## Tuesday, September 15, 2020

### How Big Are The Lepton Universality Violation Tensions With The Standard Model?

A "tension" with the Standard Model that isn't definitive proof of new physics, is normally defined as more than two sigma (less than that is "consistent" with the Standard Model prediction) and less than five sigma (which is considered a discovery of new physics if replicated and other conditions regarding vetting of the results are met).

One of the most notable tensions with the Standard Model involves violations of its assumption of lepton universality (i.e. that the electron, muon and tau lepton have identical properties apart from fundamental rest mass). So far, this is see only in in certain decays of mesons that contain valence bottom quarks (a meson is a short lived compound particle with integer spin made up of a valence quark and a valence antiquark, in addition to a sea of virtual quark and antiquarks, bound together by the strong force as mediated by gluons).

The abstract from the new preprint below sums up how strong those tensions are (which arguably approach a new physics level of treated as independent manifestations of the same new physics phenomena and multiplied). But it does not, however, list of myriad null results in different decays, nor does it fully take into account look elsewhere effects or consider issues like correlated errors, so it is somewhat overstated.

Lepton universality violations are not seen in W boson decays at the LHC, are not found in tau lepton decays or pion decays (also here), and are not found in anti-B meson and D* meson decays or in Z boson decays. There were still tensions in the data from B meson decays, but the deviations were smaller as of 2019 than they were in 2015 (also here).

# Angular analysis of Bs→f′2(1525)(→K+K−)μ+μ− decays as a probe to lepton flavor universality violation

The flavor anomalies reported in RKRKP5 and (Bsϕμ+μ) indicate lepton flavor universality violation in bsl+l quark level transition decays. The deviation from the SM prediction reported in the underlying flavor observables currently stand at the level of 2.5σ2.4σ3.3σ and 3.7σ, respectively.
In this context, we perform an angular analysis of the four-body differential decay of Bsf2(1525)(K+K)μ+μ in a model independent effective field theory framework. The decay mode Bsf2(1525)l+l undergoes similar bs neutral current quark level transition and, in principle, can provide complementary information regarding lepton flavor universality violation in bsl+l quark level transition decays. We give predictions of various physical observables such as the branching ratio, the longitudinal polarization fraction, the forward-backward asymmetry, the angular observables P1P2P4P5 and also the lepton flavor sensitive observables such as the ratio of branching ratio Rf2QFLQAFBQ1Q2Q4Q5 for Bsf2(1525)(K+K)μ+μ decays in the standard model and in the presence of several 1D and 2D new physics scenarios.
 Comments: 25 pages, 7 figures Subjects: High Energy Physics - Phenomenology (hep-ph) Cite as: arXiv:2009.06213 [hep-ph] (or arXiv:2009.06213v1 [hep-ph] for this version)
From the introduction in the body text:
Exploring and identifying the Lorentz structure of possible new physics (NP) that lies beyond the standard model (SM) is of great importance particularly in semileptonic B meson decays mediated via b → s l+ l− neutral current and b → c l ν charged current interactions. It is well known that the flavor sector could be an ideal platform to explore NP since it can provide possible indirect evidence of NP in the form of new interactions that can, in principle, be very sensitive to the existing experiments. It is also well known that, apart from the flavor sector, existence of NP is also evident from several other phenomena such as the matter antimatter asymmetry of the universe, neutrino mass, dark matter, dark energy and so on.
In the recent years, several measurements have shown hints of lepton flavor universality violation (LFUV) in the semileptonic decays of B mesons involving b → s l+ l− (l ∈ e, µ) neutral current and b → c l ν (l ∈ e/µ, τ ) charged current quark level transitions. Significant deviation from the SM expectation has been reported in various flavor observables such as RK, RK∗ , P'5 in B → K(∗) l + l− decays; B(Bs → φ µ+ µ−); RD, RD∗ , P τ D∗ , F D∗ L in B → D(∗) l ν decays and RJ/Ψ in Bc → J/Ψ l ν decays.
Here we will focus mainly on the anomalies present in B meson decays mediated via b → s l+ l− quark level transitions. The ratio of branching ratio RK and RK∗ in B → (K , K∗ )l+ l− decays are defined as:
RK(∗) = B(B → K(∗) µ+ µ−)  / B(B → K(∗) e+ e−). (1)
After the Rencontres de Moriond, 2019, the current status of several observables pertaining to b → s l+ l− quark level transition decays is as follows:
the measurement of RK from the combined data of both Run 1 and Run 2 of LHCb reports RK = 0.846+0.060 −0.054 (stat) +0.016 −0.014 (syst) in the central q^2 region (1 ≤ q^2 ≤ 6 GeV2 ) where, q^2 is the invariant mass-squared of the dilepton. The deviation from the SM value of RK ∼ 1 is found to be at the level of ∼ 2.5σ.
Similarly, the RK∗ was measured in two different q^2 bins from two different experiments where, the LHCb reports RK∗ = 0.660+0.110 −0.070 (stat) ±0.024 (syst) and Belle reports RK∗ = 0.52+0.36 −0.26 (stat) ±0.05 (syst) in the low q^2 bin (0.045 ≤ q 2 ≤ 1.1 GeV2 ) and similarly in the central q^2 bin (1.1 ≤ q 2 ≤ 6 GeV2 ), LHCb reports RK∗ = 0.685+0.113 −0.069 (stat) ±0.047 (syst) and Belle reports RK∗ = 0.96+0.45 −0.29 (stat) ±0.11 (syst).
These measurements differ from the SM prediction of RK∗ ∼ 1 at the level of ∼ 2.4σ.
In addition to RK and RK∗ , the deviation from the SM expectation is also found in the measurements of the angular distributions of B → K∗ µ+ µ−, particularly in P'5. The ATLAS and LHCb collaborations measured P'5 in the bin q^2 ∈ [4, 6] GeV2 and they differ by ∼ 3.3σ from the SM expectation.
Similarly, the CMS measurement in q^2 ∈ [4.3, 6] GeV2 and the Belle measurement in q^2 ∈ [4.3, 8] GeV2 differ by 1σ and 2.1σ, respectively from the SM expectations.
In addition, the measured value of the branching ratio B(Bs → φ µ+ µ−) is found to deviate at the level of ∼ 3.7σ from the SM expectations.
In Table I we report the current status of RK, RK∗ and P'5 . At present, the dedicated ongoing B factory programs at Belle II and LHCb emerge as promising platforms that can either confirm or refute the existence of NP in b → s l+ l− transition decays.
Our main aim is to study the impact of NP on Bs → f 0 2 (1525) µ+ µ− decay observables in a model independent effective theory formalism. The Bs → f 0 2 (1525) µ+ µ− decay mode has received less attention both from the theoretical and the experimental side and it has not been discussed earlier in detail. Although, in Ref. [18], the authors discussed the SM results for both the µ mode and τ mode of Bs → f 0 2 (1525)l+ l− along with the B → K∗ 2 (1430)l+ l− decays, but more emphasis was given to B → K∗ 2 rather than Bs → f 0 2 decays. Also the branching ratio of f 0 2 decaying into K+ K− was not considered in their numerical analysis. In Ref. [18], the authors also discussed the impact of NP on several observables coming from two different NP models such as the vector-like quark model and the family non-universal Z 0 model. Similarly, there are ample number of literatures discussing the B → K∗ 2 (1430)l+ l− decays mediated vis same b → s l+ l− quark level transition.
So far we don’t have many experimental results on electroweak penguin decays involving spin 2 particles. The experimental techniques used for Bs → φ l+ l− can be adjusted to Bs → f 0 2 (1525)l+ l− decay as well because both φ and f 0 2 (1525) decay to a pair of charged kaons which are easily detected by the LHCb detector. Since the dominating structures in K+K− spectrum are the P wave φ(1020), and there are several possible resonances around 1500 MeV/c 2, it’s a natural thing to look at this regime to study. Further, the presence of D waves in this mass region yields a richer spectrum for exploring interesting angular observables. Moreover, we will show afterwards that the branching ratio of this decay mode is found to be sizable using pQCD form factors, hence we expect hundreds of signal events to be observed by analyzing the current LHCb data available