Right, we essentially just took that as the chiral Lagrangian for the vector mesons but I didn’t check it any deeper .. I have far more in depth notes I took that I could send you
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Replying to @InertialObservr @SchreiberUrs
Here's a snapshot of how i dealt with the finding the feynman rules if it helps at all .. this is for the πωρ vertexpic.twitter.com/4ondZ0GEEK
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Replying to @InertialObservr @SchreiberUrs
i imagine this method of 'factoring' would work similarly for the ωρφ vertex .. good luck, though .. i remember that references for the vector mesons in the anti-symmetric representation took a lot of digging
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Replying to @InertialObservr
Is there a good way to translate between interaction vertices expressed a) in "antisymmetric tensor representation" for vector mesons to b) their "usual" vector representation? To re-express your Feynman rule for rho_mn - omega_mn - pi to the "usual" rho_m - omega_n - pi ?
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Replying to @SchreiberUrs
i can't seem to find the reference at the moment, but there's this wonderful detailed paper that goes over it in the appendix.. for what it's worth here's how the feynman rules for the external legs are related in the two representations .. i think you can get basically.. 1/2pic.twitter.com/OABkG90U8K
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Replying to @InertialObservr @SchreiberUrs
everything from this relationship that m*ρ_{μν} is the antisymmetric derivative of the 'usual' representation
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Replying to @InertialObservr @SchreiberUrs
Also Δ is the feynman rule for the propagator for a massive vector meson in the anti-symmetric rep
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Replying to @InertialObservr
But if we read your rho_mn literally as the usual d_m rho_n - d_n rho_m then your rho-omega-pi vertex is quartic in derivatives and would seem to be in manifest contradiction to the standard result, which is first and second order on derivatives. What's the resolution?
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Replying to @SchreiberUrs
that's a good point, i'll have to think about it in the morning (it's 2 am here) But i found the paper! Really hope this helps: https://arxiv.org/pdf/hep-ph/0608051.pdf …
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Replying to @InertialObservr
Thanks, that's useful! I am now compiling a list of references on the antisymmetric tensor rep of vector mesons, here: http://ncatlab.org/nlab/show/chiral+perturbation+theory#ReferencesAntisymmetricTensorRepOfVectorMesons …
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Replying to @SchreiberUrs
wow .. that is immensely useful, thanks!
2:09 AM - 2 Apr 2020
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