Losing the last motivation I had for an extra fermion family!

As we all know, the Standard Model(SM) of particle physics is a gauge theory of three families of quarks and leptons. Recently there were lots of discussions in the community regarding one more family of quarks and leptons, bounds on their masses and mixing with the observed fermions etc etc. Although the precision electroweak data still allows the inclusion of one more chiral family into the SM (not more than one), it hardly provides a solution to any of the problems SM suffers from. But "anything which is not forbidden must happen" attitude forces one to study the implications of four generation SM in colliders as well as cosmology. LEP II results constrains the mass of the fourth generation neutrino to lie above the Z-boson mass threshold i.e. around 45 GeV. Similarly there are various lower bounds on the charged fermions coming from precision data at LEP as well as null searches at Tevatron. From cosmology also, there are restrictions on number of light (~eV) neutrinos which prevents us from incorporating one more light neutrino into the model. One additional problem arises with the perturbativity. Since the fourth generation fermions get masses have to lie above the experimental lower bounds, their Yukawa couplings are quite large. And they become non-perturbative around few TeV scale when evolved under the Renormalization Group Equations (RGE). This demands new physics around the TeV scale which can keep the couplings perturbative. However, I have not seen any good candidate so far which can achieve this purpose. Enlarging the gauge symmetry or incorporating Supersymmetry do not help. TeV scale Extra dimensions might help although. Adding a large number of vector like particles in an ad-hoc fashion seems to work. This serious issue has to be addressed in any models involving four generations and no good models have come up so far. One motivation for fourth generation seems to come from the like sign dimuon charge asymmetry seen in Tevatron last year which was around 3 sigma deviation from SM predictions. Four generation models seems to have an explanation for this. But there are many other new physics explanation for this anomaly and there is no good reason to prefer four generation models over others. One more motivation could be related to Dark Matter. However it turns out that such a heavy neutrino will have very little abundance in the present Universe due to too much self annihilation. However if it's mass is as heavy as few TeVs then it can account for the correct abundance of Dark Matter in the present Universe. But to explain the origin of mass of such a heavy neutrino, we need non-perturbative Yukawa couplings. Also, such a heavy neutrino with SM couplings to the Z boson will give too high cross-section with a nuclei in direct detection experiments and hence will be ruled out from CDMS and XENON upper limits. Thus four generation scenario do not seem to be very motivating like the other beyond standard model frameworks. I would not be surprised if LHC rules out its existence :-)

Loss of perturbativity!

Electroweak Precision data still keeps room available to include one more chiral family into the standard model provided the quark and lepton masses are greater than some lower bound. The lower bound for the fourth generation quarks are around 200 GeV whereas for charged lepton it is around 100 GeV. The fourth generation neutrino should be more massive than

so as not to contribute to Z boson decay width which is experimentally measured very accurately and is in good agreement with three family Standard Model. Now in the standard model we have top quark yukawa coupling almost equal to 1 so as to account for its mass . Thus if we want to account for fourth generation quark masses, we have to take the corresponding yukawas large -->> Loss of perturbativity? In MSSM, the problem gets even more complicated. We have two Higgs doublet in this case, with vacuum expectation values and and their rations are denoted by . It turns out that with low value of ( close to unity) we can keep the yukawas perturbative at the electroweak scale and at the same time give rise to fourth generation quark and charged lepton masses above the experimental lower bound. However such a low value of will make the lightest Higgs boson mass at tree level very small and we have to check if loop corrections (including fourth generation) can make its mass greater than the LEP lower bound 114.5 GeV. Now suppose after taking loop corrections, we are getting Higgs mass greater than this limit as well as fourth generation masses are also above the lower bounds while keeping the yukawa perturbative. The problem is not yet solved, because when we evolve those yukawas under renormalization group, at every stage upto the grand unification scale (GUT) (assuming there is no new physics between MSSM and the GUT scale). But it turns out that (although I haven't checked it yet but there are works related to this in the literature)yukawas become non-perturbative near the TeV scale if there is not new physics between MSSM and GUT scales. People then incorporate new physics at the TeV scale which keeps the yukawas perturbative till the GUT scale. So far I have seen only one paper arXiv:0806.2064 where they have talked about adding some new vector like matter particles at the TeV scale. I personally find these vector like matter particles quite ad-hoc although they are serving this particular purpose here, I don't know how to incorporate them within the framework of some higher theories like Grand Unified Theories. But vector fields contribute differently to the beta function compared to chiral fields. Their contribution comes with opposite signs and may be that could be the reason why vector particles help the yukawas to slow down their running to keep them perturbative till the GUT scale. Anyway these are theoretical issues, but experimentally also fourth generation might have interesting signatures from colliders to dark matter search experiments as well. Will update about those issues next time :)