Saturday, March 03, 2007

Indications for Higgs with mass of 160 GeV

There have been cautious claims (see New Scientist article, the postings in the blog of Tommaso Dorigo, and the postings of John Conway in Cosmic Variance) about the possible detection of first Higgs events.

This inspires more precise considerations of the experimental signatures of TGD counterpart of Higgs. This kind of theorizing is of course speculative and remains on general qualitative level only since no calculational formalism exists and one must assume that gauge field theory provides an approximate description of the situation.

Has Higgs been detected?

The indications for Higgs comes from two sources. In both cases Higgs would have been produced as gluons decay to two b-bbar pairs and virtual b-bbar pair fuses to Higgs, which then decays either to tau-lepton pair or b-quark pair.

John Conway, the leader of CDF team analyzing data from Tevatron, has reported about a slight indication for Higgs with mass mH=160 GeV as a small excess of events in the large bump produced by the decays of Z0 bosons with mass of mZ≈ 94 GeV to tau-taubar pairs in the blog Cosmic Variance. These events have 2σ significance level meaning that the probability that they are statistical fluctuations is about 2 per cent.

The interpretation suggested by Conway is as Higgs of minimal super-symmetric extension of standard model (MSSM). In MSSM there are two complex Higgs doublets and this predicts three neutral Higgs particles denoted by h, H, and A. If A is light then the rate for the production of Higgs bosons is proportional to the parameter tan(β) define as the ratio of vacuum expectation values of the two doublets. The rate for Higgs production is by a factor tan(β)2 higher than in standard model and this has been taken as a justification for the identification as MSSM Higgs (the proposed value is tan(β)≈ 50). If the identification is correct, about recorded 100 Higgs candidates should already exist so that this interpretation can be checked.

Also Tommaso Dorigo, the blogging member of second team analyzing CDF results, has reported at his blog site a slight evidence for an excess of b-bbar pairs in Z0→ b-bbar decays at the same mass mH=160 GeV. The confidence level is around 2 sigma. The excess could result from the decays of Higgs to b-bbar pair associated with b-bbar production.

What forces to take these reports with some seriousness is that the value of mH is same in both cases. John Conway has however noticed that if both signals correspond to Higgs then it is possible to deduce estimate for the number of excess events in Z0→ b-bbar peak from the excess in tau-taubar peak. The predicted excess is considerably larger than the real excess. Therefore a statistical fluke could be in question, or staying in an optimistic mood, there is some new particle there but it is not Higgs.

mH=160 GeV is not consistent with the standard model estimate by D0 collaboration for the mass of standard model Higgs boson mass based on high precision measurement of electro-weak parameters sin(θW), α, αs , mt and mZ depending on log(mH) via the radiative corrections. The best fit is in the range 96-117 GeV. The upper bound from the same analysis for Higgs mass is 251 GeV with 95 per cent confidence level. The estimate mt=178.0+/- 4.3 GeV for the mass of top quark is used. The range for the best estimate is not consistent with the lower bound of 114 GeV on mH coming from the consistency conditions on the renormalization group evolution of the effective potential V(H) for Higgs (see the illustration here). Here one must of course remember that the estimates vary considerably.

TGD picture about Higgs briefly

Since TGD cannot yet be coded to precise Feynman rules, the comparison of TGD to standard model is not possible without some additional assumptions. It is assumed that p-adic coupling constant evolution reduces in a reasonable approximation to the coupling constant evolution predicted by a gauge theory so that one can apply at qualitative level the basic wisdom about the effects of various couplings of Higgs to the coupling constant evolution of the self coupling λ of Higgs giving upper and lower bounds for the Higgs mass. This makes also possible to judge the determinations of Higgs mass from high precision measurements of electro-weak parameters in TGD framework.

In TGD framework the Yukawa coupling of Higgs to fermions can be much weaker than in standard model. This has several implications.

  1. The rate for the production of Higgs via channels involving fermions is much lower. This could explain why Higgs has not been observed even if it had mass around 100 GeV.

  2. The radiative corrections to electro-weak parameters coming from fermion-Higgs vertices are much smaller than in standard model and cannot be used to deduce Higgs mass from the high precision measurements of electro-weak parameters. Hence one cannot anymore localize Higgs mass to the range 96-117 GeV.

  3. In standard model the large Yukawa coupling of Higgs to top, call it h, tends to reduce the quartic self coupling constant λ for Higgs in ultraviolet. The condition that the minimum for Higgs potential is not transformed to a maximum gives a lower bound on the initial value of λ and thus to the value of mH. In TGD framework the weakness of fermionic couplings implies that there is no lower bound to Higgs mass.

  4. The weakness of Yukawa couplings means that self coupling of Higgs tends to increase λ faster than in standard model. Note also that when Yukawa coupling ht to top is small (ht2< λ, see arXiv:hep-ph/9409458), its contribution tends to increase the value of βλ. Thus the upper bound from perturbative unitarity to the scalar coupling λ (and mH) is reduced. This would force the value of Higgs mass to be even lower than in standard model.

    In TGD framework new physics can however emerge in the length scales corresponding to Mersenne primes Mn=2n-1. Ordinary QCD corresponds to M107 and one cannot exclude even M89 copy of QCD. M61 would define the next candidate. The quarks of M89 QCD would give to the beta function βλ a negative contribution tending to reduce the value λ so that unitary bound would not be violated. If this new physics is accepted mH=160 GeV can be considered.

Can one then identify the Higgs candidate with mH=160 with the TGD variant of standard model Higgs? This is far from clear.

  1. Even in standard model the rate for the production of Higgs is low. In TGD the rate for the production of the counterpart of standard model Higgs is reduced since the coupling of quarks to Higgs is expected to be much smaller than in standard model. This might exclude the interpretation as Higgs.

  2. The slow rate for the production of Higgs could also allow the presence of Higgs at much lower mass and explain why Higgs has not been detected in the mass range mH<114>

  3. In TGD framework one can consider also other interpretations of the excess events at 160 GeV (taking the findings of both Dorigo's and Conway's group seriously and the fact that they do not seem to be consistent). p-Adically scaled up variants of ordinary quarks which might have something to do with the bumpy nature of top quark mass distribution.

    M89 hadron physics might be required in TGD framework by the requirement of perturbative unitarity. Thus the mesons of M89 hadron physics might be involved. By a very naive scaling by factor 2(107-89)/2=29 the mass of the pion of M89 physics would be about 70 GeV. This estimate is not reliable since color spin-spin splittings distinguishing between pion and ρ mass do not scale naively. For M89 mesons this splitting should be very small since color magnetic moments are very small. The mass of pion in absence of splitting would be around 297 MeV and 512-fold scaling gives M(π89)≈ 152 GeV which is not too far from 160 GeV. Could the decays of this exotic pion give rise to the excess of fermion pairs? Note that he mass was given erratically in the original posting. This interpretation might also allow to understand why b-pair and t-pair excesses are not consistent.

For more details see the chapter p-Adic Particle Massivation: Elementary Particle Masses of "p-Adic length Scale Hypothesis and Dark Matter Hierarchy".


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