Results and prospects of radiative and electroweak penguin decays at Belle II
CConference on Flavour Physics and CP violation (FPCP) 2020 Results and prospects of radiative and electroweak penguin decays at Belle II
Soumen Halder(On behalf of the Belle II Collaboration) ∗ Tata Institute of Fundamental Research, Mumbai 400005, India
The b → s ( d ) quark-level transitions are flavor-changing neutral current processes, which are notallowed at tree level in the standard model. These processes are very rare and constitute a potentialprobe for new physics. Belle II at SuperKEKB is a substantial upgrade of the Belle experiment. Itaims to collect 50 ab − of data with a design peak luminosity of 8 × cm − s − that is 40 timesmore than its predecessor. It has been recording data since 2019 and during these early days of theexperiment, efforts are being made to detect early signals of the above decays. We report the firstreconstrution in Belle II data of a B → K ∗ γ signal as well as future prospects for radiative andelectroweak decays at Belle II. I. INTRODUCTION
The flavor-changing neutral current processes me-diated by b → s ( d ) transitions are forbidden at treelevel in the standard model (SM). These processes canhowever proceed via higher-order amplitudes involv-ing quantum loops. Non-SM particles may contributein such loops as exemplified in Fig 1, which couldsuppress or enhance the amplitude of the decay rate.Hence, the decays mediated by b → s ( d ) transitionspotentially probe new physics (NP). In this article,we report the current status and future prospect ofBelle II for radiative penguin decays proceeding via b → s ( d ) γ and for electroweak penguin decays me-diated by b → s ( d ) (cid:96) + (cid:96) − or b → s ( d ) ν ¯ ν transitions. b s(cid:96) + ( ν (cid:96) ) (cid:96) − ( ν (cid:96) ) tW − W − ν (cid:96) ( (cid:96) ) b s(cid:96) + (cid:96) − H − H − FIG. 1: Feynman diagrams of b → s(cid:96) + (cid:96) − featuring a SMbox diagram (left) and non-SM box diagram where the W bosons are replaced by some non-SM particles such ascharged Higgs bosons (right). II. SUPERKEKB AND BELLE II
SuperKEKB is the next generation e + e − colliderlocated at Tsukuba, Japan, which plans to collide e + and e − beams at a rate 40 times higher than its pre-decessor KEKB. The Belle II detector placed at the ∗ Electronic address: [email protected] collision point of SuperKEKB is a major upgrade ofBelle. It has collected about 0.5 fb − data during itspilot run in 2018, which was aimed at ensuring thatbeam background levels are safe to install the sensitivevertex detector. Since the full detector integration in2019, Belle II has recorded 55 fb − data. The even-tual goal is to collect 50 ab − of data, which will makethe next decade very interesting for the flavor physicscommunity. A short summary on the Belle II experi-ment is available in Ref. [1]. III. ANALYSIS TECHNIQUES
The analysis techniques used to study the rare de-cays can be divided into the following two categories. • Exclusive: A specific B meson decay mode isstudied by reconstructing all of its final-stateparticles, for example, the analysis of the decay B + → K + e + e − . • Inclusive: In an inclusive analysis some of thefinal-state particles are not explicitly recon-structed. The study of B → X s γ processes is anexample of such inclusive analysis, where X s isdefined as any final state having net strangenessof one. Inclusive decay analyses are further clas-sified into two categories, namely semiinclusiveand fully inclusive. Semiinclusive analyses areperformed by combining several exclusive decaymodes. Fully inclusive analyses do not rely onspecific exclusive decays, rather they involve thereconstruction of the recoiling B meson with thehadronic or semileptonic tagging procedure. Aschematic diagram for these two types of inclu-sive analysis is shown in Fig. 2. In the hadronic-tag inclusive analyses, the momentum of the sig-nal B meson is measured, whereas this is notfeasible for the semileptonic-tag analyses due tothe presence of a neutrino. Therefore, the for-mer has a lower signal efficiency since it fullyreconstructs tag-side B meson from hadronicdecays, which have relatively smaller branching a r X i v : . [ h e p - e x ] J a n Conference on Flavour Physics and CP violation (FPCP) 2020 fractions compared to semileptonic decays. Onthe other hand, the challenge of a semileptonictag analysis lies in dealing with the relativelyhigher background level.
FIG. 2: Comparison between semileptonic and hadronictag in terms of purity and efficiency (top). Illustration ofa hadronic-tagged B → X s γ event in the center-of-massframe (bottom). IV. RADIATIVE PENGUIN B DECAYS
In this section, we discuss B decays that are me-diated by b → s ( d ) γ transitions. The leading orderFeynman diagram for this process is shown in Fig. 3. b sγW − t FIG. 3: Leading order Feynman diagram for the b → sγ process. A. First reconstrution of the penguin B decay inBelle II data Among the radiative penguin decays, B → K ∗ γ are the first to be re-observed at Belle II. The isospin asymmetry in these decays (∆ ) is defined as∆ = Γ( B → K ∗ γ ) − Γ( B + → K ∗ + γ )Γ( B → K ∗ γ ) + Γ( B + → K ∗ + γ ) , which constitutes a reliable observable as most of thetheoretical uncertainties cancel in the ratio [2]. Re-cent measurement [3] has shown evidence for isospinviolation with 3 . σ significance, drawing lots of atten-tion to these decays. If this effect is real, then it canbe observed with 5 ab − data at Belle II. The currentanalysis [4] is based on following major decay chan-nels, • B → K ∗ [ → K + π − ] γ , • B + → K ∗ + [ → K S π + ] γ , and • B + → K ∗ + [ → K + π ] γ reconstructed in a sample corresponding to 2.62 fb − .The dominant background is light-quark production e + e − → q ¯ q , also known as continuum background.These events have jetlike structure making them easilydistinguishable from B ¯ B events, where the spatial dis-tribution of particles is spherical. A boosted decisiontree classifier [5], based on several event-shape vari-ables is trained to suppress continuum background.The selection criterion on the classifier output is opti-mized by maximizing S/ √ S+B, where S and B are thenumber of signal and background events in the signalregion.Two kinematic variables called the energy difference(∆ E ) and beam-energy constrained mass ( M bc ) areused for the signal B -meson reconstruction. ∆ E is thedifference between the energy of the reconstructed B meson in the center-of-mass frame and half of the col-lision energy. M bc is the mass of the reconstructed B candidate in the center-of-mass frame with its energybeing replaced by half of the collision energy. A tightrequirement ∆ E ∈ [ − . , .
08] GeV is applied to sup-press combinatorial background. The signal yield isthen obtained by performing an unbinned maximum-likelihood fit to the M bc distribution. The combinedsignificance of the above three channels exceeds 5 σ .The obtained results are listed in Table I. TABLE I: Results of the B → K ∗ γ analysis.Signal yield Significance(stat. error only) B → K ∗ [ K + π − ] γ . ± . σB + → K ∗ + [ K + π ] γ . ± . σB + → K ∗ + [ K S π + ] γ . ± . σ B. Branching fraction measurement
The theoretical predictions of the inclusive decaysare more precise than the exclusive decays because onference on Flavour Physics and CP violation (FPCP) 2020 TABLE II: Expected fractional uncertainty on the Belle IImeasurement of BF ( ¯ B → X s γ ) for each analysis techniquein two scenarios of luminosity with E = 1 . − Belle II 50 ab − Leptonic tag 3.9% 3.2%Hadronic tag 7.0% 4.2%Semiinclusive 7.3% 5.7% they have no form factor dependence [7]. Profitingfrom that, the branching fraction of ¯ B → X s γ pro-vides an important constraint on NP models such asextended Higgs boson sector or supersymmetry [8].Relying on an effective theory approach, this allows toset stringent constraints on the Wilson coefficients C and C [10]. In a semiinclusive analysis the hadronicsystem X s is reconstructed with several exclusive de-cays that contain an odd number of kaons in the fi-nal state. We can separately measure ¯ B → X s γ and¯ B → X d γ only in the semiinclusive method. For thefully inclusive method, where only the hard photon isreconstructed at the signal side, the other B mesonis reconstructed from either hadronic or semileptonicdecays.So far, all measurements apply a threshold on thephoton energy E = [1 . , .
0] GeV, and assumptionsare made to extrapolate the results down to 1.6 GeVto be consistent with theory predictions. This extrap-olation introduces a systematic uncertainty to the re-sult. Another dominant source of uncertainty in thefully inclusive ¯ B → X s γ analysis arises from neutralhadrons faking the photon. If the threshold value E is lowered, the neutral hadron background increasescausing a larger uncertainty. So there is a trade-off be-tween the two types of uncertainty. Dedicated studieson the spatial distribution of the signals in the electro-magnetic calorimeter at Belle II, which were not triedat Belle, can help improve these systematic uncertain-ties. In the hadronic tagging method S/B is very goodat the cost of low signal efficiency [ O (0 . C. CP violation measurement
The time-integrated CP asymmetry for ¯ B → X q γ decays is defined as A CP ( ¯ B → X q γ ) = Γ( ¯ B → X q γ ) − ( B → X ¯ q γ )Γ( ¯ B → X q γ ) + ( B → X ¯ q γ ) . Deviation of A CP ( ¯ B → X s ( d ) γ ) from the SM predic-tion is a sign of NP that would modify the Wilsoncoefficients C and C [10]. The theory uncertainties[11] in these observables are quite large: A SMCP ( ¯ B → X s γ ) = [ − . , . , (1) A SMCP ( ¯ B → X d γ ) = [ − , . (2)However, the asymmetry combined for X s and X d states is expected to be small in the SM, A SMCP ( ¯ B → X s + d γ ) = O (Λ QCD /m b ) because of the CKM-matrixunitarity. The corresponding Belle measurement A SMCP ( ¯ B → X s + d γ ) = 2 . ± . ± . B ¯ B backgrounds,which are subtracted. The estimation of this asymme-try from sidebands will be more accurate with a largerdata set. In fact, using the hadronic tag method wecan precisely measure the asymmetry of both chargedand neutral ¯ B → X s γ decays and dominant peakingbackgrounds. The Belle II data set will allow for testthe assumption that the CP violating asymmetry isindependent of the X s decay mode. The systematicuncertainty due to detector asymmetry can also be re-duced using a large data set since this is also measuredfrom sidebands or control samples.The isospin asymmetry introduced earlier, can alsobe measured in the inclusive analysis of B → X s γ decays. Another reliable observable is the differenceof direct CP asymmetries between the charged andneutral B decays, ∆ A CP = A CP ( B + → X + s γ ) − A CP ( B → X s γ ), which can be shown to be propor-tional to Im( C g C γ ) [11]. In the SM, C and C are bothreal, therefore ∆ A CP is zero, but in several NP mod-els [11, 13, 14] ∆ A CP can reach the level of 10%. Sincethe distinction between charged and neutral B decaysis necessary to measure these two observables, only thesemiinclusive and hadronic-tag methods can be used.So far, measurements [15, 16] are consistent with theSM. In these studies statistical uncertainties dominateand can be improved at Belle II. Another dominantuncertainty is due to the production ratio of B + B − and B ¯ B from the Υ(4 S ) decay ( f + − /f ). At BelleII, this factor can be measured with better precisionusing double semileptonic decay ¯ B → D ∗ (cid:96) − ¯ ν . Theexpected fractional uncertainties on the Belle II mea-surements of the discussed asymmetries are shown inTable III for each analysis technique in two scenariosof luminosity. V. ELECTROWEAK PENGUIN B DECAYS
Electroweak penguin amplitudes mediate the b → s(cid:96) + (cid:96) − process. The dominant Feynman diagrams in Conference on Flavour Physics and CP violation (FPCP) 2020
TABLE III: Expected uncertainties on the Belle II mea-surements of the CP and isospin asymmetries for eachanalysis technique in two scenarios of luminosity with E = 1 . −
50 ab − A CP ( B → X s + d γ ) Leptonic tag 1.5% 0.48% A CP ( B → X s + d γ ) Hadronic tag 2.2% 0.70%∆ A CP ( B → X s + d γ ) Semiinclusive 0.98% 0.30%∆ A CP ( B → X s + d γ ) Hadronic tag 4.3% 1.3%∆ ( B → X s + d γ ) Semiinclusive 0.81% 0.63%∆ ( B → X s + d γ ) Hadronic tag 2.6% 0.85% the SM are shown in Fig.4. b s(cid:96) + (cid:96) − tW − W − ν (cid:96) b s(cid:96) + (cid:96) − t W − γ/Z FIG. 4: Feynman diagrams for the b → s(cid:96) + (cid:96) − process.Left diagram is known as box diagram and right diagramis known as penguin diagram. A. Lepton flavor universality test
Within the SM, gauge bosons couple equally to dif-ferent flavors of lepton. The only non-universality be-tween leptons is their coupling with the Higgs bosonas it depends on their mass, but still it has negligibleeffect on the BF of the decays. Therefore, the ratiosof branching fractions, referred to as R -ratios, R H [ q , q ] = (cid:82) q q dq d Γ( B → Hµ + µ − ) dq (cid:82) q q dq d Γ( B → He + e − ) dq , with H being a hadron, are expected to be unity upto corrections from the phase-space difference due todifferent masses, where q is the dilepton invariantmass squared. These R -ratios are very reliable ob-servables, as the theoretical uncertainties from CKMfactors, form factors and other hadronic effects can-cel since they are common in the numerator and de-nominator. The dilepton mass ranges correspondingto charmonium resonances are vetoed. This leadsto two dilepton square-mass regions, namely low- q ( q ∈ [1 ,
6] GeV /c ) and high- q ( q > . /c )regions. Within these two regions the SM predictionsfor R ratios are 1 with high precision. For example, R SM K [1 ,
6] = 1 . ± .
001 [19]. The main experimental challenge is understandingthe difference in reconstructed efficiency between elec-tron and muons. The most important difference is in-troduced by the bremsstrahlung process, which causeselectrons to radiate a significant amount of energy. Sofar, LHCb provided the most precise measurement ofboth R K ( ∗ ) in the low- q region [20, 21]. The R K ( ∗ ) measurement result is compatible with the SM at thelevel of 2.6 (2.5) standard deviations. FIG. 5: Measurement of R K (top) and R K ∗ (bottom) indifferent experiments. A previous measurement by Belle [22, 24] has higheruncertainty, and is consistent with both SM and LHCbmeasurement. Belle already measured R -ratios in thehigh q bins, while no measurement from LHCb hasbeen reported [22]. At Belle II electron and muonmodes has almost similar reconstruction efficiency.Using a larger data set, the future Belle II measure-ment can shed light on these R K ( ∗ ) anomalies. If the R K anomaly is real due to NP, we should be able toestablish it with 5 σ significance using around 20 ab − of Belle II data. Thanks to the clean environment,Belle II can also study inclusive B → X s (cid:96) + (cid:96) − de-cay and measure R X s . Furthermore, Belle II canmeasure individually charged and neutral channels in B → K ∗ / + (cid:96)(cid:96) . In Table IV expected resolutions of R -ratio observables are listed. onference on Flavour Physics and CP violation (FPCP) 2020 TABLE IV: Expected resolutions on the observables thattest lepton flavor universality at Belle II.Observable Belle II 5 ab − Belle II 50 ab − R K [1,6] GeV /c
11% 3.6% R K [ > /c
12% 3.6% R K ∗ [1,6] GeV /c
10% 3.2% R K ∗ [ > /c R X s [1,6] GeV /c
12% 4.0% R X s [ > /c
11% 3.4%
B. Angular analysis of B → K ∗ (cid:96) + (cid:96) − An angular analysis of B → K ∗ [ Kπ ] (cid:96) + (cid:96) − decaysprovides several observables that are sensitive to NP.The angular distributions are completely described byfour independent kinematic variables, chosen as q = M (cid:96) + (cid:96) − and three angles cos θ (cid:96) , cos θ K , and φ . Theangle θ (cid:96) is the angle between the (cid:96) + ( (cid:96) − ) momentumand the momentum of dilepton system in the B ( ¯ B )rest frame. The angle θ K is the angle between thedirection of kaon and the K ∗ momentum in the B ( ¯ B )rest frame. The angle φ is the angle between the decayplane of (cid:96) + (cid:96) − and K ∗ . These angles are described inFig. 6. FIG. 6: Definitions of angles in the B → K ∗ (cid:96)(cid:96) decay The differential decay rate in terms of angular vari-ables is given by, d Γ( ¯ B → ¯ K ∗ (cid:96) + (cid:96) − ) d cos θ (cid:96) d cos θ K dφdq = 932 π (cid:88) j I j f j (cos θ (cid:96) , cos θ K , φ ) ,d Γ( B → K ∗ (cid:96) + (cid:96) − ) d cos θ (cid:96) d cos θ K dφdq = 932 π (cid:88) j ¯ I j f j (cos θ (cid:96) , cos θ K , φ ) , where I j and ¯ I j are functions of q and depend on the K ∗ transversity amplitude [25]. The angular depen-dence of each term comes from f j (cos θ (cid:96) , cos θ K , φ ),parametrized with spherical harmonics associatedwith different polarisation states of the K ∗ anddilepton system. The self-tagging nature of the B → K ∗ (cid:96) + (cid:96) − decay allows for determining both CP-averaged and CP-asymmetric quantities that depends on the coefficients, S i = ( I i + ¯ I i ) / d Γ dq ,A i = ( I i − ¯ I i ) / d Γ dq . It is possible to exploit symmetry relations to con-struct observables that are free from form-factor un-certainties at leading order in the 1/ m b expansion [26].It is also possible to build reliable observables at low- q exploiting the form-factor cancellation. This in-cludes the so-called P (cid:48) series of observables [27] de-fined as, P (cid:48) = S √− S c S s , P (cid:48) = S √− S c S s , P (cid:48) = S √− S c S s , P (cid:48) = S √− S c S s . The LHCb reported atension in the P (cid:48) observable from the B → K ∗ µ + µ − decay [28]. Belle also performed the angular analysis[29], using its full data set with both charged and neu-tral B mesons. A 2 . σ tension was observed in P (cid:48) ofthe muon modes in the region 4 GeV /c < q < /c , which is the same region LHCb observed the P (cid:48) anomaly. A lepton-flavor-dependent measurementof P (cid:48) can lead to another observable Q (cid:48) = P (cid:48) µ − P (cid:48) e .There are no significant deviation from SM observedin the Belle measurement of Q (cid:48) .At Belle II, the uncertainty due to peaking back-ground can be reduced by including individual compo-nents in the fitting model as these components can bemore reliably modeled with a larger data set. The un-certainty in P (cid:48) , for q ∈ [4 ,
6] GeV /c with 2.8 ab − of Belle II data based on both electron and muonmodes will be comparable to the 3 fb − data resultof LHCb that uses the muon modes only. A naive ex-trapolation leads to the conclusion that the accuracythat can be achieved on the optimised observables atBelle II with 50 ab − is just 20% lower than the pre-cision that LHCb is expected to reach with 50 fb − ofdata [30]. C. Missing energy channel: B → K ( ∗ ) ν ¯ ν The semileptonic decays mediated by b → sν ¯ ν areforbidden at tree level involving a single boson ex-change. They occur via higher-order electroweak pen-guin (Fig. 8), box diagram (Fig. 9), or tree-level tran-sition involving at least two W / Z bosons (Fig. 10).An advantage of the b → sν ¯ ν transition comparedto b → s(cid:96) + (cid:96) − is the absence of photon mediated di-agrams that lead to a pair of charged leptons. As aconsequence, the factorisation of the hadronic and lep-tonic current is exact for B → K ( ∗ ) ν ¯ ν decays, whichmakes theoretical predictions more accurate. Mea-surements of the B → K ( ∗ ) ν ¯ ν decay rates would inprinciple allow the extraction of the B → K ( ∗ ) formfactors to high accuracy. B decays involving exotic Conference on Flavour Physics and CP violation (FPCP) 2020
FIG. 7: Measurement of P (cid:48) (top) and Q (cid:48) (bottom) atBelle.FIG. 8: Electroweak penguin diagram for b → sν ¯ ν . final states, e.g. dark matter candidates, are closelyrelated to this kind of signals since the missing en-ergy signatures within the detector is the same. Onemore observable which is sensitive to NP is the K ∗ longitudinal polarisation fraction ( F L ) in B → K ∗ ν ¯ ν .An angular analysis of the B → K ∗ ( → Kπ ) ν ¯ ν decaywould allow to access the K ∗ longitudinal polarisationfraction F L . Ref. [18] predicts F SM L = 0 . ± .
03. An-other study [17] shows that the NP-sensitive operator O R = e π (¯ sγ µ P R b )(¯ νγ µ (1 − γ ) ν ), where P R is right-handed chiral projection operator, in the product ex-pansion impacts F L . In other words, this observable FIG. 9: Box diagram for b → sν ¯ ν .FIG. 10: Tree-level diagram involving two bosons. is sensitive to right-handed quark current.In the SM, the branching fractions of B → K + ν ¯ ν and K ∗ ν ¯ ν are (4 . ± . × − and (9 . ± . × − ,respectively [31]. None of the decays have been ob-served. They are expected to be observed with first10 ab − of Belle II data. A larger data sample is re-quired to measure F L . Studies based on simplifiedsimulated experiments show that the uncertainty on F L will be 0.11 with 50 ab − . The expected resolu-tions on the observables are listed in Table V. VI. SUMMARY
The low-background environment with constrainedcollision kinematics at Belle II grants access to severalunique observables in rare B decays. Starting with the B → K ∗ γ decay, Belle II is on its way to re-observe TABLE V: Expected resolutions on the observables fordecays mediated by b → sν ¯ ν .Observable Belle II 5 ab − Belle II 50 ab − BF( B + → K + ν ¯ ν ) 30% 11%BF( B → K ∗ ν ¯ ν ) 26% 9.6%BF( B + → K ∗ + ν ¯ ν ) 25% 9.3% F L ( B → K ∗ ν ¯ ν ) – 0.079 F L ( B + → K ∗ + ν ¯ ν ) – 0.077 onference on Flavour Physics and CP violation (FPCP) 2020 [1] J. Bennett, J. Phys.: Conf. Ser. , 014013 (2005).[3] T. Horiguchi et al. (Belle Collaboration), Phys. Rev.Lett. , 191802 (2017).[4] M. Yonenaga et al., BELLE2-NOTE-PL-2019-021[5] T. Keck, arXiv:1609.06119 (2016).[6] M. Misiak et al., Phys. Rev. Lett. , 221801 (2015).[7] M. Misiak et al., J. High Energy Phys. , 175 (2020).[8] O. Deschamps et al., Phys. Rev. D , 073012 (2010).[9] A. Abdesselam et al. (Belle Collaboration),arXiv:1608.02344 (2016).[10] P. Gambino and M. Misiak, Nucl. Phys. B , 338(2001).[11] M. Benzke et al., Phys. Rev. Lett. , 141801 (2011).[12] L. Pesantez et al. (Belle Collaboration), Phys. Rev.Lett. , 151601 (2015).[13] R. Malm, M. Neubert and C. Schmell, J. High EnergyPhys. , 042 (2016).[14] M. Endo et al., J. High Energy Phys. , 019 (2018).[15] B. Aubert et al. (BaBar Collaboration), Phys. Rev.D , 052004 (2005).[16] S. Watanuki et al. (Belle Collaboration), Phys. Rev.D , 3 (2019).[17] W. Altmannshofer et al., J. High Energy Phys. ,022 (2009).[18] A. J. Buras et al., J. High Energy Phys. , 184(2015).[19] C. Bobeth, G. Hiller and G. Piranishvili, J. High En-ergy Phys. , 040 (2007).[20] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. , 191801 (2019).[21] R. Aaij et al. (LHCb Collaboration), J. High EnergyPhys. , 055 (2017).[22] S. Choudhury et al. (Belle Collaboration),arXiv:1908.01848 (2019).[23] J. P. Lees et al. (BaBar Collaboration), Phys. Rev. D , 032012 (2012).[24] J. T. Wei et al. (Belle Collaboration), Phys. Rev. Lett. , 171801 (2009).[25] W. Altmannshofer et al., J. High Energy Phys. ,019 (2009).[26] F. Kruger and J. Matias, Phys. Rev. D , 094009(2005).[27] S. Descotes-Genon et al., J. High Energy Phys. ,137 (2013).[28] R. Aaij et al. (LHCb Collaboration), J. High EnergyPhys. , 104 (2016).[29] S. Wehle et al., Phys. Rev. Lett. , 111801 (2017).[30] E. Kou et al., PTEP , 2 (2020).[31] A. J. Buras et al., J. High Energy Phys.02