Rare decays in quark flavour physics

Available online at www.sciencedirect.com Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 www.elsevier.com/locate/nppp Rare decays in quark flavour physics Johannes Albrecht On behalf of the collaboration a TU Dortmund, Germany Abstract Rare heavy-flavour 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. Recent results on Flavour Changing Neutral Current decays from the LHC are reviewed. An emphasis is put on the very rare decay B s μ + μ, which was recently observed by the CMS and experiments, on a recent test of lepton universality in loop processes and on the analysis of the angular distributions of the B K μ + μ decays, both by the collaboration. Keywords: Rare decay, heavy flavour, Electroweak penguin. Introduction Flavour 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 generalpurpose 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 at the LHC. Most measurements use the complete run dataset, of pp collisions at s = 7 TeV collected in and at s = 8 TeV collected in. The first part of the article discusses the very rare leptonic decays B s,d μ+ μ, followed by rare electroweak penguin transitions of the type b sμ + μ, which allow stringent tests of the Lorentz structure of In this proceedings, the inclusion of charge conjugate states are implicit, unless otherwise stated. http://dx.doi.org/.6/j.nuclphysbps.5.9.7 45-64/ 6 Published by Elsevier B.V. the electroweak penguin processes and a discussion of a recent measurement of the photon polarisation. The article closes with a test of lepton universality in B + K + l + l decays.. Leptonic decays Precise measurements of the branching fractions of the two Flavour Changing Neutral Current (FCNC) decays B s μ + μ and B μ + μ belong to the most important measurements of the field of flavour physics. Enhancements of the branching fractions of these decays are predicted in a variety of different extensions of the Standard Model, an overview is given in Ref. []. In one popular example, the Minimal Supersymmetric Standard Model (MSSM), the enhancement is proportional to tan 6 β, where tan β is the ratio of the vacuum expectation values of the two Higgs fields. For large values of tan β, this search belongs to the most sensitive probes for physics beyond the SM which can be performed at collider experiments. The B s μ + μ and B μ + μ decays are strongly suppressed by loop and helicity factors, making the SM

J. Albrecht / Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 53 branching fractions small [] B(B s μ + μ ) = (3.66 ±.3) 9, () B(B μ + μ ) = (.6 ±.9), () where the branching fraction of the B s decay is evaluated as average over all decay times, see Refs. [3, 4] for a detailed discussion. Before the start of the LHC data taking, there was a large gap between this theoretical prediction and the best experimental constraints, provided by the Tevatron experiments [5, 6]. In, the collaboration reported the first evidence for the rare decay B s μ + μ using a total dataset of fb [7]. In 3, both the and CMS collaborations updated their analyses to the full run dataset, corresponding to about 3 fb for and 5 fb for CMS. Both collaborations reported an evidence of the decay B s μ + μ with a significance of about four standard deviations [8, 9]. No significant evidence of the decay B μ + μ was found by either experiment. Figure shows the signal candidates selected by the CMS collaboration and Fig. the candidates selected by the collaboration. Anaïve combination of the results [] yields an observation of the rare decay B s μ + μ with a significance exceeding five standard deviations and measured branching fractions of B(B s μ + μ ) = (.9 ±.7) 9, (3) B(B μ + μ ) = (3.6 +.6.4 ). (4) These measurements are compatible with the SM expectation. A full combination of the likelihoods of the CMS and measurements is in preparation. Future updates on the analyses of B s,d μ+ μ with more statistics and improved analysis techniques are of great interest. Main objectives are to reduce the uncertainty on the branching fraction of B s μ + μ, to search for the decay B μ + μ and to test the SM prediction for the effective lifetime of B s μ + μ, which offers a theoretically clean probe for New Physics searches that is complementary to the branching ratio [4]. 3. Decay rates and angular observables of semileptonic b sμ + μ decays New physics can also be searched for in semileptonic b sμ + μ transitions, which offer a wealth of asymmetries and angular observables that can be studied as functions of the dimuon invariant mass squared, q. Several of these observables have been shown to have reduced theoretical uncertainties. Isospin and CP asymmetries, for example, provide powerful tests of the validity of the Standard Model because the form-factor uncertainties cancel. The isospin asymmetry of the decays B K ( ) μ + μ, A I, is defined as A I = B(B K ( ) μ + μ ) τ τ + B(B + K ( )+ μ + μ ) B(B K ( ) μ + μ ) + τ τ + B(B + K ( )+ μ + μ ), (5) where τ,+ is the lifetime of the B and B + meson, respectively. Evidence of a non-vanishing value of A I [] has not been confirmed in an update with larger statistics []. All CP asymmetries measured so far in these decays are consistent with zero [3, 4, 5], as predicted by the SM. 3.. Angular analysis of B K μ + μ The decay B K μ + μ has a branching fraction of B(B K μ + μ ) = (.5 +.6.3 ) 6 [6]. The decay has a rich angular structure that allows sensitive tests for physics beyond the Standard Model [7, 8], it can be written in three decay angles, θ l, θ K and φ, following the notation of Ref. [8], = 9 3π d 4 Γ d cos θ l d cos θ K dφdq (6) J i (q ) f i (cos θ l, cos θ K,φ), i where θ l is defined as the angle between the μ + and the B in the dimuon rest frame, θ k as angle between the kaon and the B in K rest frame and φ as angle between the plane spanned by the dimuon system and the K decay plane. The different angular terms J i are sensitive to different K polarization states and provide complementary information to the contribution of potential new particles. The ATLAS [9], CMS [] and [] collaboration have published measurements of these angular distributions using the data collected in. The number of candidates is for all three collaborations not sufficient to fit the complete angular distribution, so only a simplified distribution is fitted. Figure 3 shows the measurements of the fraction of longitudinal polarisation, F L, of the K produced in B K μ + μ decays as well as the forward-backward asymmetry, A FB. All measurements are consistent with the SM prediction. It is possible to construct observables in the decay angles of B K μ + μ such that the form factor uncertainties cancel at leading order []. Two such observables are reported in Ref [3], P 4 and P 5. The result of this measurement is shown in Fig. 4. A large discrepancy with a local significance of 3.7 standard deviations

54 J. Albrecht / Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 S/(S+B) Weighted Events / (.4 GeV) 5 4 3 CMS - L = 5 fb s = 7 TeV, L = fb s = 8 TeV data full PDF Bs μ+ μ - - B μ + μ combinatorial bkg semileptonic bkg peaking bkg S/(S+B) Weighted Events / (.4 GeV) 4 8 6 4 CMS - L = 5 fb s = 7 TeV, L = fb s = 8 TeV data full PDF Bs μ+ μ - - B μ + μ combinatorial bkg semileptonic bkg peaking bkg 4.9 5 5. 5. 5.3 5.4 5.5 5.6 5.7 5.8 5.9 m μμ (GeV) 4.9 5 5. 5. 5.3 5.4 5.5 5.6 5.7 5.8 5.9 (GeV) m μμ Figure : Plots illustrating the combination of all categories used in the categorized-bdt method (left) and the D-BDT method (right). For these plots, the individual categories are weighted with S/(S + B), where S (B) is the signal (background) determined at the B s peak position. The overall normalization is set such that the fitted B s signal corresponds to the total yield of the individual contributions. These distributions are for illustrative purposes only and were not used in obtaining the final results. Candidates / (44 MeV/c ) 6 4 8 6 4 BDT>.7 3 fb 5 55 m μ + μ [MeV/c ] Figure : Invariant mass distribution of the selected B s,d μ+ μ candidates (black dots) with BDT >.7. The result of the fit is overlaid (blue solid line) and the different components detailed: B s μ + μ (red long dashed line), B μ + μ (green medium dashed line), combinatorial background (blue medium dashed line), B (s) h+ h (magenta dotted line), B π μ + ν μ (black) and B (+) π (+) μ + μ (light blue dot- dashed line), B π μ + ν μ and B s K μ + ν μ (black dot-dashed line).

J. Albrecht / Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 55 is found in the q range of 4.3 < q < 8.68 GeV /c 4 for the observable P 5. Several attempts have been made to understand this discrepancy, both in terms of New Physics models [4, 5, 6, 7, 8, 9, 3] and in terms of a better understanding of the form factor or c c contribution to the decays [3, 3]. The data seems best to be described by reducing the SM vector current contribution. The analysis of the full datasets collected so far by the, CMS and ATLAS experiments will help to resolve the nature of this discrepancy. 3.. Branching fractions of b sμ + μ decays Any deviation seen in the angular observables of the B K μ + μ decay will impact similar b sμ + μ decays. In particular, the deviation discussed in the previous section would imply a destructive interference and thus reduced decay rates. The collaboration has measured the differential branching fractions of B K μ + μ, B + K μ + μ, B K μ + μ and B + K + μ + μ decays [, ]. All these measurements are below the SM prediction, Fig. 5 shows the differential branching fraction measurements of the decays B K μ + μ and B + K + μ + μ as an example. However, accounting for the significant uncertainties in the B K ( ) form factors, all measurements are consistent with the SM prediction. More data and reduced form factor uncertainties will help to resolve if these anomalies are first hints for new effects or only statistical fluctuations. 4. Photon polarisation Transitions of the type b sγ offer an excellent test bench for the photon polarization, which is in the SM governed by the coupling to the W ± boson and thus predicted to be almost entirely left polarised. The right handed component is proportional to m s/m b, making it vanishingly small. This prediction can, however, be modified by QCD corrections. In many extensions of the SM, the photon is differently polarised, making the photon polarization a sensitive test for new phenomena. The photon polarization is experimentally accessible in B + K + π π + γ decays [36], where the photon direction with respect to the K + π + π system is measured. The up-down asymmetry of the photon is then proportional to the photon polarization. The collaboration performed a first measurement of the photon polarization in B + K + π π + γ decays, using the full run dataset corresponding to 3 fb of data [37]. The complete dataset contains 3876 ± 53 signal candidates. To separate different resonant contributions, the dataset is split into four regions of K + π + π invariant mass, as shown in Fig. 6. Figure 6 (right) shown the measured up-down asymmetry in the four regions of interest in K + π + π invariant mass. The combined significance of all bins of the photon polarization to be different from zero is 5. standard deviations, which makes this measurement the first observation of photon polarization in radiative b-hadron decays. The interpretation of this measurement in terms of SM photon polarization is highly non-trivial, as the current understanding of the hadronic K + π + π system is limited. The resonant structure in the K + π + π invariant mass needs to be understood experimentally. Also theoretically, the conversion of the measured asymmetry into photon polarization needs more detailed studies. 5. Lepton universality Decays of the type B + K + l + l can be used to test the universal couplings of leptons in loop processes. By forming appropriate ratios, the form factor uncertainty in the SM prediction cancels, giving a very clean probe for new phenomena. An example is the ratio R K = q max q min q max q min dγ[b + K + μ + μ ] dq dq dγ[b + K + e + e, (7) ] dq dq where the dilepton mass range < q < 6GeV /c 4 is theoretically preferred. This ratio is very well predicted in the SM and its numerical value is very close to unity [38], receiving small phase space and radiative corrections of the order O( 3 ). A measurement of this ratio R K is a stringent test of new phenomena occurring in loop processes that couple differently to the different lepton flavours. Previous measurements of R K at the B-factories have measured a value consistent with unity, with an accuracy of %. BaBar has measured R K [39] in two bins of q, quoting a value of R K =.74 +.4.3 ±.6 in the range of dilepton mass squared of q,. < q < 8. GeV /c 4. Belle gives a single value across the full allowed q range [4], which is consistent with unity. The experiment has recently produced the most precise measurement of R K to date [4], using the full run dataset. The measurement of R K is performed in a double ratio of the FCNC decays to the dominant B J/ψK decay modes, to cancel uncertainties of the particle identification and trigger at first order. Furthermore, the data is split into three categories depending if the electron, the K + or rest of the event triggered

56 J. Albrecht / Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 F L Theory Binned ATLAS CMS A FB Theory Binned ATLAS CMS.8.5.6.4. -.5 5 5 q [GeV /c 4 ] 5 5 q [GeV /c 4 ] Figure 3: (left) Fraction of longitudinal polarisation, F L, of the K produced in B K μ + μ decays. (right) The forward-backward asymmetry, A FB. The datasets are collected by the ATLAS [9], CMS [] and [] collaborations. The SM prediction based on Ref. [33] and references therein is overlaid. P 4 '.8 SM Predictions.6.4 Data. -. -.4 -.6 -.8 5 5 q [GeV /c 4 ] P 5 '.8.6.4 SM Predictions Data. -. -.4 -.6 -.8 5 5 q [GeV /c 4 ] Figure 4: Observables with reduced form factor uncertainties, P 4 and P 5, measured by the collaboration [3] in B K μ + μ decays. The SM prediction, taken from Ref [] is overlaid. ] - GeV c 4-7 db/dq [ Theory Binned.5 CMS.5 5 5 q [GeV /c 4 ] ] c 4 /GeV -8 db/dq [ 5 4 3 LCSR Lattice Data + + B K μ + μ 5 5 q [GeV /c 4 ] Figure 5: (left) Differential branching fraction of the decay B K μ + μ measured by the CMS [] and [] collaborations. (right) Differential branching fraction of the decay B + K + μ + μ measured by the [] collaboration. The SM prediction, taken from Refs. [33, 34], are overlaid. A prediction for the differential branching fraction of the B + K + μ + μ decay using form-factors form the lattice [35] are also shown.

J. Albrecht / Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 57 Candidates / ( 8 MeV/c ) 35 3 5 5 5 A ud..5 -.5 -. 4 6 8 M(Kππ) [MeV/c ] 4 6 8 M(Kππ) [MeV/c ] Figure 6: (left) Background-subtracted K + π + π mass distribution of the B + K + π π + γ signal. The four intervals of interest, separated by dashed lines, are shown. (right) Up-down asymmetry of the photon with respect ot the K + π + π system in the four intervals of interest in K + π + π mass. Candidates / (4 MeV/c ) 5 3 (a) 5 5 54 56 m(k + e + e ) [MeV/c ] ) Candidates / (4 MeV/c 5 5 (b) 5 5 54 56 m(k + e + e ) [MeV/c ] Candidates / (4 MeV/c ) (c) 5 5 54 56 m(k + e + e ) [MeV/c ] ) Candidates / (4 MeV/c 4 3 (d) 5 5 54 56 m(k + e + e ) [MeV/c ] Candidates / (4 MeV/c ) 5 5 (e) 5 5 54 56 m(k + e + e ) [MeV/c ] Candidates / (4 MeV/c ) 5 5 (f) 5 5 54 56 m(k + e + e ) [MeV/c ] Figure 7: Mass distributions with fit projections overlaid of selected B J/ψ(e + e )K candidates triggered in the hardware trigger by (a) one of the two electrons, (b) by the K +, and (c) by other particles in the event. Mass distributions with fit projections overlaid of selected B + K + e + e candidates in the same categories, triggered by (d) one of the two electrons, (e) the K +, and (f) by other particles in the event. The total fit model is shown in black, the combinatorial background component is indicated by the dark shaded region and the background from partially reconstructed b -hadron decays by the light shaded region.

58 J. Albrecht / Nuclear and Particle Physics Proceedings 73 75 (6) 5 59 the event. The reconstructed invariant mass distributions of the measured candidates for both resonant and FCNC modes for the three trigger categories are shown in Fig. 7. The measurement is restricted to the theoretically favoured region, < q < 6GeV /c 4, and R K is found to be R K =.745 +.9.74 (stat) ±.36(syst), (8) which is consistent with the SM at a level of.6 standard deviations. The suppression of the value of R K at low values of q measured at both the BaBar and the experiments might hint at an interesting effect, but more data needs to be analysed to make definite statements. Also potential correlations with the anomalies described in Sec. 3 will be clarified with more experimental data. 6. Conclusion Most scenarios of physics beyond the Standard Model of particle physics predict measurable effects in the flavour sector, in particular in rare meson decays. 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