PHYSICAL REVIEW D 100, 093003 (2019) 0 Charged current b → cτν¯τ anomalies in a general W boson scenario † ‡ John D. Gómez ,1,2,* N´estor Quintero ,3, and Eduardo Rojas4, 1Instituto de Física, Universidad de Antioquia, A.A. 1226 Medellín, Colombia 2Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano, Calle 73 No. 76 A—354 Vía el Volador, Medellín, Colombia 3Facultad de Ciencias Básicas, Universidad Santiago de Cali, Campus Pampalinda, Calle 5 No. 62-00, Código Postal 76001 Santiago de Cali, Colombia 4Departamento de Física, Universidad de Nariño, A.A. 1175 San Juan de Pasto, Colombia (Received 16 August 2019; published 20 November 2019) Very recent experimental information obtained from the Belle experiment, along with that accumulated by the BABAR and LHCb experiments, has shown the existence of anomalies in the ratios RðDÞ and RðDÃÞ associated with the charged-current transition b → cτν¯τ. Although the Belle measurements are in agreement with standard model (SM) predictions, the new experimental world averages still exhibit a à à à tension. In addition, the D longitudinal polarization FLðD Þ related with the channel B → D τν¯τ observed by the Belle Collaboration and the ratio RðJ=ψÞ measured by the LHCb Collaboration also show discrepancies with their corresponding SM estimations. We present a model-independent study based on the most general effective Lagrangian that yields a tree-level effective contribution to the transition 0 b → cτν¯τ induced by a general W boson. Instead of considering any specific new physics (NP) realization, we perform an analysis by considering all of the different chiral charges to the charm-bottom and τ − ντ interaction terms with a charged W0 boson that explain the anomalies. We present a phenomenological study of parameter space allowed by the new experimental b → cτν¯τ data and with the mono-tau signature 0 pp → τhX þ MET at the LHC. For comparison, we include some of the W boson NP realizations that have already been studied in the literature. DOI: 10.1103/PhysRevD.100.093003 I. INTRODUCTION ð → ðÞτν¯ Þ ð ðÞÞ¼ BR B D τ l0 ¼ μ ð Þ R D ðÞ 0 ; e or ; 1 The B meson system has constituted a good scenario for BRðB → D l ν¯l0 Þ studying, on both theoretical and experimental levels, the – standard model (SM) as well as for exploring new physics compared with the SM predictions [5 7]. These discrep- – (NP) effects at low-energy scales. Particularly, semileptonic ancies were later confirmed by Belle [8 11] and LHCb – and leptonic B meson decays offer an excellent place to test [12 14] experiments by means of different techniques. ðÞ lepton universality (LU), so far one of the cornerstones of Theoretical progress on the SM calculations of RðD Þ has the SM. Any mismatch between the theoretical and been made recently [17–21], with average values [15,16] experimental predictions may be an indication of LU shown in Table I. Despite all of these advancements, the ðÞ violation, and therefore a hint of NP beyond the SM [1,2]. experimental measurements on RðD Þ still exhibit a The BABAR Collaboration in 2012 was the first experi- deviation from the SM expectations. Nevertheless, things ment that reported disagreement on the measurements seem to have changed, and the tension has been reduced of the ratio of semileptonic B decays (b → c transition with the new results on RðDðÞÞ that the Belle Collaboration processes) [3,4] has recently released [22] (as presented in Table I), which are now in agreement with the SM predictions within 0.2σ and 1.1σ, respectively. Incorporating these Belle results, in *[email protected] Table I we display the new 2019 world averages values † [email protected] reported by the Heavy Flavor Averaging Group (HFLAV) ‡ à [email protected] on the measurements of RðDÞ and RðD Þ [15,16], which now exceed the SM predictions by 1.4σ and 2.5σ, respec- Published by the American Physical Society under the terms of tively. To see the incidence of the very recent Belle results, the Creative Commons Attribution 4.0 International license. ð Þ ð ÃÞ Further distribution of this work must maintain attribution to in Figure 1, we plot the R D vs R D plane by showing the author(s) and the published article’s title, journal citation, the HFLAV 2018 average (green region) and the new and DOI. Funded by SCOAP3. HFLAV 2019 average (blue region) [15,16], at both 1σ and 2470-0010=2019=100(9)=093003(13) 093003-1 Published by the American Physical Society GÓMEZ, QUINTERO, and ROJAS PHYS. REV. D 100, 093003 (2019) TABLE I. Experimental status on observables related to the charged transition b → cτν¯τ. Observable Expt. measurement SM prediction RðDÞ 0.307 Æ 0.037 Æ 0.016 Belle-2019 [22] 0.299 Æ 0.003 [15,16] 0.340 Æ 0.027 Æ 0.013 HFLAV [15] RðDÃÞ 0.283 Æ 0.018 Æ 0.014 Belle-2019 [22] 0.258 Æ 0.005 [15,16] 0.295 Æ 0.011 Æ 0.008 HFLAV [15] RðJ=ψÞ 0.71 Æ 0.17 Æ 0.18 [23] 0.283 Æ 0.048 [24] ð ÃÞ −0 38 Æ 0 51þ0.21 −0 497 Æ 0 013 Pτ D . −0.16 [10,11] . [25] à FLðD Þ 0.60 Æ 0.08 Æ 0.035 [26] 0.46 Æ 0.04 [27] RðXcÞ 0.223 Æ 0.030 [28] 0.216 Æ 0.003 [28] 2σ. The black (solid 1σ and dotted 2σ) and red (dashed) observables to potentially distinguish the underlying NP contours show the SM predictions and the recent Belle [25,27,45,46]. measurements, respectively. This RðDÞ vs RðDÃÞ plot The potential NP scenarios that could explain the RðDðÞÞ illustrates how the anomalies have been significantly and RðJ=ψÞ anomalies would also affect the branching ratio − − narrowed due to the new Belle data. associated with the leptonic decay Bc → τ ν¯τ [122,123] Further hints of lepton flavor universality violation in the since all of them are generated by the same quark level − charged current b → cτν¯τ have recently been obtained by transition, b → cτν¯τ. In Ref. [122], a constraint of BRðBc → − LHCb in the measurement of the ratio [23] τ ν¯τÞ ≲ 30% is imposed by considering the lifetime of Bc, − − while a stronger bound of BRðBc → τ ν¯τÞ ≲ 10% has been ð → ψτν¯ Þ obtained in Ref. [123] from the LEP data taken at the Z peak. ð ψÞ¼BR Bc J= τ ð Þ R J= ; 2 In the SM, the branching fraction of this tauonic decay is BRðBc → J=ψμν¯μÞ given by the expression [122,123] which also shows tension with regard to the SM prediction 2 2 2 (around 2σ) [24,29–33]. In further calculations, we will use ð − → τ−ν¯ Þ ¼ τ GF j j2 2 2 1 − mτ BR Bc τ B Vcb f mB mτ 2 ; SM c 8π Bc c m the theoretical prediction of Ref. [24] (see Table I), which is Bc – in agreement with other estimations [29 33]. Additionally, ð3Þ polarization observables associated with the channel B → à D τν¯τ have been observed in the Belle experiment— à namely, the τ lepton polarization PτðD Þ [10,11] and the à à D longitudinal polarization FLðD Þ [26]. We present in Table I these measurements, as well as their corresponding SM values [25,27], which also exhibit a deviation from the experimental data. The incompatibility of these measurements with the SM could be evidence of LU violation in B decays and, there- fore, an indication of NP sensitive to the third generation of leptons. In order to understand these discrepancies, an enormous number of theoretical studies have been proposed. On the one hand, model-independent analyses of the impact of NP effective operators have been extensively studied (for the most recent ones that include the new Belle measure- ments, see Refs. [34–38]).1 On the other hand, particular NP scenarios such as charged scalars [47–63], leptoquarks (both scalar and vector) [64–66,68–98], extra gauge bosons [48,95,99–112], right-handed neutrinos [63,107–114],R- parity-violating supersymmetric couplings [25,115–121] have been studied as well. Complementary tests at the LHC searches of some of these scenarios have been also explored [45,48,53,105,106,110,115]. Furthermore, the FIG. 1. The HFLAV 2018 and HFLAV 2019 averages (green ð Þ ð ÃÞ polarizations of the τ lepton and Dà are also useful and gray regions, respectively) [15,16] in the R D vs R D plane. The black (1σ solid and 2σ dotted) and red (dashed) contours shows the SM predictions and the recent Belle mea- 1For previous works, see, for instance, Refs. [24,39–47]. surements [22], respectively. 093003-2 CHARGED CURRENT B → Cτν¯τ … PHYS. REV. D 100, 093003 (2019) 0 where GF is the Fermi constant, Vcb denotes the Cabbibo- of our discussion the possible connection with a Z boson Kobayashi-Maskawa (CKM) matrix element involved, and that appears in particular UV completions, as done, for τ − – fBc and Bc are the Bc meson decay constant and lifetime, instance, in Refs. [95,101,102,104,106,109 112]. respectively. By using the following input values, This work is organized as follows. In Sec. II,we τ ¼ð0.507 Æ 0.009Þ ps, m ¼ 6.2749 GeV, and jV j¼ briefly present the most general charged-current effective Bc Bc cb 0 ð40.5 Æ 1.5Þ × 10−3 from the Particle Data Group (PDG) Lagrangian for a general W gauge boson; then, we study its [124] and f ¼ð434 Æ 15Þ MeV from lattice QCD [125], tree-level effective contribution to the observables associ- Bc → τν¯ we get a value of ated with the semileptonic transition b c τ.