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Speaking of polarization sums for vector bosons,

the old DoPolarizationSums function has recently got a major makeover.

<https://github.com/FeynCalc/feyncalc/commit/fef289c48c9fa0fd6990e1464d5fda032add0532>

Instead of just inserting -g(mu,nu) for suitable

polarization vectors (which is for example not ok for QCD, unless

you want to add the ghost contributions explicitly), it now

can deal both with massive and massless vector bosons.

The new syntax is DoPolarizationSums[exp, k, n], where

exp is you matrix element squared, k is the four vector

of the external vector boson and n is the auxiliary vector

needed for massless bosons. In this form it can be used e.g.

for gluons. Usually one would pick n to be one of the external

momenta, such that SP[k,n]=!=0. At the end n should of course cancel

out for all gauge invariant quantities.

Now we know that in pure QED processes it is usually sufficient to

replace the polarization sum by just -g(mu,nu) to get the correct

result. Fine, for this use DoPolarizationSums[exp, k, 0].

Finally DoPolarizationSums[exp, k] means that we have a massive

vector boson, with the mass equal to SP[k,k] (e.g. W or Z)

Currently DoPolarizationSums hat two options: ExtraFactor and Contract.

ExtraFactor-> a means that the whole expression will be multiplied by a.

For example if, we are averaging over photon or gluon polarizations, it

is convenient to set ExtraFactor-> 1/2 right from the beginning.

The option Contract specifies if the inserted polarization sum should be

immediately contracted with the rest of the expression or not. The

default is True and it does make things a bit faster. Of course you can

also do e.g.

DoPolarizationSums[

Pair[Momentum[k], Momentum[Polarization[p, I]]] Pair[Momentum[q],

Momentum[Polarization[p, -I]]], p, n, Contract -> False]

to explicitly see the uncontracted polarization sum.

By the way, DoPolarizationSums automatically takes care about

uncontracting polarization vectors, so you don't need any tricks here

Last but not least, note that DoPolarizationSums must be applied for

each external boson. For example, if you have a process with two

external photons k1 and k2, you must use DoPolarizationSums for k1 and

k2 separately.

The polarization sums that get inserted for massive and massless bosons

are defined in PolarizationSum

<https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/fctools/PolarizationSum.m>

For real life examples, have a look at the included examples for e.g.

Compton scattering in QED

<https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/fcexamples/QED/QEDComptonScatteringTree.m>

Quark Gluon scattering in QCD

<https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/fcexamples/QCD/QCDGQiToGQi.m>

Gluon Gluon to Gluon Gluon scattering in QCD

https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/fcexamples/QCD/QCDGGToGGTree.m

Cheers,

Vladyslav

**Next message:**Vladyslav Shtabovenko: "Re: Reduction of SUND"**Previous message:**Vladyslav Shtabovenko: "Re: Issues with SUNSimplify"**Maybe in reply to:**Ben: "Polarization sums with dummy indices"**Next in thread:**Kyrylo Bondarenko: "Re: Polarization sums with dummy indices"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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