Assigning Goldstone Boson

[KASINATHDAS]

Hi SARAH Team,

When there are more than one Z-like vector bosons in a model those get their mass after EWSB, what is the way to know which Goldstone boson corresponds to which vector boson. As we can get more than one massless pseudo-scalar eigenstates after EWSB, how to choose which one corresponds to which massive vector boson.

The gauge group of the model is SU(2)L_SU(2)R_U(1). There is one scalar doublet for each one of the SU(2) group. There is one bi-doublet which transforms under both of the SU(2) groups.

Thanking You,
Kasinath

[FStaub]

Hi,

The masses are in Feynman gauge and mass ordered. So, if you have a heavy Z', the SM like goldstone is still at first position.

Cheers
Florian

[KASINATHDAS]

Hi Florian,

Thank you for your answer.

Is the statement true independent of any of the following ordering in matter sector for pseudo-scalars

{{sigmaH10,sigmaH20,sigmaHL,sigmaHR},{Ah,UP}}

{{sigmaH10,sigmaHL,sigmaH20,sigmaHR},{Ah,UP}}

{{sigmaHR,sigmaHL,sigmaH20,sigmaH10},{Ah,UP}}.

Here sigmaHL is the pseudo-scalar component of doublet of SU(2)L, sigmaHR is for doublet of SU(2)R, sigmaH10 and sigmaH20 are from
the bidoublet.

Since both Ah[1] and Ah[2] will be massless, Is always Ah[1] is the Goldstone boson for SU(2)L Z-like vector boson if this Z is the lightest
neutral vector boson ?

How the information for the mass ordering of Z-like boson states is related to the ordering of mass eigen states of the pseudo-scalars in SARAH ?


With regards,
Kasinath

[FStaub]

Hi,

the order of the gauge eigenstates plays no role. Ah[1] and Ah[2] won't be massless when you study your model with SPheno because all calculations are done in Feynman gauge, i.e. they have identical masses to the vector bosons, and are mass ordered.

Cheers,
Florian

[KASINATHDAS]

Hi,
Thank you for the clarification.

With regards,
Kasinath