Implications of b→s measurements
IImplications of b → s measurements a Wolfgang Altmannshofer and David M. Straub ,b Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada N2L 2Y5 Excellence Cluster Universe, TU M¨unchen, Boltzmannstr. 2, 85748 Garching, Germany
The recent updated angular analysis of the B → K ∗ µ + µ − decay by the LHCb collaborationis interpreted by performing a global fit to all relevant measurements probing the flavour-changing neutral current b → sµ + µ − transition. A significant tension with Standard Modelexpectations is found. A solution with new physics modifying the Wilson coefficient C ispreferred over the Standard Model by 3 . σ . The tension even increases to 4 . σ includingalso b → se + e − measurements and assuming new physics to affect the muonic modes only.Other new physics benchmarks are discussed as well. The q dependence of the shift in C issuggested as a means to identify the origin of the tension – new physics or an unexpectedlylarge hadronic effect. Rare B and B s decays based on the b → s flavour-changing neutral current transition are sen-sitive to physics beyond the Standard Model (SM). Recent measurements at the LHC, comple-menting earlier B -factory results, have hugely increased the available experimental informationon these decays. Interestingly, several tensions with SM predictions have shown up in the data,most notably • several tensions at the 2–3 σ level in B → K ∗ µ + µ − angular observables in 1 fb − of LHCbdata taken during 2011 ; • a 2 . σ deviation from lepton flavour universality (LFU) in B + → K + (cid:96) + (cid:96) − decays measuredby LHCb, including the full 3 fb − dataset .Several model-independent theoretical analyses , , , , , , , have shown that both anomaliescould be explained by new physics (NP). Today, the LHCb collaboration has released an updateof the analyis of B → K ∗ µ + µ − angular observables based on the full 3 fb − dataset , finding asignificant tension in particular in the angular observable P (cid:48) . The aim of this talk is to interpretthese measurements by performing a global model-independent fit to all available data. Theresults are updates of an analysis published recently (and building on earlier work , , ),incorporating the new LHCb measurements. Crucially, the fit makes use of a combined fit to B → K ∗ form factors from light-cone sum rules and lattice QCD , published recently. The effective Hamiltonian for b → s transitions can be written as H eff = − G F √ V tb V ∗ ts e π (cid:88) i ( C i O i + C (cid:48) i O (cid:48) i ) + h.c. (1)Considering NP effects in the following set of dimension-6 operators, O = m b e (¯ sσ µν P R b ) F µν , O (cid:48) = m b e (¯ sσ µν P L b ) F µν , (2) O = (¯ sγ µ P L b )(¯ (cid:96)γ µ (cid:96) ) , O (cid:48) = (¯ sγ µ P R b )(¯ (cid:96)γ µ (cid:96) ) , (3) O = (¯ sγ µ P L b )(¯ (cid:96)γ µ γ (cid:96) ) , O (cid:48) = (¯ sγ µ P R b )(¯ (cid:96)γ µ γ (cid:96) ) , (4) a Talk presented at the 50th Rencontres de Moriond (Electroweak Session), La Thuile, 20 March 2015. b Speaker. a r X i v : . [ h e p - ph ] M a r ecay obs. q bin SM pred. measurement pull¯ B → ¯ K ∗ µ + µ − F L [2 , .
3] 0 . ± .
02 0 . ± .
19 ATLAS +2 . B → ¯ K ∗ µ + µ − F L [4 ,
6] 0 . ± .
04 0 . ± .
06 LHCb +1 . B → ¯ K ∗ µ + µ − S [4 , − . ± . − . ± .
08 LHCb − . B → ¯ K ∗ µ + µ − P (cid:48) [1 . , − . ± . − . ± .
11 LHCb − . B → ¯ K ∗ µ + µ − P (cid:48) [4 , − . ± . − . ± .
16 LHCb − . B − → K ∗− µ + µ − d BR dq [4 ,
6] 0 . ± .
08 0 . ± .
10 LHCb +2 . B → ¯ K µ + µ − d BR dq [0 . ,
2] 2 . ± .
50 1 . ± .
56 LHCb +1 . B → ¯ K µ + µ − d BR dq [16 ,
23] 0 . ± .
12 0 . ± .
22 CDF +2 . B s → φµ + µ − d BR dq [1 ,
6] 0 . ± .
06 0 . ± .
05 LHCb +3 . Table 1: Observables where a single measurement deviates from the SM by 1 . σ or more (cf. for the B → K ∗ µ + µ − predictions at low q ). one can construct a χ function which quantifies, for a given value of the Wilson coefficients,the compatibility of the hypothesis with the experimental data. It reads χ ( (cid:126)C NP ) = (cid:104) (cid:126)O exp − (cid:126)O th ( (cid:126)C NP ) (cid:105) T [ C exp + C th ] − (cid:104) (cid:126)O exp − (cid:126)O th ( (cid:126)C NP ) (cid:105) . (5)where O exp,th and C exp,th are the experimental and theoretical central values and covariancematrices, respectively. All dependence on NP is encoded in the NP contributions to the Wilsoncoefficients, C NP i = C i − C SM i . The NP dependence of C th is neglected, but all correlationsbetween theoretical uncertainties are retained. Including the theoretical error correlations andalso the experimental ones, which have been provided for the new angular analysis by the LHCbcollaboration, the fit is independent of the basis of observables chosen (e.g. P (cid:48) i vs. S i observables).In other words, the “optimization” of observables is automatically built in.In total, the χ used for the fit contains 88 measurements of 76 different observables by 6experiments (see the original publication for references). The observables include B → K ∗ µ + µ − angular observables and branching ratios as well as branching ratios of B → Kµ + µ − , B → X s µ + µ − , B s → φµ + µ − , B → K ∗ γ , B → X s γ , and B s → µ + µ − . Setting the Wilson coefficients to their SM values, we find χ ≡ χ ( (cid:126)
0) = 116 . p value of 2 . b → se + e − observables c the χ deteriorates to 125 . p = 0 . S , F L , P (cid:48) ), only the first two areincluded in the fit as the last one can be expressed as a function of them ,d . c We have not yet included the recent measurement of B → K ∗ e + e − angular observables at very low q .Although these observables are not sensitive to the violation of LFU, being dominated by the photon pole, theycan provide important constraints on the Wilson coefficients C ( (cid:48) )7 . d Including the last two instead leads to equivalent results since we include correlations as mentioned above;this has been checked explicitly. oeff. best fit 1 σ σ (cid:113) χ − χ p [%] C NP7 − .
04 [ − . , − .
01] [ − . , .
02] 1 .
42 2 . C (cid:48) .
01 [ − . , .
07] [ − . , .
12] 0 .
24 1 . C NP9 − .
07 [ − . , − .
81] [ − . , − .
53] 3 .
70 11 . C (cid:48) .
21 [ − . , .
46] [ − . , .
70] 0 .
84 2 . C NP10 .
50 [0 . , .
78] [ − . , .
08] 1 .
97 3 . C (cid:48) − .
16 [ − . , .
02] [ − . , .
21] 0 .
87 2 . C NP9 = C NP10 − .
22 [ − . , .
03] [ − . , .
33] 0 .
89 2 . C NP9 = − C NP10 − .
53 [ − . , − .
35] [ − . , − .
18] 3 .
13 7 . C (cid:48) = C (cid:48) − .
10 [ − . , .
17] [ − . , .
43] 0 .
36 1 . C (cid:48) = − C (cid:48) .
11 [ − . , .
22] [ − . , .
33] 0 .
93 2 . Table 2: Constraints on individual Wilson coefficients, assuming them to be real, in the global fit to 88 b → sµ + µ − measurements. The p values in the last column should be compared to the p value of the SM, 2 . Next, we have performed fits where a single real Wilson coefficient at a time is allowed to float.The resulting best-fit values, 1 and 2 σ ranges, pulls, and p values are shown in table 2. The bestfit is obtained for new physics in C only, corresponding to a 3 . σ pull from the SM. A slightlyworse fit with a pull of 3 . σ is obtained in the SU (2) L invariant direction C NP9 = − C NP10 . Thisdirection corresponds to an operator with left-handed leptons only and is predicted by severalNP models. If we include b → se + e − observables in the fit and assume NP to only affect the b → sµ + µ − modes, the pulls of these two scenarios increase to 4 . σ and 3 . σ , respectively.Allowing NP effects in two Wilson coefficients at the same time, one obtains the allowedregions shown in fig. 1 in the C - C plane and the C - C (cid:48) plane. Apart from the 1 σ and2 σ regions allowed by the global fit shown in blue, these plots also show the allowed regionswhen taking into account only B → K ∗ µ + µ − angular observables (red) or only branching ratiomeasurements of all decays considered (green). The result that the best fit is obtained by modifying the Wilson coefficient C might be worryingas this is the coefficient of an operator with a left-handed quark FCNC and a vector-like couplingto leptons; non-factorizable hadronic effects are mediated by virtual photon exchange and thusalso have a vector-like coupling to leptons (and the left-handedness of the FCNC transition isensured by the SM weak interactions). It is therefore conceivable that unaccounted for hadroniceffects could mimic a new physics effect in C . There are at least two ways to test this possibility.1. The hadronic effect cannot violate LFU, so if the violation of LFU in R K (or any of theother observables suggested, e.g., in ) is confirmed, this hypothesis is refuted;2. There is no a priori reason to expect that a hadronic effect should have the same q dependence as a shift in C induced by NP.Let us focus on the second point. With the finer binning of the new LHCb B → K ∗ µ + µ − angularanalysis, it is possible to determine the preferred range of a hypothetical NP contribution to C in individual bins of q . To this end, we have splitted all measurements of B → K ∗ µ + µ − - - - - Re ( C ) R e ( C N P ) - - - - - Re ( C ) R e ( C ) Figure 1 – Allowed regions in the Re( C NP9 )-Re( C NP10 ) plane (left) and the Re( C NP9 )-Re( C (cid:48) ) plane (right). The bluecontours correspond to the 1 and 2 σ best fit regions from the global fit. The green and red contours correspondto the 1 and 2 σ regions if only branching ratio data or only data on B → K ∗ µ + µ − angular observables is takeninto account. (including braching ratios and non-LHCb measurements) into sets with data below 2.3 GeV ,between 2 and 4.3 GeV , between 4 and 6 GeV , and above 15 GeV (the slight overlap of thebins, caused by changing binning conventions over time, is of no concern as correlations aretreated consistently). The resulting 1 σ regions are shown in fig. 2 (the fit for the region between6 and 8 GeV is shown for completeness as well but only as a dashed box because we assumenon-perturbative charm effects to be out of control in this region and thus do not include thisdata in our global fit). We make some qualitative observations, noting that these will have tobe made more robust by a dedicated numerical analysis. • The NP hypothesis requires a q independent shift in C . At roughly 1 σ , this hypothesisseems to be consistent with the data. • If the tensions with the data were due to errors in the form factor determinations, naivelyone should expect the deviations to dominate at one end of the kinematical range whereone method of form factor calculation (lattice at high q and LCSR at low q ) dominates.Instead, if at all, the tensions seem to be more prominent at intermediate q values whereboth complementary methods are near their domain of validity and in fact give consistentpredictions . • There does seem to be a systematic increase of the preferred range for C at q belowthe J/ψ resonance, increasing as this resonance is approached. Qualitatively, this is thebehaviour expected from non-factorizable charm loop contributions. However, the centralvalue of this effect would have to be significantly larger than expected on the basis ofexisting estimates , , , , , as conjectured earlier .Concerning the last point, it is important to note that a charm loop effect does not have tomodify the H − and H helicity amplitudes e in the same way (as a shift in C induced by NPwould). Repeating the above exercise and allowing a q -dependent shift of C only in one ofthese amplitudes, one finds that the resulting corrections would have to be huge and of the samesign. It thus seems that, if the tensions are due to a charm loop effect, this must contribute toboth the H − and H helicity amplitude with the same sign as a negative NP contribution to C . e The modification of the H + amplitude is expected to be suppressed , . - - - q [ GeV ] C N P Figure 2 – Purple: ranges preferred at 1 σ for a new physics contribution to C from fits to all B → K ∗ µ + µ − observables in different bins of q . Blue: 1 σ range for C NP9 from the global fit (cf. tab. 2). Green: 1 σ range for C NP9 from a fit to B → K ∗ µ + µ − observables only. The vertical gray lines indicate the location of the J/ψ and ψ (cid:48) resonances, respectively. The new LHCb measurement of angular observables in B → K ∗ µ + µ − is in significant tensionwith SM expectations. An explanation in terms of new physics is consistent with the data.Models with a negative shift of C or with C NP9 = − C NP10 < .Arguments have been given why the tension being caused by underestimated form factoruncertainties, suggested as an explanation of the original B → K ∗ µ + µ − anomaly , doesnot seem to be supported by the data. A detailed numerical analysis of this point, with thehelp of the new LCSR result (and possibly the relations in the heavy quark limit , , as across-check) would be interesting.An important cross-check of the NP hypothesis is the q dependence of the preferred shift in C and it has been argued that also an unexpectedly large charm-loop contribution at low q nearthe J/ψ resonance could solve, or at least reduce, the observed tensions. A possible experimentalstrategy to resolve this ambiguity could contain, among others, the following steps. • Testing LFU in the B → K ∗ µ + µ − vs. B → K ∗ e + e − branching ratios and angular observ-ables, where spectacular deviations from the SM universality prediction would occur if the R K anomaly is due to NP , , , which can be accomodated in various NP models witha Z (cid:48) boson , , , , , , f or leptoquarks , , , , , ; • Searching for lepton flavour violating B decays like B → K ( ∗ ) e ± µ ∓ , because in leptoquarkmodels explaining the B → K ∗ µ + µ − anomaly, either R K ( ∗ ) deviates from one or leptonflavour is violated , and also in Z (cid:48) models these decays could arise . • Measuring the T-odd CP asymmetries , A , , , which could be non-zero in the presenceof new sources of CP violation. • Measuring BR( B s → µ + µ − ) more precisely as a clean(er) probe of C .The first three items are null tests of the SM and could unambiguously prove the presence ofnew physics not spoiled by hadronic uncertainties; the last one is at least much cleaner thansemi-leptonic decays. f Some Z (cid:48) models , , , predict LFU to hold but could still solve the B → K ∗ µ + µ − anomaly. n the theory side, the new more precise data could be used, in the spirit of fig. 2, to extractthe preferred size, q and helicity dependence of a possible hadronic effect, assuming the SM.Combined with a better understanding of the charm-loop effect and more precise estimates ofits possible size, this could shed light on the important question whether the effect observedby LHCb is the first evidence for physics beyond the Standard Model, or our understanding ofstrong interaction effects in rare semi-leptonic B decays has to be revised. Both possibilities willhave important implications. Acknowledgments
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