Rare B decays at LHCb

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.


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.

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, Λ QCD .Rare b → s decay processes can therefore be treated using an effective field theory, with a Hamiltonian where G F is the Fermi constant and the V tb V * ts 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 Λ NP , that contribute to the SM set of local operators or introduce entirely new operators with C NP ∝ 1/Λ NP .
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: thomas.blake@cern.chexample are governed by the magnetic penguin operator that is commonly labelled O 7 .The purely leptonic decay B 0 s → µ + µ − is governed by the axial-vector operator (O 10 ) and semileptonic b → s + − decays receive contributions from O 7 , O 10 and the vector operator O 9 .
In the SM, contributions to the right-handed counterparts of O 7 , O 9 and O 10 , labelled below with a prime, are highly suppressed (by m s /m b ) as are contributions to scalar, O S , or pseudoscalar, O P , operators.Contributions to these operators can be significantly enhanced in many extensions to the SM.

Radiative decays
There is a wealth of information on C 7 and C 7 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 |C 7 | 2 + |C 7 | 2 but does not distinguish between C 7 and C 7 , and measurements of time dependent CP violation in B 0 → K * 0 γ (K * 0 → K 0 π 0 ) decays, S K * 0 γ , which constrains C 7 /C 7 .These constraints on C 7 and C 7 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 C 7 and C 7 can be determined: from the lifetime dependence of B 0 s → φγ decays [2]; from measurements of the photon and proton angular distributions in radiative Λ b 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 B 0 → K * 0 γ and B 0 s → 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 B 0 → K * 0 γ and B 0 s → φγ respectively [7].These samples are far larger than the sam- ples available at the B-factories and importantly show that the various sources of background can be controlled.

Leptonic decays
The branching fraction of the decays B 0 s → µ + µ − and B 0 → µ + µ − are suppressed both by the loop-order of the process and by helicity in the SM.In the SM, the branching fractions scale as C 10 − C 10 .In extensions to the SM, in which there are large contributions to either scalar or pseudo-scalar operators (denoted C S and C P ), the branching fraction of the decay can see large enhancements, Large contributions to C S and C P often arise in models with extended Higgs sectors, e.g. in SUSY models or models with two Higgs-doublets.
In LHCb, B 0 s → µ + µ − candidates are selected using a loose pre-selection and are then classified using a BDT based on the kinematic properties of the reconstructed B 0 s candidate.The analysis procedure is described in detail in Ref. [8].The dimuon invariant mass of the candidates with a signal-like BDT response is shown in Fig. 2. LHCb observes a signal that is incompatible with the background only hypothesis at 3.5σ, providing the first evidence for the B 0 s → µ + µ − decay.Normalising the observed yield with respect to B + → J/ψ K + and B 0 → K + π − and accounting for the ratio of fragmentation fractions, f s / f d , yields   II.with BDT > 0.7 is shown in Fig. 2.This should be compared to a time-integrated SM expectation [9,10] of , which is clearly in good agreement with the observed limit.Barring fortuitous cancellation (e.g.C S = C S or C P = C P ) this rules out large contributions from either C S or C P to the branching fraction.

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 The observable S 9 is suppressed by small strong phases and is a null-test.

The
The four-body final state of the B 0 → K * 0 µ + µ − decay can be described in terms of three angles (θ , θ K and φ) and the invariant mass squared, q 2 , of the dimuon system (see for example Ref. [11]) (3) The J i are billinear combinations of K * 0 spin-amplitudes that in turn depend on the Wilson coefficients C ( ) 7 , C ( ) 9 and C ( ) 10 and B → K * 0 form-factors (the contribution from C S 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 , F L ; the forward backward asymmetry of the dimuon system, A FB ; 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 A FB , F L , S 3 and S 9 measured by the LHCb [12], BaBar [13], Belle [14] and CDF [15] experiments in six bins of q 2 .The results are consistent between the different experiments and consistent with the SM expectation (which is included in the figure).
In the SM A FB varies with q 2 and changes sign at q 2 0 ∼ 4 GeV 2 /c 4 due to the interplay between C 7 and C 9 .This behaviour is reproduced by the LHCb data.Fitting forward-and backward-going events separately as a function of q 2 gives a zero crossing point, The presence of this crossing point fixes the sign of C 7 with respect to C 9 .

The B
The B + → K + µ + µ − decay can be described by a single angle, θ , defined in the rest frame of the dimuon system [16] 15001-p.3The forward-backward asymmetry of the decay is expected to be zero in the SM.
and two parameters, the forward backward asymmetry of the dimuon system, A FB and a parameter F H .In the SM A FB is vanishingly small and F H tends to be close to zero.Both A FB and F H can be significantly enhanced in models in which C ( ) S or C ( ) P 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 B 0 s → µ + µ − the (differential) branching fraction of the decay scales as Measurements of A FB , F H and dB/dq 2 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 A FB measured by the LHCb [18], BaBar [13], Belle [14] and CDF [15] experiments in six bins of q 2 .These are largely compatible with the SM expectation but favour a smaller branching fraction at low q 2 than is predicted in the SM.The parameter F H is not shown but is also compatible with the SM.

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 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 corresponds to C (7,9,10) = 0 and C NP 7,9,10 = 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, Λ NP , 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 Λ NP 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 B 0 s → µ + µ − decay scales approximately as tan 6 β/M 4 A .At tan β = 50, the B 0 s → µ + µ − branching fraction measurement excludes regions of the m 0 : m 1 2 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).

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).

479 480FIG. 1 .
FIG.1.CLs as a function of the assumed B 0 → µ + µ − branching fraction for the combined 2011+2012 dataset.The dashed gray curve is the median of the expected CLs distribution if background and SM signal were observed.The shaded yellow area covers, for each branching fraction value, 34 % of the expected CLs distribution on each side of its median.The solid red curve is the observed CLs.

Figure 3 .
Figure 3. Angular observables in the B 0 → K * 0 µ + µ − decay: dimuon system forward backward asymmetry, A FB (top left); fraction of longitudianl polariation of the K * 0 , F L (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.

Figure 4 .
Figure 4. Differential branching fraction (left) and dimuon system forward backward asymmetry (right) of the B + → K + µ + µ − decay.The forward-backward asymmetry of the decay is expected to be zero in the SM.

Figure 6 .
Figure 6.Constraints in the m 0 : m 1 2 plane of the CMSSM at tan β = 50 from the branching fraction of B 0 s → 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].