tree level graviton scattering from a scalar

[Arash Yunesi]

Dear all

I need to calculate scattering amplitude of graviton from a scalar particle through a graviton exchange. So I need to calculate three graviton vertex. I have used xPert to calculate h^3 terms from det(-g)R and it looks good.

Then I used 

{CD -> PD, _RiemannCD -> 0, _RicciCD -> 0, _RicciScalarCD -> 0, _ChristoffelCD -> 0, PD[_][_metric] -> 0}

to change covariant derivative to partial derivative and go to flat background. 

1. Has anyone seen such a calculation? Even if it is done by brute force using hand!

2. Can I use xAct packages to calculate this scattering amplitude?

3. Any clues how I should proceed?

Best,

Arash

[Nathan Moynihan]

I've done this before using xAct, but in the end it turns out to be more useful to use the spinor helicity formalism and calculate everything by hand (the 3-graviton vertex is a 1 line calculation in this way).

Let me know if you need any help/references.

Nathan

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[ghadir jafari]

Dear Arash 

I Have done such calculation with xAct package.

See the attached file that is the graviton  3-vertex has been achieved.

Ghadir

[Arash Yunesi]

Thank you so much Ghadir. It was helpful and solved my problem.

Best,

Aresh