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When Chiral Symmetry was exact, as it was before EWSB due to the lack of mass terms for quarks, would the residual strong force have infinite range? Related to this, does the Negative Beta Function apply for the Nuclear Force, or does it only affect the Strong Force within nucleons?

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Before EWSB, chiral symmetry is still broken by the yukawas, that is there is a Higgs quarks vertex that breaks explicitly $SU(2)_L \times SU(2)_R$. Therefore, the pions would still be massive and hence mediating a short range residual nuclear force. Moreover, it doesn't make much sense thinking about 'before' the EWSB since you are looking at pions interacting with nucleons, that is at scales well below the Higgs vev. As for the last part of your question, I don't think I understand what negative beta function you are referring to.

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  • $\begingroup$ But I thought massive quarks made chiral symmetry only an approximate symmetry, and thus the symmetry breaking creates pseudo-goldstone bosons with a mass rather than massless goldstone bosons? $\endgroup$ – user43542 May 16 '14 at 13:46
  • $\begingroup$ Indeed, but the quark masses come from the yukawas, that is the couplings to the Higgs bosons. And, as I said in the answer, as long as the yukawa aren't zero (well, in fact, equal) the chiral symmetry is broken even with no Higgs vev and no quark mass. In such a case it is the interaction (eventually responsible for the masses after EWSB) that breaks chiral symmetry. $\endgroup$ – TwoBs May 16 '14 at 17:48
  • $\begingroup$ Ah, so higgs interactions exist before EWSB. So, let me get this straight, higgs interactions always give things mass, but the presence of a nonzero VEV leads to all fermions interacting always? $\endgroup$ – user43542 May 16 '14 at 20:28
  • $\begingroup$ Higgs Interactions are there before and after EWSB. $\endgroup$ – TwoBs May 16 '14 at 21:38
  • $\begingroup$ Ah! That makes sense! Another question, though. Is it that there is the POSSIBILITY for there to be a Higgs-quarks interaction vertex that breaks the symmetry, not necessarily that the interaction is something that's ACTIVELY happening? $\endgroup$ – user43542 May 16 '14 at 21:46

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