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 RðD Þ 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 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 → ð Þτν¯ Þ ð ð ÞÞ¼ BR B D τ l0 ¼ μ ð Þ R D ð Þ 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. ð Þ 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 ð Þ 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 RðDð ÞÞ 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) ‡ [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 Þ 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 0.037 0.016 Belle-2019 [22] 0.299 0.003 [15,16] 0.340 0.027 0.013 HFLAV [15] RðD Þ 0.283 0.018 0.014 Belle-2019 [22] 0.258 0.005 [15,16] 0.295 0.011 0.008 HFLAV [15] RðJ=ψÞ 0.71 0.17 0.18 [23] 0.283 0.048 [24] ð Þ −0 38 0 51þ0.21 −0 497 0 013 Pτ D . . −0.16 [10,11] . . [25] FLðD Þ 0.60 0.08 0.035 [26] 0.46 0.04 [27] RðXcÞ 0.223 0.030 [28] 0.216 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 RðD Þ plot The potential NP scenarios that could explain the RðDð ÞÞ 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 → D τν¯τ have been observed in the Belle experiment— namely, the τ lepton polarization PτðD Þ [10,11] and the 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 Þ polarizations of the τ lepton and D 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 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 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 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. In order to provide an explanation to the charged-current B anomalies, − − in Sec. III, we study different parametric models that BRðB → τ ν¯τÞ ¼ð2.16 0.16Þ%: ð4Þ c SM depend on the choices of the chiral charges and carry out a χ2 analysis to get the best candidates to adjust the It is worth mentioning that by taking the value for −3 experimental data. Based on this analysis, we explore the jVcbj¼ð39.18 0.94 0.36Þ × 10 reported by HFLAV − − two parametric model to determine the regions in parameter [15], a value of BRðB → τ ν¯τÞ ¼ð2.02 0.11Þ% is c SM space favored by two different datasets, RðDÞ and RðD Þ, obtained, which is consistent with Eq. (4). For later use in and all of the b → cτν¯τ observables, and we make a our phenomenological analysis, we will take Eq. (4) and − − comparison with some benchmark models studied in the the upper limit BRðBc → τ ν¯τÞ ≲ 10%. Moreover, we will − literature. Our main conclusions are given in Sec. IV. consider the inclusive semileptonic decay B → Xcτ ν¯τ that → τ−ν¯ is generated via the same transition, b c τ. Including W0 Oð1 2Þ II. A GENERAL BOSON SCENARIO nonperturbative corrections of the order =mb and using the 1S mass scheme, in Ref. [28], a very recent The most general Lorentz invariant Lagrangian describ- 0 estimation has been calculated, RðX Þ ¼ 0.228 0.030, ing the couplings of a general W boson to quarks and c SM 2 that is in agreement (0.2σ) with the experimental value leptons may be written as ð Þ ¼ 0 223 0 030 R Xc exp . . [28] (these values are also 0 0 Wμ collected in Table I). LW ¼ pffiffiffi ½¯ ðϵL þ ϵR Þγμ ui u d PL u d PR dj In light of the new HFLAV world average values RðDð ÞÞ eff 2 i j i j ¯ L R μ [15,16] (due to the very recent Belle measurements [22]) þ l ðϵl ν P þ ϵl ν P Þγ ν þH:c:; ð5Þ i i j L i j R j and the polarization observables PτðD Þ, FLðD Þ measured by Belle [10,11,26], in this work, we look into the where PR=L ¼ð1 γ5Þ=2 are the right-handed (RH) interpretation of these charged-current B anomalies driven 0 and left-handed (LH) chirality projectors, respectively; by a general W gauge boson scenario. Without invoking L R L R and the coefficients ϵ , ϵ , ϵl ν , and ϵl ν are arbitrary any particular NP model, we provide a model-independent uidj uidj i j i j study based on the most general effective Lagrangian given dimensionless parameters that codify the NP flavor effects, ∈ ð Þ ∈ ð Þ l l ∈ ð μ τÞ ϵL;R ϵL;R with ui u; c; t , dj d; s; b , and i, j e; ; .For in terms of the flavor-dependent couplings cb and τντ of μ simplicity, we consider leptonic flavor-diagonal inter- the currents (c¯γμP b) and (τγ¯ P ντ), respectively (see L;R L;R actions (i ¼ j). In the SM, only the LH couplings ϵL ¼ Sec. II for details), which yields a tree-level effective uidj → τν¯ g V and ϵL ¼ g are present, with g being the contribution to the b c τ transition. We implement a L uidj liνi L L χ2 ð2Þ analysis by considering all of the scenarios with different SU L gauge coupling constant, and Vuidj the correspond- chiral charges that explain the RðDð ÞÞ discrepancies. We ing CKM quark matrix element. also analyze the effect of taking into account all of the In the SM framework, the b → cτν¯τ quark level proc- charged transition b → cτν¯τ observables—namely, RðJ=ψÞ, esses are mediated by a virtual W boson exchange, which is − − PτðD Þ, FLðD Þ, RðXcÞ and BRðBc → τ ν¯τÞ. We present a described by the effective Lagrangian phenomenological analysis of parameter space allowed by 4 the experimental data, and for comparison, we include some −L ð → τν¯ Þ ¼ pGffiffiffiF ð¯γ Þðτγ¯ μ ν Þ ð Þ eff b c τ Vcb c μPLb PL τ ; 6 of the W0 boson NP realizations that have already been SM 2 studied in the literature [95,100,101,104–106,108–110]. Most of these models were implemented by considering where GF is the Fermi coupling constant and Vcb is the the previous HFLAV averages and, in addition, not all of associated CKM matrix element. According to Eq. (5),a 0 them considered the polarization observables PτðD Þ and general W boson exchange leads to additional tree-level effective interactions to the b → cτν¯τ transition; thus, the FLðD Þ; therefore, we explore which of these benchmark models are still favored (or disfavored) by the new total low-energy effective Lagrangian has the following form, b → cτν¯τ data. It is important to remark that, since we are not imple- menting any NP realizations in our analysis, we will get out 2See the review “W0-boson searches” in the PDG [124].
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− L ð → τν¯ Þ 0 eff b c τ SMþW longitudinal polarizations can be parametrized in terms of LL RL LR RR 4 the effective Wilson coefficients CV , CV , CV , and CV as GF LL μ ¼ pffiffiffi V ½ð1 þ C Þðc¯γμP bÞðτγ¯ P ντÞ 2 cb V L L follows [45,109,112] þ RLð¯γ Þðτγ¯ μ ν Þþ LRð¯γ Þðτγ¯ μ ν Þ ð Þ¼ ð Þ ðj1þ LL þ RLj2 þj LR þ RRj2Þ ð Þ CV c μPRb PL τ CV c μPLb PR τ R D R D SM CV CV CV CV ; 12 RR μ þ C ðc¯γμP bÞðτγ¯ P ντÞ ; ð7Þ V R R ð Þ¼ ð Þ ðj1 þ LLj2 þj RLj2 þj LRj2 þj RRj2 R D R D SM CV CV CV CV where CLL, CRL, CLR, and CRR are the Wilson coefficients − 1 81 ½ð1 þ LLÞ RL þð RRÞ LR Þ ð Þ V V V V . Re CV CV CV CV ; 13 associated with the NP operators, particularly the LH and RH vector operator contributions, respectively. These ð ψÞ¼ ð ψÞ ðj1þ LLj2 þj RLj2 þj LRj2 þj RRj2 R J= R J= SM CV CV CV CV Wilson coefficients depend on the choices of the chiral −1 92 ½ð1þ LLÞ RL þð RRÞ LR Þ ð Þ charges and are defined as . Re CV CV CV CV ; 14
pffiffiffi −1 LL RL 2 L L ð Þ¼ ð Þ ðj1 þ − j 2 ϵ ϵτν FL D FL D SMrD CV CV CLL ≡ cb τ ; ð8Þ V 4 2 þj RR − LRj2Þ ð Þ GFVcb MW0 CV CV ; 15 pffiffiffi R L −1 LL 2 RL 2 RR 2 2 ϵ ϵτν PτðD Þ¼PτðD Þ r ðj1 þ C j þjC j − jC j CRL ≡ cb τ ; ð9Þ SM D V V V V 2 2 4G V M 0 − j LRj − 1 77 ½ð1 þ LLÞ RL F cb W CV . Re CV CV pffiffiffi − ð RRÞ LR Þ ð Þ 2 ϵL ϵR CV CV ; 16 LR ≡ cb τντ ð Þ CV 2 ; 10 4 0 GFVcb M ¼ ð Þ ð Þ W respectively, with rD R D =R D SM. The numerical pffiffiffi formula for RðJ=ψÞ have been obtained by using the R R 2 ϵ ϵτν CRR ≡ cb τ ; ð11Þ analytic expressions and form factors given in Ref. [24]. V 4 2 − → τ−ν¯ GFVcb MW0 Similarly, the leptonic decay Bc τ will also be modified [45,112] 0 L;R L;R 0 ϵ ϵ with MW being the W boson mass, and cb and τντ the ð − → τ−ν¯ Þ¼ ð − → τ−ν¯ Þ ðj1 þ LL − RLj2 effective flavor-dependent couplings given in Eq. (5).To BR Bc τ BR Bc τ SM CV CV → τν¯ accommodate the b c τ anomalies, we will adopt the þjCRR − CLRj2Þ; ð17Þ phenomenological assumption in which the W0 boson V V couples only to the bottom-charm quarks and the third as well as the ratio RðXcÞ of inclusive semileptonic B ϵL;R ≠ 0 3 generation of leptons, i.e., the effective couplings cb decays [28], ϵL;R ≠ 0 and τντ are other from zero, while the other ones are ð Þ¼ ð Þ ð1 þ 1 147½j LLj2 þj RRj2 taken to be zero. Therefore, NP effects are negligible for R Xc R Xc SM . CV CV L;R L;R light lepton modes (e or μ), ϵ ν ¼ ϵμν ¼ 0. For simplicity, 2 2 e e μ þ 2ReðCLLÞþjCLRj þjCRLj we take these effective couplings to be real. These are the V V V − 0 714 ½ð1 þ LLÞ RL þð RRÞ LR Þ ð Þ minimal assumptions in order to provide an explanation to . Re CV CV CV CV : 18 the discrepancies and not to get in conflict or tension with another low-energy LU test; for instance, there is no In the next section, we will pay attention to the Wilson LL RL LR RR problem with LU constraints from the bottom-charm loop coefficients CV , CV , CV , and CV , given in terms of the 0 τ ϵL;R ϵL;R 0 (mediated by a W boson) contribution to the lepton decay effective couplings cb and τντ and the W boson mass, τ → lντν¯l [126]. which can provide an explanation for the b → cτν¯τ As a final remark, let us notice that such a flavor texture anomalies. assumption for the gauge interactions can be obtained by ð2Þ ð2Þ an approximated U q × U l flavor symmetry [95,104] III. PHENOMENOLOGICAL ANALYSIS or in SM gauge extensions with additional exotic fer- mions [102]. Table I shows the most recent measurements for several flavor observables. In what follows, we will denote these O A. Contribution to the charged-current values as exp, and the corresponding theoretical expres- O – b → cτν¯τ observables sions th are shown in Eqs. (12) (18). When there are no 2 correlations or they are negligible, the χ functionP is given According to the above effective Lagrangian (7), a general 2 2 0 χ ¼ W charged boson exchange will modify the observables by the sum of the squared pulls, i.e., i pulli , where associated with the semileptonic transition b → cτν¯τ. The ratios RðMÞ (M ¼ D; D ;J=ψ) and the D and τ 3We thank Saeed Kamali for the useful conversations.
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L;R L;R TABLE II. SM pulls of the all b → cτν¯τ observables. ðϵ ϵ Þ chiral charges cb ; τντ , there are four different 2P models, LL, LR, RL, and RR. As we will see in the next RðDÞ RðD Þ RðJ=ψÞ PτðD Þ F ðD Þ RðX Þ L c section, two of them (LL and RR) have already been 1.36 2.55 1.69 0.21 1.46 0.23 studied in the literature; however, the LR and RL models, as far as we know, have not been reported on yet. The same qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is true for the 3P and 4P models. ¼ðOi − Oi Þ σi2 þ σi2 σi pulli exp th = exp th. Here exp;th corre- In order to check whether it is possible to adjust the sponds to the experimental (theoretical) error. In order to deviations of the standard model predictions in these 2 account for the RðDÞ and RðD Þ correlation, the contri- models, we carried out a χ analysis with the seven bution of these observables to the χ2 function should be experimental observables mentioned above. Owing to written as the absence of the experimental measurement on − − Bc → τ ν¯τ, we used the SM estimation given in Eq. (4), ð Þþ ð Þ2 − 2ρ ð Þ ð Þ χ2 ¼ pull D pull Dpffiffiffiffiffiffiffiffiffiffiffiffiffi pull D pull D which is consistent with the strongest upper limit RðDÞ−RðD Þ ; − − 1 − ρ2 BRðBc → τ ν¯τÞ < 10% [123]. In Table II, we display the SM pulls of all of the b → cτν¯τ observables. The fit ð Þ 19 results are shown in Table III. In this fit, the number of degrees of freedom is given by dof ¼ 7 − p, where p is the where ρ ¼ −0.203 is the RðDÞ−RðD Þ correlation reported χ2 = by HFLAV [15,16]. This effect is important since the number of parameters. The goodness of fit min dof is of experimental methodology and the theoretical expressions order 1 for 2P models (except for the RL model); for the 3P χ2 ∼ 1 4 are quite similar for these observables. This correlation and the 4P models, min=dof . and 1.8, respectively. does not significantly modify the best-fit point for all So, the 2P models represent the best candidates to adjust the models presented here. We neglected the remaining corre- experimental anomalies. It is important to note that the ð ψÞ lations. From Eq. (5), it is possible to obtain several models observables that generate more tension are R J= and ð Þ by turning on some of the couplings, while the remaining FL D , even though these experiments have large uncer- ones are set equal to zero. In order to adjust the exper- tainties. By comparing Tables II and III, we can see that, with respect to the SM, the models with an additional W0 imental anomalies, any model must contain a charm- bottom interaction term in the quark sector and the decrease the pulls for RðDÞ and RðD Þ without increasing corresponding τ-ντ interaction term in the lepton sector; the pulls of the other observables. In order to keep the this means that it is necessary to have at least two nonzero couplings in the perturbative regime, we took the mass of 0 0 ¼ 1 couplings in the Lagrangian (5). These models will be the W boson as MW TeV. There is no tension with the referred to as 2P models, and the corresponding models current LHC constraints for the MW0 (which are above with three and four nonzero couplings will be referred to as 4 TeV) since we are assuming zero couplings to the SM 3P and 4P, respectively. Depending on the choices for the fermions of the first family.
TABLE III. By turning on the parameters of the second column [keeping the remaining parameters of Lagrangian (7) equal to zero], we obtain several effective models at low energies. The models in rows 3–6 have two free parameters (the chiral couplings), and in the following, they will be referred to as 2P models. In the same sense, we will refer to the models in rows 7–9 as 3P models. In the last row, the model with all the parameters turned on is shown. The pulls for each observable are shown in columns 3–8, the minimum value for the χ2 is shown in column 9, and the best-fit point for the chiral charges is shown for each model in the last four columns, for a gauge 2 0 ¼ 1 χ ∼ 1 boson mass MW TeV. All 2P models have an acceptable value for min=dof , except the model with RH coupling to quarks and LH coupling to leptons. The goodness of fit decreases for the 3P and 4P models since, for them, the number of parameters increases χ2 while min stays at nearly the same value.
Pulli Best-fit point ð Þ ð Þ ð ψÞ ð Þ ð Þ ð Þ ð → τν¯Þ χ2 ϵL ϵR ϵL ϵR Parameters on R D R D R J= Pτ D FL D R Xc BR Bc min cb cb τν τν ðϵL ϵL Þ −0 045 −0 93 −0 27 −0 345 −0 276 cb; τν . 0.032 1.53 0.21 1.46 . . 5.49 . . ðϵL ϵR Þ −0 047 −0 013 −0 94 −0 27 cb; τν . 0.027 1.53 . 1.46 . . 5.44 0.584 0.897 2P ðϵR ϵL Þ −0 059 −0 26 −0 322 cb; τν 2.57 0.46 1.55 0.19 1.52 . . 12.28 . 0.271 ðϵR ϵR Þ −0 047 −0 013 −0 121 −0 27 cb; τν . 0.027 1.53 . 1.46 . . 5.44 0.584 0.897 ðϵL ϵR ϵL Þ −0 20 −0 91 −0 27 −0 051 cb; cb; τν 0.31 . 1.52 0.22 1.41 . . 5.34 0.272 . 0.326 ðϵR ϵL ϵR Þ −0 21 −0 91 −0 27 −0 038 3P cb; τν; τν 0.31 . 1.52 0.011 1.41 . . 5.29 0.466 . 1.082 ðϵL ϵL ϵR Þ −0 048 −7 4 10−7 −0 94 −0 27 cb; τν; τν . 0.027 1.53 . × 1.46 . . 5.44 0.666 0.008 0.764 ðϵL ϵR ϵL ϵR Þ −0 21 −4 1 10−6 −0 91 −0 27 −0 105 −0 469 4P cb; cb; τν; τν 0.31 . 1.52 . × 1.41 . . 5.29 1.016 . 0.009 .
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ðϵL ϵL Þ 0 ¼ 0 5 0 ¼ 1 FIG. 2. The 95% C.L. allowed parameter space in the cb; τντ plane for (a) MW . TeV and (b) MW TeV. The purple region is obtained by considering only RðDð ÞÞ from the HFLAV 2019 average, while the green one is obtained by taking into account all of the b → cτν¯τ observables. The black star and red hatched region represent the ACDFR model [105] and the GMR analysis [106], respectively. See the text for details.
As the next step in our analysis, we will explore in a more experimental uncertainties. This effect is in agreement with detailed way the four 2P models LL, LR, RL, and RR, which the analysis presented in Ref. [36]. It is remarkable that the according to our χ2 analysis are the best candidates to RðDð ÞÞ HFLAV 2019 averages allow the solution L L address the charged-current B anomalies. By considering ðϵτν ; ϵ Þ¼ð0; 0Þ; this result is consistent with the SM τ cb two different datasets, RðDÞ and RðD Þ, and all of the b → and does not require NP explanations. cτν¯τ observables, we determine the regions in the parameter In order to improve our analysis, we will include some of space favored by the experimental data. the benchmark models that have already been studied in the literature [95,104–106]: LL CV ≠ (a) In Ref. [105], Abdullah, Calle, Dutta, Flor´ez, and A. scenarios ( LL 0) 0 0 Restrepo considered a simplified W model (referred to In this scenario, we consider a W boson that couples by us as the ACDFR model) which preferentially only to LH quark and LH lepton currents inducing the couples to the bottom and charm quarks and τ leptons, μ V semitauonic operator ðc¯γμP bÞðτγ¯ P ντÞ, i.e., C ≠ 0. 0 0 L L LL through the NP couplings gq and gl, respectively. In Figs. 2(a) and 2(b), we show the 95% confidence They showed that for W0 masses in the range [250, ðϵL ϵL Þ 0 0 level (C.L.) allowed parameter space in the cb; τντ 750] GeV and couplings gq ¼ gl ¼ 0.1, such scenario 0 ¼ plane, associated with the couplings in Eq. (8), for MW could be probed at the LHC with a luminosity of 0 5 0 ¼ 1 −1 . TeV and MW TeV, respectively. In order to see 100 fb . This model is represented in Figs. 2(a) the impact of the polarization measurements [10,11,26], the and 2(b) by the black stars. We notice that for MW0 ¼ purple region is obtained by considering the HFLAV 2019 0.5 TeV the ACDFR model is enabled both for HFLAV ð Þ ð Þ averages on R D and R D [16], while the green region is 2019 and all observables, while for MW0 ¼ 1 TeV, it is obtained by taking into account all of the b → cτν¯τ still allowed by HFLAV 2019. ð Þ observables—namely, RðD Þ, RðJ=ψÞ, FLðD Þ, and (b) In Ref. [106], Greljo, Martin, and Ruiz performed PτðD Þ (see Table I)—and considering the upper limit a study (referred to by us as the GMR analysis) of − − BRðBc → τ ν¯τÞ < 10%. It is observed that the allowed the connection between NP scenarios addressing the region for RðDð ÞÞ is significantly reduced to two sym- RðDð ÞÞ anomalies and the mono-tau signature at the metrical regions when all of the b → cτν¯τ observables LHC, pp → τhX þ MET. By using current ATLAS are considered. This is due mainly to the effect of the [127] and CMS [128] data, they constrained different — 0 polarization FLðD Þ, whereas observables such as RðJ=ψÞ scenarios particularly those regarding a W boson and PτðD Þ have little influence due to their large scenario—and they found that [106]
093003-6 CHARGED CURRENT B → Cτν¯τ … PHYS. REV. D 100, 093003 (2019) 0 2 → τν¯ L L MW b c τ observables, respectively. It is found that the ϵ ϵτν ¼ð0.14 0.03Þ ð20Þ cb τ TeV allowed region for RðDð ÞÞ is significantly reduced to fourfold symmetrical regions when all of the b → cτν¯τ for W0 masses in the range [0.5, 3.5] TeV, which is in observables are considered. As in the LL scenarios pre- L L 2 viously discussed, this is mainly due to the effect of the agreement with the value ϵ ϵτν ¼ 0.107ðM 0 =TeVÞ cb τ W polarization F ðD Þ. For further discussion, we consider obtained in [48]. This result is represented by the red L hatched region in Figs. 2(a) and 2(b). We can appreciate some benchmark models: (a) The authors of Refs. [109,110] presented a model that the allowed parameter region by RðDð ÞÞ HFLAV where the SM is extended by the gauge group 2019 and all b → cτν¯τ observables of our analysis are 0 0 SUð3Þ × SUð2Þ × SUð2Þ × Uð1Þ , with g and g consistent and overlap with this region. C L V V being the corresponding new gauge couplings. After (c) In Refs. [95,104] the authors introduced a color- 0 the spontaneous symmetry breaking SUð2Þ ×Uð1Þ → neutral SUð2Þ triplet of massive vector bosons that V L Uð1Þ , new heavy vector bosons are generated. In couple predominantly with third generation fermions Y addition, the SM fermion content is accompanied by (both quarks gq and gl leptons), with an underlying ð2Þ new heavy vectorlike fermions (both quarks and dynamics generated by an approximated U q × leptons) that mix with the RH fermions of the SM, ð2Þ U l flavor symmetry; however, in light of new which is required in order to provide an explanation of experimental measurements, this model is disfavored the RðDð ÞÞ anomalies. Since the results in [109,110] unless a fine-tuning of the couplings is carried out. are very similar, for simplicity, we will consider the analysis of Ref. [110] for comparison (referred to as the V B. RR scenarios (CRR ≠ 0) 3221 gauge model). Translating the notation in [110] R 23 R 3 0 ϵ ¼ g c ϵτν ¼ g c In this scenario, the W is the gauge boson associated into ours, we have cb V q and τ V N, with 23 3 with the interaction between the RH quark and RH lepton cq ;cN coefficients that encode the flavor dependence. 0 ¼ 2 1σ currents involving a RH sterile neutrino. This RH current Given that MW gVvV= [110], a viable solution interpretation to the RðDð ÞÞ anomalies have been discussed to the anomalies is obtained for a vacuum expectation ≃ 2000 ≃ Oð1–3Þ recently in the literature within different NP realizations value (VEV) of vV GeV, gV , and 23 ¼ 3 ≃ 1 0 1000 ≲ [63,107–114]. We plot in Figs. 3(a) and 3(b) the 95% C.L. cq cN , implying W masses in the range R R 0 ð Þ ≲ 3000 allowed parameter space in the ðϵ ; ϵτν Þ plane for masses MW GeV to avoid the perturbative limit cb τ ≃ M 0 ¼ 1 and 1.2 TeV, respectively. The purple and green [110]. By taking representative values of vV W 2000 ≃ 1–1 2 regions are obtained by taking into account only RðDÞ and GeV and gV . , the 3221 gauge model is RðD Þ from the HFLAV 2019 averages [16] and all the depicted by the blue squared in Figs. 3(a) and 3(b)
ðϵR ϵR Þ 0 ¼ 1 0 ¼ 1 2 FIG. 3. The 95% C.L. allowed parameter space in the cb; τντ plane for (a) MW TeV and (b) MW . TeV. The purple region is obtained by considering only RðDð ÞÞ from HFLAV 2019 averages, while the green one is obtained by taking into account all of the b → cτν¯τ observables. The black diamond, blue squared, red hatched region, and orange circle represent the NU-LRSM model [100,101], 3321 gauge model [109,110], GMR analysis [106], and USM-LRSM [108], respectively. See the text for details.
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ðϵL ϵR Þ ðϵR ϵL Þ 0 ¼ 1 FIG. 4. The 95% C.L. allowed parameter space in the cb; τντ and cb; τντ planes for a mass value of MW TeV.
for MW0 ¼ 1 and 1.2 TeV, respectively. According (d) A class of LRSM (parity symmetric and asymmetric) to our analysis, this model is disfavored by the new that implemented vectorlike fermions to generate quark data. We have also checked that, for W0 masses higher and lepton masses via a universal seesaw mechanism than 1.2 TeV, this is still disfavored. However, as (USM) have been studied in Ref. [108] to explain discussed in [111], there is a freedom in the flavor the anomalies. In the USM-LRSM, the mass of the 23 3 M 0 ¼ M ¼ structure of the cq ;cN couplings, and it is possible to RH chargedpffiffiffi gauge boson is given by W WR 23 ≠ 3 κ 2 κ ∼ 2 get, in general, different values cq cN than the ones gR R= , with R TeV being the VEV of the χ assumed in [110]. neutral member of the doublet R (for details, see (b) In the GMR analysis [106] previously discussed, the Ref. [108]p),ffiffiffi and the effectivep couplingsffiffiffi are simply 0 ϵR ¼ 2 ϵR ¼ 2 authors also found that, for RH W models, the cb gR= and τντ gR= . Taking the lower solution is ≃ 1 2 mass limit MWR . TeV (obtained for the parity asymmetric case [108]), the USM-LRSM is repre- 0 2 R R MW ϵ ϵτν ¼ð0.6 0.1Þ ; ð21Þ sented by the orange circle in Fig. 3(b). This setup is cb τ ð Þ TeV allowed by both RðD Þ and all of the b → cτν¯τ observables. which is represented by the red hatched region in Figs. 3(a) and 3(b), which is consistent with the value 2 RL LR CV ≠ CV ≠ ϵR ϵR ¼ 0 55 ð 0 Þ C. and scenarios ( RL 0 and LR 0) cb τντ . MW =TeV obtained in [48]. Again, the allowed parameter region by RðDð ÞÞ HFLAV Finally, we consider a class of scenarios where the quark 2019 and all b → cτν¯τ observables of our analysis and lepton currents with different quiralities projection 0 are consistent and overlap with this region. couple to the W boson, i.e., semitauonic operators of μ μ (c) In Refs. [100,101], the anomalies have been addressed the types ðc¯γμPRbÞðτγ¯ PLντÞ and ðc¯γμPLbÞðτγ¯ PRντÞ that V ≠ 0 V ≠ 0 within the framework of the nonuniversal left-right implies CRL and CLR , respectively. For a repre- symmetric model (NU-LRSM) with enhanced cou- sentative mass value of MW0 ¼ 1 TeV, we display in Fig. 4 plings to the third generation. In terms of our notation, the 95% C.L. allowed parameter space for the couplings in we have the result that, in the NU-LRSM, the effective the LR (left panel) and RL (right panel) scenarios. The case R R l ϵ ¼ j j ϵ ¼ j j 0 ≥ 1 couplings are cb gR VRcb and τντ gR VR3τ , with of MW TeV requires higher effective coupling values. l gR being the RH gauge coupling, VRcb and VR3τ the RH For the LR case, it can be inferred that the allowed region quark and lepton mixing element, respectively. It is for RðDð ÞÞ is reduced to fourfold symmetrical regions l 0 ≃ 1 ≃ 1 j j ≃ 1 assumed that, taking MW TeV, gR , VR3τ , when all of the b → cτν¯τ observables are considered. While and jVRcbj ≃ jVcbj [100,101], as shown by the black for the RL case, the permitted region is barely reduced diamond in Fig. 3(a), the model accommodates the when all observables are taken into account. In both tension in RðDð ÞÞ. One can observe that this frame- scenarios, it is found that a NP solution (0, 0) is admissible. work is still allowed by the HFLAV 2019 average, but So far, particular NP models realization of such LR and not with all observables data. RL scenarios have not been studied in the literature.
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However, interestingly enough, recently Bhattacharya et al. 2P models represent the best candidate to adjust the [129] have explored the possibility of how the measure- experimental charged current B anomalies. ¯ 0 þ − ment of CP-violating observables in B → D μ ν¯μ can be Next, we studied all of the possible combinations of 2P used to differentiate the NP scenarios. Particularly, they models (LL, RR, LR, and RL scenarios) and took into found that the only way to generate sizable CP-violating account two different datasets: RðDð ÞÞ only and all b → 0 effects is with LH and RH W bosons (with sizable mixing) cτν¯τ observables; we determined the regions in parameter that contribute to b → clν¯l [129]. space favored by these observables for different values of the W0 boson mass preferred in the literature. For the LL IV. CONCLUSIONS and RR scenarios, we obtained that part of the allowed parametric space is consistent with the mono-tau signature Motivated by the new HFLAV world average values on ð Þ pp → τ X þ MET at the LHC. In order to improve the the ratios RðD Þ, due to the recent Belle measurements, we h discussion, we included in our analysis some of the W0 addressed the anomalies RðDð ÞÞ related to the charged- 0 boson NP realizations that have already been studied in the current transition b → cτν¯τ within a general W boson LL and RR scenarios. We found which of these benchmark scenario. In order to provide a robust analysis, we consid- models are favored or disfavored by the new data. ered in addition the available experimental information on Regarding the LR and RL scenarios, as far as we know, all of the charged transition b → cτν¯τ observables—namely, these have not been previously reported in the literature, the ratios RðJ=ψÞ, RðXcÞ and the polarizations PτðD Þ, − − and our results showed that it would be interesting to study F ðD Þ, as well as the upper limit BRðB → τ ν¯τÞ < 10%. L c a particular NP model since this could generate CP- We carried out a model-independent study, based on the ¯ 0 → þμ−ν¯ most general effective Lagrangian given in terms of the violating effects in B D μ, as discussed in [129]. ϵL;R ϵL;R flavor-dependent couplings cb and τντ of the currents μ c¯γμPL;Rb and τγ¯ PL;Rντ, that yields a tree-level effective ACKNOWLEDGMENTS 0 contribution generated by a general W boson. With the We are grateful to William A. Ponce and Carlos E. Vera χ2 above-mentioned observables, we performed a analysis for their contributions at the early stage of this work. N. Q. ϵL;R by considering the cases of two, three, and four nonzero cb acknowledges support from the Dirección General de ϵL;R and τντ couplings (with different chiral charges), referred to Investigaciones, Universidad Santiago de Cali, under as the 2P, 3P, and 4P models, respectively. It is found that the Project No. 935-621118-3.
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