According to simple argument of John Conway based on branching ratios of Z^{0} and standard model Higgs to τ-τbar and b-bbar, Z^{0}→ τ-τbar excess predicts that the ratio of Higgs events to Z^{0} events for Z^{0}→ b-bbar is related by a scaling factor

[B(H→ b-bbar)/B(H→ τ-τbar)]:[B(Z^{0}→ b-bbar)/B(Z^{0}→ τ-τbar)] ≈ 10/5.6=1.8

to that in Z^{0}→ 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.

- 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. - 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).
- In TGD framework the details of the dynamics leading to the final states involving Z
^{0}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 Z^{0}→ τ-τbar and Z^{0}→ 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

_{b}^{2}/m_{τ}^{2}→ B(H→ b-bbar)/B(H→ τ-τbar)×X ,X=(ε

^{2}(q)/ε^{2}(L))× (x_{τ}^{2}/x_{b}^{2}).Generalizing the simple argument of Conway one therefore has

(H/Z)

^{0}(b-bbar)= 1.8 × (ε^{2}_{Q}/ε^{2}_{L})×(x_{τ}^{2}/x_{b}^{2})× (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.

- 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/Z
^{0})(b-bbar) by a factor of 1/9. To my best understanding, this improves the situation considerably (see for yourself). - 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, ε^{2}itself is given by either α_{K}Q_{K}^{2}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.

^{0}→ 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".

## 2 comments:

Hi Matti,

I do not know much about TGD...

What I can say is that of course both "signals" (Conway's 2-sigma and the Z->bb plot's wiggling around, whose significance is probably zero) are fluctuations.

On that, as Nanni Moretti once put it, I bet a testicle - not two, but one I am willing to.

In any case, I think the Tevatron would not be able to measure the ratio of BR of such a particle into tau or b, even if it was real. We need the LHC anyway for that...

Cheers,

T.

Dear quantum diaries survivor,

I agree about the possible fate of the signals. Perhaps their deeper purpose was to stimulate me to think in more detail about what TGD can say about Higgs.

In later posting "Still about Higgs" I consider also interpretation in terms of decays of pion of scaled up QCD suggested, or dare I say, predicted, by TGD. A scaling argument taking into account the delicacy related to rho-pi color magnetic splitting gives for the mass estimate 154 GeV which is quite near to that of the bump. This interpretation could be easily killed by looking for monochromatic photon pairs at 76 GeV.

Best Regards,

Matti

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