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R(D) and R(D*) anomalies and their phenomenological implications
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Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184 www.elsevier.com/locate/nppp
R( D) and R(D∗ ) anomalies and their phenomenological implications Xin-Qiang Li Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, Hubei 430079, China
Abstract Recently, BaBar, Belle and LHCb have found hints of lepton flavour universality violation in B → D(∗) τ¯ντ decays, i.e., the measured ratios R(D(∗) ) = B(B → D(∗) τ¯ντ )/B(B → D(∗) ¯ν ) ( = e/μ) show a combined 3.8 σ deviation from the SM predictions. In this talk, we will discuss two possible solutions to the observed R(D) and R(D∗ ) anomalies: one with an EW-scale charged scalar and the other with a TeV-scale scalar leptoquark transforming as (3, 1, − 13 ) under the SM gauge group. Their phenomenological implications for the other decays are also briefly discussed. Keywords: R(D(∗) ) anomalies, Lepton-flavour-universality violation, charged scalar, TeV-scale scalar leptoquark
1. Introduction Lepton flavour universality (LFU) tests are among the most powerful probes of the Standard Model (SM) and New Physics (NP) beyond it. They can be pursued by constructing ratios of process rates that differ only in the charged lepton flavour, where common systematical, parametric and hadronic uncertainties are cancelled out to some extent. Interestingly, the BaBar [1, 2], Belle [3, 4, 5, 6] and LHCb [7, 8] collaborations have recently measured the ratios R(D(∗) ) = B(B → D(∗) τ¯ντ )/B(B → D(∗) ¯ν ) ( = e/μ), for which our averages are [9]1 R(D)avg =0.400 ± 0.049 , R(D∗ )avg =0.310 ± 0.017 ,
(1)
with a correlation of −19%, as displayed in Fig. 1. This implies a 3.8σ deviation from the SM predictions: RSM D =0.301 ± 0.003 [9, 11] , RSM D∗ =0.252 ± 0.003 [12] .
(2)
1 We average the new Belle result [5] with the HFAG average of the remaining measurements [10], which takes correlations between the different measurements into account to a certain extent.
http://dx.doi.org/10.1016/j.nuclphysbps.2017.03.072 2405-6014/© 2017 Elsevier B.V. All rights reserved.
Figure 1: Average of R(D(∗) ) measurements, displayed as red filled ellipses (68% CL and 95% CL). The SM prediction is shown as a black ellipse (95% CL), and the individual measurements as contours (68% CL): Belle (blue), BaBar (green), and LHCb (yellow).
X.-Q. Li / Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184
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Furthermore, the shapes of the differential distributions dΓ(B → D(∗) τ¯ντ )/dq2 have been made available by Belle and BaBar [2, 3], yielding additional information to distinguish NP from the SM as well as different NP models from each other. The observed R(D(∗) ) anomalies have motivated a lot of studies; for a review, see e.g., refs. [13, 14, 15, 16]. In this talk, we will discuss two possible NP solutions to the observed R(D(∗) ) anomalies: one with an EW-scale charged scalar [9, 17] and the other with a TeV-scale scalar leptoquark transforming as (3, 1, − 13 ) under the SM gauge group [18, 19, 20]. Their phenomenological implications for other decays mediated by the same quark-level transitions as in B → D(∗) τ¯ντ are also briefly discussed [9, 20, 21].
In Fig. 2 we show the fit results for B → Dτ¯ντ data in the complex δτcb plane (upper), and the B → D∗ τ¯ντ data in the complex Δτcb plane (lower), together with the constraints from B(Bc → τ¯ντ ) ≤ 40% [9, 20, 22]. For the B → Dτ¯ντ data, we find that the q2 -distribution selects a part of the R(D) ring that is closer to zero; while it favours a non-zero value for δτcb as well, where the preferred central value has a negative real part, opposite to the one from R(D). All constraints are consistent at 95 % CL with the SM, as is their combination.
2. Solution with an EW-scale charged scalar The NP contributions to charged-current semileptonic processes can be studied in a model-independent manner. We discuss firstly the case with an EW-scale colour-neutral charged scalar, which naturally lead to observable effects in b → cτ¯ντ transition, while b → c¯ν remains unaffected, since the charged-scalar couplings to fermions are proportional to the corresponding fermion masses. Specifically, the resulting low-energy effective Lagrangian is given by Leff = −
4G F Vcb cbτ τPL ντ ] , (3) c¯ (gL PL + gcbτ √ R PR ) b [¯ 2
where V represents the CKM matrix and PL,R = (1 ∓ γ5 )/2 are the usual chiral projectors. The Wilson coefficients gcbτ L,R are complex parameters which encode details of the underling theory at high energies. Without further assumptions on the flavour structure in Eq. (3), the only related observables are R(D), R(D∗ ), dΓ(B → D(∗) τ¯ντ )/dq2 , and the τ polarization asymmetry Aτ (D∗ ) measured firstly by Belle [5]. Note that B → Dτ¯ντ and B → D∗ ν¯ τ depend only on the scalar and pseudo-scalar combinations of the couplings gcbτ L,R , δτcb ≡
cbτ 2 2 (gcbτ (gcbτ − gcbτ L + gR )(m B − mD ) R )m B , Δτcb ≡ L , mτ (m ¯b −m ¯ c) mτ (m ¯b +m ¯ c) (4)
respectively, which we consequently choose to display the corresponding constraints. This implies that any value of R(D(∗) ) can at first be trivially explained in this scenario. However, the differential distributions give rise to additional non-trivial constraints on the parameter space when combined with R(D(∗) ).
Figure 2: Model-independent fits in the complex δτcb - (upper) and Δτcb planes (lower). The dark rings stem from R(D(∗) ), the lighter discs from dΓ(B → D(∗) τ¯ντ )/dq2 , the dark-green disc from B(Bc → τ¯ντ ) ≤ 40% [9, 20, 22] and the dashed line from Aλ (D∗ ). The yellow areas represent the global fit in each sector. All coloured areas correspond to 95% CL regions, only the dashed line corresponds to 68% CL.
For the B → D∗ τ¯ντ data, the picture is different: although compatible with zero by itself, the differential distribution tends to exclude the part of the R(D∗ ) ring
X.-Q. Li / Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184
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This makes it possible to analyze the compatibility of b → cτ¯ντ and b → uτ¯ντ data. Details of our predictions for Bu → τ¯ντ , B → πτ¯ντ , Λb → Λc (p)τ¯ντ observables can be found in ref. [9]. 3. Solution with a TeV-scale scalar leptoquark As a second solution to the B → D(∗) τ¯ντ data, we consider the model proposed by Bauer and Neubert, where a TeV-scale scalar leptoquark φ transforming as (3, 1, − 13 ) under the SM gauge group is added to the SM, and its couplings to fermions are described by [19] L L Lφint = u¯ cL λul lL φ∗ − d¯Lc λdν νL φ∗ + u¯ cR λRul lR φ∗ + h.c. , (6)
Figure 3: Constraints from R(D(∗) ), dΓ(B → D(∗) τ¯ντ )/dq2 , R(Xc ) = 0.222 ± 0.007 [9, 23], and the bound B(Bc → τ¯ντ ) ≤ 40% in the δτcb − Δτcb plane, assuming real couplings.
that is closer to zero, resulting in a global fit that excludes the SM even more strongly than R(D∗ ) alone. Specifically, it disfavours the negative real solution for Δτcb , which is again seen in Fig. 3, where now only one of the four solutions in the δτcb − Δτcb plane is favoured. The R(D(∗) )-rings in the complex δτcb - and Δτcb -planes yield four solutions when these parameters are chosen real, as shown in Fig. 3. The differential distributions exclude two of these solutions very clearly, and somewhat favour the one with very large Δτcb , as also observed for complex parameters. However, once the constraints from the ratio of inclusive decays R(Xc ) = B(B → Xc τ¯ντ )/B(B → Xc ¯ν ) = 0.222 ± 0.007 [9, 23] and the bound B(Bc → τ¯ντ ) ≤ 40% [9, 20, 22] are taken into account, we find that only one solution remains, indicated by the yellow area in Fig. 3. We therefore conclude that, when both the gcbτ L and cbτ gR couplings are included at the same time, the current B → D(∗) τ¯ντ data do not show clear signs of inconsistency and can be explained simultaneously by chargedscalar NP. Note that this option has been ignored in ref. [24], leading to the statement that scalar contributions alone could not explain R(D(∗) ) together with the measured differential distributions. In order to study the potential complementarity between b → c and b → u probes of charged-scalar contributions, we have also considered as a benchmark the universality relation ubτ gcbτ L,R /gL,R = mc,b /mu,b .
(5)
L L , λdν and λRul are the coupling matrices in where λul fermion mass basis. The resulting effective Hamiltonian induced by φ exchange at tree level is given by [19, 20] 4G F Heff = √ Vcb CV (Mφ ) c¯ γμ PL b τ¯ γμ PL ντ 2 + CS (Mφ ) c¯ PL b τ¯ PL ντ 1 − CT (Mφ ) c¯ σμν PL b τ¯ σμν PL ντ , (7) 4
where CV , CS , CT are the Wilson coefficients of the corresponding operators at the matching scale μ = Mφ , and are given explicitly as L L∗ λbν λcτ , CV (Mφ ) = √ τ 4 2G F Vcb Mφ2
CS (Mφ ) = CT (Mφ ) = −
L λbν λR∗ τ cτ
. √ 4 2G F Vcb Mφ2
(8)
(9)
Taking Mφ = 1 TeV as a benchmark and performing a two-dimensional χ2 fit, Freytsis, Ligeti and Ruderman found four best-fit solutions for the operator coefficients [18] ⎧ ⎪ ( 0.35, −0.03), PA ⎪ ⎪ ⎪ ⎪ ⎪ 2.41), PB ⎨ ( 0.96, L L∗ L R∗ (λbντ λcτ , λbντ λcτ ) = ⎪ . (10) ⎪ ⎪ (−5.74, 0.03), PC ⎪ ⎪ ⎪ ⎩ (−6.34, −2.39), PD It is noted that only the solution PA is adopted by Bauer and Neubert [19], arguing that the other three require significantly larger couplings. It would be worth investigating whether the four best-fit solutions could be discriminated from each other using the processes mediated by the same effective operators given by eq. (7). To this end, in addition to B → D(∗) τ¯ντ , we examine their
X.-Q. Li / Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184
184 0.14
4. Conclusion
0.12
Motivated by the observed R(D(∗) ) anomalies, we have discussed two possible NP solutions: one with an EW-scale charged scalar and the other with a TeVscale scalar leptoquark. Their phenomenological implications for other decays mediated by the same quarklevel transitions have also been discussed. Future precise measurements from LHCb and Belle II are urgently need to further clarify these anomalies.
ddq2
0.10 0.08 0.06 0.04 PC
0.02
PA SM
0.00
0.2
0.3
q2
0.4
0.5
0.175
Acknowledgements
0.150
ddy
0.125 0.100 0.075 0.050
PC
0.025
SM
0.000
PA
0.80
0.85
0.90
y
0.95
1.00
1.05
Figure 4: The qˆ 2 distributions of the differential branching fraction dB(B → Xc τ¯ντ )/dqˆ 2 (upper) and the τ-energy spectrum dB(B → Xc τ¯ντ )/dy (lower).
effects on Bc → τ¯ντ , Bc → γτ¯ντ and B → Xc τ¯ντ decays. It is found that the solutions PB and PD are already excluded by the decay Bc → τ¯ντ , because the predicted decay widths have already overshot the total width ΓBc : ⎧ ⎪ 2.22 × 10−2 ΓBc , ⎪ ⎪ ⎪ ⎪ ⎪ 2.45 × 10−2 ΓBc , ⎪ ⎪ ⎨ − − 1.33 ΓBc , Γ(Bc → τ ν¯ τ ) = ⎪ ⎪ ⎪ ⎪ −2 ⎪ 2.39 × 10 ΓBc , ⎪ ⎪ ⎪ ⎩ 1.31 ΓBc ,
SM PA PB , PC PD
(11)
The remaining two solutions result in two effective Hamiltonians that differ by a sign, but give almost the same predictions as in the SM for the D∗ and τ longitudinal polarizations as well as the lepton forwardbackward asymmetries in B → D(∗) τ¯ντ decays. For the observables B(Bc → τ¯ντ ), B(Bc → γτ¯ντ ), RD(∗) (q2 ), dB( B¯ → D(∗) τ¯ντ )/dq2 and B(B → Xc τ¯ντ ), on the other hand, the two solutions give sizable enhancements relative to the SM predictions, as shown e.g., in Fig. 4. Finally, due to the spin-half nature of Λb and Λc baryons, the semi-leptonic Λb → Λc ¯ν decays, which are mediated by the same quark-level transition as in B¯ → D(∗) ¯ν decays, can provide additional polarization observables through angular decay distribution. Detailed analyses of these baryonic decays in these two NP scenarios can be found in refs. [9, 21].
The author thanks the organizers for the fruitful TAU’16 workshop, and acknowledges the collaborations with Alejandro Celis, Martin Jung, Antonio Pich, Ya-Dong Yang, and Xin Zhang for the works reported here. XL is supported by the NNSFC under contract Nos. 11675061 and 11435003, and the self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (CCNU15A02037). [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
J. P. Lees, et al., Phys. Rev. Lett. 109 (2012) 101802. J. P. Lees, et al., Phys. Rev. D88 (7) (2013) 072012. M. Huschle, et al., Phys. Rev. D92 (7) (2015) 072014. A. Abdesselam, et al., arXiv:1603.06711. A. Abdesselam, et al., arXiv:1608.06391. S. Hirose, Talk at the TAU’ 16 workshop, these proceedings. R. Aaij, et al., Phys. Rev. Lett. 115 (11) (2015) 111803, [Addendum: Phys. Rev. Lett.115,no.15,159901(2015)]. K. D. Bruyn, Talk at the TAU’16 workshop, these proceedings. A. Celis, M. Jung, X.-Q. Li, A. Pich, in preparation. Y. Amhis et al., arXiv:1412.7515, and online update at http://www.slac.stanford.edu/xorg/hfag. D. Bigi, P. Gambino, arXiv:1606.08030. S. Fajfer, J. F. Kamenik, I. Nisandzic, Phys. Rev. D85 (2012) 094025. A. Crivellin, in: 51st Rencontres de Moriond on QCD and High Energy Interactions La Thuile, Italy, March 19-26, 2016, 2016. Z. Ligeti, in: 27th International Symposium on Lepton Photon Interactions at High Energy (LP15) Ljubljana, Slovenia, August 17-22, 2015, 2016. N. Kosnik, arXiv:1610.00447. G. Ricciardi, arXiv:1610.04387. A. Celis, M. Jung, X.-Q. Li, A. Pich, JHEP 01 (2013) 054. M. Freytsis, Z. Ligeti, J. T. Ruderman, Phys. Rev. D92 (5) (2015) 054018. M. Bauer, M. Neubert, Phys. Rev. Lett. 116 (14) (2016) 141802. X.-Q. Li, Y.-D. Yang, X. Zhang, JHEP 08 (2016) 054. X.-Q. Li, Y.-D. Yang, X. Zhang, arXiv:1611.01635. R. Alonso, B. Grinstein, J. Martin Camalich, arXiv:1611.06676. Z. Ligeti, F. J. Tackmann, Phys. Rev. D90 (3) (2014) 034021. Y. Sakaki, M. Tanaka, A. Tayduganov, R. Watanabe, Phys. Rev. D91 (11) (2015) 114028. R. Aaij, et al., Phys. Rev. Lett. 113 (2014) 151601. M. Davier, A. Hoecker, B. Malaescu, Z. Zhang, Eur. Phys. J. C71 (2011) 1515, [Erratum: Eur. Phys. J.C72,1874(2012)].
Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184 www.elsevier.com/locate/nppp
R( D) and R(D∗ ) anomalies and their phenomenological implications Xin-Qiang Li Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, Hubei 430079, China
Abstract Recently, BaBar, Belle and LHCb have found hints of lepton flavour universality violation in B → D(∗) τ¯ντ decays, i.e., the measured ratios R(D(∗) ) = B(B → D(∗) τ¯ντ )/B(B → D(∗) ¯ν ) ( = e/μ) show a combined 3.8 σ deviation from the SM predictions. In this talk, we will discuss two possible solutions to the observed R(D) and R(D∗ ) anomalies: one with an EW-scale charged scalar and the other with a TeV-scale scalar leptoquark transforming as (3, 1, − 13 ) under the SM gauge group. Their phenomenological implications for the other decays are also briefly discussed. Keywords: R(D(∗) ) anomalies, Lepton-flavour-universality violation, charged scalar, TeV-scale scalar leptoquark
1. Introduction Lepton flavour universality (LFU) tests are among the most powerful probes of the Standard Model (SM) and New Physics (NP) beyond it. They can be pursued by constructing ratios of process rates that differ only in the charged lepton flavour, where common systematical, parametric and hadronic uncertainties are cancelled out to some extent. Interestingly, the BaBar [1, 2], Belle [3, 4, 5, 6] and LHCb [7, 8] collaborations have recently measured the ratios R(D(∗) ) = B(B → D(∗) τ¯ντ )/B(B → D(∗) ¯ν ) ( = e/μ), for which our averages are [9]1 R(D)avg =0.400 ± 0.049 , R(D∗ )avg =0.310 ± 0.017 ,
(1)
with a correlation of −19%, as displayed in Fig. 1. This implies a 3.8σ deviation from the SM predictions: RSM D =0.301 ± 0.003 [9, 11] , RSM D∗ =0.252 ± 0.003 [12] .
(2)
1 We average the new Belle result [5] with the HFAG average of the remaining measurements [10], which takes correlations between the different measurements into account to a certain extent.
http://dx.doi.org/10.1016/j.nuclphysbps.2017.03.072 2405-6014/© 2017 Elsevier B.V. All rights reserved.
Figure 1: Average of R(D(∗) ) measurements, displayed as red filled ellipses (68% CL and 95% CL). The SM prediction is shown as a black ellipse (95% CL), and the individual measurements as contours (68% CL): Belle (blue), BaBar (green), and LHCb (yellow).
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182
Furthermore, the shapes of the differential distributions dΓ(B → D(∗) τ¯ντ )/dq2 have been made available by Belle and BaBar [2, 3], yielding additional information to distinguish NP from the SM as well as different NP models from each other. The observed R(D(∗) ) anomalies have motivated a lot of studies; for a review, see e.g., refs. [13, 14, 15, 16]. In this talk, we will discuss two possible NP solutions to the observed R(D(∗) ) anomalies: one with an EW-scale charged scalar [9, 17] and the other with a TeV-scale scalar leptoquark transforming as (3, 1, − 13 ) under the SM gauge group [18, 19, 20]. Their phenomenological implications for other decays mediated by the same quark-level transitions as in B → D(∗) τ¯ντ are also briefly discussed [9, 20, 21].
In Fig. 2 we show the fit results for B → Dτ¯ντ data in the complex δτcb plane (upper), and the B → D∗ τ¯ντ data in the complex Δτcb plane (lower), together with the constraints from B(Bc → τ¯ντ ) ≤ 40% [9, 20, 22]. For the B → Dτ¯ντ data, we find that the q2 -distribution selects a part of the R(D) ring that is closer to zero; while it favours a non-zero value for δτcb as well, where the preferred central value has a negative real part, opposite to the one from R(D). All constraints are consistent at 95 % CL with the SM, as is their combination.
2. Solution with an EW-scale charged scalar The NP contributions to charged-current semileptonic processes can be studied in a model-independent manner. We discuss firstly the case with an EW-scale colour-neutral charged scalar, which naturally lead to observable effects in b → cτ¯ντ transition, while b → c¯ν remains unaffected, since the charged-scalar couplings to fermions are proportional to the corresponding fermion masses. Specifically, the resulting low-energy effective Lagrangian is given by Leff = −
4G F Vcb cbτ τPL ντ ] , (3) c¯ (gL PL + gcbτ √ R PR ) b [¯ 2
where V represents the CKM matrix and PL,R = (1 ∓ γ5 )/2 are the usual chiral projectors. The Wilson coefficients gcbτ L,R are complex parameters which encode details of the underling theory at high energies. Without further assumptions on the flavour structure in Eq. (3), the only related observables are R(D), R(D∗ ), dΓ(B → D(∗) τ¯ντ )/dq2 , and the τ polarization asymmetry Aτ (D∗ ) measured firstly by Belle [5]. Note that B → Dτ¯ντ and B → D∗ ν¯ τ depend only on the scalar and pseudo-scalar combinations of the couplings gcbτ L,R , δτcb ≡
cbτ 2 2 (gcbτ (gcbτ − gcbτ L + gR )(m B − mD ) R )m B , Δτcb ≡ L , mτ (m ¯b −m ¯ c) mτ (m ¯b +m ¯ c) (4)
respectively, which we consequently choose to display the corresponding constraints. This implies that any value of R(D(∗) ) can at first be trivially explained in this scenario. However, the differential distributions give rise to additional non-trivial constraints on the parameter space when combined with R(D(∗) ).
Figure 2: Model-independent fits in the complex δτcb - (upper) and Δτcb planes (lower). The dark rings stem from R(D(∗) ), the lighter discs from dΓ(B → D(∗) τ¯ντ )/dq2 , the dark-green disc from B(Bc → τ¯ντ ) ≤ 40% [9, 20, 22] and the dashed line from Aλ (D∗ ). The yellow areas represent the global fit in each sector. All coloured areas correspond to 95% CL regions, only the dashed line corresponds to 68% CL.
For the B → D∗ τ¯ντ data, the picture is different: although compatible with zero by itself, the differential distribution tends to exclude the part of the R(D∗ ) ring
X.-Q. Li / Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184
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This makes it possible to analyze the compatibility of b → cτ¯ντ and b → uτ¯ντ data. Details of our predictions for Bu → τ¯ντ , B → πτ¯ντ , Λb → Λc (p)τ¯ντ observables can be found in ref. [9]. 3. Solution with a TeV-scale scalar leptoquark As a second solution to the B → D(∗) τ¯ντ data, we consider the model proposed by Bauer and Neubert, where a TeV-scale scalar leptoquark φ transforming as (3, 1, − 13 ) under the SM gauge group is added to the SM, and its couplings to fermions are described by [19] L L Lφint = u¯ cL λul lL φ∗ − d¯Lc λdν νL φ∗ + u¯ cR λRul lR φ∗ + h.c. , (6)
Figure 3: Constraints from R(D(∗) ), dΓ(B → D(∗) τ¯ντ )/dq2 , R(Xc ) = 0.222 ± 0.007 [9, 23], and the bound B(Bc → τ¯ντ ) ≤ 40% in the δτcb − Δτcb plane, assuming real couplings.
that is closer to zero, resulting in a global fit that excludes the SM even more strongly than R(D∗ ) alone. Specifically, it disfavours the negative real solution for Δτcb , which is again seen in Fig. 3, where now only one of the four solutions in the δτcb − Δτcb plane is favoured. The R(D(∗) )-rings in the complex δτcb - and Δτcb -planes yield four solutions when these parameters are chosen real, as shown in Fig. 3. The differential distributions exclude two of these solutions very clearly, and somewhat favour the one with very large Δτcb , as also observed for complex parameters. However, once the constraints from the ratio of inclusive decays R(Xc ) = B(B → Xc τ¯ντ )/B(B → Xc ¯ν ) = 0.222 ± 0.007 [9, 23] and the bound B(Bc → τ¯ντ ) ≤ 40% [9, 20, 22] are taken into account, we find that only one solution remains, indicated by the yellow area in Fig. 3. We therefore conclude that, when both the gcbτ L and cbτ gR couplings are included at the same time, the current B → D(∗) τ¯ντ data do not show clear signs of inconsistency and can be explained simultaneously by chargedscalar NP. Note that this option has been ignored in ref. [24], leading to the statement that scalar contributions alone could not explain R(D(∗) ) together with the measured differential distributions. In order to study the potential complementarity between b → c and b → u probes of charged-scalar contributions, we have also considered as a benchmark the universality relation ubτ gcbτ L,R /gL,R = mc,b /mu,b .
(5)
L L , λdν and λRul are the coupling matrices in where λul fermion mass basis. The resulting effective Hamiltonian induced by φ exchange at tree level is given by [19, 20] 4G F Heff = √ Vcb CV (Mφ ) c¯ γμ PL b τ¯ γμ PL ντ 2 + CS (Mφ ) c¯ PL b τ¯ PL ντ 1 − CT (Mφ ) c¯ σμν PL b τ¯ σμν PL ντ , (7) 4
where CV , CS , CT are the Wilson coefficients of the corresponding operators at the matching scale μ = Mφ , and are given explicitly as L L∗ λbν λcτ , CV (Mφ ) = √ τ 4 2G F Vcb Mφ2
CS (Mφ ) = CT (Mφ ) = −
L λbν λR∗ τ cτ
. √ 4 2G F Vcb Mφ2
(8)
(9)
Taking Mφ = 1 TeV as a benchmark and performing a two-dimensional χ2 fit, Freytsis, Ligeti and Ruderman found four best-fit solutions for the operator coefficients [18] ⎧ ⎪ ( 0.35, −0.03), PA ⎪ ⎪ ⎪ ⎪ ⎪ 2.41), PB ⎨ ( 0.96, L L∗ L R∗ (λbντ λcτ , λbντ λcτ ) = ⎪ . (10) ⎪ ⎪ (−5.74, 0.03), PC ⎪ ⎪ ⎪ ⎩ (−6.34, −2.39), PD It is noted that only the solution PA is adopted by Bauer and Neubert [19], arguing that the other three require significantly larger couplings. It would be worth investigating whether the four best-fit solutions could be discriminated from each other using the processes mediated by the same effective operators given by eq. (7). To this end, in addition to B → D(∗) τ¯ντ , we examine their
X.-Q. Li / Nuclear and Particle Physics Proceedings 287–288 (2017) 181–184
184 0.14
4. Conclusion
0.12
Motivated by the observed R(D(∗) ) anomalies, we have discussed two possible NP solutions: one with an EW-scale charged scalar and the other with a TeVscale scalar leptoquark. Their phenomenological implications for other decays mediated by the same quarklevel transitions have also been discussed. Future precise measurements from LHCb and Belle II are urgently need to further clarify these anomalies.
ddq2
0.10 0.08 0.06 0.04 PC
0.02
PA SM
0.00
0.2
0.3
q2
0.4
0.5
0.175
Acknowledgements
0.150
ddy
0.125 0.100 0.075 0.050
PC
0.025
SM
0.000
PA
0.80
0.85
0.90
y
0.95
1.00
1.05
Figure 4: The qˆ 2 distributions of the differential branching fraction dB(B → Xc τ¯ντ )/dqˆ 2 (upper) and the τ-energy spectrum dB(B → Xc τ¯ντ )/dy (lower).
effects on Bc → τ¯ντ , Bc → γτ¯ντ and B → Xc τ¯ντ decays. It is found that the solutions PB and PD are already excluded by the decay Bc → τ¯ντ , because the predicted decay widths have already overshot the total width ΓBc : ⎧ ⎪ 2.22 × 10−2 ΓBc , ⎪ ⎪ ⎪ ⎪ ⎪ 2.45 × 10−2 ΓBc , ⎪ ⎪ ⎨ − − 1.33 ΓBc , Γ(Bc → τ ν¯ τ ) = ⎪ ⎪ ⎪ ⎪ −2 ⎪ 2.39 × 10 ΓBc , ⎪ ⎪ ⎪ ⎩ 1.31 ΓBc ,
SM PA PB , PC PD
(11)
The remaining two solutions result in two effective Hamiltonians that differ by a sign, but give almost the same predictions as in the SM for the D∗ and τ longitudinal polarizations as well as the lepton forwardbackward asymmetries in B → D(∗) τ¯ντ decays. For the observables B(Bc → τ¯ντ ), B(Bc → γτ¯ντ ), RD(∗) (q2 ), dB( B¯ → D(∗) τ¯ντ )/dq2 and B(B → Xc τ¯ντ ), on the other hand, the two solutions give sizable enhancements relative to the SM predictions, as shown e.g., in Fig. 4. Finally, due to the spin-half nature of Λb and Λc baryons, the semi-leptonic Λb → Λc ¯ν decays, which are mediated by the same quark-level transition as in B¯ → D(∗) ¯ν decays, can provide additional polarization observables through angular decay distribution. Detailed analyses of these baryonic decays in these two NP scenarios can be found in refs. [9, 21].
The author thanks the organizers for the fruitful TAU’16 workshop, and acknowledges the collaborations with Alejandro Celis, Martin Jung, Antonio Pich, Ya-Dong Yang, and Xin Zhang for the works reported here. XL is supported by the NNSFC under contract Nos. 11675061 and 11435003, and the self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (CCNU15A02037). [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
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