Are we overlooking Lepton Flavour Universal New Physics in $b\to s\ell\ell$ ?

The deviations with respect to the Standard Model (SM) that are currently observed in $b \to s \ell\ell$ transitions (the so-called flavour anomalies) can be interpreted in terms of different New Physics (NP) scenarios within a model-independent effective approach. We reconsider the determination of NP in global fits from a different perspective by removing one implicit hypothesis of current analyses, namely that NP is only Lepton-Flavour Universality Violating (LFUV). We examine the roles played by LFUV NP and Lepton-Flavour Universal (LFU) NP altogether, providing new directions to identify the possible theory beyond the SM responsible for the anomalies observed. New patterns of NP emerge due to the possibility of allowing at the same time large LFUV and LFU NP contributions to $C_{10\mu}$, which provides a different mechanism to obey the constraint from the $B_s \to\mu^+\mu^-$ branching ratio. In this landscape of NP, we discuss how to discriminate among these scenarios in the short term thanks to current and forthcoming observables. While the update of $R_K$ will be a major milestone to confirm the NP origin of the flavour anomalies, additional observables, and in particular the LFUV angular observable $Q_5$, turn out to be central to assess the precise NP scenario responsible for the observed anomalies.


Introduction
This addendum presents an update of our recent work [1], where we identified the patterns of New Physics (NP) suggested by b → s + − measurements. It also updates some of the NP scenarios considered in Ref. [2]. Keeping the theoretical framework and the rest of the data set unchanged, we update the value of the Lepton-Flavour-Universality-Violating (LFUV) observable: as announced recently by the LHCb collaboration [3], corresponding to the average of Run-1 and part of Run-2 (2015-2016) measurements. The correlations with the (finely binned) measurements of B(B → Kµ + µ − ) [4] are tiny and are neglected here. Also Belle has presented new results for R K * in three bins [5] combining the data from charged and neutral channels: Our theory treatment for this observable follows the same strategy as described in [1] for Q 4,5 where we introduced a nuisance parameter accounting for the relative weight of each isospin component. In addition, we include a brief discussion on the impact of these measurements in two models, where we also take into account the new values of R D ( * ) from Belle [6] 1 .

Global fits
Tabs. 1-3 and Fig. 1 update the corresponding tables and plots of Ref. [1] based on fits to the global set of data ("All") or restricted to quantities measuring Lepton Flavour Universality Violation (LFUV).
While we do not observe any significant difference in the 1D scenarios with "All" data compared to Ref. [1], the pulls for the LFUV 1D fits get reduced by half a sigma, except the scenario C NP 9µ = −C 9 µ which favours an SM-like R K (see Ref. [9]). Also now the C NP 9µ b.f.p. scenario coincides in the "All" and LFUV fits. Concerning 2D scenarios, the same picture arises except that C NP 9e is now centered around zero and small contributions to right-handed currents (RHCs) seem slightly favoured (C 9 µ > 0, C 10 µ < 0) 2 . Indeed these contributions tend to increase the value of R K as can be seen from the explicit 1 We also update B(Bs → µ + µ − ) including the latest ATLAS measurement [7] and the most recent lattice update of fB s [8]. The comparison between v1 and v2 of this addendum shows the relatively small numerical impact of such updates.
2 Interestingly these small contributions also reduce a bit the mild tension between P 5 at large and low-recoil pointed out in [9] compared to the scenario with only C NP 9µ .  Table 1. Most prominent 1D patterns of New Physics in b → sµµ. The Pull SM is quoted in units of standard deviation. The p-value of the SM hypothesis is 8.6% for the fit "All" and 4.5% for the fit LFUV. We have checked also the scenario with only C NP 10µ but its significance in the "All" fit is only at the 4.0σ level and 3.9σ for the LFUV fit.

Impact on NP models
In complement with the above EFT analysis, we focus on the interpretation of two NP scenarios: the (C 9µ , C 9 µ ) scenario (which is especially interesting when R K is rather close to 1) and Scenario 8 (which allows for correlations between b → s + − and R D ( * ) ).
The (C 9µ , C 9 µ ) scenario is naturally generated in a Z model with opposite couplings to right-handed and left-handed quarks. This setup was already proposed in Ref. [11] within the context of a gauged L µ − L τ symmetry with vector-like quarks. The latter (of masses m D and m Q ) are charged under L µ − L τ and have the same SM quantum numbers as right-handed down quarks and left-handed quark doublets, respectively. The vector-like quarks couple to the SM ones and to a scalar φ which breaks the L µ − L τ symmetry with couplings Y D,Q . We show the update of Fig. 2 of Ref. [11] assuming Y D,Q = 1 in the left panel of Fig. 3. Since the current fit allows for C 9 µ = 0 at the one sigma level, the SU (2) singlet vector-like quark can still be decoupled [12]. Scenario 8 of Ref. [2] allows for a model-independent connection between the anomalies in b → s + − and b → cτ ν, which are also at the 4σ level [13]. Such a correlation arises in the C (1) = C (3) scenario as expressed in terms of gauge-invariant dimension-6 operators [14], which stems naturally from models with an SU (2) singlet vector leptoquark [15][16][17]. The operator involving third generation leptons explains R D ( * ) and the one with second generation ones give a LFUV effect in b → sµ + µ − . The constraint from b → cτ ν and SU (2) L invariance leads generally to large contributions to the operatorsγ µ P L bτ γ µ P L τ , which enhances b → sτ + τ − processes [18], but also mixes into O 9 and generates C U 9 at µ = m b [19]. Therefore, scenario 8 is reproduced in this setup with an additional correlation between C U 9 and R D ( * ) . Assuming a generic flavour structure so that small CKM elements can be neglected [18,19], we get Realisations of this scenario in specific NP models yield also an effect in C 7 generally [19]. However, since this effect is model dependent (and in fact small in some UV complete models [20,21]), we neglect it here, leading to the right plot of Fig. 3. Note that this scenario has a pull of 7.0 σ due to the inclusion of R D ( * ) , which increases ∆χ 2 SM by ∼ 20. Finally, in Ref. [22] it was recently found that a 2HDM with right-handed neutrinos leads to the scenario 9 in Table 5. Figure 2. Updated plots of Ref. [2] corresponding to Scenarios 6,7,8 and the new Scenario 9.

Summary
In summary, we observe after all updates (R K , R K * and B(B s → µ + µ − )) a very similar picture to the one previously found in Ref. [1] with some peculiarities. 1D global fits with all observables remain basically unchanged showing the preference for C NP 9µ scenario over C NP 9µ = −C NP 10µ , albeit with a slightly reduced difference of pulls. If only LFUV observables are considered the situation is reversed, as already happened in [1], but now with an increase of the difference in significances. The main differences arise in the 2D scenarios, where those including RHCs, (C NP 9µ , C 10 µ ) or (C NP 9µ , C 9 µ = −C 10 µ ), can accommodate better the new values, enhancing their significances compared to [1]. Finally, scenarios including LFU NP discussed in [2] stay practically unchanged but with some preference for scenarios 8 and 6, with a (V − A) structure for the LFUV-NP and a V or (V + A) structure for the LFU-NP. We have included an additional scenario 9 that exhibits a significance of 5.3σ. Now the amount on LFU is very sensitive to the structure of the LFUV component.