be modified somewhat. That's where you have
terms proportional to m^2: the (m^2 A) terms. Since it's proportional to the
2nd power, that means the "Inertia Field" has to enter somehow in quadratic
form. Since these are gauge fields, gauge symmetry forces the relevant
terms to be part of something that involves covariant derivatives.
Therefore,
m^2 A
has to be the "frozen" value of a term that looks like
(D M)+ (D M)
at the lowest orders of energy.
All quantum fields in QFT have 0 rest mass. So that raises an
interesting question:
What if you took the free field to be massless and
introduced the (psi' m psi) term and (m^2 A) term
as perturbations?
Hendrik van Hees
> What about the Z* boson which decays into the Higgs & Z?
> At 206.6GeV this would be very interesting for my theory.
I fear you will have to wait until LHC. Now they are able to look at
their peak around 115 GeV and Maiani gave them yesterday one more month
beam time at LEP, so let's wait what happens with the now claimed Higgs
found.
Igor Ivanov
>
> Assuming that a 115 GEV Higgs has or soon will be found,
> what are the implications for supersymmetry versus the
> nonsupersymmetric standard model? (My understanding is
> this implication?)
OK, first -- a general remark on Higgs sectors of various theories.
When we discuss the Higgs mechanism within the Standard Model (SM),
we implicitly assume that there is only one Higgs doublet, which,
after symmetry is broken, gives rise to the only physical Higgs boson.
This is what people call the SM Higgs boson.
Well, nothing within the SM itself or within the Higgs mechanism
rules out more complicated variants of the Higgs sectors.
The most popular is two Higgs doublet model (2HDM), but people also
consider Higgs sectors containing additional Higgs singlets etc.
In principle, any such theory can be called the Standard Model,
because the spectrum of other physical particles is the same as
in the original SM.
So, let us focus on 2HDM. After symmetry breaking,
we are left with 4 different Higgs particles:
* two neutral and CP-even bosons: h (the lighter) and H (the heavier);
* one neutral and CP-odd boson: A
* one charged boson: H+ (with its antiparticle H-).
The principal point is that the 2HDM model allows for
ANY masses of all these bosons. This is simply because
the CP conserving 2HDM has 5 free parameters that parameterize
the Higgs potential (7 parameters for the CP-violating case).
Thus, for any arbitrary choice of the masses of all
these bosons, one can construct the corresponding 2HDM that would
nicely describe this spectrum.
In particular, in the decoupling regime -- when the lightest Higgs boson
h
is sufficiently light, while all other Higgs bosons are much heavier --
the properties of h resemble very closely the propetries of
the SM Higgs boson. Therefore, simply observing the Higgs boson
at Mh=115 GeV says NOTHING about the true structure of the Higgs sector.
Period.
It is only after one starts investigating the detailed propetries
of the observed boson (mostly, the coupling constants to various
particles),
that one can draw any conclusions about this.
Now -- about the supersymmetry. There are several supersymmetric
theories,
the most 'economic' of them being the minimal supersymmetric standard
model
(MSSM). In MSSM one has to introduce precisely 2 Higgs doublets,
and it turns out that the Higgs potential has fewer degrees of freedom
than in a general 2HDM.
In particular, the masses of the Higgs bosons become interconnected
in a very particular way. All this tempts one to conclude that
the MSSM has a great deal of predictive power.
Unfortunately, MSSM contains also a zoo of new particles -- the
superpartners
of known particles. This part of the theory is absolutely unknown
and contains a lot of free parameters as well: the masses of sparticles,
their mixing, their couplings etc. These parameters can significantly
affect the masses of the Higgs bosons via radiative corrections.
In fact, everythings becomes so complicated even at the 1 loop level,
that no one is even trying to track down the effect of every single
parameter on the (lightest) Higgs boson mass.
Nevertheless, one still can predict something within the MSSM.
And some predictions can be based on the sole observation of the
lightest
Higgs boson with mass 115 GeV.
> Second, if we assume the 115 GEV Higgs exists -and- is a
> part of or related to a supersymmetric constellation of
> sparticles, what is the implication for things like the
> mass of the lightest supersymmetric particle, and the
> neutralino, etc.?
First, this value is not so far from the upper boundary
that can be in principle achieved for Mh within MSSM (around 125 GeV).
It turns out then that Mh=115 GeV favors the large tan(beta) regime.
I.e. MSSM with tan(beta)=10 can have Mh=115 GeV; MSSM with tan(beta)=5
also can.
But tan(beta)=2 does not work!
Then, the effect of light enough squarks (superpartners of quarks)
is to push Mh down. For example, M_squark = 200 GeV or lower
is definitely forbidden. With such light squarks you do not get
Mh=115 GeV even for the optimal choice of other parameters
(within MSSM, that is). M_squark = 500 GeV or higher is already quite
OK.
That's almost everything we can say by now.
So, conclusions:
-- the observed(?) Higgs boson can be a member of almost any Higgs
sector,
including that of 2HDM and MSSM. I do not understand the claims
that the observed Higgs boson is incompatible with predictions
of supersymmetric theories.
-- some conclusions can be drawn from the mere
fact of existence of Mh=115 GeV Higgs boson; but there are very few of
them.
-- if no other Higgs-like particle is observed, then we have to
scrupulously investigate the properties of the observed Higgs
in order to distunguish among various theories (SM, 2HDM, MSSM, other).
I hope, that helps clarifying the issue.
--
Igor Ivanov
John Baez
Aaron Bergman <aber...@Princeton.EDU> wrote:
>In article <200009130552...@math-cl-n03.ucr.edu>,
>ba...@galaxy.ucr.edu (John Baez) wrote:
>>Aaron Bergman wrote:
>> >Unfortunately, the model has trouble with mass relations or something
>> >like that, I think.
>> Really? There are a bunch of versions of this model, which give
>> different relations between masses of particles.
>I read it in hep-th/9701078. I haven't actually seen it myself. It also
>talks about a "disturbing Fermion doubling".
Connes' original "Essay on physics and non-commutative geometry" was
published in 1990. This contained 3 different models. Then came two
papers by Connes and Lott, "Particle physics and noncommutative geometry"
and "The metric aspect of noncommutative geometry", in 1990 and 1991.
In his 1995 paper "Noncommutative geometry and reality", Connes made some
major changes in his theory. He made a bunch more changes and included
gravity in his 1996 paper "Gravity coupled with matter and the foundation
of noncommutative geometry". The last big step that I know about was his
paper with Chamseddine, "The spectral action principle". I don't know
which if any models has a "disturbing fermion doubling.
In 1997, Daniel Kastler and others used this latest version of Connes'
theory to predict the Higgs mass. They give a prediction of 182 +/- 17
GeV.
>>>It's too bad, really, especially as the model actually gives almost
>>>exactly the standard model gauge group.
>> I'm not sure what you mean here.
>You're right. Looking back at the paper, I misread it -- it went from
>the two point model to the Standard Model so fast that I missed the
>transition.
You gotta keep an eye on these grand unification shell games. Look
away for a minute and they'll be acting like they "derived" the
Standard Model gauge group and so on - when in fact they slipped
this stuff in by hand!
Aaron Chou
> Assuming that a 115 GEV Higgs has or soon will be found,
> what are the implications for supersymmetry versus the
> nonsupersymmetric standard model? (My understanding is
> that a light Higgs favors supersymmetry. How strong is
> this implication?)
If baryogenesis occurs at the electroweak scale through the
sphaeleron mechanism, then the standard model predicts a low
Higgs mass < ~40 GeV. This is already ruled out by current
limits. Electroweak baryogenesis through the MSSM predicts
a higher mass < ~110 GeV. See Carlos Wagner's talks/papers
for details.
Caveats: baryogenesis could be GUT mediated or occur through
some other mechanism. Also, the MSSM is just a toy model with
a lot of assumptions made for simplicity.
Jeff Berryhill
Igor Ivanov <i.iv...@fz-juelich.de> writes:
> When we discuss the Higgs mechanism within the Standard Model (SM),
> we implicitly assume that there is only one Higgs doublet, which,
> after symmetry is broken, gives rise to the only physical Higgs boson.
> This is what people call the SM Higgs boson.
>
> Well, nothing within the SM itself or within the Higgs mechanism
> rules out more complicated variants of the Higgs sectors.
> The most popular is two Higgs doublet model (2HDM), but people also
> consider Higgs sectors containing additional Higgs singlets etc.
> In principle, any such theory can be called the Standard Model,
> because the spectrum of other physical particles is the same as
> in the original SM.
It should be noted, and of course you probably know this,
that the experimental result of the "rho parameter"
$\rho = M^2_W/(M^2_Z \cos^2 \theta_W)$
which is measured to be very close to 1.0, *very strongly constrains*
the types of SU(2) representations allowed for the Higgs sector.
The theoretical value for the rho parameter depends strongly on the
weak isospin of the SU(2) representation of the Higgs, and is
identically 1 at tree level for *isodoublets*, so doublets seemingly
have a very privileged status amongst possible Higgs theories.
Introducing anything other than doublets (SU(2) triplets and singlets)
requires severe theoretical contortions in order to make the
rho parameter come out to be unity (contributions to rho of the
various reps cancelling just so). That said, there is no limit
on the *number* of doublets one can introduce, which is why multi-Higgs
doublet models are so freely discussed.
> So, conclusions:
>
> -- the observed(?) Higgs boson can be a member of almost any Higgs sector,
> including that of 2HDM and MSSM. I do not understand the claims
> that the observed Higgs boson is incompatible with predictions
> of supersymmetric theories.
>
> -- some conclusions can be drawn from the mere fact of existence
> of Mh=115 GeV Higgs boson; but there are very few of them.
>
> -- if no other Higgs-like particle is observed, then we have to
> scrupulously investigate the properties of the observed Higgs
> in order to distunguish among various theories (SM, 2HDM, MSSM, other).
>
> I hope, that helps clarifying the issue.
That about sums it up. Experimental information about the Higgs sector
is notoriously difficult to extract. That's why it takes gigabucks
to do the job.
J. J. Lodder
> Not a lot as I gather from postings in sci.physics.research.
> John Baez stated supersymmetry theories have yet to recover the standard
> model in a convincing way.
>
> What about the Z* boson which decays into the Higgs & Z?
> At 206.6GeV this would be very interesting for my theory.
And this week's latest news:
It has been decided at CERN to extend LEP's life by -one- month,
postponing closedown from end sept to nov 2,
in order to verify or disprove the claims for a low mass Higgs
being seen at the very limit of LEP's energy range.
"The decision to extend LEP's experimental programme sets the scene for
a nail-biting finish to the accelerator's already illustrious career."
See www.cern.ch for the press release,
Jan
Cl.Massé
>>> So the Higgs field is nothing more and nothing less than the
>>> representation of a Universal Inertia Field.
> >It is really amazing the heap of hidden assumptions you make.
> >Only some examples: why should psi be a field?
> Because we're discussing Quantum Field Theory? I mean, if you want to
> consider alternative theories (like Bohm's interpretation of
> Quantum Mechanics, or a pre-quantized theory like classical electromagnetism
> augmented with a stochastic zero-point field) that's fine. But none
> of these have, as of yet, met the same standard of explanatory
> power of Quantum Field Theory.
Still another heap of hidden assumptions I give up detailing.
Just a question, why second quantization and not third, forth, ...
> >Why should an electron be pointlike?
> That wasn't assumed or even mentioned.
That's why I called it *hidden* assumption.
> But it is true that the electron
> is pointlike within current powers of resolution.
But it could not be *under* current powers of resolution, and the
theory would have to change dramatically. BTW, which sort of
punctuality do we measure? One is already lost with the first
quantization.
> >Why should even be a term psi' m psi?
> There CAN'T be a psi' m psi term, since that would violate gauge
> symmetry. But that's what's already present in QED (for
> instance).
Ok, a psi' whatever psi term. And if it were only a place holder,
a cupboard where we put all the skeletons? The Dirac equation
permits it, but that doesn't imply that it exists in a form or
another.
> >A last question : What gives its property of inertia to a
> >photon?
> A photon has no rest mass.
Then take a system of non coherent photons which has a rest mass.
Inertia is a property of *energy*.
> All quantum fields in QFT have 0 rest mass. So that raises an
> interesting question:
>
> What if you took the free field to be massless and
> introduced the (psi' m psi) term and (m^2 A) term
> as perturbations?
I have another idea. What if a mass term arose through
self-interaction of massless fields? As the self-interaction is
already treated, a quantum of matter no more interact with itself,
which set the quantum of mass, i.e. the lepton mass. That is
consistent with the correlation between the mass of a particle and
the forces it is sensible to.
A very simple, and not new, idea indeed, but so difficult to
implement. The Higgs boson is a solution of facility, but Nature
doesn't let buy itself.
John Baez
Igor Ivanov <i.iv...@fz-juelich.de> wrote:
>First, this value is not so far from the upper boundary
>that can be in principle achieved for Mh within MSSM (around 125 GeV).
>It turns out then that Mh=115 GeV favors the large tan(beta) regime.
>I.e. MSSM with tan(beta)=10 can have Mh=115 GeV; MSSM with tan(beta)=5
>also can. But tan(beta)=2 does not work!
Thanks for your very informative post! I enjoyed it a lot. It's
nice to hear exactly what we can and cannot conclude from at 115 GeV
Higgs.
It's just the above passage that I found difficult to follow.
What's tan(beta)? I don't think you explained that terminology.
Mark William Hopkins
seS...@SPAMfree.frSPAM> writes:
>I have another idea. What if a mass term arose through
>self-interaction of massless fields?
Then in the lowest order of energy it will look like the Higgs field,
*independent* of its origin. That's the real point of calling the
Higgs field necessary.
All the Standard Model with the Higgs mechanism does is take in the
lowest common denominator of what HAS to be there. At the same time
it doesn't say of what ALL has to be there.
I think the actual mechanism is much simpler: it's nothing more than
the effects of the g_55 component of a 5-dimensional vacuum metric
being seen in terms of an effective field theory representation in
4 dimensions.
Igor Ivanov
>
> Thanks for your very informative post! I enjoyed it a lot. It's
> nice to hear exactly what we can and cannot conclude from at 115 GeV
> Higgs.
Thanks for the encouraging words. Not everyone can boast
of such a comment from John Baez! :)
> It's just the above passage that I found difficult to follow.
> What's tan(beta)? I don't think you explained that terminology.
tan(beta) is a key parameter of a 2HDM (and consequently, of MSSM).
When you introduce two Higgs doublets phi_1 and phi_2, and write
down the Higgs potential, then you find that the minimum occurs at some
( 0 ) ( 0 )
phi_1 = ( v_1 ) phi_2 = ( v_2 )
So, we get two vacuum expectation values v_1 and v_2.
(If we don't want an explicitly CP-violating theory, there should not
be any relative phase between v_1 and v_2.)
These two parameters are not independent, since they determine the
mass of the gauge bosons in an unambigous way, like:
m_W^2 = g^2*(v_1^2 + v_2^2)/2
The conclusion is that we are free to choose only their ratio v2/v1.
This is precisely the parameter called tan(beta):
tan(beta) = v2/v1
Such a presentation of this ratio is convenient, since the angle beta
turns out to be the mixing angle between the charged (the upper)
components
of the two doublets. For example, the physical charged Higgs boson H+ is
H+ = -sin(beta)*phi_1^{+} + cos(beta)*phi_2^{+}
and so on.
Now -- why tan(beta) is important for phenomenology.
It is important because it enters the expressions for coupling constants
of the Higgs bosons with matter. Since the mass of the lightest Higgs
boson
is significantly shifted by radiative corrections, this shift
will certainly feel the value of tan(beta). For example, at
tan(beta) = 1.5, the upper bound on Mh is about 100-105 GeV (in MSSM),
while for large tan(beta) it can be pushed up to 125-130 GeV.
--
Igor Ivanov
John Baez
Mark William Hopkins <whop...@alpha2.csd.uwm.edu> wrote:
>All the Standard Model with the Higgs mechanism does is take in the
>lowest common denominator of what HAS to be there. At the same time
>it doesn't say of what ALL has to be there.
>
>I think the actual mechanism is much simpler: it's nothing more than
>the effects of the g_55 component of a 5-dimensional vacuum metric
>being seen in terms of an effective field theory representation in
>4 dimensions.
I suggested this a while ago here on sci.physics.research: we
were talking about the history of the Kaluza-Klein model, and how
it got discarded at one point because it predicted an unobserved
scalar field g_{55} - the dilaton. Then I asked: could the dilaton
be the Higgs? And someone posted something saying that would be
interesting... but we never worked out whether this idea made the
slightest bit of sense.
So: have you found a scenario where you get a dilaton that interacts
with fermions and the W and Z in a way that could mimic the Higgs?
I don't see how to do this. There are lots of different strategies,
but all of them seem to have obstacles. For starters, where's your
SU(2) x U(1) gauge theory coming from? Are you putting it in from
the start or hoping to get those gauge fields to appear via the
Kaluza-Klein trick? If the latter, I guess you need more than
5 dimensions: you need your extra dimensions to form a manifold with
SU(2) x U(1) symmetry.
(I'm ignoring QCD for now to keep life simple: I'll be very happy
if you can show me a way to get the Weinberg-Salam model, complete
with Higgs, from a Kaluza-Klein theory.)
Cl.Massé
> >self-interaction of massless fields?
Mark William Hopkins wrote :
> Then in the lowest order of energy it will look like the Higgs
> field, *independent* of its origin. That's the real point of
> calling the Higgs field necessary.
Perhaps, but as the Higgs field hasn't be introduced, there is no
Higgs particle, which makes a great difference. The Higgs field
could only be a function of psi and the gauge field, and that to
all order of everything.
> I think the actual mechanism is much simpler: it's nothing more
> than the effects of the g_55 component of a 5-dimensional vacuum
> metric being seen in terms of an effective field theory
> representation in 4 dimensions.
Or the block diagonal elements in a Kaluza-Klein-like theory?
Along the lines of Chang, Kenneth, Macrae, and Mansouri? [Phys.
Rev. D _13_(1976)235] Good idea.
--
~~~~ %20cl...@free.fr%20 LPF
God doesn't understand supersymmetry.
Charles Torre
>
> I suggested this a while ago here on sci.physics.research: we
> were talking about the history of the Kaluza-Klein model, and how
> it got discarded at one point because it predicted an unobserved
> scalar field g_{55} - the dilaton. Then I asked: could the dilaton
> be the Higgs? And someone posted something saying that would be
> interesting... but we never worked out whether this idea made the
> slightest bit of sense.
>
of the main players was N. Manton. In the simplest formulation (to
me anyway) of KK theory, it is pretty clear how the gauge groups and
matter content arise. I will dig through my files tomorrow, but I think
you can get the Higgs to come out ok. But for fermions, well, I guess
you need supersymmetry? And what about that chiral fermion problem
pointed out by Witten? Anyway, if I can find something interesting
I'll try to post it.
In the meantime, what I do remember is this. If you try, just for fun,
a purely bosonic model in which the "big" spacetime is a fiber bundle
over the "real" spacetime with fibers given by G/H, G the KK symmetry
group and H a closed subgroup, then the gauge group is the normalizer
of H in G, modulo H. (Here by KK theory I mean that the big spacetime
is a Lorentz manifold N with isometry group G, orbits G/H,
and the G-invariant metrics on the big spacetime are built from the metric,
YM field and Higgs-like stuff down on the small spacetime N/G.)
Heh. Quite an unreadable load of rubbish, eh? To say it all plainly takes
more typing, and I gotta run...
-charlie
John Baez
>I recall that a number of papers were written on this issue. Perhaps one
>of the main players was N. Manton. In the simplest formulation (to
>me anyway) of KK theory, it is pretty clear how the gauge groups and
>matter content arise. I will dig through my files tomorrow, but I think
>you can get the Higgs to come out ok.
That's cool. If so, I guess the Higgs *has* to be a dilaton, i.e. one
of the components of the metric g_{ij} where both i and j point in
compactified directions, since this is the only way I see to get
scalar fields. But I'd like to be reassured on this point.
In particular, it would be cool if there were some choice of
compact manifold K such that gravity on R^4 x K looked like
Yang-Mills fields with gauge group SU(2) x U(1) together with
a scalar field that couples to the gauge bosons and itself
in a way that mimics the Higgs of the Weinberg-Salam model!
But how the heck can we get the usual "Mexican hat" shaped
potential for the Higgs?
>But for fermions, well, I guess you need supersymmetry?
Well, I guess you really just need fermions in your higher-dimensional
theory to get fermions when you compactify it. If you want to get
silly, you can even do gravity coupled to Yang-Mills and fermions on
R^4 x K, and then see what it looks like down on R^4. This of course
defeats the original point of Kaluza-Klein theories, which was to make
everything be "gravity".
>And what about that chiral fermion problem pointed out by Witten?
Right, that may be the killer. I'm always confused, though: if
it turns out that a right-handed neutrino exists, does the chiral
fermion problem go away? Or would it only go away if we had a right-
handed neutrino which coupled to all gauge fields just like the left-
handed one does? (Which apparently we do not!)
Paul D. Shocklee
> Right, that may be the killer. I'm always confused, though: if
> it turns out that a right-handed neutrino exists, does the chiral
> fermion problem go away? Or would it only go away if we had a right-
> handed neutrino which coupled to all gauge fields just like the left-
> handed one does? (Which apparently we do not!)
Yes, you need the same coupling to both chiralities.
I think it would also go away, though, if the fundamental theory was
left-right symmetric and the chirality of the low-energy theory was
due to some some sort of spontaneous symmetry breaking. There are
a lot of papers on left-right symmetric models in which the extra
gauge bosons are just more massive than the ordinary ones. I don't
know if you could still get this to work with a Kaluza-Klein
reduction of 11-dimensional supergravity though, because the
Standard Model gauge group is already just small enough to fit
with 7 extra dimensions.
Incidentally, there is another possible loophole to the chiral fermion
problem that was mentioned in Witten's original paper, namely torsion,
but I don't know if there are any convincing models that exploit this.
--
Paul Shocklee
Graduate Student, Department of Physics, Princeton University
Researcher, Science Institute, Dunhaga 3, 107 Reykjavík, Iceland
Phone: +354-525-4762
John Gonsowski
> Mark William Hopkins wrote :
[unnecessary quoted text deleted by angry gods]
> Perhaps, but as the Higgs field hasn't be introduced, there is no
> Higgs particle, which makes a great difference. The Higgs field
> could only be a function of psi and the gauge field, and that to
> all order of everything.
> > I think the actual mechanism is much simpler: it's nothing more
> > than the effects of the g_55 component of a 5-dimensional vacuum
> > metric being seen in terms of an effective field theory
> > representation in 4 dimensions.
> Or the block diagonal elements in a Kaluza-Klein-like theory?
> Along the lines of Chang, Kenneth, Macrae, and Mansouri? [Phys.
> Rev. D _13_(1976)235] Good idea.
>
> --
> ~~~~ %20cl...@free.fr%20 LPF
> God doesn't understand supersymmetry.
Yes the 5 extra dimensions for some are just the 5 extra dimensions that
Spin(6) adds to the the 10 gravity dimensions of Spin(5). You can still
get a Higgs particle from this. The weak bosons get mass from this and
the Higgs particle could be a black hole merger of the weak bosons.
These are Irving Ezra Segal/Tony Smith ideas. God doesn't understand our
supersymmetry perhaps cause it doesn't exist at least in the
supergravity/superstring sense... John
Mark William Hopkins
>I think it would also go away, though, if the fundamental theory was
>left-right symmetric and the chirality of the low-energy theory was
>due to some some sort of spontaneous symmetry breaking.
You can turn any asymmetric model into one that's symmetric simply by
duplicating the Lagrangian into 2 mutually disconnected mirror image
sectors. Since the sector with the left-weak force then remains disconnected
from the sector with the right-weak force, they will be invisible to one
another except by their gravity.
The only way you'd even know it existed is by the fact that there would
be a lot of gravity out there which is unaccounted for by visible matter.
Since the planetary systems' formation are the nearly exclusive consequence
of gravity, as well as the formation of individual stars and planets, that
means that both kinds of matter would cluster into the same celestial
bodies and there would probably not be any purely sector 1 or sector 2
bodies out there.
In other words, our own Earth, itself, would have an invisible counterpart
which is illuminated by the invisible counterpart of our sun, under the
radiation of the invisible counterpart of the electromagnetic force. It
could even have its own life and even civilizations on it. All of this
would literally be in the same space we're in, but completely oblivious
to us since the duplicated Lagrangian would have no inter-sector
interaction terms in it to allow either sector to "see" the other.
Jonathan Thornburg
Mark William Hopkins <whop...@alpha2.csd.uwm.edu> wrote:
>our own Earth, itself, would have an invisible counterpart
>which is illuminated by the invisible counterpart of our sun, under the
>radiation of the invisible counterpart of the electromagnetic force. It
>could even have its own life and even civilizations on it. All of this
>would literally be in the same space we're in, but completely oblivious
>to us since the duplicated Lagrangian would have no inter-sector
>interaction terms in it to allow either sector to "see" the other.
The science fiction novel
John Cramer
"Twistor"
Avon paperback, 1991, ISBN 0-380-71027-7
also published in hardcover, but I don't have the pub info handy :(
takes precisely this as its theme, with our chief protagonists being
a grad student and a postdoc who discover a way to "rotate our state
vector" back and forth between our universe and the invisible-counterpart
universe.
The author is a physics professor at U of Washington (Seattle),
and the physics is nicely handled. There's even an appendix detailing
which parts of the novel's "physics" are genuine and which are fictional.
IMHO it's an excellent novel, and I think many s.p.r. readers might
enjoy reading it.
--
-- Jonathan Thornburg <jth...@thp.univie.ac.at>
http://www.thp.univie.ac.at/~jthorn/home.html
Universitaet Wien (Vienna, Austria) / Institut fuer Theoretische Physik
"He who joyfully marches to music in rank and file has already earned
my contempt. He has been given a large brain by mistake, since for
him the spinal cord would fully suffice." -- Albert Einstein
Gerry Quinn
(Mark William Hopkins) wrote:
>In other words, our own Earth, itself, would have an invisible counterpart
>which is illuminated by the invisible counterpart of our sun, under the
>radiation of the invisible counterpart of the electromagnetic force. It
>could even have its own life and even civilizations on it. All of this
>would literally be in the same space we're in, but completely oblivious
>to us since the duplicated Lagrangian would have no inter-sector
>interaction terms in it to allow either sector to "see" the other.
But direct measurements of gravity made with, for example, large iron
spheres would not contain any contribution from the other sector.
Therefore, reconciling the size of the earth with the measured force of
gravity would necessitate reducing our estimate of the earth's 'normal
matter' density by a factor of two compared to its current value of 5.5.
This would create certain difficulties - for example it would be
incompatible with a large iron core.
The bravest science fictional solution might be to make both versions
hollow, thus multiplying planets and civilisations not by two but by
four!
- Gerry Quinn
John Baez
Gerry Quinn <ger...@indigo.ie> wrote:
>In article <8qtegf$hb0$1...@uwm.edu>, whop...@alpha2.csd.uwm.edu
>(Mark William Hopkins) wrote:
>>In other words, our own Earth, itself, would have an invisible counterpart
>>which is illuminated by the invisible counterpart of our sun, under the
>>radiation of the invisible counterpart of the electromagnetic force.
>>All of this
>>would literally be in the same space we're in, but completely oblivious
>>to us since the duplicated Lagrangian would have no inter-sector
>>interaction terms in it to allow either sector to "see" the other.
>But direct measurements of gravity made with, for example, large iron
>spheres would not contain any contribution from the other sector.
>Therefore, reconciling the size of the earth with the measured force of
>gravity would necessitate reducing our estimate of the earth's 'normal
>matter' density by a factor of two compared to its current value of 5.5.
Hey! That's a nice simple way to prove that theory is wrong.
Good thinking.
Mark William Hopkins
>I think the actual mechanism is much simpler: it's nothing more than
>the effects of the g_55 component of a 5-dimensional vacuum metric
>being seen in terms of an effective field theory representation in
>4 dimensions.
From John Baez:
>So: have you found a scenario where you get a dilaton that interacts
>with fermions and the W and Z in a way that could mimic the Higgs?
>I don't see how to do this. There are lots of different strategies,
>but all of them seem to have obstacles. For starters, where's your
>SU(2) x U(1) gauge theory coming from? Are you putting it in from
>the start or hoping to get those gauge fields to appear via the
>Kaluza-Klein trick?
You're getting Kaluza-Klein mixed up with higher-dimensional relativity.
They're actually 2 separate fields, especially nowadays after the
older K-K formulation (where potentials are represented as g5n
components) has been replaced by the gauge theoretic formulation (where
the potentials are represented as gauge potentials in a U(1) bundle).
Another example: the "black hole" solutions for 5-D Riemannian space are
totally different from the Riessner-Nordstroem solutions, which would be
what you get if you with in a U(1) bundle space. See [5]. So, 5-D
relativity and Yang-Mills relativity (for lack of a better term) are
really two separate things entirely.
The extra dimension can be linked with a Brans-Dicke scale (see [2]), or
possibly with a dilation scale. In the latter case, I think you recover Weyl
Space (defined and discussed in [3]) as the effective 4-D formulation of a
5-D Riemannian vacuum.
If not, then Weyl Space is still a 5-D space when treated as a bundle. In
that case, the way your extra dimension fits in is as the extra dimension
corresponding to the inclusion of the scale relativity group D(1).
So then, you're actually looking at a D(1) x SU(2) x U(1)
bundle. A representation of the Higgs mechanism via broken D(1)
symmetry has been formulated in [3].
The only drawback is that the symmetry-breaking terms have to be
written in by hand. They should come out for free by taking the
effective 4-D form of a 5-D vacuum field.
That's the missing piece in the puzzle.
In a sense, what I said about the tie-in between Higgs, scalar fields and
g55 is trivial since:
(a) the Campbell embedding theorem already guarantees you that ANY 4-D
Riemannian space can be represented as a u = 0 hypersurface in a
5-D vacuum, where u is the 5th coordinate.
and the converse:
(b) the Jordan decomposition of a 5-D vacuum yields the old scalar+
bivector+gravity decomposition. Nowadays, Jordan has been
repackaged into an effective field theory for 5-D vacuums and
studied in its own right, independent of any connections to an
older K-K. This is Wesson's Space-Time-Matter. See [1] below.
The only non-trival part is showing that when you embed a Riemannian
space with a Higgs source term and then apply Wesson's STM to extract out the
4-D effective field, the scalar part will be the Higgs, itself.
Among the speculations about the possible meanings of a 5th dimension is
that it is closely linked to a mass scale or to a Brans-Dicke scale (see [2]
below for an interesting comparison of the two).
As related in [1] and references found from there, actually testing for
the existence of a 5th dimension proves to be exceedingly subtle.
Evidence for the fact that there IS a universal scalar field along the
lines of an effective g55 term, that this field actually dominates the
total energy content of the Universe (and is, in fact, none other than
the Dark Energy or "quintessence") is provided in [4].
References & Additional Notes:
[1] Wesson P.S., Ponce de Leon, J., 1992.
Journal of Mathematical Physics 33, 3383.
Develops the mathematical machinery behind the S-T-M effective field
theory.
See also, Weeson P.S., et. al., 1996.
International Journal of Modern Physics, 11, 3247,
where the physical interpretation of S-T-M is developed.
[2] Fukui, T., Overduin, J.M., 1999.
The Relation of Generalized Scalar-Tensor Theory with the 5-D
Space-Time-Matter Theory.
General Relativity and Gravitation, 31 (8), 1151-1168.
Links a generalized Brans-Dicke theory to Wesson's STM.
[3] Drechsler, W. 1999.
Mass Generation by Weyl-Symmetry Breaking,
Foundations of Physics, 29, (9), 1999.
Provides an equivalence expressing the Higgs mechanism in terms of
D(1) symmetry breaking over Weyl Space.
[4] Guzm\'an, F.S., Matos, T., 2000.
Scalar field as dark matter in spiral galaxies
Classical and Quantum Gravity, 17, L9-L16.
And its sequel:
Matos, T., Guzm\'an, F.S., Arturo Ure\~na-L\'opez, L., 2000.
Scalar fields as dark matter in the universe.
Classical and Quantum Gravity, 17, 1707-1712.
Provides evidence (including results of numerical simulations) that
relate the "quintessence" to a universal scalar field, such as
described as the effective scalar field of a g55 term in 5-D
vacuum.
The title is actually a misnomer, since they're only trying to account
for the more recently discovered "quintessence" (a.k.a., Dark Energy),
not the better-known Dark Matter phenomenon, itself.
[5] Me, "The 5 Dimensional Black Hole", 1997.
Series of sci.physics.research articles posted in late March & early
April 1998, in which the general 5-D spherically symmetric, stationary
cylindrical metric was derived.
squ...@my-deja.com
> but the problem (to my mind) is that this is put in more or less "by
> hand", namely by cleverly choosing the finite-dimensional
> algebra mentioned above. In other words, it seems to me that at this
> stage, his model no longer puts out more than he puts in.
Well, this is to be expected, as the SM is most probabely only the low
energy limit of something else. We can hardly expect it to arise
naturally. However, the existance of suitably coupled scalar fields is
illuminated.
Best regards, squark.
Sent via Deja.com http://www.deja.com/
Before you buy.
Mark William Hopkins
>Hey! That's a nice simple way to prove that theory is wrong.
Of course, there are a lot of ways to rescue the basic idea that the
symmetry is hidden in an unseen or virtually unseen sector.
An interesting case in point:
add in the right neutrino, coupled to the left-neutrino by Higgs. Then
duplicate the way the rest of the Standard Model Lagrangian is linked to
the left neutrino, with a similar sector linked to the right-neutrino.
Both sectors remain coupled to the same Higgs.
The left-to-right neutrino cross-over provides a channel for sector 1 and
sector 2 to mix. This means you can have a broken symmetry in which the
universe is sector 1 dominated or sector 2 dominated.
John Baez
>In article <200009130552...@math-cl-n03.ucr.edu>,
> ba...@galaxy.ucr.edu (John Baez) wrote:
>> The more sophisticated models include the SU(3) for the strong force,
>> but the problem (to my mind) is that this is put in more or less "by
>> hand", namely by cleverly choosing the finite-dimensional
>> algebra mentioned above. In other words, it seems to me that at this
>> stage, his model no longer puts out more than he puts in.
>Well, this is to be expected, as the SM is most probably only the low
>energy limit of something else. We can hardly expect it to arise
>naturally.
I believe that the Standard Model must indeed "arise naturally" from
simpler underlying laws - just as galaxies, planets and the cacti
in my back yard arise naturally. I want to understand how it arose.
I have no problem with it arising as the low-energy limit of something
that looks quite different. But I want to see where the Standard
Model gauge group comes from. I know most people have given up on
this, but I think that's premature. I'm an optimist: I bet the laws
of physics make more sense than we now realize.
John Baez
Mark William Hopkins <whop...@alpha2.csd.uwm.edu> wrote:
>You're getting Kaluza-Klein mixed up with higher-dimensional relativity.
>They're actually 2 separate fields, especially nowadays after the
>older K-K formulation (where potentials are represented as g5n
>components) has been replaced by the gauge theoretic formulation (where
>the potentials are represented as gauge potentials in a U(1) bundle).
Hmm, I'm not sure what distinction you're drawing here: merely one of
formulation, or a matter of essentially different theories?
The people I read define a Kaluza-Klein theory on the spacetime M to
be general relativity or supergravity on M x K, together with some
ansatz on the geometry of the compact manifold K. To quote Witten's
"Search for a Realistic Kaluza-Klein Theory":
The [original] Kaluza-Klein theory, as noted above, also has
a non-abelian generalization, which has been extensively discussed
over the years. In this generalization, one starts with general
relativity in 4+n dimensions, possibly with additional matter
fields, or with a cosmological constant. Instead of assuming the
ground state to be M^{4+n}, Minkowski space of 4+n dimensions,
one assumes the ground state to be a product space M^4 x B, where
B is a compact space of dimension n. M^4 x B should be a solution
of the classical equations of motion, or possibly, as will be
discussed later, a minimum of some effective potential.
This is the sort of thing I usually mean by "Kaluza-Klein theory",
which is what I was talking about when...
Hmm, now I've completely lost track of what we were talking about.
Oh yeah: how to get a Standard-Model-like Higgs to pop out naturally as
the dilaton in some Kaluza-Klein theory. So I'm still wondering if
anyone has pulled this trick. The stuff Charles Torre posted about,
by Manton, didn't strike me as particularly "natural" - though I should
reread that post. And I'll have to reread your post too, now that I've
expressed my confusion about the first sentence quoted above.
Mark William Hopkins
>Well, this is to be expected, as the SM is most probably only the low
>energy limit of something else. We can hardly expect it to arise
>naturally.
But Einstein extracted the GR from its Newtonian limit by systematic
use of certain principles even though the end result doesn't look anything
like the starting point. So there's no reason to believe that just because
A is the low energy limit of B that B can't be induced from A.
This is not the actual problem behind the difficulty of getting at the
generalization. The actual problem is that there untold numbers of fields
out there which are invisible and unknown except by their gravity that
comprises nearly all the mass and energy content of the universe. Entire
sectors in the particle and force spectrum probably exist but which may not
ever be directly visible (except by gravity).
In other words, the spectrum described by SM is only a VERY small subset
of what very likely exists. That's way too much indeterminacy to be able
to pull off an Einstein.
Unless, of course you can find the right principle. For instance, if you
require the total zero point energy density for all particles and fields
to be finite (and to be small, no less!), this places a restriction on the
numbers and masses of fermions and bosons. For one, it means there have to
be as many boson degrees of freedom as fermion degrees of freedom.
Currently, there are 96 fermion degrees of freedom known (if you believe
the quark model, and represent neutrinos by 4-components owing to their
non-zero mass); but only 28 boson degrees of freedom known (counting the
Higgs).
That means either
(a) the quark model is totally wrong,
(b) or generations are not fundamental (which implies then that there have
to be maybe 4 or 8 fermion degrees in addition to the 24 of the 1st
generation and maybe 2 or 4 additional boson degrees in addition to
the known 28),
or (c) there are at least 68 unknown boson states out there!
And if it's (c), then this is a serious understatement because in order
to satisfy the mass constraints to you're going to need EVEN MORE fermion
degrees of freedom which are currently unknown.
Mark William Hopkins
>And I'll have to reread your post too, now that I've expressed my confusion
>about the first sentence quoted above.
Actually, you restated what I said: that the old Kaluza-Klein (in 5-D
Riemannian space) was supplanted by Kaluza-Klein on bundles. The extra
dimensions of modern K-K combine with the base space to form a *non*
Riemannian space, with a Riemannian base that's still only 4-D.
This is in contrast to a higher dimensional relativity theory which takes
5-D Riemannian space as its base and may, itself, include extra
Kaluza-Klein dimensions.
When they shifted to new and improved K-K, they bumped everything up a
notch. Where before A was grouped with the g's, and F grouped with the
Gammas, afterwards A was grouped with the Gammas, and F with the Rs.
That's actually the same shift in going from canonical Quantum Gravity
(which tries to quantize the g's) to gauge Gravity (which starts
essentially with the connection Gamma).
John Baez
Mark William Hopkins <whop...@alpha2.csd.uwm.edu> wrote:
>From John Baez:
>>And I'll have to reread your post too, now that I've expressed my confusion
>>about the first sentence quoted above.
>Actually, you restated what I said: that the old Kaluza-Klein (in 5-D
>Riemannian space) was supplanted by Kaluza-Klein on bundles. The extra
>dimensions of modern K-K combine with the base space to form a *non*
>Riemannian space, with a Riemannian base that's still only 4-D.
Now I'm even more confused. Yes, I said that nowadays we use
"Kaluza-Klein theory" to stand for general relativity on a bundle
of the form M x K with M four-dimensional and K compact. But for
this very reason, M x K is *indeed* a Riemannian manifold - or more
precisely, a Lorentzian one.