Tuesday, March 28, 2017

\(B\)-meson \(b\)-\(s\)-\(\mu\)-\(\mu\) anomaly remains at 4.9 sigma after Moriond

There was no obvious announcement of new physics at Moriond 2017, one that would have settled supersymmetry or other bets in a groundbreaking direction, but that doesn't mean that the Standard Model is absolutely consistent with all observations.

In recent years, the LHCb collaboration has claimed various deviations of their observations of mostly \(B\)-meson decays from the Standard Model predictions. A new paper was released yesterday, summarizing the situation after Moriond 2017:
Status of the \(B\to K^*\mu^+\mu^−\) anomaly after Moriond 2017
Wolfgang Altmannshofer, Christoph Niehoff, Peter Stangl, David M. Straub (the German language is so effective with these one-syllable surnames, isn't it?) and Matthias Rindfleischetikettierungsüberwachungsaufgabenübertragungsgesetz have looked at the tension with the newest data.

The Good-lookers, Matterhorn (1975): In the morning, they started their journey at CERN (or in Bern). I've made the would-be witty replacement of Bern with CERN so many times that I am not capable of singing this verse reliably correctly anymore!

The new data include the angular distribution of the decay mentioned in the title, as measured by the major (ATLAS and CMS) detectors.

Microscopically, at the level of quarks and leptons, these decays of the \(B\)-mesons correspond to the\[

b\to s + \mu^+ + \mu^-

\] transformation of the bottom-quark.

There seems to be a deviation from the Standard Model. But they see that the deviation doesn't seem to visibly depend on \(q^2\) and it's independent of the helicities, too. The first fact encourages them to explain the "extra processes" by an extra four-fermion interaction including the fermions \(b,s,\mu,\mu\). There are various tensor structures that allow you to contract the four spinors in the four-fermion interactions and once they look carefully, the deviation from the Standard Model seems to be maximally hiding in the new physics (NP) term in the Hamiltonian:\[

\HH_{\rm eff} &= -\frac{4 G_F}{\sqrt{2}} V_{tb} V^*_{ts} \frac{e^2}{16\pi^2} \cdot C_9 O_9 + {\rm h.c.},\\
O_9 &= (\bar s \gamma_\mu P_L b) (\bar \ell \gamma^\mu \ell)

\] There are numerous other possible terms a priori, up to \(O_{10}\). Also, analogous operators may have primes and the prime indicates the replacement of \(P_L\) with \(P_R\).

If you memorize this song about quarks, you should understand all the four-fermion interactions unless you will conclude that the song is about cheese, as one of the singers did. The ladies from the girl band – those on the first photograph ever posted on the web – are planning a comeback and look for donations.

At any rate, only the evidence in favor of a nonzero coefficient \(O_9\) from new physics seems strong enough to deserve the paper – and the TRF blog post – and the best fit value of \(C_9\) seems to be negative and\[

C_9 = -1.21 \pm 0.22

\] which means that the experimental data indicate that \(C_9\) is nonzero (it should be zero in the Standard Model) at the 4.9-sigma level. Not bad. Well, there is also a similar but weaker anomaly for \(C_{10}\) that multiplies a similar operator with an extra \(\gamma_5\) and whose best fit is:\[

O_{10} &= (\bar s \gamma_\mu P_L b) (\bar \ell \gamma^\mu \gamma_5 \ell)\\
C_{10} &= +0.69\pm 0.25

\] which differs from the Standard Model's zero by 2.9 sigma. The numbers make it clear that the hypothesis that \(C_{9}=-C_{10}\) is rather compatible with the data, too, within one sigma, and the best fit for this \(C_{9}=-C_{10}\) is \(-0.62\pm 0.14\) or so, a 4.2-sigma deviation from zero (I believe that \(-0.62\pm 0.14\) should really be multiplied by \(\sqrt{2}\) but let me not make this confusion too visible).

The German/Ohio authors translate this effect to various other parameterizations of the LFUs (lepton flavor universality parameters) and if I understand the ultimate claim well, they basically say that similar anomalies from ATLAS+CMS, LHCb, and Belle seem to be consistent with each other and with the extra new physics term that was proposed above.

Some skeptics could say that these anomalies could be due to some difficult QCD effects. But the bottom-quark is pretty heavy and therefore "ignoring" the gluy, sticky environment around itself so I tend to think that the deviation from the Standard Model is rather exciting.

I've made fun of the German language so I want to make sure that the U.S. readers don't think that they're untouchable. ;-)

If it exists, the authors say, the clear deviations from the Standard Model could be made very strong by the experiments very soon.

Theoretically, I would try to explain this four-fermion interaction by the exchange of a new gauge boson or a scalar particle but I am not capable of giving you a more refined let alone stringy inspired detailed story about this new effect at this moment.

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