# negative cross-section for chiral interaction

Hi,

I have a FCNC-type Lagrangian of the form

X Gmu ( a + b G5 ) y v + Y Gmu ( c + d G5 ) x V

where capital letters denote antiparticles, Gmu is the Dirac gamma matrix, G5 is gamma5, x and y are fermions, and v is a (complex) vector (so it carries an index like v_mu or V_mu).

I am interested in the process v V -> y Y -- so the vector is annihilating

If I set a = c, b = d (which is required to make this Lagrangian hermitian) and make neither of these vanish, then I get a negative cross-section. On the other hand, if I set any of the following :: b = d = 0, a = c = 0, a = - c, b = -d :: then I get a positive cross-section.

Any idea why this might be?

Thanks,
Sam

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Neil Christensen
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 Revision history for this message Neil Christensen (neil-christensen-qft) said on 2014-02-26: #1

You are probably breaking gauge invariance. In Feynman gauge, CalcHEP includes unphysical polarizations in the external spin-1 states as well as physical polarizations. The contributions from the unphysical polarizations are cancelled by the Goldstone and ghost contributions. The cancellation is protected by gauge invariance. But, if you have broken gauge invariance, you break the cancellation and can get negative cross sections.

If your model is correct except for the Goldstone bosons and ghosts, you may want to try Unitary gauge where the Goldstones and ghosts are removed anyway. Usually the calculation takes longer in Unitary gauge and loss of precision at very high energy is potentially worse in Unitary gauge because of the growth of k_mu k_nu / M^2, but depending on your process, you may be fine.

I should also mention that if the vector fields are massless (as in the case of the gluon), you must use Feynman gauge in CalcHEP. This means, you are required to correctly add ghosts. If your spin-1 field is massless and the gauge boson of a U(1) gauge group, then you do not need ghosts. But, you still need to mark the particle as a gauge particle in the "aux" column. See the manual for details.

Best wishes,
Neil

 Revision history for this message samwell187 (samwell187) said on 2014-02-26: #2

Thanks Neil Christensen, that solved my question.