P3H22103 TTP22062 KEKTH2464 Global fit to bcτνanomalies 2022 mid-autumn Syuhei IguroabTeppei Kitaharacdefand Ryoutaro Watanabeg

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P3H–22–103, TTP22–062, KEK–TH–2464

Global ﬁt to b→cτ ν anomalies 2022 mid-autumn

Syuhei Iguro,(a,b) Teppei Kitahara,(c,d,e,f) and Ryoutaro Watanabe(g)

(a) Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology (KIT),

Engesserstraße 7, 76131 Karlsruhe, Germany

(b) Institute for Astroparticle Physics (IAP), KIT, Hermann-von-Helmholtz-Platz 1,

76344 Eggenstein-Leopoldshafen, Germany

(d) Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,

Nagoya 464–8602, Japan

(e) KEK Theory Center, IPNS, KEK, Tsukuba 305–0801, Japan

(f) CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,

Chinese Academy of Sciences, Beijing 100190, China

(g) INFN, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy

igurosyuhei@gmail.com,teppeik@kmi.nagoya-u.ac.jp,wryou1985@gmail.com

Dated: October 18, 2022

Abstract

Recently, the LHCb collaboration announced a preliminary result of the test of lepton

ﬂavor universality (LFU) in B→D(∗)semi-leptonic decays: RLHCb2022

D= 0.441 ±0.089

and RLHCb2022

D∗= 0.281 ±0.030 based on the LHC Run 1 data. This is the ﬁrst result

of RDfor the LHCb experiment, and its precision is comparable to the other B-factory

data. Interestingly, those data prefer the violation of the LFU again. A new world

average of the data from the BaBar, Belle, and LHCb collaborations is RD= 0.358 ±

0.027 and RD∗= 0.285 ±0.013. Including this new data, we update a circumstance

of the b→cτν measurements and their implications for new physics. Incorporating

recent developments for the B→D(∗)form factors in the Standard Model (SM), we

observe a 4.1σdeviation from the SM predictions. Our updates also include; model-

independent new physics (NP) formulae for the related observables; and the global

ﬁttings of parameters for leptoquark scenarios as well as single NP operator scenarios.

Furthermore, we show future potential to indirectly distinguish diﬀerent new physics

scenarios with the use of the precise measurements of the polarization observables in

B→D(∗)τν at the Belle II and the high-pTﬂavored-tail searches at the LHC. We also

discuss an impact on the LFU violation in Υ →l+l−.

Keywords: Beyond Standard Model, Bphysics, Eﬀective Field Theories

arXiv:2210.10751v4 [hep-ph] 28 May 2024

Contents

1 Introduction 1

1.1 Summary of the current status: 2022 mid-autumn ............... 1

1.2 Preliminaries of our analysis ............................ 4

2 General formulae for the observables 6

3 Fit analysis 10

3.1 EFT: single operator scenario ........................... 11

3.2 LQ scenarios .................................... 13

3.3 UV completion of U1LQ ............................. 17

4 The LFU violation in Υ decays 18

5 Conclusions and discussion 22

A Leptoquark interactions 25

1 Introduction

The semi-tauonic B-meson decays, B→D(∗)τ ν, have been intriguing processes to measure

the lepton ﬂavor universality (LFU):

RD≡B(B→D τ ντ)

B(B→D ℓ νℓ), RD∗≡B(B→D∗τ ντ)

B(B→D∗ℓ νℓ),(1.1)

since it has been reported that the measurements by the BaBar [1,2], Belle [3–7] and

LHCb [8–10] collaborations indicate deviations from the Standard Model (SM) predictions,

where ℓ=e, µ for the BaBar/Belle and ℓ=µfor the LHCb. See Table 1for the present

summary.

A key feature of the deviation is that the measured RD(∗)are always excesses compared

with the SM predictions and thus imply violation of the LFU. Then it has been followed by

a ton of theoretical studies to understand its implication from various points of view, e.g.,

see Ref. [11] and references therein. A conﬁrmation of the LFU violation will provide an

evidence of new physics (NP).

1.1 Summary of the current status: 2022 mid-autumn

Three years have passed since the previous experimental report of RD(∗)measurements from

the Bfactories [7]. In the meantime, the Belle II experiment ﬁnally started taking data

Experiment RD∗RDCorrelation

BaBar [1,2] 0.332 ±0.024 ±0.018 0.440 ±0.058 ±0.042 −0.27

Belle [3] 0.293 ±0.038 ±0.015 0.375 ±0.064 ±0.026 −0.49

Belle [4,5] 0.270 ±0.035+0.028

−0.025 – –

Belle [6,7] 0.283 ±0.018 ±0.014 0.307 ±0.037 ±0.016 −0.51

LHCb [9,10] 0.280 ±0.018 ±0.029 – –

LHCb [8,18] 0.281 ±0.018 ±0.024 0.441 ±0.060 ±0.066 −0.43

World average [19] 0.285 ±0.010 ±0.008 0.358 ±0.025 ±0.012 −0.29

Table 1. Current status of the independent experimental RD(∗)measurements. The ﬁrst and second

errors are statistical and systematic, respectively.

from 2020 [12,13], and the CMS collaboration has developed an innovative data recording

method, called “BParking” since 2019 [14–17], although their oﬃcial ﬁrst results are still

being awaited.

On the other hand, the LHCb collaboration has shown their results in 2015 and 2017

with the LHCb Run 1 dataset, and thus it was ﬁve years passed. Then, now, the LHCb

collaboration reported their preliminary result of RDand also RD∗with the LHCb Run 1

dataset [18],

RLHCb2022

D= 0.441 ±0.060 ±0.066 ,

RLHCb2022

D∗= 0.281 ±0.018 ±0.024 .(1.2)

The τis reconstructed in τ→µνν and the result supersedes the previous result performed

in 2015 [8].

In Table 1, we summarize the current status of the RD(∗)measurements including the

new LHCb result. It is found that the new LHCb result is consistent with the previous

world average evaluated in the HFLAV 2021 report [20] within the experimental uncertainty.

The combined average of the experimental data gives p(χ2) = 32% with χ2/dof = 9.21/8

for the p-value among all data, compared with the previous HFLAV average of 28% with

χ2/dof = 8.8/7 written in Ref. [20]. The ampliﬁed p-value indicates consistency among the

data. New world averages of the RD(∗)measurements are [19]

RD= 0.358 ±0.025 ±0.012 ,

RD∗= 0.285 ±0.010 ±0.008 ,(1.3)

and RD–RD∗correlation of −0.29.

Reference RDRD∗PD

τ−PD∗

τFD∗

LRJ/ψ RΛcRΥ(3S)

Bernlochner, et al. [22] 0.288(4) 0.249(3) – – – – – –

Iguro, Watanabe [23] 0.290(3) 0.248(1) 0.331(4) 0.497(7) 0.464(3) – – –

Bordone, et al. [24,25] 0.298(3) 0.250(3) 0.321(3) 0.492(13) 0.467(9) – – –

HFLAV2021 [20] 0.298(4) 0.254(5) – – – – – –

Refs. [26–28] – – – – – 0.258(4) 0.324(4) 0.9948

Data 0.358(28) 0.285(13) – 0.38 +0.53

−0.55 0.60(9) 0.71(25) 0.271(72) 0.968(16)

Table 2. Summary of the SM predictions for the B→D(∗)τν and related observables. The current

combined results of the experimental measurements are also written in the last line. See the main

text for the deﬁnitions of the observables.

Regarding the combined average, an important analysis is given in Ref. [21]. The authors

pointed out that evaluations of the D∗∗ distributions in the SM background involve nontrivial

correlations that aﬀect the RD(∗)measurements. Their sophisticated study shows that the

combined RD(∗)average is slightly sifted, which is beyond the scope of our work.#1

Recent SM predictions for RSM

D(∗)have been obtained in Refs. [20,23–25] as summarized

in Table 2. The diﬀerence of these SM values is mainly due to development of the B→D(∗)

form factor evaluations both by theoretical studies and experimental ﬁts, whose details can

be found in the literature. In our work, we will employ the work of Ref. [23] as explained

soon later.

A further concern for the SM evaluation is long-distance QED corrections to B→

D(∗)ℓν, which remains an open question. They depend on the lepton mass as being of

O[αln(mℓ/mB)] and hence it could provide a few percent correction to violation of the

LFU in the semileptonic processes [29–32]. This will be crucial in future when the Belle II

experiment reaches such an accuracy.

In Fig. 1, we show the latest average of the RD–RD∗along with the several recent SM

predictions. A general consensus from the ﬁgure is that the deviation of the experimental

data from the SM expectations still remains. For instance, applying the SM prediction from

{HFLAV2021 [20], Ref. [22], Ref. [23], Refs. [24,25]}, one can see {3.2σ, 4.0σ, 4.1σ, 3.6σ}

deviations corresponding to p-value = {1.2×10−3,6.4×10−5,4.8×10−5,2.7×10−4}(∆χ2=

{13.8,19.3,19.9,16.4}for 2 degrees of freedom), respectively.

In addition to these deviations in the LFU measurements, τ- and D∗-polarization observ-

ables in B→D(∗)τν also provide us important and nontrivial information. This is because

these observables can potentially help us to pin down the NP structure that causes these

deviations [33–50]. We refer to the τlongitudinal-polarization asymmetry in B→D(∗)τν

and the fraction of the D∗longitudinal mode in B→D∗τν as PD(∗)

τand FD∗

L, respectively.

#1Instead, a comparison among the two previous and new world averages is shown in Fig. 1.

+HFLAV 2021

+Bernlochner, et al.

+Iguro, Watanabe

+Bordone, et al.

HFLAV 2021

New combined average

Bernlochner et al.

0.25 0.30 0.35 0.40 0.45

0.24

0.26

0.28

0.30

0.32

0.34

0.36

RD*

Figure 1. A world average of the latest RDand RD∗experimental results (red, 1, 2, 3σcontours),

compared with the previous HFLAV 2021 average (dashed orange) [20] and with Ref. [21] (dashed

blue) which includes the nontrivial D∗∗ contribution. On the other hand, the several SM predictions

are shown by crosses [22–25].

See Refs. [42,51,52] for their explicit deﬁnitions.

In recent years, the ﬁrst measurements for some of the above polarization observables

have been reported by the Belle collaboration. It is summarized as PD∗

τ=−0.38 ±

0.51 +0.21

−0.16 [4] and FD∗

L= 0.60 ±0.08 ±0.04 [53]. See also Table 2. Although the exper-

imental uncertainty in FD∗

Lis still large, this result already has important implications for

a tensor-operator NP as pointed out in Ref. [42]. Although PD

τis the most striking ob-

servable to disentangle the leptoquark (LQ) scenarios that can explain the discrepancy, the

experimental study does not exist so far.

Note that the D∗longitudinal polarization in the electron mode has also been measured,

FD∗

L(B0→D∗+eν)≡FD∗

L= 0.56 ±0.02 [53]. This is comparable to the SM prediction

of 0.534 ±0.002 [23]. The FD∗

Land FD∗

Lmeasurements have the same level of signiﬁcance

(1.5σand 1.3σ, respectively).

1.2 Preliminaries of our analysis

Main points of this paper are that (i) we provide state-of-the-art numerical formulae for the

observables relevant to the semi-tauonic Bdecays and (ii) we revisit to perform global ﬁts

to the available RD(∗)measurements with respect to NP interpretations. It will be given by

incorporating following updates and concerns:

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P3H–22–103,TTP22–062,KEK–TH–2464Globalfittob→cτνanomalies2022mid-autumnSyuheiIguro,(a,b)TeppeiKitahara,(c,d,e,f)andRyoutaroWatanabe(g)(a)InstituteforTheoreticalParticlePhysics(TTP),KarlsruheInstituteofTechnology(KIT),Engesserstraße7,76131Karlsruhe,Germany(b)InstituteforAstroparticlePhysics(IAP),KIT,...

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