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Prepared for submission to June 12, 2017

A Challenge to Universality in B Decays

Gregory Ciezarek1, Manuel Franco Sevilla2, Brian Hamilton3, Robert Kowalewski4, Thomas Kuhr5, Vera Luth¨ 6, Yutaro Sato7

One of the key assumptions of the of fundamental is that the interactions of the charged , namely , , and taus, differ only because of their different . While precision tests comparing processes involving electrons and muons have not revealed any definite violation of this assumption, recent studies involving the higher- lepton have resulted in observations that challenge lepton universality at the level of four standard deviations. A confirmation of these results would point to new particles or interactions, and could have profound implications for our understanding of physics.

1Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands 2University of California at Santa Barbara, Santa Barbara, California 93106, USA 3University of Maryland, College Park, Maryland 20742, USA 4University of Victoria, Victoria, British Columbia, Canada V8P 5C2 5Ludwig Maximilians University, 80539 Munich, Germany 6SLAC National Accelerator Laboratory, Stanford, California 94309, USA 7Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan

ore than 70 years of research have led account precision measurements of the tau and masses and − − − − to an elegant and concise theory of particle interac- lifetimes and the decay rates τ → e νeντ and µ → e νeνµ , M tions at the sub-nuclear level, commonly referred to the equality of the weak coupling strengths of the tau and muon as the Standard Model (SM) [1, 2]. Based on information ex- was confirmed [6]. On the other hand, a recent determination of tracted from experiments, theorists have combined the theory of the radius, derived from very precise measurements of the electroweak (EW) interactions with in muonic hydrogen [9] differs by about 4% (QCD), the theory of strong interactions, and experiments have from measurements of normal hydrogen atoms and e-p scattering validated this theory to an extraordinary degree. Any observation data. Studies of the origin of this puzzling difference are under- that is proven to be inconsistent with SM assumptions would way [10]. They are aimed at a better understanding of the proton suggest a new type of interaction or particle. radius and structure, and may reveal details of the true impact of In the framework of the SM of particle physics the fundamen- muons and electrons on these interactions. tal building blocks, and leptons, are each grouped in three Recent studies of purely leptonic and semileptonic decays − − (∗) − generations of two members each. The three charged leptons, the of B of the form B → τ ντ and B → D ` ν`, with − − − (e ), the muon (µ ) and the tau (τ ) are each paired ` = e, µ, or τ, have resulted in observations that seem to challenge with a very low mass, electrically neutral , νe,νµ , and ντ . lepton universality. These weak decays involving leptons are The electron, a critical component of , was discovered by well understood in the framework of the SM, and therefore offer J.J. Thomson [3] in 1897. The discovery of the muon in cosmic a unique opportunity to search for unknown phenomena and rays by C. D. Anderson and S. H. Neddermeyer [4] in 1937 came processes involving new particles, for instance, a yet undiscovered as a surprise, similarly surprising was the first observation of charged partner of the Higgs [11]. Such searches have been τ+τ− pair production by M. Perl et al. [5] at the SPEAR e+e−

arXiv:1703.01766v3 [hep-ex] 8 Jun 2017 performed on data collected by three different experiments, the storage ring in 1975. As far as we know, all leptons are point-like LHCb experiment at the proton-proton (pp) collider at CERN in particles, i.e. they have no substructure. Europe, and the BABAR and Belle experiments at e+e− colliders The three generations are ordered by the mass of the charged in the U.S.A. and in Japan. ± ± lepton ranging from 0.511MeV for e to 105MeV for µ , and Measurements by these three experiments favor larger than ± 1,777MeV for τ [6]. These mass differences lead to vastly dif- expected rates for semileptonic B decays involving τ leptons. Cur- ferent lifetimes, from the stable electron to 2.2µs for muons, and rently, the combined significance of these results is at the level of 0.29ps for taus. Charged leptons participate in electromagnetic four standard deviations, and the fact that all three experiments and weak, but not strong interactions, whereas only un- report an unexpected enhancement has drawn considerable atten- dergo . The SM assumes that these interactions tion. A confirmation of this violation of lepton universality and an of the charged and neutral leptons are universal, i.e., the same for explanation in terms of new physics processes are a very exciting the three generations. prospect! In the following, details of the experimental techniques Precision tests of lepton universality have been performed and preliminary studies to understand the observed effects will over many years by many experiments. To date no definite vi- be presented, along with prospects for improved sensitivity and olation of lepton universality has been observed. Among the complementary measurements at current and future facilities. most precise tests is a comparison of decay rates of K mesons, − − − − K → e νe versus K → µ ν µ [7][8]. Furthermore, taking into A Challenge to Lepton Universality in Decays — 2/10

` The first factor is universal for all semileptonic B decays, contain- (a) (a) ing a flavor mixing parameter [14], in this case |Vcb| [15] ∗ ⌫¯` V ` for b → c quark transitions, and p , the 3-momentum of the b ub D(∗) b Vcb W /H B in the B rest frame, in this case a D(∗) meson. The four 0 W B, B¯ u¯ ⌫¯` c helicity [18] amplitudes H+,H−,H0 and Hs capture the impact u,¯ d¯ 0,( ) +,( ) D ⇤ ,D ⇤ of hadronic effects. They depend on the of the me- u,¯ d¯ 2 2 2 ∗ 2 ` son and on q . The kinematic range, m` ≤ q ≤ (mB − mD ) , (b) is sensitive to the lepton mass m` and the charm meson mass (b) ∗ ` ⌫¯` mD . The much larger mass of the τ not only impacts the rate, W but also the kinematics of the decays via the Hs amplitude. All ⌫¯` b Vcb ¯0 ∗ − b LQ B, B c four amplitudes contribute to B → D ` ν`, while only H0 and Hs ¯0 − B, B c ¯ 0,( ) +,( ) contribute to B → D` ν , which leads to a higher sensitivity of u,¯ d D ⇤ ,D ⇤ ` ¯ 0,( ) +,( ) ¯ u,¯ d D ⇤ ,D ⇤ u,¯ d this decay mode to the scalar contribution Hs. u,¯ d¯ − − Measurements of the ratios of semileptonic branching frac- Figure 1. Diagrams for SM decay processes: (a) B → ` ν` (∗) − tions remove the dependence on |Vcb|, lead to a partial cancella- (c) with a purely leptonic final state and (b) B → D ` ν`) involving a charm meson and lepton pair and mediated by a tion of theoretical uncertainties related to hadronic effects, and − reduce of the impact of experimental uncertainties. Current SM ` (W ). b Vub predictions [19, 20, 21] are B W /H u¯ ⌫¯`Standard model predictions of B meson decay rates B(B → Dτ−ν ) SM τ 0 300 ± 0 008 (4) RD = − = . . According to the SM, purely leptonic and semileptonic decays of B(B → De νe) − B mesons are mediated by the W boson, as shown schematically ∗ − SM B(B → D τ ντ ) ∗ 0 252 ± 0 003 (5) in Figure1. B mesons are assumed to be composed of a b-quark RD = ∗ − = . . . B(B → D e νe) and an anti-quark, either B−(b,u) or B0(b,d), whereas charm ∗ mesons (the spin-0 D and spin-1 D state) contain a c-quark and The predicted ratios relative to B(B → D∗µ−ν ) are identical 0(∗) +(∗) µ an anti-quark, D (c,u) or D (c,d). within the quoted precision. For purely leptonic B decays, the SM prediction of the total decay rate Γ, which depends critically on the lepton mass squared B meson production and detection m2 ` , is B meson decays have been studied at pp and e+e− colliding beam + − 2 2  2 2 facilities, operating at very different beam energies. The e e SM − − GF mB m` 2 m` 2 Γ (B → ` ν ) = |Vub| 1 − × f . (1) colliders operated at a fixed energy of 10.579GeV in the years ` 8π m2 B B 1999 to 2010. At this energy, about 20 MeV above the kinematic − The first factor contains the Fermi constant GF = 1.1663797 × threshold for BB production, e+ and e annihilate and produce −5 −2 10 GeV and the B meson mass, mB = 5.279GeV. All hadronic a particle, commonly refered to as ϒ (4S), which decays almost effects, due to the binding of quarks inside the meson, are en- exclusively to B+B− or B0B0 pairs. The maximum production capsulated in the decay constant fB. Recent lattice QCD cal- rate for these ϒ (4S) → BB events of 20 Hz was achieved at KEK, culations [12] predict fB = (0.191 ± 0.009)GeV. Taking into compared to the multi-hadron non-BB background rate of about − account the current world averages for the B lifetime, τB = 80 Hz. (1.638 ± 0.004)ps [13], and the quark mixing parameter [14] for B mesons from ϒ (4S) decays have very low momenta, ≈ b → u transitions,|Vub| [15], the expected branching fraction, i.e., 300MeV, and therefore their decay products are distributed al- the frequency of this decay relative to all decay modes, is [16] most isotropically in the rest frame of the ϒ (4S). For this reason, SM − − +0.10 −4 the BABAR [22, 23] and Belle [24] detectors were designed to B (B → τ ντ ) = (0.75 ) × 10 . (2) −0.05 cover close to 90% of the total solid angle, thereby enabling the − − Decays to the lower mass charged leptons, e and µ , are strongly reconstruction of all final state particles from decays of the two B suppressed by spin effects and have not yet been observed. mesons, except for neutrinos. Both detectors consist of cylindri- The differential decay rate, dΓ, for semileptonic decays in- cal layers of sensors surrounding the beam pipe, plus endcaps to (∗) 2 2 volving D mesons depends on both m` and q , the invariant cover the small polar angles. Constraints from energy-momentum mass squared of the lepton pair [17], conservation allow events containing a single neutrino to be dis- SM (∗) − 2 2 ∗ 2  2 2 criminated from those containing multiple undetected particles. dΓ (B → D ` ν ) GF |Vcb| |p (∗) | q m ` = D 1 − ` This feature also allows for an effective suppression of non-BB q2 3 2 q2 d 96π mB background and misreconstructed events. | {z } universal and phase space factors The LHC pp collider operated at total energies of 7 and 8 TeV (3) from 2008 to 2012. In inelastic pp collisions, high energy ,   m2  3m2  the carriers of the strong between the quarks inside the pro- × (|H |2 + |H |2 + |H |2) 1 + ` + ` |H |2 . tons, collide and produce a pair of B (mesons or ) + − 0 2q2 2q2 s along with a large number of other charged and neutral particles, | {z } hadronic effects in roughly one of hundred pp interactions. The B hadrons are A Challenge to Lepton Universality in B Meson Decays — 3/10

Figure 2. Belle (a) and LHCb (b) single event displays illustrating the reconstruction of semileptonic B meson decays: Trajectories of charged particles are shown as colored solid lines, energy deposits in the calorimeters are depicted by red bars. The Belle display is an end view perpendicular to the beam axis with the silicon detector in the center (small orange circle) and the device measuring the + − − 0 − 0 − + − − particle velocity (dark purple polygon). This is a ϒ (4S) → B B event, with B → D τ ν¯τ , D → K π and τ → e ντ ν¯e, and the B+ decaying to five charged particles (white solid lines) and two . The trajectories of undetected neutrinos are marked as dashed yellow lines. The LHCb display is a side view with the proton beams indicated as a white horizontal line with the interaction point far to the left, followed by the dipole magnet (white trapezoid) and the Cherenkov detector (red lines). The area close to the interaction point is enlarged above, showing the tracks of the charged particles produced in the pp interaction, the B0 path (dotted ¯0 ∗+ − ∗+ 0 + 0 − + − − orange line), and its decay B → D τ ν¯τ with D → D π and D → K π , plus the µ from the decay of a very short-lived τ . typically produced at small angles to the beam and with high and identify electrons in BABAR and Belle. Muons are identified momenta, features that determined the design of the LHCb detec- as particles penetrating a stack of steel absorbers interleaved with tor [25, 26], a single arm forward spectrometer, covering the polar large area gaseous detectors. angle range of 3−23 degrees. The high momentum and relatively long B hadron lifetime result in decay distances of several cm. − − Measurements of B → τ ντ decays Very precise measurements of the pp interaction point, combined The decays B− → τ−ν with two or three neutrinos in the final with the detection of charged particle trajectories from B decays τ state have only been observed by BABAR and Belle. These which do not intersect this point, are the very effective, primary two experiments exploit the BB pair production at the ϒ (4S) method to separate B decays from background. resonance via the process e+e− → ϒ (4S) → BB. These BB pairs All three experiments rely on several layers of finely seg- can be tagged by the reconstruction of a hadronic or semileptonic mented silicon strip detectors to locate the beam-beam interaction decay of one of the two B mesons, referred to as Btag. If this point and decay vertices of long-lived particles. A combination decay is correctly reconstructed, all remaining particles in the of silicon strip detectors and multiple layers of gaseous detec- event originate from the other B decay. tors measure the trajectories of charged particles, and determine BABAR and Belle have independently developed two sets of their momenta from the deflection in a magnetic field. Examples algorithms to tag BB events. The hadronic tag algorithms [27, 28] of reconstructed signal events recorded by the LHCb and Belle search for the best match between one of more than a thousand experiments are shown in Figure2. possible decay chains and a subset of all detected particles in For a given momentum, charged particles of different masses, the event. The efficiency for finding a correctly matched Btag is primarily and , are identified by their different ve- unfortunately quite small, 0.3%. The benefit of reconstructing locities. All three experiments make use of devices which sense all final state particles is that the total energy, Emiss, and vector Cherenkov , emitted by particles with velocities that ex- momentum, ~pmiss, of all undetected particles of the other B decay ceed the in a chosen radiator material. For lower can be inferred from energy and momentum conservation. The 2 2 velocity particles, Belle complements this with time-of-flight squared of all undetected particles, mmiss = Emiss − 2 2 measurements. BABAR and Belle also measure the velocity- ~pmiss, is used to distinguish events with one neutrino (mmiss ≈ 0) dependent energy loss due to ionization in the tracking detectors. from events with multiple neutrinos or other missing particles 2 Arrays of cesium iodide crystals measure the energy of photons (mmiss > 0). A Challenge to Lepton Universality in B Meson Decays — 4/10

The semileptonic tag algorithms exploit the large branching 70 Data Belle fractions for B decays involving a charm meson, a charged lepton Fit and associated neutrino, B → D(∗)`+ν , with `+ = e+, µ+. The 60 non BB background ` BB background efficiency for finding these tag decays is about 1%. However, the 50 Signal presence of the neutrino leads to weaker constraints on the Btag and signal B decay. 40 − − 30 Measurements of B → τ ντ decays are based on leptonic τ − − − − Events / (0.05 GeV) decays, τ → e νeντ and τ → µ ν µ ντ , and on semileptonic 20 decays, − → − and − → − 0 , which together account τ π ντ τ π π ντ 10 for 70% of all τ− decays. Thus, the signature for signal events is − − a single charged particle, either a charged lepton, a π , or a π 0.0 0.5 1.0 0 accompanied by a π , plus a Btag. (GeV) Eextra The presence of multiple neutrinos precludes the use of kine- Figure 3. Extraction of the B− → τ−ν yield from Belle data: matic constraints to effectively suppress backgrounds from other τ Results of a fit to the E distribution for the sum of signal and B decays. A variable that is sensitive to backgrounds with addi- extra backgrounds [29] for a subset of events with τ− → π−ν tional photons or undetected charged particles due to efficiency τ candidates. The green histogram at the bottom indicates the and acceptance losses is E , the sum of the energy deposits in extra predicted signal distribution. the calorimeter which are not associated with the tag or signal B decay. Figure3 shows a Eextra distribution measured by Belle − − for a subset of events with τ → π ντ . Signal events have low At LHCb, only decays of B¯0 mesons producing a µ− and D∗+ values of Eextra, while background events extend to higher values. meson are selected. Muons are favored over electrons because The signal yield is determined from a fit to the data using signal of their higher detection efficiency and momentum resolution. and background distributions based on data control samples and The D∗+ meson is reconstructed exclusively in D∗+ → D0(→ Monte Carlo simulation. The sum of the fitted signal yields for K−π+)π+ decays. B mesons produced at LHCb have a flight the four subsamples of purely leptonic and semileptonic τ decays, path of order 1 cm. This feature is exploited to reject the bulk of corrected for the efficiency of the tag and signal B decays, is used the background, by requiring that the charged particles from the − − to determine the B → τ ντ branching fraction. B candidate and no other tracks originate from a common vertex As shown in Figure4, current measurements by Belle [ 29, 30] that is significantly separated from the pp collision point. The and BABAR [31, 32] are of limited precision due to very small reduction in signal efficiency due to the use of a single decay chain signal samples and high backgrounds, and uncertainties in the is compensated by the very large production rate of B mesons at Btag efficiencies. The combination of these four measurements the LHC. The direction of the B momentum is inferred from the − constitutes the first observation of a purely leptonic B decay. reconstructed pp collision point and D∗+µ− vertex, its magnitude While the early measurements favored somewhat larger values, is unknown. LHCb approximates the B momentum by equating the current average [33] of its component parallel to the beam axis to that of the D∗+µ− combination, rescaled by the ratio of the B mass to the measured − − −4 B(B → τ ντ ) = (1.06 ± 0.19) × 10 . (6) D∗+µ− mass. The yields for the signal, normalization, and various back- is compatible with the SM prediction (compare Eq. 1), which is ground contributions are determined by maximum likelihood fits lower by 1.4 standard deviations. to the observed data distributions. Control samples are used to validate the simulated distributions and constrain the size and (∗) − Measurements of B → D τ ντ decays kinematic features of the background contributions. 2 ∗ As defined in Eqs.4 and5, RD(∗) correspond to the ratio of All three experiments rely on the variables mmiss, E` , the en- (∗) − (∗) − 2 branching fractions for B → D τ ντ (signal) and B → D ` ν` ergy of the charged lepton in the B rest frame, and q . BABAR (normalization). BABAR and Belle events containing such decays and Belle restrict the data to q2 > 4 GeV2 to enhance the con- ∗ are selected by requiring a hadronic Btag, a D or , and a tribution from signal decays. BABAR performs the fit in two charged lepton `− = e−, µ−. Charged and neutral D candidates dimensions whereas LHCb covers the whole q2 range in four are reconstructed from combinations of pions and kaons with intervals, thus performing a fully three-dimensional fit. Belle 2 invariant masses compatible with the D meson mass. The higher- performs a one-dimensional fit to the mmiss distribution in the low ∗0 ∗+ ∗ 2 2 2 mass D and D mesons are identified by their D → Dπ and mmiss region (mmiss < 0.85 GeV ) dominated by the normaliza- D∗ → Dγ decays. In signal decays, the lepton `− originates tion decays, combined with a fit to a multivariate classifier in the − − 2 2 ∗ from the τ → ` ντ ν` decay, leading to a final state with three high mmiss region. This classifier includes mmiss, E` , Eextra, and 2 neutrinos and resulting in a broad mmiss distribution, while in additional kinematic variables. normalization decays the lepton originates from the B decay with Figure5 shows one-dimensional projections of the data and 2 ¯ a single neutrino and therefore mmiss ≈ 0. Non-BB backgrounds the fitted contributions from signal, normalization, and back- 2 and misreconstructed events are greatly suppressed by the Btag grounds decays. For BABAR (and likewise for Belle) the mmiss reconstruction. The remaining background is further reduced by distributions show a narrow peak at zero (Figure5 a,d), domi- multivariate selections. nated by normalization decays with a single neutrino, whereas A Challenge to Lepton Universality in B Meson Decays — 5/10

BABAR (ST) 1.7 ± 0.8

+0.58 ± ± BABAR (HT) 1.83 -0.55 0.440 0.072 0.332 0.030

Belle (ST) 1.25 ± 0.39 0.302 ± 0.032

+0.29 ± ± Belle (HT) 0.72 -0.27 0.375 0.069 0.293 0.041

LHCb 0.336 ± 0.040 0 1 2 3 0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 - - -4 B(B → τ ντ) [10 ] R(D) R(D*) − − Figure 4. Comparison of measurements with SM predictions: The branching fraction B(B → τ ντ ) (left), the ratios RD (center), and RD∗ (right) by BABAR [31, 32, 28], Belle [29, 30, 34, 35], and LHCb [36]. The data points indicate statistical and total uncertainties. ST and HT refer to the measurements with semileptonic and hadronic tags, respectively. The average values of the measurements and their combined uncertainties, obtained by the Heavy Flavor Averaging Group [33, 37], are shown in red as vertical lines and bands, and the expectations from the SM calculations [16, 19, 20] are shown in blue.

8001 1 1 (a) BABAR (b) BABAR (c) BABAR 2 0.8 0.8 3000.8 m2 > 1 GeV 600 200 miss 0.6 0.6 2000.6 ) 400 ) 2 2 0.4 1000.4 0.4 100 2000.2 0.2 0.2

0 0 0 −4 −2 0 2 4 6 8 10 12 −4 −2 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 01 01 01 −2 (d) −1 0 1 2 3 4 150−2 (e) 0 2 4 6 8 10 1500 (f) 0.5 1 2 1.5 2 2 Data mmiss > 1 GeV 0.8 B → Dτν 0.8 0.8 * 1000 B D Events/(0.1 GeV)

Events/(0.05 GeV → τν Events/(0.25 GeV 0.6 1000.6 1000.6 B → Dlν B → D*lν 5000.4 B → D**(l/τ)ν 0.4 0.4 Bkg. 50 50 0.2 0.2 0.2

0 0 0 0−4 −2 0 2 4 6 8 10 12 0−4 −2 0 2 4 6 8 10 12 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 −2 −1 0 1 2 3 4 −2 0 2 4 6 8 10 0 0.5 1 1.5 2 2 2 2 2 * mmiss [GeV ] mmiss [GeV ] E l [GeV] ) )

2 2 4000 20000 (g) −0.40 < q2 < 2.85 GeV2 LHCb (h) q2 > 9.35 GeV2 LHCb 4000 (i) q2 > 9.35 GeV2 LHCb

Data 15000 3000 3000 DataB → D*τν

B →B D* →τ D*Hν c(→ lνX')X B D*H ( l X')X →B → D**lc →ν ν 2000 2000 10000 B → D**lν B → D*µν Events / (0.3 GeV B → D*µν Events / (0.3 GeV CombinatorialCombinatorial Events / (0.075 GeV) 5000 MisidentifiedMisidentified µ µ 1000 1000

0 0 0 −2 −1 0 1 2 3 4 −2 0 2 4 6 8 10 0 5000.5 10001 15001.5 20002 25002.5 2 2 2 2 * mmiss [GeV ] mmiss [GeV ] Eµ [GeV] 2 Figure 5. Extraction of the ratios RD and RD∗ by maximum likelihood fits: Comparison of the projections of the measured mmiss ∗ and E` distibutions (data points) and the fitted distributions of signal and background contributions for the BABAR fit [28] to the D` samples (a-c) and D∗` samples (d-f), as well the LHCb fit [36] to the D∗+` sample (g-i). The D` samples in (a-c) show sizable 0 ∗+ − 0 ∗+ − ∗ contributions from B → D ` ν` and B → D τ ντ decays, where the low energy or originating from a D → Dπ or D∗ → Dγ transition was undetected. The BABAR data exclude q2 < 4 GeV2, where the contributions from signal decays is very small. ∗ 2 2 The E` distributions in (c) and (f) are signal enhanced by the restriction mmiss > 1GeV . The LHCb results are presented for two 2 0 ∗+ − different q intervals, the lowest, which is free of B → D τ ντ decays (g), and the highest where this contribution is large (h,i). the signal events with three neutrinos extend to about 10 GeV2. the signal region (Figure5 h) because of the sizable uncertainty − ∗ For B → D` ν` decays, there is a sizable contribution from in the estimation of the Bsig momentum. The E` distributions ∗ − B → D ` ν` decays, for which the pion or photon from the (Figure5 c,f,i) provide additional discrimination, since a lepton D∗ → Dπ or D∗ → Dγ decay was not reconstructed. For LHCb, from a normalization decay has a higher average momentum than − − the peak at zero is somewhat broader and has a long tail into a lepton originating from secondary τ → ` ντ ν` decay in a A Challenge to Lepton Universality in B Meson Decays — 6/10

(a) BABAR (HT) Belle (HT) ` 0.45 b LHCb Belle (ST) B LQ HFAG average SM expectation u¯ 0.4 ⌫¯` ) * 0.35 (b) ` R(D ⌫¯` b 0 LQ 0.3 B, B¯ c ¯ 0,( ) +,( ) u,¯ d D ⇤ ,D ⇤ u,¯ d¯ 0.25 Figure 7. Diagrams for non-SM decay processes: (a) 0.25 0.3 0.35 0.4 0.45 0.5 0.55 − − B → ` ν` with a purely leptonic final state and (b) (∗) − R(D) B → D ` ν`, involving a charm meson and lepton pair and Figure 6. RD and RD∗ measurements: Results from mediated by a spin-0 lepto-quark (LQ). BABAR [28], Belle [34, 35], and LHCb [36], their values and 1-σ contours. The average calculated by the Heavy Flavor In the SM, these B decays are mediated by a virtual charged Averaging Group [37] is compared to SM − predictions [19, 20, 21]. ST and HT refer to the measurements vector boson, a particle of spin 1, usually referred to as the W with semileptonic and hadronic tags, respectively. (as indicated in the diagram in Figure 1) which couples equally to all leptons. If a hitherto unknown existed that interacted differently with leptons of higher mass like the τ−, this signal B decay. could change the B decay rates and their kinematics. Among the background contributions, semileptonic B decays Among the simplest explanations for the observed rate in- − to D∗∗ mesons (charm mesons of higher mass than the D∗ mesons) creases for decays involving τ would be the existence of a new 0− − are of concern, primarily because their branching fractions are vector boson, W , similar to the SM W boson, but with a not well known. These D∗∗ states decay to a D or D∗ meson greater mass, and with couplings of varying strengths to different plus additional particles that, if not reconstructed, contribute to leptons and quarks. This could lead to changes in RD and RD∗ , ∗∗ − but not in the kinematics of the decays, which are observed to the missing momentum of the decay. As a result, B → D ` ν` 2 be consistent with the SM. However, this choice is constrained decays have a broader mmiss distribution than normalization de- ∗ by searches for W 0− → tb¯ decays [42, 43] at the LHC collider cays. They can be distinguished from signal decays by their E` distributions which extend to higher values. At LHCb, an impor- at CERN, as well as by precision measurements of µ [44] and (∗) tant background arises from B → D HcX decays, where Hc is τ [45] decays. a charm hadron decaying either leptonically or semileptonically, Another potentially interesting candidate would be a new and X refers to additional low mass hadrons, if present. These type of , a particle of spin 0, similar to the recently decays produce m2 and E∗ spectra that are similar to those of discovered neutral Higgs [46, 47], but electrically charged. This miss ` − signal events (Figure5 h,i). charged Higgs (H ) was proposed in minimal extensions of the SM [48], which are part of broader theoretical frameworks such Figure4 shows the measured values for RD and RD∗ by − BABAR [28], Belle [34, 35], and LHCb [36]. These results as [49]. The H would mediate weak decays, similar to the W − (as indicated in Figure 1), but couple differently include a recent measurement of RD∗ by Belle that employs a 2 semileptonic tag, but do not include earlier results from BABAR [38, to leptons of different mass. The q and angular distributions 39] and Belle [40, 41] based on partial data sets. The averages of would be impacted by this kind of mediator because of its different the measurements [37] are spin. Another feasible solution might be [50], hypo- RD = 0.397 ± 0.040stat ± 0.028syst, (7) thetical particles with both electric and color (strong) charges that

RD∗ = 0.316 ± 0.016stat ± 0.010syst. (8) allow transitions from quarks to leptons and vice versa, and offer a unified description of three generations of quarks and leptons. Both values exceed the SM expectations. Taking into account Among the ten different types of leptoquarks, six could contribute the correlations (Figure6), the combined difference between the to B → D(∗)τν decays [51]. A diagram of a spin-0 state mediat- measured and expected values has a significance of about four ing quark-lepton transitions is shown in Figure7 for the B decay standard deviations. modes under study. BABAR and Belle have studied the implications of these hy- Interpretations of results pothetical particles in the context of specific models [28, 34]. The The results presented here have attracted the attention of the measured values of RD and RD∗ do not support the simplest of the physics community, and have resulted in several potential expla- two-Higgs doublet models (type II), however, more general Higgs nations of this apparent violation of lepton universality for decays models with appropriate parameter choices can accommodate involving the τ lepton. these values [52, 53, 54]. Some of the models could A Challenge to Lepton Universality in B Meson Decays — 7/10

also explain the measured values of RD and RD∗ [55, 56, 57], compatibility with the SM predictions. Detailed studies of the evading constraints from direct searches of leptoquarks in ep col- overall physics goals and precision measurements that can be lisions [58] at HERA [59, 60] and pp collisions at LHC [61, 62]. achieved by Belle II and LHCb are ongoing. (∗) The three-body kinematics of B → D τντ decays should In recent years, several experiments have examined decay permit further discrimination of new physics scenarios based rates and angular distributions for B+ decays involving a K(∗)+ on the decay distributions of final state particles. The q2 spec- meson and a lepton pair, B+ → K(∗)+µ+µ− and B+ → K(∗)+e+e−. trum [28, 34] and the momentum distributions of the D(∗) and In the framework of the SM these decays are very rare, since they electron or muon [35] have been examined. Within the uncer- involve b → s quark transitions. LHCb [64] recently published a tainties of existing measurements, the observed shapes of these measurement of the ratio, distributions are consistent with SM predictions. + + + − B(B → K µ µ ) +0.090 RK = = 0.745−0 074 ± 0.036, (9) Conclusions and outlook B(B+ → K+e+e−) . While the observed enhancements of the leptonic and semilep- tonic B meson decay rates involving a τ lepton relative to the a value that is 2.6 standard deviations below the SM expectation expectations of the SM of electroweak interactions are intriguing, of about 1.0. Earlier measurements by Belle [65], CDF [66], their significance is not sufficient to unambiguously establish a and BABAR [67] had significantly larger uncertainties and were violation of lepton universality at this time. However, the fact fully consistent with lepton universality. Some theoretical models that these unexpected enhancements have been observed by three include new types of interactions that can explain this result. For experiments operating in very different environments deserves instance, leptoquarks which can mediate this decay and result further attention. in higher rates for electrons than muons [68, 69]. BABAR [67], LHCb [70] and Belle [71] have analyzed angular distributions for At present, the measurements are limited by the size of the the four decay modes and observed general agreement with SM available data samples and uncertainties in the reconstruction predictions, except for local deviations, the most significant by efficiencies and background estimates. It is not inconceivable LHCb at the level of 3.4 standard deviations. Also here, more data that the experiments have underestimated these uncertainties, or are needed to enhance the significance of these measurements missed a more conventional explanation. Furthermore, while and find possible links to B decays involving leptons. it is unlikely, it cannot be totally excluded that the theoretical τ SM predictions are not as firm as presently assumed. Currently, If the currently observed excess in the ratios RD and RD∗ the experimenters are continuing their analysis efforts, refining is confirmed, experimenters will use their large data samples their methods, enhancing the signal samples by adding additional to measure properties of signal events and learn about the na- decay modes, improving the efficiency and selectivity of the ture of the new particles and interactions that contribute to these tagging algorithms, as well as the Monte Carlo simulations, and decays [72, 73]. scrutinizing all other aspects of the signal extraction. In conclusion, we can expect much larger event samples from In the near future, LHCb will make several important contri- the upgraded LHCb and Belle experiments in the not too distant − future. These data will be critical to the effort to understand butions, among them their first measurement of the B → Dτ ντ ∗ − whether the tantalizing results obtained to date are an early in- decay, which will also improve results for B → D τ ντ . Fur- − − + − dication of beyond-the-SM physics processes or the result of thermore, the τ → π π π ντ decay mode will be included. In addition, searches for lepton universality violation in semilep- larger-than-expected statistical or systematic deviations. A confir- tonic decays of other B mesons and baryons are being planned. mation of new physics contributions in these decays would shake Beyond that, LHCb will continue to record data at the highest pp the foundations of our understanding of matter and trigger an collision energy available. By the end of 2017, the accumulated intense program of experimental and theoretical research. data sample is expected to increase by a factor of three. In the longer term future, LHCb is planning to further enhance the data Acknowledgements rate capability and record much larger event samples. We recognize the contributions and dedication of our colleagues At KEK in Japan, the e+e− collider is undergoing a major in the large international collaborations supporting the operation upgrade and is expected to enlarge the data sample by almost of the BaBar (M.F.S., R.K., V.L.), Belle (T.K., Y.S.) and LHCb two orders of magnitude over a period of about ten years. In (G.C., B.H.) detectors, the data processing and the data analyses parallel, the capabilities of the Belle detector are also being up- on which the results presented in this Review are based. None of graded. The operation of this new and more powerful detector is this would have been achieved without the efforts of the teams at expected to start in 2018. The much larger event samples and the SLAC, KEK and CERN who achieved excellent beam conditions constrained BB kinematics will allow more precise measurements and delivered high luminosities of the e+e− and pp storage rings of kinematic distributions and detailed studies, for instance, of over many years. We acknowledge support from the Organisation ∗ the τ polarization in B → D τντ decays. The feasibility of such for Scientific Research (NWO) of the Netherlands, the US Na- − − a measurement was recently presented [63]. For B → τ ντ de- tional Science Foundation and Department of Energy, the Natural cays, which currently have statistical and systematic uncertainties Sciences and Engineering Research Council (NSERC) of Canada, of 30% or more for individual measurements, the substantially the Excellence Cluster of the DFG of Germany: Origin and Struc- larger data samples are expected to lead to major reductions in ture of the , and the Japan Society for the Promotion of these uncertainties allowing more accurate assessments of the Science (JSPS). A Challenge to Lepton Universality in B Meson Decays — 8/10

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