The LHCb experiment, bolstered up by the 10^12 b-hadrons to be produced
yearly in its interaction region, is an excellent place to study rare B decays.
Flavor-changing neutral currents are forbidden at tree level in the Standard
Model. They proceed through loop diagrams and hence are indirectly sensitive to
New Physics through the effect of new particles on observable quantities. In
this paper, we present preparation studies of the three most promising B rare
decay analyzes. These aim at the observation of the photon polarization in B_s
to phi gamma, the measurement of the angular distribution of the B^0 to K* mu^+
mu^- decay, and the search for the yet unobserved B_s to mu^+ mu^- decay. The
current analysis strategies and the expected sensitivities are presented.Comment: To be published in the proceedings of DPF-2009, Detroit, MI, July
  2009, eConf C090726; one reference adde

Bettler, Marc-Olivier

English

arXiv

The LHCb experiment, bolstered up by the $10^{12}$ $b$-hadrons to be produced yearly in its interaction region, is an excellent place to study rare $B$ decays. Flavor-changing neutral currents are forbidden at tree level in the Standard Model. They proceed through loop diagrams and hence are indirectly sensitive to New Physics through the effect of new particles on observable quantities. In this paper, we present preparation studies of the three most promising $B$ rare decay analyzes. These aim at the observation of the photon polarization in $B^{0}_s \to \phi \gamma$, the measurement of the angular distribution of the $B^{0} \to K^{*0} \mu^{+} \mu^{-}$ decay, and the search for the yet unobserved $B^{0}_s \to \mu^{+} \mu^{-}$ decay. The current analysis strategies and the expected sensitivities are presented.The LHCb experiment, bolstered up by the 10^12 b-hadrons to be produced yearly in its interaction region, is an excellent place to study rare B decays. Flavor-changing neutral currents are forbidden at tree level in the Standard Model. They proceed through loop diagrams and hence are indirectly sensitive to New Physics through the effect of new particles on observable quantities. In this paper, we present preparation studies of the three most promising B rare decay analyzes. These aim at the observation of the photon polarization in B_s to phi gamma, the measurement of the angular distribution of the B^0 to K* mu^+ mu^- decay, and the search for the yet unobserved B_s to mu^+ mu^- decay. The current analysis strategies and the expected sensitivities are presented

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LHCb-CONF-2009-03806/10/2009Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009 1Search for New Physics in B Rare Decays at LHCbMarc-Olivier Bettler, on behalf of the LHCb collaborationEcole Polytechnique Fe´de´rale de Lausanne, Lausanne, SwitzerlandThe LHCb experiment, bolstered up by the 1012 b-hadrons to be produced yearly in its interaction region,is an excellent place to study rare B decays. Flavor-changing neutral currents are forbidden at tree level inthe Standard Model. They proceed through loop diagrams and hence are indirectly sensitive to New Physicsthrough the effect of new particles on observable quantities. In this paper, we present preparation studies ofthe three most promising B rare decay analyzes. These aim at the observation of the photon polarization inBs → φγ, the measurement of the angular distribution of the B0→ K∗0µ+µ− decay, and the search for theyet unobserved B0s → µ+µ− decay. The current analysis strategies and the expected sensitivities are presented.1. IntroductionThe Standard Model (SM) is successful in explain-ing almost all observations in particle physics experi-ments so far. Nevertheless, there are reasons to con-sider it as a low energy effective limit of a more gen-eral theory. In that prospect, observables for pro-cesses where the SM contribution is highly suppressedare particularly interesting. Within the SM, flavor-changing neutral current processes are highly sup-pressed since they are forbidden at tree level andcan only proceed via loops diagrams. If New Physics(NP) exists, new particles can also contribute to thoseprocesses in the loop diagrams, modifying observablequantities with respect to the SM prediction.The LHCb detector [1] will take advantage of the co-pious bb production cross-section expected at LHC [2].It is a single-arm forward spectrometer primarily opti-mized for the study of CP-violation and rare b-hadrondecays. The detector is characterized by its precisevertex detector, powerful particle identification capa-bilities and versatile trigger. Nominally, LHCb willoperate at a luminosity L = 2× 1032 cm−2 s−1, giving2 fb−1 of data per year (107 seconds). The analyzespresented in this document are applied to Monte Carlosimulated data with a full detector response, includ-ing pile-up (multiple pp collisions in a single bunchcrossing) and spill-over (signal coming from particlesproduced in a previous bunch crossing).B physics requires excellent vertexing capabilities,momentum resolution and particle identification. Thestudy of rare decays demands high background rejec-tion and trigger performance. LHCb was designedto fulfill these requirements. Its Vertex Locator pro-vides an impact parameter resolution of 14µm ±35µm/pT[ GeV/c] that results in a B proper-time res-olution of σ(τ) ≈ 40–100 fs depending on the decaymode. The tracking system yields a momentum reso-lution of σ(p)/p ≈ 0.4%, leading to an invariant massresolution of 20 MeV/c2 and 15 MeV/c2 forB0s→ µ+µ−and B0 → K∗0µ+µ−, respectively.2. B0s → φγ Photon PolarizationThe branching fraction of this decay, B(B0s→ φγ)=(57+18 +12−15 −11) × 10−6 [3], was recently measured bythe Belle collaboration and is in agreement with theSM prediction. In the SM the polarization of thephoton is precisely predicted. B0s → XsγL andB0s → XsγR are allowed transitions under helicityconservation, whereas the crossed transitions are sup-pressed by a factor msmb . An observable ψ is definedfrom the B0s transition amplitude ratio astanψ ≡∣∣∣∣∣A(B0s→ φγR)A(B0s→ φγL)∣∣∣∣∣ ,which is proportional to ms/mb and very small in theSM. In extensions of the SM, such as the Left-RightSymmetric Model [4] and the unconstrained MSSM [5]predict large values for ψ. The measurement of thephoton polarization thus provides a null test for theSM.The photon polarization is measured indirectly,through the time-dependent decay rate [6]. For thedecay of B0s (B0s) mesons, the decay rate is:Γ{B0s ,B0s}→φγ(t) ∝ e−Γst{cosh∆Γst2−A∆ sinh ∆Γst2±C cos ∆mst∓ S sin ∆mst}. (1)Unlike Belle and BaBar analyzes studying CP asym-metry in B0 → K0Spi0γ [7, 8] decay, we consider ananalysis without flavor tagging. Thus, adding the B0sand B0s contributions, the two last terms of Eq. (1)cancel out. Furthermore, since in the SM ∆Γs is ex-pected to be non-zero in the B0s system, the decay rateis sensitive to ψ, through A∆ = sin 2ψ cosϕ. Hereϕ represents the decay weak phase, that is approxi-mately zero in the SM. Note that, in the SM, a flavortagged analysis is not expected to provide a bettersensitivity on the measure of ψ, because C < 1 % andϕ ≈ 0.The main experimental issue is to understand thebias on the B0s lifetime coming from the trigger and2 Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009Figure 1: LHCb sensitivity to AFB with the unbinnedB0→ K∗0µ+µ− analysis for 2 fb−1, with 1σ and 2σ LHCbexperimental error bands, allowing the extraction of thezero-crossing point value q20 . This simulation assumes theSM with q20 = 3.97 GeV2/c4.oﬄine cuts for the φ selection. For 2 fb−1, the ex-pected signal yield is 11000 events with a B/S < 0.6and a B0s mass resolution of 92 MeV/c2 [9]. This yield,leads to an expected resolution of 0.1 for the photonpolarization observable ψ [10].There are others channels considered to probe pho-ton polarization, such as Λb → Λ0γ , Λb → Λ∗(→pK−)γ, and B+→ φK+γ .3. B0→ K∗0µ+µ− Angular AnalysisThis decay branching fraction B(B0→ K∗0µ+µ−)= (9.8± 2.1)×10−7 [11] is in agreement with the SM.Asymmetries related to angular distributions are the-oretically well predicted because hadronic uncertain-ties cancel out in the ratios. The forward-backwardasymmetry of θ`, the angle between the µ− and theB0flight direction in the di-muon rest frame is suchan observable. Thus, the shape of AFB as a functionof the di-muon invariant mass squared, q2, is calcu-lated for the SM and for extension models. The zero-crossing point of AFB (q20 such that AFB(q20) = 0) is aparticularly interesting observable. Its SM predictionis q20 = 4.36+0.33−0.31 GeV2/c4 [12].The AFB for this channel was already measured atBaBar, Belle and CDF [13–15] and exhibits sometension with respect to the SM prediction. However,the statistics is very low: the Belle analysis, the mostsensitive so far, is based on 230 events only. LHCbexpects 7000 events per 2 fb−1, with B/S ≈ 0.2.The challenge for this analysis is the understandingof the biases on angular observables induced by de-tector and reconstruction effects. It is worth to notethat the zero-crossing point value is little sensitive tothose biases, making its measurement particularly in-teresting with early data.Figure 2: A(4)T observable, defined in [19]. The SM predic-tion is shown by the dashed line, with 1σ and 2σ theoret-ical uncertainty bands. The dotted line depicts a particu-lar SUSY scenario with positive mass insertion and largegluino mass, with 1σ and 2σ LHCb experimental errorbands (the solid line showing the central value of the toyexperiments).The LHCb strategy for this decay consists of differ-ent methods of increasing sensitivity but also increas-ing requirements in statistics and acceptance under-standing.The first method is a binned analysis for AFB, com-bined with a linear fit to extract the zero-crossingpoint value [16]. With a few hundreds of pb−1, thismethod will already compete with current measure-ments. With 2 fb−1, the expected resolution on q20 is0.5 GeV2/c4 and LHCb expects to reach the theoreti-cal precision with 10 fb−1 of data.The second method consists of an unbinned analysisfor AFB, with no linear assumption around the zero-crossing point [17]. This analysis yields a sensitivitysimilar to the binned analysis. Figure 1 depicts the ex-pected AFB shape obtained by the unbinned analysisfor the SM and with 2 fb−1.The next step is a full angular analysis, based on thethree angles, which, with the di-muon invariant mass,completely define the decay kinematics [18]. Usingthe three angle distributions, a number of asymme-tries and transversity amplitudes can be computed.The full angular analysis requires a good knowledgeof detector acceptance effects and an integrated lumi-nosity of at least 2 fb−1.A thorough study has assessed the sensitivity tovarious observables [19], of which some were shown todiffer significantly between SM and NP scenarios. Anexample of the sensitivity achievable with 10 fb−1 foran observable particularly sensitive to NP is shown inFig. 2.Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009 34. B0s→ µ+µ− Branching FractionWithin the SM, the B0s → µ+µ− branching ratiois expected to be B(B0s→ µ+µ−) = (3.35 ± 0.32) ×10−9 [20]. In the MSSM, this decay receives addi-tional contributions from new particles, e.g. for largetanβ values, the ratio of the Higgs vacuum expecta-tion values, the branching ratio is then proportionalto tanβ to the sixth power, and can be considerablyenhanced [21]. The latest upper limit given by theCDF experiment is 3.6× 10−8 at 90% CL [22].The current LHCb strategy for the B0s → µ+µ−decay search [23] can be summarized as follows. Anefficient selection is applied with the goal to removeobvious background with minimal loss of signal events.The analysis relies on three independent variables re-lated to, the di-muon invariant mass, the particle iden-tification of the daughters, and geometrical informa-tion from the decay topology. Since the three vari-ables are uncorrelated, they can be calibrated inde-pendently. For each event, likelihood values are cal-culated for each of the three variables, under the signaland background hypotheses. Calibration methods forthese values, both for signal and for background, aredesigned to rely solely on real data. The compati-bility of the obtained likelihood distributions is testedagainst various B0s→ µ+µ− branching ratio hypothe-ses, using the CL modified frequentist analysis [24].The final result is either a measurement or an upperlimit of the branching fraction.The branching fraction is expressed as:B(B0s→ µ+µ−) =Nsig2 σbb Lint fs sig,where Nsig is the number of signal events, σbb is thebb production cross-section, Lint the integrated lumi-nosity, fs the probability of a b quark to hadronizein a B0s meson, and sig the product of the recon-struction, trigger, and selection efficiencies. Since thenumber of B0s produced, 2σbb Lint, will not be pre-cisely known, the use of a normalization channel ofwell-known branching fraction is required to obtainan absolute measurement of the branching fraction orupper limit.The B0s→ µ+µ− branching fraction is then:B(B0s→ µ+µ−) = Bnorm ×fnormfs× normsig× NsigNnorm ,where fnorm, norm and Nnorm are the quantities forthe normalization channel, with definitions analogousto those of the signal channel.Possible normalization channels are B+ →J/ψ(µµ)K+ and B0→ K+pi− . Particular care hasbeen taken to analyze the signal and normalizationchannels in a common way such as to cancel any largesystematic effects in the efficiency ratio.The main systematics arise from the ∼ 13% un-certainty on the ratio fB0fs orfB+fs. With sufficientstatistics, all other systematic uncertainties are ex-pected to get much smaller than that, as the analysisrelies solely on data. To eliminate the factor fnormfs ,the B0s→ D−s pi+ decay mode could be used in the fu-ture a normalization channel, if its absolute branchingfraction can be measured more precisely at Belle.The expected sensitivity of LHCb to the B0s →µ+µ− decay as a function of the integrated luminosityis shown in Fig. 3. The solid line in the left plot showsthe expected upper limit, at 90% confidence level, onthe branching fraction when no signal is observed, forpp collisions at√s = 8 TeV. The branching fractionfor which a 5σ discovery (or for which a 3σ evidence)is expected, is shown on the right plot for 14 TeV col-lisions.The left plot also indicates the expected limit fromthe Tevatron experiments, extrapolating the currentresults to 8 fb−1 of data per experiment. It shows thatLHCb can compete with the Tevatron with approxi-mately 0.1 fb−1 of data and overtake its expected limitwith about 0.2 fb−1. In that time frame, the detectormay not be fully understood yet. Therefore, an alter-native robust analysis is designed using variables witha physical content similar to the ones of the standardanalysis, but avoiding the use of error estimates. Thisimplies a modified selection and definition of the geo-metrical likelihood. The robust analysis sensitivity isalso depicted in Fig. 3 (left), as a red dashed curve.The robust analysis presents a sensitivity comparablewith the one of the standard analysis. Therefore, itconstitutes a valuable option for the early data.About 3 fb−1 (10 fb−1) are enough for a 3σ evidence(5σ observation) if the branching fraction is equal tothe SM prediction. Any enhancement driven by NPwill be observed sooner. Particularly, if the branchingfraction is as high as 2×10−8, as predicted in Ref. [21],a 5σ discovery is possible with very little luminosity(< 0.4 fb−1).5. ConclusionThe large bb production cross-section expected atLHC, together with the characteristics of LHCb, leadsto a good performance in the search for NP in FCNCdecays. Rare B decays are particularly interestingbecause of the precise theoretical predictions for someof their observables, and they provide stringent test ofthe SM and its extensions. Expected sensitivities forLHCb’s analyzes of the most promising rare B decayswere presented.One year of data taken in nominal conditions yieldsto the observation of the photon polarization in theB0s → φγ decay to a 10% level and to the measure-ment of the AFB zero-crossing point to a 0.5 GeV2/c44 Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009Figure 3: Expected 90% CL upper limit on B(B0s→ µ+µ−) in absence of signal for 8 TeV collisions (left) andB(B0s→ µ+µ−) at which a 5σ discovery (stars) or a 3σ evidence (solid blue curve) is expected for 14 TeV collisions(right), as a function of the integrated luminosity. On the exclusion plot, the black curve is the result of the standardanalysis, and the red dashed curve is the result of the robust analysis. The background estimate has conservatively beenset to its 90% CL upper limit in the exclusion plot, and similarly the dashed curves indicates the 90% CL upper andlower limit in the observation case. The Tevatron limit is calculated by extrapolating the current result to 8 fb−1 perexperiment.resolution in the B0→ K∗0µ+µ− decay mode. Thesame amount of data allows to set a limit on theB0s→ µ+µ− branching fraction down to the SM pre-diction if no signal is observed, strongly constrainingNP models with high tanβ values. In case the branch-ing fraction is enhanced, an observation of NP is pos-sible.In the long term, a full angular analysis of theB0→ K∗0µ+µ− can be performed and bringing en-hanced sensitivity in probing for NP. A 5σ discoveryof the B0s→ µ+µ− decay is possible if the branchingfraction is at the SM level with about 10 fb−1. 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Search for New Physics in B Rare Decays at LHCb

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