Gluons and quarks
Raphanus
a composite of two quarks of differing (anti-) colors?
Phillip Helbig---remove CLOTHES to reply
<1967d6ef-639a-4891...@z66g2000hsc.googlegroups.com>,
Raphanus <lester...@gmail.com> writes:
> What is the best argument as to why a gluon could not be considered as
> a composite of two quarks of differing (anti-) colors?
Why do you think they are not? Gluons consist of quark-antiquark pairs
with colour combinations such as red and anti-green. See, for example,
page 291 of Donald H. Perkins's INTRODUCTION TO HIGH ENERGY PHYSICS.
Or by "two quarks" you do NOT mean quark-antiquark pair? Or by
"differing (anti-) colors" you mean something other than in my example?
Marc Nardmann
> What is the best argument as to why a gluon could not be considered as
> a composite of two quarks of differing (anti-) colors?
Phillip Helbig replied:
> Why do you think they are not? Gluons consist of quark-antiquark pairs
> with colour combinations such as red and anti-green. See, for example,
> page 291 of Donald H. Perkins's INTRODUCTION TO HIGH ENERGY PHYSICS.
I don't have access to that book right now. But within the framework of
the Standard Model of particle physics, gluons are something completely
different than composites of two quarks. For example, quarks have a
nonzero mass, whereas gluons are massless and therefore move at the
speed of light. Gluons cause the strong force between quarks. If you
wanted to explain the strong force without gluons, you would have to
postulate some direct interaction between quarks. What would it be? (I
guess that every possible Lagrangian you might write down would not be
renormalisable in four spacetime dimensions.) Think about Feynman
diagrams: which ones would be allowed? What would the Feynman rules look
like? (Would the QCD gauge group SU(3) turn up anywhere in such a
theory? How?) I am certainly not an expert on QCD (not even a
physicist), but I bet that one cannot construct a consistent theory of
this form which agrees with the experimental evidence.
-- Marc Nardmann
Raphanus
remove CLOTHES to reply) wrote:
> In article
> <1967d6ef-639a-4891-b34d-e99428b04...@z66g2000hsc.googlegroups.com>,
>
> Raphanus <lester.we...@gmail.com> writes:
> > What is the best argument as to why a gluon could not be considered as
> > a composite of two quarks of differing (anti-) colors?
>
> Why do you think they are not? Gluons consist of quark-antiquark pairs
> with colour combinations such as red and anti-green. See, for example,
> page 291 of Donald H. Perkins's INTRODUCTION TO HIGH ENERGY PHYSICS.
>
> Or by "two quarks" you do NOT mean quark-antiquark pair? Or by
> "differing (anti-) colors" you mean something other than in my example?
You understand my question correctly. Thanks. According to the LBL
particle tables the gluon is indicated as having zero mass and the
quarks are massive. Is the gluon mass explained because m+(-m)=0?
Thanks.
Chalky
> Raphanus <lester.we...@gmail.com> wrote:
> > What is the best argument as to why a gluon could not be considered as
> > a composite of two quarks of differing (anti-) colors?
>
> Phillip Helbig replied:
>
> > Why do you think they are not? Gluons consist of quark-antiquark pairs
> > with colour combinations such as red and anti-green. See, for example,
> > page 291 of Donald H. Perkins's INTRODUCTION TO HIGH ENERGY PHYSICS.
>
> I don't have access to that book right now. But within the framework of
> the Standard Model of particle physics, gluons are something completely
> different than composites of two quarks. For example, quarks have a
> nonzero mass, whereas gluons are massless and therefore move at the
> speed of light. Gluons cause the strong force between quarks. If you
> wanted to explain the strong force without gluons, you would have to
> postulate some direct interaction between quarks. What would it be?
The originally defined strong force (now renamed the residual strong
force) was modelled as a meson exchange between nucleons, with that
meson now modelled as a quark /antiquark pair. Personally speaking, I
don't have any problem with envisaging that interaction as a quark /
antiquark vacuum fluctuation constrained by the speed of light.
Whithin that context, the gluon would seem to reduce to merely a
postulated physical mechanism for effecting that speed of light
constraint on the vacuum fluctuation.
Phillip Helbig---remove CLOTHES to reply
<Marc.N...@bigfoot.de> writes:
> Raphanus <lester...@gmail.com> wrote:
>
> > What is the best argument as to why a gluon could not be considered as
> > a composite of two quarks of differing (anti-) colors?
>
> Phillip Helbig replied:
>
> > Why do you think they are not? Gluons consist of quark-antiquark pairs
> > with colour combinations such as red and anti-green. See, for example,
> > page 291 of Donald H. Perkins's INTRODUCTION TO HIGH ENERGY PHYSICS.
>
> I don't have access to that book right now. But within the framework of
> the Standard Model of particle physics, gluons are something completely
> different than composites of two quarks. For example, quarks have a
> nonzero mass, whereas gluons are massless and therefore move at the
> speed of light. Gluons cause the strong force between quarks. If you
> wanted to explain the strong force without gluons, you would have to
> postulate some direct interaction between quarks. What would it be?
Sorry, my fingers were quicker than my brain. Mesons are
quark-antiquark pairs (but colourless (such as red and anti-red)).
Gluons have colour combinations such as red/anti-green.
A photon is massless yet in some contexts can be thought of as an
electron-positron pair. Can a gluon be thought of as a quark-antiquark
pair in some contexts?
Phillip Helbig---remove CLOTHES to reply
<4411923c-c615-44ce...@26g2000hsk.googlegroups.com>,
Raphanus <lester...@gmail.com> writes:
See my correction in another post in this thread.
Rock Brentwood
> What is the best argument as to why a gluon could not be considered as
> a composite of two quarks of differing (anti-) colors?
The "consists of" relation is not well-defined in quantum field
theory. The particle worldlines form a tapestry that does not admit a
clear-cut delineation into "this segment is this particle, that
segment is that".
The relevant feature is that the Lagrangian has terms of the form
psi-bar (A^a Q_a) psi
where A is the gauge field, Q = (Q_a Y^a) the gauge charge operator.
Q_a operates linearly on the vector space containing psi, so if (e_A)
is a basis for psi, and (e^A) a basis for psi-bar, then (Q_a e_B) =
sum(T^C_{aB} e_C) and (e^C Q_a) = sum (T^C_{aB} e^B). Thus, putting
all this together, you end up proving that Q has the form equivalent
to a linear operator
A = (sum A^a T^C_{aB} e_C x e^B).
So the gauge field has the same formal structure as a superposition of
femion/anti-fermion pairs.
Consequently, this also means there are fundamental processes
(vertices) of the form A^a <-> psi^B + psi_C with amplitude
(T^C_{aB}). So it behaves as a femion/anti-fermion pair in that
respect.
HOWEVER ... since the gauge field is NON-Abelian, one has CUBIC and
QUARTIC interactions involving the gauge fields, themselves. This
means processes like A -> A+A, or A -> A+A+A or A+A -> A+A. The
imagery of gauge bosons as non-elementary bound states of fermions and
anti-fermions doesn't quite fit here. Because then you have fermion/
anti-fermion pairs coming and going, literally, out of nowhere;
whereas, pair production and annihilation is normally tied to the
emission or absorption of a gauge boson of energy.
Plus the picture of gauge bosons as composite leads to the idea that
there should be a breakdown; analogous to what you see in solid state
physics where fermions pair up into quasi-bosons.
The "elementary"-ness of the "particles" is NOT assessed by any such
relation as "made out of", but by their behavior under transformation
groups. If the state space comprising a system transforms as an
irreducible sector, then it's an elementary system ... regardless of
what "it's made up of" or "what it looks like inside". If it
transforms as a tensor product of state spaces, so that its state
space is reducible, then it's considered composite.
Gluons, in this respect, are elementary. Not composite.
FrediFizzx
<hel...@astro.multiCLOTHESvax.de> wrote in message
news:g911gf$huq$1...@online.de...
Yes, gluons are theorized to fluctuate very briefly to a _virtual_
quark-antiquark pair just like photons can fluctuate to a virtual
electron-positron pair. I have often wondered how one might represent
an interaction with diagrams if a fluctuation happens at the vertex of
an interaction?
Best,
Fred Diether
Co-moderator sci.physics.foundations
Tom Roberts
> The originally defined strong force (now renamed the residual strong
> force) was modelled as a meson exchange between nucleons, with that
> meson now modelled as a quark /antiquark pair.
Yes, mesons consist of a quark/antiquark pair (and observable ones are
necessarily color singlets). But in the standard model, the "exchange"
you mention is of GLUONS, not a meson. Of course there are high-order
diagrams that could look sort of like such a "meson exchange" if one
squints hard enough, but the standard model Lagrangian has no such vertex.
> Personally speaking, I
> don't have any problem with envisaging that interaction as a quark /
> antiquark vacuum fluctuation constrained by the speed of light.
Perhaps you don't have any "problem" with that, but that's not at all
how the standard model describes such things. The exchange of a gluon
between quarks is NOT equivalent to the "exchange of a quark/antiquark
pair" -- the former is essentially fundamental, but there's no way to do
the latter directly (i.e. without a boatload of gluons).
> Whithin that context, the gluon would seem to reduce to merely a
> postulated physical mechanism for effecting that speed of light
> constraint on the vacuum fluctuation.
I know of no such "constraint" -- virtual particles are in general off
mass shell and are not constrained by the speed of light. In the
standard model, gluons are gauge bosons, and are fundamental in their
own right, not as some sort of adjunct to "vacuum fluctuations".
As should be clear, I am not an expert on this. I have
an experimentalist's "working knowledge" of the standard
model, not a theorist's deep understanding.
Tom Roberts
ganes...@gmail.com
remove CLOTHES to reply) wrote:
> <Marc.Nardm...@bigfoot.de> writes:
>
> - Show quoted text -
I dont know the right answer, but electron-positron annihilation
produces a photon, while on the other hand,
quark anti-quark produces a meson but not a gluon.
Chalky
> Chalky wrote:
> > The originally defined strong force (now renamed the residual strong
> > force) was modelled as a meson exchange between nucleons, with that
> > meson now modelled as a quark /antiquark pair.
>
> Yes, mesons consist of a quark/antiquark pair (and observable ones are
> necessarily color singlets). But in the standard model, the "exchange"
> you mention is of GLUONS, not a meson.
I quote from http://en.wikipedia.org/wiki/Gluon
One consequence is that gluons are not directly involved in the
nuclear forces. The force mediators for these are other hadrons called
mesons
Chalky
remove CLOTHES to reply) wrote:
> Sorry, my fingers were quicker than my brain. Mesons are
> quark-antiquark pairs (but colourless (such as red and anti-red)).
> Gluons have colour combinations such as red/anti-green.
Gluons, presumably, can also be colourless as in the gluon holding a
meson together.
> A photon is massless yet in some contexts can be thought of as an
> electron-positron pair. Can a gluon be thought of as a quark-antiquark
> pair in some contexts?
Gluons can't be isolated. The ones I have come across before have a
quark at one end and an antiquark at the other end.
Is this is ALWAYS the case?
When such a gluon is stretched sufficiently, it 'snaps' producing a
further quark / antiquark pair at the junction.
Is this is ALWAYS the case too?
Chalky
> On Aug 29, 8:04 am, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
> remove CLOTHES to reply) wrote:
> > A photon is massless yet in some contexts can be thought of as an
> > electron-positron pair. Can a gluon be thought of as a quark-antiquark
> > pair in some contexts?
>
> I dont know the right answer, but electron-positron annihilation
> produces a photon, while on the other hand,
> quark anti-quark produces a meson but not a gluon.
Look at it the other way round.
Example of gluon decaying into quark/antiquark pair at:
http://en.wikipedia.org/wiki/Higgs_boson
Containment requires that you can't isolate gluons.
Chalky
> > The originally defined strong force (now renamed the residual strong
> > force) was modelled as a meson exchange between nucleons, with that
> > meson now modelled as a quark /antiquark pair.
> > don't have any problem with envisaging that interaction as a quark /
> > antiquark vacuum fluctuation constrained by the speed of light.
>
> Perhaps you don't have any "problem" with that, but that's not at all
> how the standard model describes such things. The exchange of a gluon
> between quarks is NOT equivalent to the "exchange of a quark/antiquark
> pair"
Perhaps not, but I was describing the nuclear force between nucleons,
NOT the strong force between quarks.
> the former is essentially fundamental,
No, it is merely considered to be fundamental within the context of
the standard model.
> but there's no way to do
> the latter directly (i.e. without a boatload of gluons).
See Yukawa's original paper.
> > Whithin that context, the gluon would seem to reduce to merely a
> > postulated physical mechanism for effecting that speed of light
> > constraint on the vacuum fluctuation.
>
> I know of no such "constraint"
Let us keep matters simple for you by ignoring the Higgs field, thus
making all virtual particles massless.
The temporal extension of the vacuum fluctuation is constrained by its
energy, via Heisenberg's uncertainty relationship.
The spatial extension is constrained by its momentum, via the same
relationship.
Since p = E/c, the relationship between spatial and temporal extension
is constrained by the speed of light.
QED.
Gerry Quinn
says...
> "Phillip Helbig---remove CLOTHES to reply"
> > A photon is massless yet in some contexts can be thought of as an
> > electron-positron pair. Can a gluon be thought of as a
> > quark-antiquark
> > pair in some contexts?
>
> Yes, gluons are theorized to fluctuate very briefly to a _virtual_
> quark-antiquark pair just like photons can fluctuate to a virtual
> electron-positron pair.
And in the right environment, doubtless a photon could also fluctuate to
a quark-antiquark pair, and a gluon to an electron-positron pair.
> I have often wondered how one might represent
> an interaction with diagrams if a fluctuation happens at the vertex of
> an interaction?
The point about vertexes is that they are small. Magnify stuff enough
(i.e. calculate exactly enough), and maybe vertexes will look
complicated.
- Gerry Quinn
Chalky
correct and develop my own posting.
On Aug 31, 12:44 am, Chalky <chalkys...@bleachboys.co.uk> wrote:
> On Aug 29, 4:04 am, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
> remove CLOTHES to reply) wrote:
>
> > Sorry, my fingers were quicker than my brain. Mesons are
> > quark-antiquark pairs (but colourless (such as red and anti-red)).
> > Gluons have colour combinations such as red/anti-green.
>
> Gluons, presumably, can also be colourless as in the gluon holding a
> meson together.
Apparently not. According to
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/gluons.html
colourless gluons don't exist. Consequently, the only way I can see
for holding mesons together with gluons, is to assume that all mesons
comprise a superposition of all three colours (and anticolours).
Presumably, this is why
Tom Roberts <tjroberts...@sbcglobal.net> wrote:
"there's no way to do the latter directly (i.e. without a boatload of
gluons)".
> Gluons can't be isolated. The ones I have come across before have a
> quark at one end and an antiquark at the other end.
>
> Is this is ALWAYS the case?
Clearly not, as in the case of the strong force within nucleons.
In fact, I am beginning to doubt that it is ever the case, except for
the fact that it seems to be required for the meson.
Can anyone clarify?
> When such a gluon is stretched sufficiently, it 'snaps' producing a
> further quark / antiquark pair at the junction.
>
> Is this is ALWAYS the case too?
Actually, I quoted this from memory of a New Scientist article in the
1990s.
The closest reference I have found recently is
http://en.wikipedia.org/wiki/Three_jet_event
Does anyone know what the colour relationship is supposed to be
between the resultant quark and antiquark?
Furhermore, within the context of that original New Scientist article,
if a stretched gluon splits in the middle, this should then result in
2 quarks and 2 antiquarks in total. Does anyone know what the colour
relationship between these 2 pairs is supposed to be?
Hendrik van Hees
> I dont know the right answer, but electron-positron annihilation
> produces a photon, while on the other hand,
> quark anti-quark produces a meson but not a gluon.
Electron-positron annihilation creates (at least) two photons.
Kinematics (energy-momentum conservation) doesn's allow the
annihilation to one photon.
The analogous QCD process would be quark-anti-quark annihilation to
two gluons.
The analogon for the formation of meson-bound states in QCD for QED is
the formation of positronium as a bound state. While the latter can
be calculated with help of resummed perturbation theory
(Bethe-Salpeter ladder approximation) this is not sensible for mesons
in QCD.
--
Hendrik van Hees Institut für Theoretische Physik
Phone: +49 641 99-33342 Justus-Liebig-Universität Gießen
Fax: +49 641 99-33309 D-35392 Gießen
http://theory.gsi.de/~vanhees/faq/
ganes...@gmail.com
I would like someone to correct me on this, if incorrect.
My argument is related to asymptotic freedom for quark-anti quark
interaction.
First let me start with electron-positron interaction.
For a electron-positron interaction, the running coupling constant
increases with decreasing distance and as they move closer and
closer, the force between them becomes stronger and stronger, and
finally they annihilate to form photons.
Lets take the running coupling constant at p^2
g(p^2) = g^2/{1 + K. log(p^2/M^2)}
where K = g^2/4.pi^2{11N/3 - 2n_f/3) > 0
with N = 3 for SU(3), and n_f = 2 (one quark, and one anti-quark)
One also gets the derivative d(g(p^2))/dp^2 < 0 for all p
Now both g(p^2) and d(g(p^2))/dp^2 -> 0 as p -> infinity
So at very close distance i.e at v. high energies,
the quark and anti quark dont "see" each other at all. Also since
d(g(p^2))/dp^2 = 0 at p = inf, the "force" between them continues to
be zero even for small perturbations. Again in effect they dont "see"
each other at all.
Hence they cannot "move" towards each other to annihilate each
other and form a gluon.
However the above argument does not prevent a gluon from converting
itself to a quark-antiquark process. Hence we do get a reaction in
which a quark-antiquark is produced from a gluon.
ganesh
Gerry Quinn
says...
> In article <6hpdshF...@mid.individual.net>, fredi...@hotmail.com
> says...
> > "Phillip Helbig---remove CLOTHES to reply"
>
> > > A photon is massless yet in some contexts can be thought of as an
> > > electron-positron pair. Can a gluon be thought of as a
> > > quark-antiquark
> > > pair in some contexts?
> >
> > Yes, gluons are theorized to fluctuate very briefly to a _virtual_
> > quark-antiquark pair just like photons can fluctuate to a virtual
> > electron-positron pair.
>
> And in the right environment, doubtless a photon could also fluctuate to
> a quark-antiquark pair, and a gluon to an electron-positron pair.
Oops - the photon can do this, but of course the gluon can't... there is
nothing to carry the colour charge.
> > I have often wondered how one might represent
> > an interaction with diagrams if a fluctuation happens at the vertex of
> > an interaction?
>
> The point about vertexes is that they are small. Magnify stuff enough
> (i.e. calculate exactly enough), and maybe vertexes will look
> complicated.
Or (since I'm in the business of clarification right now) Feynmann
Diagrams are DIAGRAMS. However it's also true that in most
circumstances you can probably think of the highest energy stuff as
being concentrated around the vertexes.
On a really large scale, Feynman diagrams approximate to real particle
tracks.
- Gerry Quinn
Chalky
> In article <MPG.232422701243dbe989...@news.indigo.ie>, ger...@indigo.ie
> says...
>
> > In article <6hpdshFmv0d...@mid.individual.net>, fredifi...@hotmail.com
> > says...
> > > Yes, gluons are theorized to fluctuate very briefly to a _virtual_
> > > quark-antiquark pair just like photons can fluctuate to a virtual
> > > electron-positron pair.
>
> > And in the right environment, doubtless a photon could also fluctuate to
> > a quark-antiquark pair, and a gluon to an electron-positron pair.
>
> Oops - the photon can do this, but of course the gluon can't... there is
> nothing to carry the colour charge.
Which brings us back to my earlier question about real mesons. If
gluons can only be coloured, how can they hold together the quark-
antiquark pair of a positive (or a negative) pi meson, which is a
colour singlet? Presumably the solution to this problem must be
covered in the standard model?
Chalky
> You understand my question correctly. Thanks. According to the LBL
> particle tables the gluon is indicated as having zero mass and the
> quarks are massive. Is the gluon mass explained because m+(-m)=0?
> Thanks.
No. the (rest) mass of an up quark is ~ 3 MeV as is its antiparticle.
For a down quark, this is ~ 6 Mev
Compare to mass of pion, ~ 137 MeV and mass of nucleon, ~ 938 MeV
I couldn't say, offhand, precisely where these massenergy differences
come from, but you certainly can't get the figures to balance, even
approximately, by simply adding together rest masses.
I note from a first reading of
http://teachers.web.cern.ch/teachers/archiv/HST2002/feynman/Pion%20exchange.pdf
that gluons are believed to be responsible fore about half of the
momentum of such hadrons, but, even then, it looks like you would need
to assume that the composite quarks are in highly relativistic states
of motion relative to each other, in order to get the numbers to add
up, even approximately.
(I would be happy to get corrected on this, of course, by anyone with
a more in depth knowledge of the subject)
Chalky
> Which brings us back to my earlier question about real mesons. If
> gluons can only be coloured, how can they hold together the quark-
> antiquark pair of a positive (or a negative) pi meson, which is a
> colour singlet? Presumably the solution to this problem must be
> covered in the standard model?
In case nobody else answers this question, I have eventually managed
to find the following link
http://teachers.web.cern.ch/teachers/archiv/HST2002/feynman/Pion%20exchange=
.pdf
which does indeed indicate (fig 5) that the pion is modelled as a
transforming through all three colour/anticolour pairs, with the
gluons mediating those colour exchanges within the pion.
I found this article more clearly written (and diagrammed) than
anything I have read on the subject hitherto, and would recommend it
to anyone else who is still confused.
(Fig 7 is particularly relevant to the OP's original question.)
Raphanus
> On Sep 6, 2:18 pm, Chalky <chalkys...@bleachboys.co.uk> wrote:
>
> > Which brings us back to my earlier question about real mesons. If
> > gluons can only be coloured, how can they hold together the quark-
> > antiquark pair of a positive (or a negative) pi meson, which is a
> > colour singlet? Presumably the solution to this problem must be
> > covered in the standard model?
>
> In case nobody else answers this question, I have eventually managed
2002/feynman/Pion%20ex...
> which does indeed indicate (fig 5) that the pion is modelled as a
> transforming through all three colour/anticolour pairs, with the
> gluons mediating those colour exchanges within the pion.
>
> I found this article more clearly written (and diagrammed) than
> anything I have read on the subject hitherto, and would recommend it
> to anyone else who is still confused.
>
> (Fig 7 is particularly relevant to the OP's original question.)
The link seems to have been abridged...or? (The "ex..." at the point
of the line break seems suspicious.)
In any case I can't get it to work.