EPJ Web of Conferences 49, 15001 (2013) DOI: 10.1051/epjconf/20134915001 C Owned by the authors, published by EDP Sciences, 2013
Rare B decays at LHCb T. Blake1 , a on behalf of the LHCb collaboration 1
CERN, Switzerland
Abstract. Rare B meson decays are an ideal place to search for the effects of new particles that could arise in extensions to the Standard Model and couple to the flavour sector. Measurements of the rare B decay processes at LHCb are presented. The relationship between these different measurements is described. Finally, the implication of these measurements for SUSY/Exotic searches is discussed.
1 Introduction The phrase “rare decay” is often used to describe a set of flavour changing neutral current processes that, are forbidden at tree level, and are mediated by electroweak box and penguin type diagrams in the Standard Model. These processes include: radiative b → sγ transitions; decays of B mesons to a pair of opposite charge leptons and semileptonic b → s`+ `− (where ` = e, µ, τ) decays. In many extensions to the SM, these rare decay processes can receive contributions from new virtual particles that can enhance (or suppress) the branching fraction of the decays or change the angular distribution of the B decay products.
example are governed by the magnetic penguin operator that is commonly labelled O7 . The purely leptonic decay B0s → µ+ µ− is governed by the axial-vector operator (O10 ) and semileptonic b → s`+ `− decays receive contributions from O7 , O10 and the vector operator O9 . In the SM, contributions to the right-handed counterparts of O7 , O9 and O10 , labelled below with a prime, are highly suppressed (by m s /mb ) as are contributions to scalar, OS , or pseudoscalar, OP , operators. Contributions to these operators can be significantly enhanced in many extensions to the SM.
3 Radiative decays 2 Effective field theory for b → s processes The phenomenology of rare B meson decays is a multiscale problem; at one end, the electroweak-scale of the weak interaction and at the other end, ΛQCD . Rare b → s decay processes can therefore be treated using an effective field theory, with a Hamiltonian X X 4G F Heff = − √ Vtb Vts∗ CSM OSM + CNP ONP , 2 SM NP
(1)
where G F is the Fermi constant and the Vtb Vts∗ the product of CKM matrix elements. The O are local operators with different Lorentz structures and the C are Wilson coefficients that contain information on the heavy degrees of freedom (the top-quark, W ± , Z 0 and Higgs in the SM). Finally, in extensions to the SM it is possible to have new particles, at a mass scale ΛNP , that contribute to the SM set of local operators or introduce entirely new operators with CNP ∝ 1/ΛNP . Different processes receive contributions from different local operators. Radiative decays of B mesons, which at the quark level correspond to a b → sγ transition, for a e-mail:
[email protected]
There is a wealth of information on C7 and C70 from measurements of radiative b → sγ decays at the B-Factories and CLEO-c, see for example Ref. [1]. The two most stringent constraints come from measurements of the inclusive branching fraction, B(b → sγ), which constrains |C7 |2 + |C70 |2 but does not distinguish between C7 and C70 , and measurements of time dependent CP violation in B0 → K ∗0 γ (K ∗0 → K 0 π0 ) decays, S K ∗0 γ , which constrains C7 /C70 . These constraints on C7 and C70 are shown in Fig. 5. Unfortunately both measurements are challenging in a hadronic environment and are unlikely to be improved by LHCb. At LHCb however, additional constraints on C7 and C70 can be determined: from the lifetime dependence of B0s → φγ decays [2]; from measurements of the photon and proton angular distributions in radiative Λb decays [3, 4] and from asymmetries in B decays to final states containing a photon, a pseudoscalar and a vector meson such as B+ → φK + γ [5, 6]. To highlight the potential of the radiative decay programme of LHCb, the K + π− γ and K + K − γ invariant mass of B0 → K ∗0 γ and B0s → φγ candidates, in a data sample of 1 fb−1 , are shown in Fig. 1. Signals of 5279 ± 93 and 601 ± 36 candidates are seen for B0 → K ∗0 γ and B0s → φγ respectively [7]. These samples are far larger than the sam-
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2 .0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20134915001
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TABLE I. Expected and observed limits on the B 0 → µ+ µ− branching fractions for the 2012 and for the combined LHCb 2011+2012 datasets.
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+ 0 FIG. 1. CLs as a function of the assumed → µ+2µ)− branchM(K K γ)B(MeV/c ing fraction for the combined 2011+2012 dataset. The dashed gray curve is the median of the expected CLs distribution if < 10.3 × 10−10 at 95 % CL [8], respectively. The pbackground and SM signal were observed. The shaded yellow area covers, for each branching fraction value, 34 % of the exvalue for Bs0 → µ+ µ− changes from 18 % to 11 % and 0 ++ − − + − 0 on each side of components its median.are: Thethe solid s distribution theFigure Bs →1.µK µπ γbranching increases σ (left) and K fraction K γ (right) invariant by mass∼of0.3 selected Bpected → K ∗0CL γ and B0s → φγ candidates. The fit +1.8 +1.7 + curve − +s . + − 0 0 + − 0 −9 (red dashed); Λ → red −9 is the observed CL signal dotted); combinatorial background p K γ (purple dot-dashed); B → K π π and B → K K π . This shift from (0.8(green ) × 10 to (1.4 ) × 10 b s −1.3 −1.3 (black long-dashed and blue dotted); partially reconstructed decays with one or more missing particles (blue dashed and black dotted). is compatible with the systematic uncertainty previously
assigned to the background shape [8]. The values of the Bs0 → µ+ µ− branching fraction obtained with the 2011 andples 2012 datasets areB-factories compatible within 1.5σ. show that available at the and importantly The 2011 and 2012 results are combined by computing the various sources of background can be controlled. the CLs and performing the maximum-likelihood fit simultaneously to the eight and seven BDT bins of the 2011 and4 2012 datasets, respectively. The parameters that Leptonic decays are considered 100 % correlated between the two datasets + 0 K +π +−− the areThe fs /fbranching → J/ψKof+ )the and B(B 0B→ fraction decays d , B(B s → µ µ ), and transition the Crystal function describing B0 → µ+point µ− areofsuppressed bothBall by the loop-order of the theprocess signal and mass theSM. mass distribution of the by lineshape, helicity in the In the SM, the branch0 0 B(s) h+ h"− scale background, BDT and mass ing→fractions as C10 − Cthe extensions to thedistriSM, 10 . In 0are large − + 0(+) 0(+) + or in which there contributions to either scalar butions of the B → π µ νµ and B →π µ µ− 0 pseudo-scalar operators (denoted C and C ), the branchS of theP B → µ+ µ− backgrounds and the SM predictions s 0fraction + of − the decay can see large enhancements, ing and B → µ µ branching fractions. The distribution of the expected and observed events in bins of BDT in the simultaneous analysis of signal regions obtained from the 4m2µ 0 + − datasets, 0 2 the 2011 and 2012 are summarized in Table II. B(Bs → µ µ ) ∝ 1 − 2 |C S − CS | + mB
2m2µ 0 2 |C P − C P0 + 2 (C10 − C10 )| . (2) M The expected and observed upperB limits for the B 0 → µ+ µ− channel obtained from the combined 2011+2012 Large contributions to CSinand C P often models datasets are summarized Table I andarise the inexpected with extended Higgs sectors, e.g. in SUSY models or and observed CLs values as a function of the branching models with two Higgs-doublets. fraction are shown in Fig. 1. The observed CLb value LHCb, B0 → µ+ µ− candidates are selected using at CLIn s+b = 0.5 sis 89 %. The probability that backa loose pre-selection are then a BDT ground processes can and produce theclassified observedusing number of 0 based + − −4 on the kinematic properties of the reconstructed B0s Bs → µ µ candidates or more is 5 × 10 and correcandidate. The analysis procedureofis3.5σ. described detail sponds to a statistical significance The in value of 0 + The − in Ref. [8]. dimuon invariant mass of the candidates the Bs → µ µ branching fraction obtained from the fit is with a signal-like BDT response is shown in Fig. 2. LHCb observes a signal that is incompatible with the background −9for only s0hypothesis providing+0.5 the first evidence B(B → µ+ µ− )at=3.5σ, (3.2 +1.4 −1.2 (stat) −0.3 (syst)) × 10 0 + − the Bs → µ µ decay. and is Normalising in agreement the SM The thewith observed yieldexpectation. with respect to B+ in→ 0 + − + 0 + − variant theaccounting B(s) → µ for µ the candidates J/ψ Kmass anddistribution B → K π ofand ratio of fragmentation fractions, f s / fd , yields −9 B(B0s → µ+ µ− ) = (3.2 +1.5 . −1.2 ) × 10
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Figure 2. Dimuon invariant mass of B0s → µ+ µ− canidates0 FIG. 2. Invariant distribution of the selected s → with signal-like BDT mass responses. The fit components are: B the + − µ µ µ+candidates (black dots) with 0.7 in the comB0s → µ− signal (red long-dashed); B0 →BDT µ+ µ−>(green mediumbined 2011+2012 dataset. The result of the fit is overdashed); B0 → K + π− , B0 → π+ π− and other B(s) → h+ h− peaking laid (blue solid line) and the different components detailed: backgrounds (pink dotted); B0 → π− µ+ νµ (black short-dashed); Bs0 → µ++ µ− − (red long dashed), B 0 → µ+ µ− (green medium B → πµ µ (light blue +dot-dashed); combinatorial0 background 0 "− dashed), B(s) → h h (pink dotted), B → π − µ+ νµ (blue medium dashed). (black short dashed) and B 0(+) → π 0(+) µ+ µ− (light blue dot dashed), and the combinatorial background (blue long dashed). 496 497 498 499 500 501 502 503 504
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This should be compared to a time-integrated SM expectation 10]value of The[9, true of the Bs0 → µ+ µ− branching fraction is contained in the interval [1.1, 6.4] × 10−9 at 95 % CL, 0 µ+ µ−upper ) = (3.5 ± 0.3) 10−9branching , where theB(B lower limit are×the fracs →and tions = 0.975 and = 0.025, s+bagreement which evaluated is clearly at in CL good with CL thes+b observed respectively. results are in good with limit. Barring These fortuitous cancellation (e.g. agreement CS = CS0 or 0 the andrules upper derived fromfrom integrating C P =lower C P ) this outlimits large contributions either CS the profile obtained from the unbinned fit. or C P tolikelihood the branching fraction. In summary, a search for the rare decays Bs0 → µ+ µ− and B 0 → µ+ µ− is performed using 1.0 fb−1 and 1.1 fb−1
5 Semileptonic decays
The most stringent experimental constraints on axialvector and vector operators come from semileptonic B meson decays, in particular from the branching fraction and
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Figure 3. Angular observables in the B0 → K ∗0 µ+ µ− decay: dimuon system forward backward asymmetry, AFB (top left); fraction of longitudianl polariation of the K ∗0 , FL (top right), a term proportional to the asymmetry between the two transverse amplitudes (S 3 ). The observable S 9 is suppressed by small strong phases and is a null-test.
angular distribution of B0 → K ∗0 µ+ µ− and B+ → K + µ+ µ− decays. 5.1 The B0 → K ∗0 µ+ µ− decay
The four-body final state of the B0 → K ∗0 µ+ µ− decay can be described in terms of three angles (θ` , θK and φ) and the invariant mass squared, q2 , of the dimuon system (see for example Ref. [11]) 9
X d4 Γ = Ji (q2 ) fi (cos θ` , cos θK , φ). dq2 d cos θ` d cos θK dφ i=0 (3) The Ji are billinear combinations of K ∗0 spin-amplitudes that in turn depend on the Wilson coefficients C7(0) , C9(0) and (0) C10 and B → K ∗0 form-factors (the contribution from CS and C P to the angular distribution is small). The dominant theoretical uncertainties arise from the form-factors and can be mitigated by forming angular observables in which the form-factor uncertainties can be cancelled. Due to the limited size of the available data samples (900 candidates in LHCb), the angular distribution is simplified by transforming the φ angle or integrating over two of the three angles. This leaves four free parameters: the fraction of longitudinal polarisation of the K ∗0 , FL ; the
forward backward asymmetry of the dimuon system, AFB ; and a parameter that is sensitive to the asymmetry between the transverse K ∗0 spin amplitudes, S 3 . In the preliminary LHCb result, the fourth parameter, S 9 , is suppressed by small strong phases and is expected to be close to zero. Figure 3 shows the values of AFB , FL , S 3 and S 9 measured by the LHCb [12], BaBar [13], Belle [14] and CDF [15] experiments in six bins of q2 . The results are consistent between the different experiments and consistent with the SM expectation (which is included in the figure). In the SM AFB varies with q2 and changes sign at 2 q0 ∼ 4 GeV2 /c4 due to the interplay between C7 and C9 . This behaviour is reproduced by the LHCb data. Fitting forward- and backward-going events separately as a function of q2 gives a zero crossing point, 2 4 q20 = 4.9+1.3 −1.1 GeV /c .
The presence of this crossing point fixes the sign of C7 with respect to C9 . 5.2 The B+ → K + µ+ µ− decay
The B+ → K + µ+ µ− decay can be described by a single angle, θ` , defined in the rest frame of the dimuon system [16]
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1 dΓ[B+ → K + µ+ µ− ] 3 = (1 − FH )(1 − cos2 θ` ) Γ dcos θ` 4 1 + FH + AFB cos θ` , 2
(4)
and two parameters, the forward backward asymmetry of the dimuon system, AFB and a parameter FH . In the SM AFB is vanishingly small and FH tends to be close to zero. Both AFB and FH can be significantly enhanced in models in which CS(0) or C P(0) are large or in models which give rise to new local operators that have a tensor-like Lorentz structure (which can occur in Leptoquark models) [17]. In contrast to the decay B0s → µ+ µ− the (differential) branching fraction of the decay scales as dB ∝|(C10 + C010 ) f+ (q2 )|2 + dq2 |(C9 + C09 ) f+ (q2 ) +
2mb (C7 + C07 ) fT (q2 )|2 . M B + MK (5)
Measurements of AFB , FH and dB/dq2 at LHCb are described in Ref. [18]. Using 1 fb−1 of integrated luminosity, LHCb observers 1232 ± 40 candidates with an excellent signal-to-background ratio. Figure 4 shows the differential branching fraction and of AFB measured by the LHCb [18], BaBar [13], Belle [14] and CDF [15] experiments in six bins of q2 . These are largely compatible with the SM expectation but favour a smaller branching fraction at low q2 than is predicted in the SM. The parameter FH is not shown but is also compatible with the SM.
measurements, more stringent constraints are achieved on non-SM contributions to the Wilson coefficients. Unfortunately, the individual measurements and the global combination is in good agreement with the SM (which corre0 NP sponds to C(7,9,10) = 0 and C7,9,10 = 0). Translating these constraints on the Wilson coefficients into constraints on the masses of new particles in extensions to the SM is highly model dependent. In models that would introduce tree-level FCNC’s , the constraints on the Wilson coefficients typically imply the mass scale of the new particles, ΛNP , is O(10 − 100 TeV). In many SUSY/Exotic scenarios, the new particle contributions are loop-supressed and typically enter with the same CKMlike hierachy as the SM. In such scenarios, the constraints from rare decay measurements are weakened but still imply ΛNP is in the range 100 GeV − 1 TeV. Studies have also been carried out in specific models. In the CMSSM for example (Ref. [19]), the branching fraction of the B0s → µ+ µ− decay scales approximately as tan6 β/MA4 . At tan β = 50, the B0s → µ+ µ− branching fraction measurement excludes regions of the m0 : m 21 plane with masses below 1 TeV. At these large values of tan β the indirect constraints from rare decay measurements can be stronger than the limits from direct searches at ATLAS and CMS (see Fig. 6).
7 Conclusion The rare decay programme of LHCb is a very active area. New results will appear in the near future from the full 2011 and 2012 data sets and 3 fb−1 of integrated luminosity. This larger data set will enable LHCb to improve its existing measurements and will open up new avenues of exploration in rare b → s and rare b → d processes (that have not been discussed in these proceedings).
6 Implications of recent measurements A global combination of the various rare decay measurements has been made by several groups. An example from Ref. [20] is shown in Fig. 5. By combining several
References [1] S. Descotes-Genon, D. Ghosh, J. Matias, M. Ramon, JHEP 06, 099 (2011), 1104.3342
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Figure 5. Constraints on C7(0) (left) from measurements of B(b → sγ) (yellow doughnut), B(b → s`+ `− ), where ` = µ, e (large brown circle), S K ∗ γ (purple cross) and the angular analysis of B0 → K ∗0 µ+ µ− (complex green region). Constraints on C9(0) and C1 0(0) (center and right) from measurements of B(b → s`+ `− ) (brown doughnut), B(B+ → K + µ+ µ− ) (twin blue bands), B(B0s → µ+ µ− ) (wide grey (0) band in C10 plane) and the angular analysis of B0 → K ∗0 µ+ µ− (complex green region). The constraints are given at the 90% CL. The combined constraint is also shown (in red). The SM point corresponds to the intercept of the dashed lines. Figure reproduced from Ref. [20].
Figure 6. Constraints in the m0 : m 1 plane of the CMSSM at 2 tan β = 50 from the branching fraction of B0s → µ+ µ− (yellow region) and direct searches (red and black lines) at CMS with up to 5 fb−1 of integrated luminosity. The allowed region is also indicated (in green). Figure reproduced from Ref. [19].
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