First, we consider fits to NP scenarios which affect muon modes only. In Tables8.1and8.2, we give the fit results for several one- or two-dimensional hypothesis for NP contributions to the various operators, with two different datasets: either we include all available data from muon and electron channels presented in the previous section (column “All”, 180 measurements), or we include only LFUV observables, i.e. RK and RK∗ from LHCb and Belle andQi (i= 4,5) from Belle (column
“LFUV”, 22 measurements). In both cases, we include also the b → sγ observables, as well as B(B → Xsµ+µ−) and B(Bs → µ+µ−). The SM point yields a χ2 corresponding to a p-value of 11.0% for the fit “All” and 8.0% for the fit “LFUV” [197].
All LFUV
1D Hyp. Best fit 1σ/2σ PullSM p-value Best fit 1σ/ 2σ PullSM p-value C9µNP -0.98 [−1.15,−0.81]
5.6 65.4 % -0.89 [−1.23,−0.59]
3.3 52.2 %
[−1.31,−0.64] [−1.60,−0.32]
CNP9µ =−C10µNP -0.46 [−0.56,−0.37]
5.2 55.6 % -0.40 [−0.53,−0.29]
4.0 74.0 %
[−0.66,−0.28] [−0.63,−0.18]
C9µNP=−C90µ -0.99 [−1.15,−0.82]
5.5 62.9 % -1.61 [−2.13,−0.96]
3.0 42.5 %
[−1.31,−0.64] [−2.54,−0.41]
C9µNP=−3C9eNP -0.87 [−1.03,−0.71]
5.5 61.9 % -0.66 [−0.90,−0.44]
3.3 52.2 %
[−1.19,−0.55] [−1.17,−0.24]
Table 8.1: Most prominent 1D patterns of NP inb→sµ+µ−. PullSMis quoted in units of standard deviation.
−3.0−2.4 −1.8 −1.2−0.6 0.0 0.6 1.2 1.8 2.4 3.0 planes for the corresponding two-dimensional hypotheses, using all available data (fit “All”). We also show the 3σ regions for the data subsets corresponding to specific experiments. Constraints fromb→sγ observables, B(B →Xsµµ) and B(Bs→µµ) are included in each case (see text).
We start by discussing NP hypotheses for the fit “All”. New available experimental data have further increased the significance of already prominent hypotheses in previous studies, namely, the first three hypotheses (C9µNP, C9µNP =−C10µNP and C9µNP =−C90µ) already identified in Refs. [113, 153]. The PullSMof current estimates exceeds 5σ in each case, however hypotheses can hardly be distinguished on this criterion, and as we will discuss in Section 8.5, the Qi observables will be very powerful tools to lift this quasi-degeneracy. We do not observe any significant differences in the 1D scenarios with “All” data compared to our previous analysis in Ref. [136].
Further scrutiny of the differences between our current most updated fits and the results from our earlier analysis [136], reveals that the scenario C9µNP = −C90µ, which would predict RK = 1 and RK∗ < 1 [113, 192, 193, 211, 212], has an increased significance in the “All” fit. Also, the best-fit point for the scenario C9µNP now coincides in the “All” and LFUV fits, as opposed to our previous conclusions in Ref. [136]. On the other hand, NP solutions based on C10µNP only show a significance in the “All” fit at the level of 4.0σ (3.9σ for the LFUV fit), which explains its absence from Tab.8.1 as in Ref. [136].
Besides providing the results for “simple” one- and two-dimensional hypotheses, we discuss five additional illustrative examples of NP hypotheses with specific chiral structures, leading to correlated shifts in Wilson coefficients. These hypotheses are:
1. (C9µNP=−C90µ,C10µNP =C100µ), 2. (C9µNP=−C90µ,C10µNP =−C100µ), 3. (C9µNP=−C10µNP,C90µ=C100µ), 4. (C9µNP=−C10µNP,C90µ=−C100µ), 5. (C9µNP,C90µ=−C100µ).
Concerning the 2D scenarios collected in Tab.8.2, no significant changes can be be identified with respect to Ref. [136]. Nevertheless, with an RK value closer to one, scenarios with right-handed currents (RHC) seem to emerge. Indeed, hypothesis 5 has now the highest PullSM, indicating that
8.2. Global analyses of b→s`` data 137 small contributions to RHC are slightly favoured (C90µ > 0,C100µ < 0) 2. Note that these RHC contributions tend to increase the value of RK while C9µNP <0 tend to decrease it. From a model-independent point of view, the also very competitive Hypothesis 1 is particularly interesting to yield a low value forRK∗ (especially if a contribution C7NP > 0 is allowed). TakingC10µNP =−C100µ (i.e.
Hypothesis 2) reduces the significance from 5.9σ to 5.3σ, similarly to Hypotheses 3 and 4 with the signature structureC9µNP=−C10µNP (irrespective of the relative sign taken to constrainC90µ=±C100µ).
Finally, the comparison between Hyps. 4 and 5 shows that the scenarioC90µ=−C100µ(left-handed lepton coupling for right-handed quarks) prefers to be associated withCNP9µ (vector lepton coupling for left-handed quarks) rather than C9µNP = −C10µNP (left-handed lepton coupling for left-handed quarks).
Up to now, we have discussed scenarios where NP contributions occur only in b → sµµ transitions. It is also interesting to consider scenarios with NP in both muon and electron channels, in particular (C9µNP,C9eNP), with a SM pull of 5.3σ and a p-value of 66.2%. While CNP9µ ∼ −1 is preferred over the SM with a significance around 5σ, C9e is compatible with the SM already at 1σ, in agreement with the LFUV data included in the fit. New data included in our updated analysis [197] has induced a change on the central value of C9e: whereas the fit of Ref. [136]
suggested a patternC9e >0, now we observe C9e.0.
All LFUV
2D Hyp. Best fit PullSM p-value Best fit PullSM p-value (CNP9µ,C10µNP) (-0.91,0.18) 5.4 68.7 % (-0.16,0.56) 3.4 76.9 % (CNP9µ,C70) (-1.00,0.02) 5.4 67.9 % (-0.90,-0.04) 2.9 55.1 % (C9µNP,C90µ) (-1.10,0.55) 5.7 75.1 % (-1.79,1.14) 3.4 76.1 % (CNP9µ,C100µ) (-1.14,-0.35) 5.9 78.6 % (-1.88,-0.62) 3.8 91.3 % (C9µNP,CNP9e ) (-1.05,-0.23) 5.3 66.2 % (-0.73,0.16) 2.8 52.3 % Hyp. 1 (-1.06,0.26) 5.7 75.7 % (-1.62,0.29) 3.4 77.6 % Hyp. 2 (-0.97,0.09) 5.3 65.2 % (-1.95,0.25) 3.2 66.6 % Hyp. 3 (-0.47,0.06) 4.8 55.7 % (-0.39,-0.13) 3.4 76.2 % Hyp. 4 (-0.49,0.12) 5.0 59.3 % (-0.48,0.17) 3.6 84.3 % Hyp. 5 (-1.14,0.24) 5.9 78.7 % (-2.07,0.52) 3.9 92.5 %
Table 8.2: Most prominent 2D patterns of NP in b → sµ+µ−. The last five rows correspond to Hypothesis 1: (C9µNP = −C90µ,C10µNP = C100µ), 2: (C9µNP = −C90µ,C10µNP = −C100µ), 3: (C9µNP =
−C10µNP,C90µ=C100µ), 4: (C9µNP=−C10µNP,C90µ=−C100µ) and 5: (C9µNP,C90µ=−C100µ).
In Fig.8.1we show the corresponding constraints for the fit “All” under the three hypotheses (C9µNP,C10µNP), (C9µNP,C9µ0) and (C9µNP,C9eNP), as well as the 3σ regions according to the results from individual experiments (for each region, we add the constraints fromb→sγ observables, B(B → Xsµ+µ−) and the average for B(Bs→ µ+µ−)). As expected, the LHCb results drive most of the effect, with a clear exclusion of the origin, i.e. the SM point.
We can now move to the LFUV fit in Fig.8.2, where we consider the same hypotheses favoured by global analyses. Note that this restricted subset of observables excludes the SM point with a higher significance, even though the p-value of the SM has increased with respect to Ref. [136]
as a result of including new data points with little resolution (Belle measurements of RK and
2Interestingly, these small contributions also reduce slightly the mild tension betweenP50 at large and low recoils pointed out in Ref. [212] compared to the scenario with onlyC9µNP.
−3.0−2.4 −1.8 −1.2−0.6 0.0 0.6 1.2 1.8 2.4 3.0 for the corresponding two-dimensional hypotheses, using only LFUV observables (fit “LFUV”).
Constraints from b→ sγ observables, B(B → Xsµµ) and B(Bs →µµ) are included in each case (see text).
RK∗). Contrarily, the p-value of the SM for the fit “All” has not followed the same trend and currently stays at the same level as in 2017, hence no overall improvement of the SM in describing current data. While the same pattern of hierarchies is observed for this fit compared to our 2017 analysis [136], the PullsSM for some of 1D fits get reduced by half a standard deviation. It is important to stress that this fit favours regions similar to the fit “All” dominated by different b→sµµ-related observables (B →K∗µµoptimised angular observables as well as low- and large-recoil branching ratios forB →Kµµ,B →K∗µµandBs→φµµ). This is also shown in Tabs.8.1 and8.2, where the scenarios with the highest pulls are confirmed with significances between 3 and 4σ, but get harder to distinguish on the basis of their significance.
C7NP C9µNP C10µNP C70 C90µ C100µ
Best fit +0.01 -1.10 +0.15 +0.02 +0.36 -0.16
1σ [−0.01,+0.05] [−1.28,−0.90] [−0.00,+0.36] [−0.00,+0.05] [−0.14,+0.87] [−0.39,+0.13]
2σ [−0.03,+0.06] [−1.44,−0.68] [−0.12,+0.56] [−0.02,+0.06] [−0.49,+1.23] [−0.58,+0.33]
Table 8.3: 1 and 2σ confidence intervals for the NP contributions to Wilson coefficients in the 6D hypothesis allowing for NP inb→sµ+µ− operators dominant in the SM and their chirally-flipped counterparts, for the fit “All”. The PullSM is 5.1 σ and thep-value is 81.6%.
Finally, we extend our analyses to include a six-dimensional fit allowing for NP contributions to all relevant Wilson coefficients C7(0),9(0)µ,10(0)µ. The associated SM pull to this fit has shifted from 3.6σ in Ref. [113] to 5.1 σ, if one considers the fit “All” described above. Corresponding 1 and 2σ CL intervals are given in Tab. 8.3, with the pattern:
C7NP &0,C9µNP<0,C10µNP >0,C70 &0,C90µ>0,C100µ.0 (8.2.7) whereC9µ is compatible with the SM beyond 3σand all the other coefficients at 1σ. No significant changes are observed in the updated 6D fit with respect to the result of the same fit in Ref. [136], except for a slight increase in the PullSMand the preference for a negative C100µ.
8.2. Global analyses of b→s`` data 139
Scenario Best-fit point 1σ 2σ PullSM p-value
Scenario 5
Table 8.4: Most prominent patterns for LFU and LFUV-NP contributions from Fit “All”. Sce-narios 5 to 8 were introduced in Ref. [211]. SceSce-narios 9 (motivated by 2HDMs [213]) and 10 to 13 (motivated by Z0 models with vector-like quarks [214]) are new.