PRDPRVDAQPhysical Review DPhys. Rev. D2470-00102470-0029American Physical Society10.1103/PhysRevD.100.011701RAPID COMMUNICATIONSB-meson charged current anomalies: The post-Moriond 2019 statusB-MESON CHARGED CURRENT ANOMALIES: THE …DEBJYOTI BARDHAN AND DIPTIMOY GHOSHBardhanDebjyoti^{1}^{,*}GhoshDiptimoy^{2}^{,†}Department of Physics, Ben-Gurion University, Beer-Sheva 8410501, IsraelDepartment of Physics, Indian Institute of Science Education and Research, Pune 411008, India

bardhan@post.bgu.ac.il

diptimoy.ghosh@iiserpune.ac.in

10July20191July201910010117017May2019Published by the American Physical Society2019authorsPublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP^{3}.

In this paper, we discuss the impact of the recent Belle result on the various theoretical explanations of the RD and RD* anomalies. The pure tensor explanation, which was strongly disfavored by the measurements of FLD* and high-pTpp→τν searches before Moriond, is now completely allowed because of the reduction of the experimental world average. Moreover, the pure right-chiral vector solution (involving right-chiral neutrinos) has now moved into the 2σ allowed range of the LHC pp→τν searches. We also critically reexamine the bound on B(Bc-→τ-ν¯τ) from large electron-positron collider data and show that the bound is considerably weaker than the number 10% often used in the recent literature.

Israel Science Foundation10.13039/501100003977780/17Kreitman FoundationRamanujan Fellowships of the Department of Science and Technology

The Belle Collaboration has recently published results for RD and RD* with a semileptonic tag [1,2], and their result is consistent with the Standard Model (SM) expectation within 1.2σ. Consequently, the experimental world average has moved towards the SM. However, the tension between the experimental world average and the SM expectation is still more than 3σ, and thus it is interesting to reexamine the status of the various New Physics (NP) explanations in view of the new world average. In Table I, we collect all the experimental results related to this anomaly.

I10.1103/PhysRevD.100.011701.t1

Observables, their SM predictions, and the experimentally measured values. The pre-Moriond experimental averages for RD and RD* are based on Refs. [3–11].

SM predictionMeasurementRD0.300±0.008[12]0.407±0.046 (pre-Moriond)[13]0.299±0.011[14]0.334±0.031[1,2,13]RD*0.258±0.005[13,15–17]0.306±0.015 (pre-Moriond)[13]0.297±0.015[1,13]PτD*-0.47±0.04[15]-0.38-0.53+0.55[3,4]FLD*0.46±0.040.60±0.087[18]RJ/ψ0.2900.71±0.25[19]

The most general effective Lagrangian for the decay b→cτ-ν¯τ involving mass dimension-6 operators and only left-chiral neutrinos can be written as Leffb→cτν=−4GFVcb2(CVLL[c¯γμPLb][τ¯γμPLν]+CVRL[c¯γμPRb][τ¯γμPLν]+CSLL[c¯PLb][τ¯PLν]+CSRL[c¯PRb][τ¯PLν]+CTLL[c¯σμνPLb][τ¯σμνPLν]+H.c.).If one uses power-counting rules arising from linearly realized SU(2)×U(1) gauge invariance, it turns out that the Wilson coefficient (WC) CVRL, with the possibility of lepton nonuniversality, is only generated at the mass dimension-8 level [20]. Thus, it is expected to be suppressed compared to the other WCs as long as the scale of NP is not too close to the Higgs vacuum expectation value; thus, we will ignore it in this analysis.

If one also assumes the existence of light right-chiral neutrino(s), as was first done in Ref. [21] to solve the RD anomaly, five additional operators can be constructed by the replacement PL→PR in the leptonic currents of Eq. (1). In particular, a pure right-chiral vector current, namely, Leffb→cτν⊃−4GFVcb2CVRR[c¯γμPRb][τ¯γμPRν]+H.c.,was considered by several authors [22–24], and we will include it in our analysis.

As the experimental situation for RD and RD* is far from clear, we do not try to perform a fit to the WCs; for an early global fit, see Ref. [25]. Instead, we show how RD and RD* vary with respect to the WCs and overlay the current 1σ experimental world average and the corresponding currently allowed values of the WCs.

In Fig. 1, we show this for two WCs CVLL and CVRR, assuming them to be real. It can be seen from the left panel that CVLL=CVLL(SM)=1 is now at the edge of the 1σ allowed region for RD. This is due to the fact the new experimental world average for RD is now consistent with the SM expectation at approximately 1σ level. So, the anomaly is mostly driven by RD*. In order to be consistent with both RD and RD* simultaneously at the 1σ level, CVLL has to be in the range CVLL:[1.045,1.107]. So, there has not been a qualitative change in the situation after the new Belle measurement. Similarly, the allowed range for CVRR now is |CVRR|:[0.305,0.480]. The lower edge of this range, |CVRR|=0.305, is now consistent with the 2σ upper bound |CVRR|=0.32 from the LHC pp→τν searches [26]

Note, however, that for |CVRR|=0.305, the value of RD(*) is at the lower edge of the experimental 1σ allowed region. Moreover, the sensitivity of the current high-pT measurements is not enough to constrain the left-handed scenario CVLL≈1.05. Thus, the right-handed scenario is statistically worse than the CVLL solution.

(the bound from LHC pp→τν+X searches was also studied in Refs. [27,28]). Note that both the WCs CVLL and CVRR can be generated by a single U1(3,1,2/3) leptoquark mediator [24,29–32].110.1103/PhysRevD.100.011701.f1

Variations of RD and RD* against Re[CVLL] and Re[CVRR]. The green horizontal regions correspond to the experimental 1σ average from Table I, and the grey vertical regions correspond to the ranges of the WCs that produce RD and RD* values within their 1σ experimental world average. Note that CVLL(SM)=1, CVRR(SM)=0.

Variations of RD and RD* with respect to CTLL and CSLL=-8CTLL are shown in Fig. 2. It can be seen from the left panel of Fig. 2 that a simultaneous solution of RD and RD* is possible for CTLL in the range CTLL:[-0.021,-0.013]. We remind the readers that the corresponding value of CTLL before the recent Belle result was CTLL∼0.35[20,33], which was strongly disfavored by both the LHC pp→τν searches [26,34,35] as well as the measurement of FLD*[36]. The new allowed range for CTLL, on the other hand, is completely safe. Thus, this has been a qualitative change after the new Belle measurement. The specific relation CSLL≈-8CTLL (at the mb scale) shown in the right panel is interesting because it is generated by a single S1(3¯,1,1/3) leptoquark mediator [37]. The allowed range of the WC in this case is [0.113, 0.170], which, as can be seen from Fig. 3, produces B(Bc-→τ-ν¯τ) less than its SM value and thus is completely safe.

210.1103/PhysRevD.100.011701.f2

Variations of RD and RD* against Re[CTLL] and Re[CSLL]=−8Re[CTLL].

310.1103/PhysRevD.100.011701.f3

Variation of B(Bc-→τ-ν¯τ) with respect to Re[CSLL] and Im[CSLL].

Another single mediator solution that has been discussed in the literature is the so-called R2(3,2,7/6) leptoquark [38,39], which, contrary to the S1(3¯,1,1/3) leptoquark mediator, generates CSLL≈+8CTLL (see the sign difference) at the mb scale.

Note that the relation CSLL=±8CTLL is approximately true only at the mb scale. It is obtained by QCD renormalization group flow from the leptoquark matching scale (≈fewTeV) where the actual relations are CSLL=±4CTLL.

In the left panel of Fig. 4, we show this case, assuming real values of the WCs. It can be seen that the combination Re[CSLL]=+8Re[CTLL] at most can produce RD and RD* at the lower edge of their 1σ experimental world average if a simultaneous solution is desired (for Re[CSLL]=+8Re[CTLL]≈−0.12). A much better description of the data is possible if imaginary WCs are assumed as shown in the right panel of Fig. 4. The case of imaginary WCs in this context was first discussed in Ref. [40] and later also in Refs. [39,41–44]. In this case, one needs Im[CSLL]=+8Im[CTLL] in the range [0.480, 0.820], which gives B(Bc-→τ-ν¯τ)>10%; see Fig. 3. However, the authors of Ref. [45] claimed an upper bound of 10% on this branching ratio, arising from the large electron-positron collider (LEP) data taken on the Z peak. Thus, the Im[CSLL]=+8Im[CTLL] solution seems to be in slight tension if the 10% upper bound is taken at face value. While some authors [41] expressed concerns about the validity of this bound, not much effort was made to estimate as to how much this bound can be relaxed. We discuss this later in the paper.410.1103/PhysRevD.100.011701.f4

Variations of RD and RD* against Re[CSLL]=+8Re[CTLL] and Im[CSLL]=+8Im[CTLL].

As the operator CSRL alone cannot explain RD and RD* simultaneously, we do not discuss it anymore.

Here, we would like to make a couple of comments on the impact of FLD* and PτD* on the various scenarios. In all the scenarios explaining the RD and RD* anomalies, the variation of PτD* is less than approximately 2.5% from the SM prediction. Unfortunately, this is also true about FLD*, the only exception being the Im[CSLL]=8Im[CTLL] solution in which case the variation can be 5%–10% below the SM. Thus, distinguishing the various explanations by either PτD* or FLD* looks difficult at the moment.

LEP bound onB(Bc-→τ-ν¯τ)

As mentioned earlier, the authors of Ref. [45] used the LEP data [46] collected at the Z peak to put an upper bound on the branching fraction of Bc-→τ-ν¯τ. As this constraint has potentially interesting consequences for the RD and RD* anomalies, we will revisit it in detail.

In Ref. [46], the L3 Collaboration obtained an upper bound on the number of B-→τ-ν¯τ events, N(B-→τ-ν¯τ)<3.8. Based on this, they provided an upper bound, B(B-→τν¯τ)<5.7×10-4at90%C.L.As N(B-→τ-ν¯τ)∝fb→B-×B(B-→τν¯τ), where fb→B- is the inclusive probability that a b quark hadronizes into a Bc- or a Bu- meson, and for which Ref. [46] uses a value fb→B-=0.382±0.025, the bound in Eq. (3) can be translated into the following bound: fb→B-×B(B-→τν¯τ)<2.035×10-4.

Separating the total number of events into those coming from Bu- and Bc- decays, we get fb→Bu-B(Bu-→τ-ν¯τ)+fb→Bc-B(Bc-→τ-ν¯τ)<2.035×10-4.This gives B(Bc-→τ-ν¯τ)<(2.035×10-4fb→Bu-B(Bu-→τ-ν¯τ)-1)×fb→Bu-fb→Bc-B(Bu-→τ-ν¯τ).

The quantities B(Bu-→τ-ν¯τ) and fb→Bu- are known experimentally: B(Bu-→τ-ν¯τ)=(1.06±0.20)×10-4[4,47]fb→Bu-=0.412±0.008[4,47](LEP)fb→Bu-=0.340±0.021[4,47](Tevatron).Note that the hadronization fractions in Z decays do not necessarily need to be identical to those in pp¯ collisions because of the different momentum distributions of the b quark in these processes; in pp¯ collisions, the b quarks have momenta close to mb, rather than approximately mZ/2 in Z decays. In fact, CDF and LHCb collaborations have reported evidence for a strong pT dependence of he Λb0 fraction [48–51]. The LHCb and the ATLAS collaborations have also studied the pT dependence of fb→Bs/fb→Bd[52,53], but the results are not conclusive yet.

Therefore, we use the measurement of fb→Bu- from LEP only and plot the upper bound on B(Bc-→τ-ν¯τ) as a function of fb→Bu-/fb→Bc- in Fig. 5. The upper bound B(Bc-→τ-ν¯τ)=10% corresponds to fb→Bu-/fb→Bc-≈4×10-3.

In order to find a real upper bound on B(Bc-→τ-ν¯τ), we need to know the value of fb→Bu-/fb→Bc-, or at least a lower bound on fb→Bu-/fb→Bc-. Moreover, we need to know fb→Bu-/fb→Bc- at LEP, and with the exact kinematical cuts used in Ref. [46].

Reference [45] tries to find the ratio fb→Bu-/fb→Bc- from measurements of Rπ+/K+ and Rπ+/μ+ defined as Rπ+/K+=fb¯→Bc+fb¯→Bu+B(Bc+→J/ψπ+)B(Bu+→J/ψK+)Rπ+/μ+=B(Bc+→J/ψπ+)B(Bc+→J/ψμ+ν).

It then follows that fb¯→Bc+fb¯→Bu+B(Bc+→J/ψμ+νμ)B(Bu+→J/ψK+)=Rπ+/K+Rπ+/μ+⇒fb¯→Bc+fb¯→Bu+=B(Bu+→J/ψK+)B(Bc+→J/ψμ+νμ)Rπ+/K+Rπ+/μ+.

Using Rπ+/μ+=0.0469±0.0054[54]Rπ+/K+=LHCb(0.683±0.02)×10-2[55]=CMS(0.48±0.08)×10-2[56]B(Bu-→J/ψK-)=(9.99±0.36)×10-4[4],we get fb¯→Bc+fb¯→Bu+=(1.22-1.75)×10-4B(Bc+→J/ψμ+νμ)(using[55])fb¯→Bc+fb¯→Bu+=(0.74-1.40)×10-4B(Bc+→J/ψμ+νμ)(using[56]).As the LHCb and CMS measurements of Rπ+/K+ are about 2.5σ away from each other, we consider them separately and do not use their average. Moreover, while the LHCb Collaboration uses the cuts 0<pT(Bc+),pT(Bu+)<20GeV and 2.0<η<4.5 in their analysis (at s=8TeV), the CMS Collaboration uses pT(Bc+),pT(Bu+)>15GeV and |η|<1.6 (at s=7TeV). Thus, the discrepancy could be due to the dependence of fb¯→Bc+/fb¯→Bu+ on kinematics.

Plugging Eqs. (18) and (19) into Eq. (6), one can obtain a bound on B(Bc-→τ-ν¯τ) directly as a function of B(Bc+→J/ψμ+νμ). This is shown in the right panel of Fig. 6.

510.1103/PhysRevD.100.011701.f5

B(Bc-→τ-ν¯τ)|max as a function of fb→Bu-/fb→Bc-. The width of the plot corresponds to the uncertainties in Eqs. (7) and (8).

Using B(Bc+→J/ψμ+νμ)≤2.5×10-2, as used in Ref. [45], we get fb¯→Bc+/fb¯→Bu+≳3×10-3 and B(Bc-→τ-ν¯τ)≲14% from the CMS data, the latter being similar but slightly weaker than that in Ref. [45].

We would like to make two comments at this stage:

The bound on B(Bc-→τ-ν¯τ) depends linearly on B(Bc+→J/ψμ+νμ). As B(Bc+→J/ψμ+νμ) has not yet been measured, a model independent bound is not possible. Moreover, even the SM calculation, and in particular the uncertainty, is not fully under control at the moment. Thus, a precise bound on B(Bc-→τ-ν¯τ) cannot be obtained currently.

Even in the presence of better information on B(Bc+→J/ψμ+νμ), Eqs. (18) and (19) provide values of fb¯→Bc+/fb¯→Bu+ at the LHC and for the specific kinematic regions used in Refs. [55,56]. As discussed before, the value of fb¯→Bc+/fb¯→Bu+ at LEP may be different from the above 1) because of a larger average pT of the b mesons produced at LEP and 2) because bb¯ pairs produced at LEP are in the color singlet state, contrary to most of the bb¯ pairs produced at the LHC, which are in the color octet state.

In view of the above, we try to estimate the ratio fb¯→Bc+/fb¯→Bu+ at LEP using the event generator Pythia8 [57,58], which has the hadronization model tuned to provide a good description of the available experimental data. The results are shown in Table II. In each of the cases presented in Table II, we have generated 1 million events in order to reduce the statistical uncertainty. In case I, we have used the same pT and η cuts as in Ref. [56], and we get a value fb→Bc-/fb→Bu-=1.06×10-3, which is much smaller than fb→Bc-/fb→Bu-=3×10-3, which was used to obtain a bound B(Bc-→τ-ν¯τ)≤10%. Note that, from Eq. (19), fb→Bc-/fb→Bu-=1.06×10-3 would correspond to B(Bc+→J/ψμ+νμ)≈6×10-2 (see the left panel of Fig. 5), which is much larger than the values considered in Ref. [45]. In the third row of Table II, we changed the pT cut to pT<15GeV in order to check the pT dependence of the hadronization fractions. In this case, we get fb→Bc-/fb→Bu-=1.89×10-3, which is considerably larger than that in case I. This is consistent with the general findings in Refs. [48–53] and confirms that the measurement of fb→Bc-/fb→Bu- from LHCb [Eqs. (15) and (18)], which uses pT(Bc+),pT(Bu+)<20GeV, is indeed not expected to be the same as that measured by CMS [Eqs. (16) and (19)], which used pT(Bc+),pT(Bu+)>15GeV. In rows 4 and 5 of Table II, we considered bb¯ production through only the Z boson (produced bb¯ are in QCD singlet state) and through only QCD interactions (produced bb¯ are in QCD triplet state) respectively. We observed only an approximately 10% variation in the fb→Bc-/fb→Bu- between these two cases.

II10.1103/PhysRevD.100.011701.t2

Hadronization fractions calculated from Pythia8.

fb→Bu-fb→Bc-fb→Bc-fb→Bu-ILHC 7 TeVpT(Bc+,Bu+)>15GeV0.2552.7×10-41.06×10-3|η|<1.6IILHC 7 TeVpT(Bc+,Bu+)<15GeV0.3015.7×10-41.89×10-3|η|<1.6IIILHC 7 TeVqq¯→Z→bb¯ onlypT(Bc+,Bu+)>15GeV0.3744.1×10-41.09×10-3|η|<1.6IVLHC 7 TeVgg→bb¯ and qq¯→g→bb¯pT(Bc+,Bu+)>15GeV0.2552.5×10-40.98×10-3|η|<1.6VLEP (at the Z peak)0.424.5×10-41.07×10-3

Finally, at the Z peak, we obtain fb→Bu-=0.42, fb¯→Bs=0.094 (not shown in the table), and fb→Bc-/fb→Bu-=1.07×10-3, the first two numbers being consistent with their experimental measurements [13,47]. Using the number fb→Bc-/fb→Bu-=1.07×10-3, from Fig. 5, we get B(Bc-→τ-ν¯τ)≤39%.We warn the readers that this bound should only be taken as an estimate because, after all, Pythia only uses a hadronization model adjusted to describe a large amount of available experimental data well (as we saw, indeed it reproduced the correct values for fb→Bu- and fb¯→Bs), and the value of fb→Bc- obtained from Pythia is based on neither any first principle calculation nor on direct experimental data.

610.1103/PhysRevD.100.011701.f6

Variations of fb¯→Bc+/fb¯→Bu+ and B(Bc-→τ-ν¯τ)|max with respect to B(Bc+→J/ψμ+νμ).

To summarize, in this short paper, we have shown the following:

The recent Belle results on RD and RD* have interesting implications on the various possible effective field theory explanations of the data. The most important is that the pure tensor explanation is now completely allowed both by the measurement of FLD* and the high-pTpp→τν searches by ATLAS and CMS.

The solution in terms of a pure right-chiral vector current (involving right-chiral neutrinos) has now moved into the 2σ allowed range of the LHC pp→τν searches.

The upper bound on the branching fraction of Bc-→τ-ν¯τ from the LEP data is much weaker than the bound 10% used in the recent literature. Our estimate of this bound, based on the hadronization model implemented in Pythia8, is approximately 40%. This bound, while being independently important, may also have interesting implications on the various scalar-pseudoscalar explanations of the RD and RD* data.

ACKNOWLEDGMENTS

The research of D. B. was supported in part by the Israel Science Foundation (Grant No. 780/17) and by the Kreitman Foundation Post-Doctoral Fellowship. D. G. would like to acknowledge support through Ramanujan Fellowships of the Department of Science and Technology, Government of India.

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