LLHCb: Status and Prospects on the b Anomalies
A. Hicheur *† LHCb Collaboration / Federal University of Rio de Janeiro.E-mail:
Since the start of the Large Hadron Collider program, direct searches for Beyond Standard Model(BSM) particles have constrained their mass scale to limits which are now above the energyreach of the current collider. As a result, studies of indirect probes of BSM physics have gaineda considerable momentum, both experimentally and theoretically. The flavour anomalies in b hadron decays are now recognized as an important laboratory for the indirect detection of BSMphysics. This short review presents several key analyses in this area, and some prospects withfuture data. BEAUTY202021-24 September 2020Kashiwa, Japan (online) * Speaker. † also at U. Constantine, Algeria. © Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ h e p - e x ] J a n Flavour Anomalies
A. Hicheur
1. Introduction
Heavy Flavour decays are usually described by low energy effective Hamiltonians forming anEffective Field Theory (EFT) (see, e.g. reference [1] for a review). The Hamiltonians are written as: H = ∑ i V iCKM C i ( µ ) O i ( µ ) , (1.1)where C i ( µ ) are the Wilson coefficients integrating out the physics above the scale µ (short range), O i ( µ ) are current operators which matrix elements represent the low energy (non-perturbative/longrange) hadronic physics, and µ is the renormalization scale (typically ∼ V iCKM represents the flavour coupling associated to an operator O i , i.e., Cabibbo-Kobayashi-Maskawa (CKM) matrix elements for SM operators. The Wilson coefficients thusrepresent the quantities which are impacted by the intervention of BSM physics.For the semileptonic tree decays, the coupling of the mediating W boson does not discriminatebetween lepton flavours in the SM. On the contrary, a BSM mediator might exhibit differentcouplings between light and heavy leptons. This is referred to as Lepton Flavour UniversalityViolation (LFUV). Such an effect could also occur for the semileptonic loop decays b → s (cid:96)(cid:96) wherethe dominant operators are O , O , O . Loop decays could also be the ground of new dynamicsinvolving Lepton Flavour Violation (LFV) where leptons of different flavours are produced together.A review of various LHCb analyses is proposed. Several of them exhibit deviations from SM thatcan be explained consistently with theoretical models.
2. Semileptonic tree decays
The dominant decays ( b → c (cid:96) − ¯ ν ) of this kind are generically written as H b → H c (cid:96) − ¯ ν where H b is a b hadron and H c is a charm hadron. The search for a possible LFUV is performed throughthe measurement of the ratio: R ( H c ) = B ( H b → H c τ − ¯ ν ) B ( H b → H c µ − ¯ ν ) , (2.1)where B denotes the branching fraction. A BSM mediating heavy boson might couple preferentiallyto the tau lepton, as in Fig.1, and thus produce a R ( H c ) ratio different from the expected SM-basedcalculations. - ,H - Wb c - tn Figure 1: b → c τ − ¯ ν semileptonic transition with a mediating W or charged Higgs boson as derived from2HDM models discussed e.g. in Ref. [2]. The modes ¯ B → D +( ∗ ) (cid:96) − ¯ ν have drawn attention both at the b factories and the LHCb experi-ment. The LHCb collaboration has been focusing so far on R ( D ∗ + ) , where D ∗ + is reconstructed via D ∗ + → D ( → K − π + ) π + . The τ lepton is reconstructed in the muonic mode, τ − → µ − ¯ ν µ ν τ [3],or the hadronic mode τ → πππ ( π ) ν τ [4]. The discriminating variables include the missing mass,1 Flavour Anomalies
A. Hicheur m miss = ( P B − P D ∗ − P µ ) , the momentum transfer q = ( P B − P D ∗ ) , the muon energy E ∗ µ , the τ lifetime (for the hadronic mode) and a Boost Decision Trees classifier [5] to reject double-charmdecays of the type B → DDX (for the hadronic mode). The muonic tau analysis [3] obtained ameasurement of R ( D ∗ + ) = . ± . ( stat ) ± . ( syst ) while the hadronic tau study [4] gives R ( D ∗ + ) = . ± . ( stat ) ± . ( syst ) ± . ( BF ) , where the last uncertainty is due to theexternal branching fraction of the normalizing channel ¯ B → D ∗ + π − π + π − . The latest HFLAVaveraging [6] in the R ( D ) − R ( D ∗ ) plane, including the recent Belle collaboration R ( D ( ∗ ) ) mea-surements [7], is shown in Fig.2. Compared to an averaged series of SM-based predictions [8], adiscrepancy of 3.1 σ is observed. Figure 2: Average of R ( D ) and R ( D ∗ ) [6]. A similar measurement with the decays B − c → J / ψ (cid:96) − ¯ ν , R ( J / ψ ) , has been per-formed recently by the LHCb collaboration for the τ muonic mode [9], leading to R ( J / ψ ) = . ± . ( stat ) ± . ( syst ) which lies 2 σ above the range of the known theoreticalestimates [10]. b → s (cid:96)(cid:96) transitions At quark level, these transitions proceed through the diagrams shown in Fig.3. The operatorscontributing to these decays are not evenly distributed in the q = m (cid:96)(cid:96) range: at low q , O dominates(for transitions to non-scalar hadrons), in the central q region below the charmonium resonances, O and O interfere, and at high q O and O interfere. At the hadron level, the modes investigatedby LHCb are B + → K ∗ + (cid:96) + (cid:96) − , B → K (cid:96) + (cid:96) − , B → K ∗ (cid:96) + (cid:96) − , B s → φ (cid:96) + (cid:96) − , and Λ b → Λ (cid:96) + (cid:96) − .A series of studies [11] have dealt with the dynamics of the muonic modes, (cid:96) = µ , to infer thedifferential decay rate d Γ dq , as illustrated in Fig.4. The data is systematically below the SM-basedtheoretical predictions, with local discrepancies exceeding 3 σ . Attempting to explore this intriguingbehaviour, angular analyses were performed for B → K ∗ µ + µ − [11](c), B s → φ µ + µ − [11](b)and Λ b → Λ µ + µ − [12]. Quantities such as P (cid:48) = S √ F L ( − F L ) have been built to reduce the hadronicuncertainties [13] from the coefficients S and F L (fraction of the K ∗ longitudinal polarization) ofthe angular distribution. For B → K ∗ µ + µ − , the discrepancy reported in previous studies for P (cid:48) seems to be persistent as shown in Fig.5(left). The fit for the deviations from SM to the real parts of2 Flavour Anomalies
A. Hicheur the C and C Wilson coefficients gives the results depicted in Fig.5(right). Considering only C ,the deviation from SM is determined to be 3.3 σ . Figure 3: b → s (cid:96)(cid:96) (left) penguin and (right) box transitions. ] c / [GeV q ] / G e V c · - [ q / d B d LCSR Lattice Data
LHCb - m + m + K fi + B ] c / [GeV q ] c G e V [ q ) / d µµ φ → s B d B ( LHCb
SM pred.Data
Figure 4: d Γ dq distribution for (left) B + → K + µ + µ − and (right) B s → φ µ + µ − . The J / ψ and ψ ( S ) q regionsare vetoed. The points represent the data measurements and the rectangles or band represent the SM-basedpredictions. ] c / [GeV q - - ' P ( S ) y / J ( S ) y CombinedRun 1 2016
SM from DHMV
LHCb − . − . − . − . . . . . . ∆ R e ( C ) − . − . − . − . . . . . . ∆ R e ( C ) flavio v2.0.0 LHCb
Run 12016Run 1 + 2016
Figure 5: (left) Evolution of P (cid:48) (see text) as a function of q for B → K ∗ µ + µ − and (right) resulting 1,2,3 σ contours, using all the angular variables, of the deviations from SM of the real parts of the C and C Wilsoncoefficients.
Another way to probe the presence of New Physics is to measure the ratio R X = B ( H b → X µ + µ − ) B ( H b → Xe + e − ) ,where X denotes a hadronic system comprising a strange quark. The LHCb collaboration studied R K ( B + → K + (cid:96) + (cid:96) − ) [14], R K ∗ ( B → K ∗ (cid:96) + (cid:96) − ) [15] and R pK with the decay Λ b → pK − (cid:96) + (cid:96) − [16].For R K , the explored q range is [ . , ] GeV / c , i.e. below the charmonium radiative tails,and above backgrounds of the type B + → K + φ ( → (cid:96) + (cid:96) − ) . The R K ∗ analysis uses two bins in q , [ . , . ] GeV / c (above the photon pole) and [ . , ] GeV / c . Finally, R pK is measured withthe requirements q ∈ [ . , . ] GeV / c and m ( pK ) < . / c .3 Flavour Anomalies
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The obtained measurements are R K = . + . − . ( stat ) + . − . ( syst ) (1 . < q < / c ); R K ∗ = . + . − . ( stat ) ± . ( syst ) for 0 . < q < . / c and 0 . + . − . ( stat ) ± . ( syst ) for 1 . < q < / c . All these values are systematically below the SM-based predictionsby 2.2 σ to 2.5 σ [17]. With the Λ b → pK − (cid:96) + (cid:96) − decay, a first observation of Λ b → pK − e + e − isobtained with a similar Run 1 and part of Run 2 data set, as illustrated in Fig.6, leading to themeasurement of the ratio R pK = . + . − . ( stat ) ± . ( syst ) . For all these numbers, the uncertaintywill be reduced soon with the addition of the remainder of Run 2 data. ] c ) [GeV/ - m + m - pK ( m · c C a nd i d a t e s p e r M e V / - m + m - pK fi b L Combinatorial - m + m - K + K fi s B - m + m *0 K fi B LHCb ] c ) [GeV/ - e + e - pK ( m · c C a nd i d a t e s p e r M e V / - e + e - pK fi b L Combinatorial - e + e p - pK fi b L y / J - pK fi b L - e + e - K + K fi s B - e + e *0 K fi B LHCb
Figure 6: Invariant mass distributions of (left) Λ b → pK − µ + µ − and (right) Λ b → pK − e + e − candidates. Thefit shapes of the Λ b → pK − (cid:96) + (cid:96) − signals and the main backgrounds are overlaid. Figure 7 shows the impact of the R K ∗ measurements by BaBar and LHCb, as well as thecombination of the LFUV and angular parameters from all the experiments, on the New Physicscontributions to the Wilson coefficients C and C , as derived in Ref. [18]. Combining all anomalousdata, C departs by more than 6 σ from its SM-based prediction. Figure 7: The 1,2,3 σ contours for the New Physics contributions to the C and C Wilson coefficients using(left) only the LFUV data from Belle and LHCb and (right) combining all data from angular analyses andLFUV. The fits are provided in Ref. [18]. Flavour Anomalies
A. HicheurTable 1: Expected precisions for R X = B ( H b → X µ + µ − ) / B ( H b → Xe + e − ) . The numbers are taken fromRef. [28] R X Run 1&2 (9 fb − ) Run 3 (23 fb − ) Run 4 (50 fb − ) Run 5 (300 fb − ) R K R K ∗ R φ R pK R π B → (cid:96)(cid:96) For these purely leptonic modes, the combination of the most recent results of the ATLAS[19], CMS [20] and LHCb [21] experiments, giving B ( B s → µ + µ − ) = ( . + . − . ) × − and B ( B → µ + µ − ) < . × − at 95% confidence level (CL), shows that B s → µ + µ − is 2 σ belowthe SM-based predictions. First attempts by LHCb of measuring the ditauon [22] and dielectron [23]modes lead to the results B ( B s → τ + τ − ) < . × − , B ( B → τ + τ − ) < . × − , B ( B s → e + e − ) < . × − and B ( B → e + e − ) < . × − at 95% CL.
5. LFV searches
The hints of LFUV in b → s (cid:96)(cid:96) decays have motivated recent LFV searches, seeking to observedecays of the type b → s (cid:96)(cid:96) (cid:48) or B → (cid:96)(cid:96) (cid:48) . A first study of B + → K + µ ± e ∓ [24] lead to the establishmentof the 95% CL limits: B ( B + → K + µ − e + ) < . × − and B ( B + → K + µ + e − ) < . × − .Another analysis on B + → K + µ − τ + [25], characterized by the original use of the decay B ∗ s → B + K + to constraint the τ four-momentum, obtained the less stringent limit B ( B + → K + µ − τ + ) < . × − . For what concerns the LFV leptonic modes, the decays B ( s ) → e ± µ ∓ [26] and B ( s ) → τ ± µ ∓ [27] have been studied , setting the 95% CL limits to B ( B s → e ± µ ∓ ) < . × − , B ( B → e ± µ ∓ ) < . × − , B ( B s → τ ± µ ∓ ) < . × − and B ( B → τ ± µ ∓ ) < . × − .
6. Prospects and summary
Most analyses presented have been published on a partial LHCb data set and are currently beingupdated. The second column of Table 1 shows the expected precisions for the R X measurements forthe full Run1+Run2 statistics.On the longer term, the third, fourth and fifth columns of Table 1 show the evolution of theexpected sensitivities for the future runs of data taking. For the tree semileptonic decays, the LFUratios R ( D ) , R ( D + ) , R ( D ( ∗ ) s ) , R ( Λ ( ∗ ) c ) , R ( J / ψ ) and R ( p ) (from Λ b → p τν ) are foreseen during thefirst phase of Run 3. Figure 8 shows the evolution of the R ( H c ) ratios throughout the periods of datataking.The available results on the anomalies in the b -hadron decays show a combination of deviations,which has triggered an intense activity on the phenomenological side in studies aiming at constrainingthe Wilson coefficients and probing possible contributions of New Physics [18, 30, 31]. The 6 to5 Flavour Anomalies
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Year . . . . . . . P r o j ec t e dun ce rt a i n t y Belle − II R D Belle − II R D ∗ LHCb R D LHCb R D ∗ LHCb R J/ψ
LHCb R D s LHCb R Λ c Figure 24: Projected uncertainty for various R H c ratios from the Belle-II and LHCb experiments(years are indicative). The Belle-II uncertainties include estimates of the evolution of thesystematic uncertainties. The systematic uncertainties at LHCb are assumed to scale with theaccumulated statistics until they reach limits at 0 . .
004 and 0 .
012 for R D ∗ , R D and R J/ψ ,and 0 .
006 for both R D s and R Λ c . Year . . . . . . . P r o j ec t e dun ce rt a i n t y Belle − II R K Belle − II R K ∗ LHCb R K LHCb R K ∗ LHCb R φ LHCb R pK Figure 25: Projected uncertainty for various R H s ratios from the Belle-II and LHCb experiments(years are indicative) in the range ∼ < q < /c . The Belle-II values include estimatesof the evolution of the systematic uncertainties (for R K ∗ , the charged and neutral channels havebeen combined). The LHCb uncertainties are statistical only (the precision of all measurementswill be dominated by the size of the available data samples except for R K and R K ∗ at 300 fb − ). Figure 8: Evolution of the sensitivity on the semileptonic ratios R ( H c ) as reported in Ref. [29]. σ deviation from SM derived for C is subject to interpretations, which try to account for whatis observed in both b → c tree transitions and b → s loop decays. Explanations based on vectorLeptoquarks [32] and the “4321” model [33] have become popular. Any explored paradigm willhave to satisfy the constraints of the B s meson mixing and B + c meson lifetime. References [1] G. Buchalla et al. , Rev. Mod. Phys. (1996) 1125-1144[2] J.F. Gunion, E.H. Haber, G.L. Kane, S. Dawson, The Higgs Hunter’s Guide , Front.Phys. (2000) 1-404[3] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2015) 111803[4] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2018) 171802[5] L. Breiman, J.H. Friedman, R.A. Olshen and C.J. Stone, Classification and regression trees , Wadsworthinternational group (1984) Belmont, California, USA[6] Heavy Flavor Averaging Group, Y. Amhis et al. , arXiv:1909.12524, latest results and plots available at https://hflav.web.cern.ch/ [7] Belle Collaboration, A. Abdesselam et al. , arXiv:1904.08794[8] D. Bigi, P. Gambino, Phys. Rev.
D94 (2016) 094008; F.Bernlochner et al. , Phys. Rev.
D95 (2017)115008 ; D.Bigi et al. , JHEP (2017) 061; S.Jaiswal et al. , JHEP (2017) 060[9] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2018) 121801[10] A.Yu.Anisimov et al. , Phys. Lett.
B452 (1999) 129; M.A.Ivanov et al. , Phys. Rev.
D73 (2006) 054024;E.Hernandez et al. , Phys. Rev.
D74 (2006) 074008[11] LHCb collaboration, R. Aaij et al. , a: JHEP (2014) 133; b: JHEP (2015) 179; c: PRL 125 (2020)011802; d: JHEP (2015) 115[12] LHCb collaboration, R. Aaij et al. , JHEP (2018) 146 Flavour Anomalies
A. Hicheur[13] Descotes-Genon et al. , JHEP (2013) 137[14] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2019) 191801[15] LHCb collaboration, R. Aaij et al. , JHEP (2017) 055[16] LHCb collaboration, R. Aaij et al. , JHEP (2020) 040[17] Non-exhaustive: C. Bobeth et al. JHEP (2007) 040; M.Bordone et al. , Eur. Phys. J. C76 (2016) 440;W. Altmannshofer et al. , Phys. Rev.
D96 (2017) 055008[18] M. Alguero et al. , Eur. Phys. J.
C79 (2019) 8, 714; Eur. Phys. J.
C80 (2020) 6, 511 (addendum).[19] ATLAS collaboration, ATLAS-CONF-2020-049[20] CMS collaboration, CMS-PAS-BPH-20-003[21] LHCb collaboration, LHCb-CONF-2020-002[22] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2017) 251802[23] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2020) 211802[24] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2019) 241802[25] LHCb collaboration, R. Aaij et al. , JHEP (2020) 129[26] LHCb collaboration, R. Aaij et al. , JHEP (2018) 078[27] LHCb collaboration, R. Aaij et al. , Phys. Rev. Lett. (2019) 211801[28] LHCb collaboration, R. Aaij et al. , arXiv:1808.08865, LHCB-PUB-2018-009, CERN-LHCC-2018-027[29] S. Bifani et al. , J. Phys. G: Nucl. Part. Phys. 46 (2019) 023001[30] J. Aebischer et al. , arXiv:1903.10434[31] D. M. Straub, flavio package, arXiv:1810.08132[32] D. Buttazzo et al. , JHEP 11 (2017) 044[33] L. Di Luzio et al. , Phys. Rev. D96 , (2017) 115011; JHEP (2018) 081(2018) 081