Rare beauty and charm decays at LHCb

Rare heavy flavor decays are an ideal place to search for the effects of potential new particles that modify the decay rates or the Lorentz structure of the decay vertices. The LHCb experiment, a dedicated heavy flavour experiment at the LHC at CERN. It has recorded the worlds largest sample of heavy meson and lepton decays. The status of the rare decay analyses with 1\,fb$^{-1}$ of $\sqrt s = 7\,$TeV and 1.1\,fb$^{-1}$ of $\sqrt s = 8\,$TeV of $pp$--collisions collected by the LHCb experiment in 2011 and 2012 is reviewed. The worlds most precise measurements of the angular structure of $B^0\rightarrow K^{*0} \mu^+ \mu^-$ and $B^+\rightarrow K^{+} \mu^+ \mu^-$ decays is discussed, as well as the isospin asymmetry measurement in $B\rightarrow K^{(*)} \mu^+ \mu^-}$ decays. The first evidence for the very rare decay $B^0_s \rightarrow \mu^+ \mu^-$ is presented together with the most stringent upper exclusion limits on the branching fraction of decays of $B^0$, $D^0$ and $K^0_s$ mesons into two muons. This note finishes with the discussion of searches for lepton number and lepton flavor violating $\tau$ decays.


Introduction
Flavor changing neutral current (FCNC) processes are forbidden at tree level in the Standard Model (SM), but can proceed via loop level electroweak penguin or box diagrams. In extensions to the SM, new virtual particles can enter in these loop level diagrams, modifying the decay rate or Lorentz structure of the decay vertex. Possible deviations from the SM predictions of these observables could lead to the discovery of yet unknown phenomena. The search for these deviations is a complementary approach to direct searches at general purpose detectors and can give sensitivity to new particles at higher mass scales than those accessible directly.
This article reviews some of the most sensitive probes for possible extensions of the Standard Model that were measured by the LHCb collaboration at the time of the HCP conference (November 2012). Most measurements use a dataset of 1 fb −1 of √ s = 7 TeV of pp-collisions collected in 2011. The search for B 0 s → µ + µ − uses a combined dataset of 1 fb −1 of √ s = 7 TeV and 1.1 fb −1 of √ s = 8 TeV, recorded in 2011 and 2012. The first part of the article discusses rare electroweak penguin transitions of the type 1 b → sµ + µ − , which allow stringent tests of the Lorentz structure of the electroweak penguin processes. The second part discusses searches for purely leptonic decays of K 0 s , D 0 and B mesons, which are particularly sensitive to new scalar interactions. The last class of analyses discussed is the search for lepton and baryon number violating τ decays. a e-mail: albrecht@cern.ch 1 In this proceedings, the inclusion of charge conjugate states are implicit, unless otherwise stated.
The implications of the presented measurements on possible extensions of the SM, most notably supersymmetric extensions, is discussed in a separate contribution in these proceedings [1].

Angular analysis and CP asymmetries in
The decay B 0 → K * 0 µ + µ − has a branching fraction of B(B 0 → K * 0 µ + µ − ) = (1.05 +0. 16 −0.13 ) × 10 −6 [2]. It allows the construction of several observables with small hadronic uncertainties, that are sensitive to physics beyond the Standard Model (see [3,4] and references therein). The LHCb collaboration performs an angular analysis in bins of the squared dimuon invariant mass (q 2 ) and the three angles θ l , θ k and φ [8]. θ l is defined as the angle between the µ + and the B 0 in the dimuon rest frame, θ k as angle between the kaon and the B 0 in K * 0 rest frame and φ as angle between the plane spanned by the dimuon system and the K * 0 decay plane.
The differential branching ratio as a function of q 2 as well as the following observables have been measured (the observables are fully defined in [4,[9][10][11]): A FB , the forward-backward asymmetry of the dimuon system; F L , the fraction of K * 0 longitudinal polarization; S 3 , the transverse asymmetry, which is also often referred to as 1 2 (1 − F L )A 2 T and S 9 , a CP averaged quantity corresponding to the imaginary component of the product of the longitudinal and transverse amplitudes of the K * 0 . The measurement of these observables is shown in Fig. 1  Preliminary LHCb ure 4: The A F B , F L , S 3 and S 9 measured by the experiments BaBar [25], Belle [27], CDF [28] and LHCb [26]. parison with the SM prediction, taken from [22] is also shown. Reproduced from [26].
Isospin asymmetry in the decays B → K ( * ) l + l − he isospin asymmetry of the decays B → Kl + l − and B → K * µ + µ − are defined as: , ere τ 0,+ is the B 0,+ lifetime. In the SM this quantity is expected to be at percent level, slightly larger and posi very low q 2 . Measurements of this quantity have been performed by the BaBar [25] and Belle [27] experime ng electrons and muons and by CDF [28] and LHCb [29] , using muons. These results are shown in Fig. 5. measurements are consistent with each other and they are consistent with SM predictions for the B → K * l ays. For the B → Kl + l − decays the measurements are in agreement with each other but they show a tens h respect to naive expectations. In particular the LHCb collaboration reported a deviation from zero at the le about 4 standard deviations [29]. At present there is no theoretical explanation for this large isospin asymmet Conclusions easurements in flavour physics have a great track record in paving the way to big discoveries in particle phys st NP scenarios predict deviation from SM expectations in rare B-meson decays. Sensitive probe for NP are tonic decays B s,d → µ + µ − and the rare semi-leptonic decays B → K * l + l − . The most recent measurement Figure 1. The observables A FB , F L , S 3 and S 9 measured in B 0 → K * 0 µ + µ − decays by the BABAR [5], Belle [6], CDF [7] and LHCb [8] experiments. The SM prediction, from Ref. [9], is also shown. Figure  other collaborations [5][6][7][8]. All observables are found to be consistent with each other and with the SM predictions. The LHCb results are the most precise measurements of these observables. A particularly sensitive probe for new phenomena is q 2 0 , the zero-crossing point of A FB . It is theoretically very clean as the form factor uncertainties cancel at first order. The LHCb collaboration has reported the worlds first measurement as q 2 0 = 4.9 +1.1 −1.3 GeV 2 /c 4 , in good agreement with the SM prediction. This measurement strongly disfavours scenarios with a flipped sign of the Wilson coefficient C 7 .
The direct CP asymmetry in the B 0 → K * 0 µ + µ − system, is predicted to be of order 10 −3 in the Standard Model. It was measured 1.0 fb −1 of 7 TeV data [12] to be integrated over the six q 2 bins. This measurement is consistent with the Standard Model prediction, it is the most precise measurement of A CP in B 0 → K * 0 µ + µ − decays to date.

Angular analysis of
The angular analysis of B + → K + µ + µ − decays is performed analogously to the analysis of B 0 → K * 0 µ + µ − decays. The angular distribution of B + → K + µ + µ − decays is given as [13,14] 1 Γ where A FB denotes the forward backward asymmetry and F H the so called flat parameter. The SM predictions for both parameters are very small. Both A FB and F H can be significantly enhanced in models with large operators C ( ) The LHCb collaboration has measured A FB and F H with 1 fb −1 of data collected at √ s = 7 TeV [15], as shown in in Fig. 2. The measurement is found in good agreement with the SM predictions.

Isospin asymmetry in
The isospin asymmetry of the decays B → K ( * ) µ + µ − , A I , is defined as Equation (1) is used to describe the signal angular distribution. The background angular and mass shapes are treated as independent in the fit. The angular distribution of the background is parameterised by a second-order Chebychev polynomial, which is observed to describe well the background away from the signal mass window (5230 < m K + µ + µ − < 5330 MeV/c 2 ).
The resulting values of A FB and F H in the bins of q 2 are indicated in Fig. 3 and in Table 1. The measured values of A FB are consistent with the SM expectation of zero asymmetry. The 68% confidence intervals on A FB and F H are estimated using pseudoexperiments and the Feldman-Cousins technique [34]. This avoids potential biases in the estimate of the parameter uncertainties that come from using event weights in the likelihood fit or from the boundary condition (|A FB | ≤ F H /2). When estimating the uncertainty on A FB (F H ), F H (A FB ) is treated as a nuisance parameter (along with the background parameters in the fit). The maximum-likelihood estimate of the nuisance parameters is used when generating the pseudo-experiments. The resulting confidence intervals ignore correlations between A FB and F H and are not simultaneously valid at the 68% confidence level.  where τ 0,+ is the lifetime of the B 0 and B + meson respectively. For the B → K * µ + µ − system, in the SM, A I is predicted to be −0.01 [17] with a slight increase at low values of q 2 . For the B → Kµ + µ − system, the SM calculation of A I predicts a similar expectation close to zero [18]. The most precise measurement of A I is performed by the LHCb collaboration [19]. The measurement of B → K * µ + µ − is consistent with the SM prediction. The B → Kµ + µ − measurement shows a deviation from zero with a significance of greater than four standard deviations [19].

Searches in leptonic meson decays
Decays of K 0 , D 0 and B 0 s or B 0 mesons into a muon pair are discussed in this section. The leptonic final state allows precise calculations of the expected rates and the two muon final state is experimentally a very clean signature. Both features together are making these decays very powerful tests of the Standard Model.

Search for K
The rare decay K 0 s → µ + µ − can give insight into the shortdistance structure of ∆S = 1 FCNC transitions. This decay is highly suppressed in the SM, the predicted branching fraction is B(K 0 s → µ + µ − ) = (5.0 ± 1.5) × 10 −12 [20,21]. Contributions from possible extensions of the SM, e.g. from new light scalar particles, can enhance the branching fraction.
The LHCb dataset of 1 fb −1 contains about 10 13 K 0 s decays inside the detector acceptance. Signal candidates are separated from the background using BDT based selection. Main sources of residual background originate from semileptonic decays and K 0 s → π + π − decays, where both pions are misidentified as muons. The latter can be separated from signal candidates exploiting the excellent mass resolution of the LHCb spectrometer. The contribution of K 0 L → µ + µ − is found to be negligible for this analysis. The number of expected signal events is evaluated using a relative normalization to K 0 s → π + π − decays. This normalization reduces the systematic uncertainties which need to be considered in this analysis. The modified frequentist method [22,23], CL s , is used to evaluate the consistency of the observed pattern of events with the background and signal plus background hypotheses. The expected upper exclusion limit is at 95% CL B(K 0 s → µ + µ − ) < 1.1 × 10 −8 and the observed limit is found to be B(K 0 s → µ + µ − ) < 1.1 × 10 −8 . This limit constitutes an improvement of a factor 30 with respect to the previous best limit.
The LHCb collaboration has performed an analysis using 0.9 fb −1 of data at √ s = 7 TeV [26]. The background is reduced using a multivariate discriminant based on geometrical and kinematic information. The signal events are normalized to the D * ± → D 0 (→ π + π − )π ± channel, which allows to reduce common systematic uncertainties. The event yield is determined from a two dimensional fit on the dimuon invariant mass and the difference between the D * ± mass and D 0 mass. The observed pattern of events is compatible with the background expectations and an upper limit on the branching fraction of B(D 0 → µ + µ − ) < 1.3 × 10 −8 is determined at 95% CL, using the CL s method. This is the worlds most stringent limit on this decay.

Evidence for B
The search for the loop-and helicity suppressed decays B 0 s → µ + µ − and B 0 → µ + µ − constitute a very stringent test of possible extensions of the SM, specially those with an extended scalar sector. The LHCb collaboration observes an excess of signal candidates in the channel B 0 s → µ + µ − [27], which is inconsistent with the background hypothesis with a significance of 3.5 standard deviations. This measurement provides the first evidence for this decay, the measured branching fraction is consistent with the SM expectation. The B 0 s → µ + µ − candidates with a high signal likelihood are shown in Fig. 3. The measurement is discussed in more detail in a separate contribution of these proceedings [28].

Search for forbidden τ − decays
Lepton flavor violating (LFV) τ − decays only occur in the Standard Model from neutrino mixing. Many extensions beyond the SM predict enhancements, up to observable values which are close to the current experimental bounds.
The neutrinoless decay τ − → µ + µ − µ − is a particular sensitive mode in which to search for LFV at LHCb as the experimental signature with the three muon final state is very clean and the inclusive τ − production cross-section at LHCb is very large, about 80 µb. The composition of the τ − production can be calculated from the bb and cc [29] cross-sections measured at the LHCb experiment and the inclusive branching ratios b → τ and c → τ [30]. About 80% of the produced τ − -leptons originate from D − s decays.
LHCb has performed a search for the decay τ − → µ + µ − µ − using 1.0 fb −1 of data [31]. The signal events are normalized to the D − s → φ(µ + µ − )π − channel. The upper limit on the branching fraction was found to be at 90 % C.L, determined using the CL s method. This has to be compared with the current best experimental upper limit from the Belle collaboration: 2.1 × 10 −8 at 90 % C.L. The large integrated luminosity that will be collected by the upgraded LHCb experiment will provide a sensitivity corresponding to an upper limit of a few times 10 −9 [32].
The large τ − sample can be exploited by searching for the baryon number and lepton number violating decays τ − → pµ − µ − and τ − →pµ + µ − . Both decays have |B − L| = 0 which is predicted by many NP models. The analysis for these channels [33] follows closely that of the τ − → µ + µ − µ − mode as described above.

Conclusion
Most scenarios of physics beyond the Standard Model of particle physics predict measurable effects in the flavor sector, in particular in rare meson or lepton decays. No sign of physics beyond the Standard Model has yet been observed and stringent limits on its scale have been set. An angular analysis of the rare electroweak penguin decays B 0 → K * 0 µ + µ − and B + → K + µ + µ − has been performed as well as a measurement of the isospin asymmetry in B → K ( * ) µ + µ − decays. The measurements are of unprecedented precision and, besides the isospin asymmetry in agreement with the SM prediction.
Sensitive probes for NP are the purely leptonic decays of B, D 0 and K 0 s mesons, all of which have been analysed by the LHCb collaboration. The first evidence on the decay B 0 s → µ + µ − has been measured and the most stringent upper exclusion limits on the other decays have been obtained. The LHCb collaboration has also pioneered the analysis of lepton flavour violating τ − decays by performing the first of such searches at a hadron collider.
Most measurements presented in this proceedings use 1 fb −1 of data collected at √ s = 7 TeV, about one third of the total dataset recorded by the LHCb experiment. Updates of the analyses with significantly improved sensitivity are expected in the coming year and beyond.