More about Higgs candidate

As I told in previous positng, 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.

According to simple argument of John Conway based on branching ratios of Z⁰ and standard model Higgs to τ-τbar and b-bbar, Z⁰→ τ-τbar excess predicts that the ratio of Higgs events to Z⁰ events for Z⁰→ b-bbar is related by a scaling factor

[B(H→ b-bbar)/B(H→ τ-τbar)]:[B(Z⁰→ b-bbar)/B(Z⁰→ τ-τbar)] ≈ 10/5.6=1.8

to that in Z⁰→ τ-τbar case. The prediction seems to be too high which raises doubts against the identification of the excecss in terms of Higgs.

In a shamelessly optimistic mood and forgetting that mere statistical fluctuations might be in question, one might ask whether the inconsistency of τ-τbar and b-bbar excesses could be understood in TGD framework.

1. The couplings of Higgs to fermions need not scale as mass in TGD framework. Rather, the simplest guess is that the Yukawa couplings scale like p-adic mass scale m(k)=1/L(k), where L(k) is the p-adic length scale of fermion. Fermionic masses can be written as m(F)= x(F)/L(k), where the numerical factor x(F)>1 depends on electro-weak quantum numbers and is different for quarks and leptons. If the leading contribution to the fermion mass comes from p-adic thermodynamics, Yukawa couplings in TGD framework can be written as h(F)= ε(F) m(F)/x(F), ε<< 1. The parameter ε should be same for all quarks resp. leptons but need not be same for leptons and quarks so that that one can write ε (quark)= ε_Q and ε (lepton)= ε_L. This is obviously an important feature distinguishing between Higgs decays in TGD and standard model.

2. The dominating contribution to the mass highest generation fermion which in absence of topological mixing correspond to genus g=2 partonic 2-surface comes from the modular degrees of freedom and is same for quarks and leptons and does not depend on electro-weak quantum numbers at all (p-adic length scale is what matters only). Topological mixing inducing CKM mixing affects x(F) and tends to reduce x(τ), x(b), and x(t).

3. In TGD framework the details of the dynamics leading to the final states involving Z⁰ bosons and Higgs bosons are different since one expects that it fermion-Higgs vertices suppressed to the degree that weak-boson-Higgs vertices could dominate in the production of Higgs. Since these details should not be relevant for the experimental determination of Z⁰→ τ-τbar and Z⁰→ b-bbar distributions, then the above argument can be modified in a straightforward manner by looking how the branching ratio R(b-bbar)/R(τ-τbar) is affected by the modification of Yukawa couplings for b and τ. What happens is following:

   B(H→ b-bbar)/B(H→ τ-τbar)= m_b²/m_τ² → B(H→ b-bbar)/B(H→ τ-τbar)×X ,

   X=(ε²(q)/ε² (L))× (x_τ²/x_b²).

   Generalizing the simple argument of Conway one therefore has

   (H/Z)⁰(b-bbar)= 1.8 × (ε²_Q/ε²_L )×(x_τ²/x_b²)× (H/Z)⁰(τ-τbar).

   Since the topological mixing of both charged leptons and quarks of genus 2 with lower genera is predicted to be very small (see this) , x_τ/x_b≈ 1 is expected to hold true. Hence the situation is not improved unless one has ε_Q/ε_L<1 meaning that the coupling of Higgs to the p-adic mass scale would be weaker for quarks than for leptons.

Can one then guess then value of r and perhaps even Yukawa coupling from general arguments?

1. The actual value of r should relate to electro-weak physics at very fundamental level. The ratio r=1/3 of Kähler couplings of quarks and leptons is certainly this kind of number. This would reduce the prediction for (H/Z⁰)(b-bbar) by a factor of 1/9. To my best understanding, this improves the situation considerably (see for yourself).

2. Kähler charge Q_K equals electro-weak U(1) charge Q_U(1). Furthermore, Kähler coupling strength which is RG invariant equals to U(1) coupling strength at the p-adic length scale of electron but not generally (see this). This observation encourages the guess that, apart from a numerical factor of order unity, ε² itself is given by either α_KQ_K² and thus RG invariant or by α_U(1)Q_U(1)². The contribution of Higgs vacuum expectation to fermionic mass would be roughly a fraction 10^-2-10^-3 about fermion mass in consistency with p-adic mass calculations.

Of course, it might turn out that fake Higgs is in question. What is however important is that the deviation of the Yukawa coupling allowed by TGD for Higgs from those predicted by standard model could manifest itself in the ratio of Z_0→ b-bbar and Z⁰→ τ-τbar excesses.

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