4.8 sigma evidence for the B meson anomaly: what could be its TGD based explanation?

Sabine Hossenfelder (see this) told that 4.8 sigma evidence for B meson anomaly manifesting itself in the decays of B meson to K^* meson plus muon pair has been reported (see this). Below is the abstract of the article telling about the finding (see this).

An analysis of the decay amplitudes of B⁰; K^*0→ K⁺π ^-μ ⁺μ ^- is presented, using proton-proton collision data recorded by the LHCb experiment at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 8.4 fb^-1. The amplitudes are constructed from Legendre polynomials in the μ⁺μ⁺ invariant mass squared region 1.1 22/c⁴. CP-averaged observables are obtained from the amplitudes.

Some of these observables present deviations with respect to the Standard Model, which can be interpreted as shifts in the effective Wilson coefficients. This model-independent approach enables tests of theoretical predictions that can help disentangle hadronic effects from potential contributions from physics beyond the Standard Model. This allows flexibility in the choice of q² binning for global analyses. Depending on the binning scheme, the deviation of the Wilson coefficient C₉ from its Standard Model expectation varies from 4.3σ to 4.8σ.

A large variety of models explaining the B meson anomaly have been proposed. Perhaps the simplest model for the anomaly is in terms of a heavier partner Z^‘ of Z⁰ boson. The anomaly reduces to that associated with the vertex involving a transformation of the b quark to s quark by CKM mixing by the emission of Z^‘ boson.

Since a very short distance phenomenon is in question this can be approximately described in effective QFT approach by a purely local interaction terms as product of the neutral weak current involving b and s quark and muon pair. This description is completely analogous to the description of weak interactions in terms of the four-fermion vertex in the original Fermi model.

As in the Fermi model, the interaction term is space-time integral for the product of weak currents involving Z^‘ propagator proportional to the inverse mass squared of Z^‘ having spatial dimension 2. The spatial dimension of the product of weak fermion currents coefficient of is determined by d=-6. In the parameterization the mass squared gives a proportionality constant proportional to cutoff mass squared 1/μ ². The index of C₉ is a convention for labelling various non-local interaction terms of the effective action of the standard model. There is no perturbative expansion since effective action is in question and the interaction term gives a simplified description for the loops responsible for the appearance of heavier particles in the interaction vertex making possible the anomaly.

Google Gemini informs that there are two kinds of models possibly explaining the anomaly in terms of Z^‘. If the Z^‘ gauge coupling is comparable to the Standard Model electroweak couplings g_Z^‘ ∼ 0.1 – 1.0, global fits to the b → l⁺l^- data typically restrict its mass to the range (1-7) TeV. Why this range?

1. The lower bound is ∼ 1-2 TeV: direct searches at ATLAS and CMS rule out lighter Z^‘ bosons. If Z^‘ were lighter than this and coupled directly to muons, it would have already appeared as a striking resonant “peak” in dimuon μ⁺μ^- invariant mass distributions at the LHC.
2. The Upper Bound ∼ 5-7 TeV: If the mass is any higher, its effect on the low-energy Wilson coefficients C₉ would become too weak to explain the observed deviations in B-meson decays, unless the couplings are artificially dialed up to mathematically unstable levels.

If the couplings are allowed to be much larger (approaching the perturbative limit where quantum field theory calculations remain reliable), the Z^‘ can hide at much higher energy scales: M_Z^‘ ∼ 10-30 TeV In this scenario, a heavy Z^‘ is too massive to be directly produced at the LHC, but its virtual “ghost” signature would still be heavy enough to generate the required modifications to the Wilson coefficients. Testing a Z^‘ in this range requires future facilities like the Future Circular Collider (FCC) or a high-energy muon collider.

TGD predicts a hierarchy of scale up copies of the standard model physics. p-Adic length scale hypothesis involves the conjecture is that these copies are labelled by 3 kinds of Mersenne primes: ordinary Mersenne primes M_k =2^k-1, Gaussian Mersennes M_G,k =(1+i)^k-1 and Eisensteinian Mersenne primes (see this). Ordinary hadron physics correspond to M₁₀₇ =2¹⁰⁷-1, there is evidence for M₈₉ hadron physics, which would be the scaled up version of ordinary hadron physics with 512 times higher mass scale and also for the M_G,79 hadron physics with mass scale higher by a factor 2¹⁴. The next candidate would be M₆₁ hadron physics with mass scale higher by factor 2²³. Therefore M_G,79 remains the only option.

Ordinary weak bosons correspond to M₈₉ and this would mean that for M_G,79 weak physics, the mass scales of weak bosons are by a factor 32 higher than for the standard model weak interactions. For the scaled up version of the ordinary Z⁰ boson with mass .09 TeV this would predict a mass M= 2.88 TeV. This mass belongs to the region allowed by coupling strength which are of same scale as for the standard model.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.