Probing the R-parity violating supersymmetric effects in the exclusive b\to c\ell^{-}\bar{\nu}_{\ell} decays

# Probing the R-parity violating supersymmetric effects in the exclusive b→cℓ−¯νℓ decays

Jie Zhu, Hua-Min Gan, Ru-Min Wang, Ying-Ying Fan, Qin Chang, Yuan-Guo Xu
Institute of Theoretical Physics, Xinyang Normal University, Xinyang, Henan 464000, China
Institute of Particle and Nuclear Physics, Henan Normal University, Xinxiang, Henan 453007, China
E-mail:ruminwang@sina.comE-mail:yuanguoxv@163.com

Motivated by recent results from the LHCb, BABAR and Belle collaborations on decays, which significantly deviate from the Standard Model and hint the possible new physics beyond the Standard Model, we probe the R-parity violating supersymmetric effects in and decays. We find that (i) and are sensitive to the constrained slepton exchange couplings; (ii) the normalized forward-backward asymmetries of decays have been greatly affected by the constrained slepton exchange couplings, and their signs could be changed; (iii) all relevant observables in the exclusive decays and the ratios are sensitive to the slepton exchange coupling, could be enhanced by the constrained slepton exchange coupling to reach each 95% confidence level experimental range from BABAR, Belle and LHCb, but it could not reach the lower limit of the 95% confidence level experimental average. Our results in this work could be used to probe R-parity violating effects, and will correlate with searches for direct supersymmetric signals at the running LHCb and the forthcoming Belle-II.

PACS Numbers: 13.20.He, 11.30.Fs, 12.60.Jv

## 1 Introduction

The semileptonic decays are very important processes in testing the Stand Model (SM) and in searching for the new physics (NP) beyond the SM, for example, the extraction of the Cabbibo-Kobayashi-Maskawa matrix element . The semileptonic decays have been measured by the CLEO[1], Belle[2, 3], BABAR[5, 6, 4, 7] and LHCb [8] collaborations. For the ratios with or , the experimental averages from the Heavy Flavor Averaging Group [9] are

 R(D)Exp.=0.391±0.050, R(D∗)Exp.=0.322±0.021, (1)

the SM predictions [10, 11] are

 R(D)SM=0.297±0.017, R(D∗)SM=0.252±0.003, (2)

the experimental measurements of and differ from their SM predictions by 1.7 and 3.0 deviations, respectively, and these hint the possible NP beyond the SM.

The exclusive decays have been studied extensively in the framework of the SM and various NP models, for instance, see Refs. [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]. The R-parity violating (RPV) supersymmetry (SUSY) is one of the respectable NP models that survived electroweak data [35, 36, 37, 38, 39, 40, 41, 42, 43]. In this paper, we will explore the RPV effects in the leptonic and semileptonic exclusive decays. We constrain relevant RPV parameter spaces from present experimental measurements and analyze their contributions to the branching ratios, the differential branching ratios, the normalized forward-backward (FB) asymmetries of the charged leptons, and the ratios of the branching ratios of relevant semileptonic decays.

The paper is organized as follows. In section 2, we briefly review the theoretical results of the exclusive decays in the RPV SUSY model. In section 3, using the constrained parameter spaces from relevant experimental measurements, we make a detailed classification research on the RPV effects on the quantities which have not been measured or not been well measured yet. Our conclusions are given in section 4.

## 2 The exclusive b→cℓ−¯νℓ decays in the SUSY without R-parity

In the RPV SUSY model, the similar processes have been studied in Ref. [38], and we will only give the final expressions in this section.

The branching ratio for the pure leptonic decays can be written as [38]

 B(B−c→ℓ−m¯νℓn)=∣∣ ∣∣GF√2Vcb−∑iλ′n3i~λ′∗m2i8m2~diR+∑iλinm~λ′∗i234m2~ℓiLμBcmℓ∣∣ ∣∣2τBc4πf2BcmBcm2ℓ[1−m2ℓm2Bc]2, (3)

where .

The differential branching ratios for the semileptonic decays could be written as [38]

 dB(B→Dℓ−¯νℓn)dsdcosθ=τB√λD27π3m3B(1−m2ℓms)2[ND0+ND1cosθ+ND2cos2θ], (4)

with

 ND0 = ∣∣ ∣∣GF√2Vcb−∑iλ′n3i~λ′∗m2i8m2~diR∣∣ ∣∣2[fD+(s)]2λD+∣∣ ∣∣GF√2Vcb−∑iλ′n3i~λ′∗m2i8m2~diR (5) +∑iλinm~λ′∗i234m2~ℓiLsmℓm(¯mb−¯mc)∣∣ ∣∣2m2ℓm[fD0(s)]2(m2B−m2D)2s, ND1 = ⎧⎪⎨⎪⎩∣∣ ∣∣GF√2Vcb−∑iλ′n3i~λ′∗m2i8m2~diR∣∣ ∣∣2+Re⎡⎢⎣⎛⎜⎝GF√2Vcb−∑iλ′n3i~λ′∗m2i8m2~diR⎞⎟⎠† (6) ×∑iλinm~λ′∗i234m2~ℓiLsmℓm(¯mb−¯mc)⎤⎥⎦⎫⎬⎭2m2ℓmfD0(s)fD+(s)√λD(m2B−m2D)s, ND2 = −∣∣ ∣∣GF√2Vcb−∑iλ′n3i~λ′∗m2i8m2~diR∣∣ ∣∣2[fD+(s)]2λD(1−m2ℓms), (7)

The differential branching ratios for the semileptonic decays could be written as [38]

 dB(B→D∗ℓ−m¯νℓn)dsdcosθ=τB√λ∗D27π3m3B(1−m2ℓms)2[ND∗0+ND∗1cosθ+ND∗2cos2θ], (8)

with

where , the kinematic factor , and the is the angle between the momentum of meson and the charged lepton in the c.m. system of .

The normalized forward-backward asymmetry of the charged lepton are given as [38]

 ¯AFB(B→D(∗)ℓ−m¯νℓn)=ND(∗)12ND(∗)0+2/3ND(∗)2. (12)

From above expressions, we can see that, unlike the contributions of the squark exchange couplings and the SM contributions, the slepton exchange couplings will not be suppressed by and helicity.

## 3 Numerical Results and Discussions

In the numerical calculations, the main theoretical input parameters are the transition form factors, the decay constant of meson, the masses, the mean lives, the CKM matrix element, etc. For the transition form factors, the traditional approaches to calculate the relevant transition form factors are the heavy quark effective theory  [10, 23], the Lattice QCD techniques [12, 13] and the pQCD factorization approach with and without Lattice QCD input [26, 27, 28], we will use the form factors based on the heavy quark effective theory [10, 23]. The decay constant of meson is taken from Ref. [44], and the rest of the theoretical input parameters are taken from the Particle Data Group (PDG) [45]. Notice that we assume the masses of the corresponding slepton are 500 GeV. For other values of the slepton masses, the bounds on the couplings in this paper can be easily obtained by scaling them by factor of .

In our calculation, we consider only one NP coupling at one time and keep its interference with the SM amplitude to study the RPV SUSY effects. To be conservative, the input parameters and the experimental bounds except for and at confidence level (CL) will be used to constrain parameter spaces of the relevant new couplings. Noted that we do not impose the experimental bounds from and , since their experimental measurements obviously deviate from their SM predictions, and we leave them as predictions of the restricted parameter spaces of the RPV couplings, and then compare them with the experimental results.

Due to the strong helicity suppression, the squark exchange couplings have no very obvious effects on the differential branching ratios and the normalized FB asymmetries of the semileptonic exclusive decays. So we will only focus on the slepton exchange couplings in our follow discussions. For the slepton exchange couplings, and , which contribute to both and transitions, the stronger constraints are from the exclusive decays [37, 41], nevertheless, the RPV weak phases of the two slepton exchange couplings are not obviously constrained by current experimental measurements.

### 3.1 The exclusive b→ce−¯νe decays

First, we focus on slepton exchange couplings contribute to five decay modes, , , , and decays. The branching ratios of four semileptonic processes have been accurately measured by CLEO [1], Belle [2] and BABAR [6, 5] collaborations. The 95% CL ranges of the experimental average values from the PDG [45] are listed in the second column of Table 1. The SM predictions at 95% CL are presented in the third column of Table 1.

Using the experimental bounds of relevant exclusive decays at 95% CL, we obtain the slepton exchange couplings . At present, the strongest bounds on the slepton exchange couplings come from the exclusive decays, with 500 GeV slepton masses [37], which will be used in our numerical results. In addition, the experimental bounds at the 95% CL listed in the second column of Table 1 are also considered to further constrain the slepton exchange couplings. Our numerical results of relevant branching ratios, which consider the constrained slepton exchange couplings, are listed in the last column of Table 1, and we can see that the constrained slepton exchange coupling has significant effects on , which could be suppressed 2 orders or enhanced 3 orders by the constrained slepton exchange couplings. Nevertheless, the constrained slepton exchange couplings have no significant effects on the branching ratios of relevant semileptonic decays.

For and decays, since the flavor symmtry implies , the slepton exchange RPV contributions to and are very similar to each other. So we would take decays as examples. The similar in the exclusive and decays.

Fig. 1 shows the constrained RPV effects of on , , and . The SM results are also displayed for comparing. Comparing the RPV SUSY predictions to the SM ones, we have the following remarks.

• As shown in Fig. 1 (a-b), is very sensitive to both moduli and weak phases of the couplings, and this is due to that the slepton exchange coupling effects on is increased by .

• As displayed in Fig. 1 (c-d), there are no obvious RPV effect on , since the present accurate experimental measurements of give very strongly constraints on the slepton exchange couplings. For the same reason, the branching ratios of relevant semileptonic decays are not sensitive to both moduli and weak phases of the couplings, so we do not display them in Fig. 1.

• Fig. 1 (e) shows us that the constrained couplings provide quite obvious effects on , its sign could be changed, nevertheless, this quantity is tiny. Fig. 1 (f) shows that there is no obvious RPV effect on .

### 3.2 The exclusive b→cμ−¯νμ decays

Now we pay attention to the contributions of the slepton exchange couplings to , , , , decays. The four semi-leptonic decay branching ratios have been accurately measured by CLEO [1], Belle [2] and BABAR [6, 5] collaborations. The experimental average values and the SM predictions at 95% CL are listed in the second and third column of Table 2, respectively.

We get the slepton exchange couplings from the exclusive decays, which are a lot weaker than ones from the exclusive decays, with 500 GeV slepton masses [41]. Taking the strongest bounds from the exclusive decays and further considering the experimental bounds from the exclusive decays, we predict the constrained slepton exchange effects in the exclusive decays, which are given in the last column of Table 2 and displayed in Fig. 2. From Table 2 and Fig. 2, we make the following points.

• As displayed in Fig. 2 (a-b), has some sensitivities to both modulus and weak phases of the couplings, and it has maximum at .

• Fig. 2 (c-d) shows that the constrained slepton exchange couplings have no obvious contribution to , and they are strongly constrained by present experimental data.

• As displayed in Fig. 2 (e-f), the constrained slepton exchange couplings also have no obvious contribution to at all range. Noted that, the slepton exchange coupling effects on are very different from ones on displayed in Fig. 1 (e-f), since the bounds on are about 3 times smaller than ones on (the same order of magnitude) and is 1000 times larger than .

### 3.3 The exclusive b→cτ−¯ντ decays

In this subsection, we concentrate on the contributions of the slepton exchange couplings in , , , and decays. The precise measurements of these semileptonic branching ratios have been reported by BABAR, Belle and LHCb [4, 7, 3, 8]. The 95% CL experimental ranges of the average data from PDG [45] and the 95% CL SM predictions are listed in the second and the third columns of Table 3, respectively.

Fig. 3 displays the allowed parameter spaces of the couplings from the 95 CL experimental bounds of the exclusive decays. Both the moduli and the weak phases of are obviously constrained by current experimental measurement. The bounds on is obtained for the first time.

Now we discuss the constrained effects in the exclusive decays. Our numerical predictions are given in the last column of Table 3. Fig. 4 shows the sensitivities of branching ratios to both moduli and weak phases of , and Fig. 5 shows the constrained slepton exchange effects on the differential branching ratios and the normalized FB asymmetries of decays.

As displayed in Fig. 4 (a-b), is very sensitive to both moduli and weak phases of , so the future experimental measurements on will give quite strong bound on . As displayed in Fig. 4 (c-d), is sensitive to but not very sensitive to their weak phases. We also can see that present experimental measurements of give strong bounds on this branching ratio. As displayed in Fig. 4 (e-f), is very sensitive to both moduli and weak phases of couplings, could have maximum at and , and they could catch the lower limits of present 95% CL experimental averages.

In Fig. 5 (a), we show another RPV prediction with the green “-” labeled with “SM+RPVII”, which is constrained by all above mentioned 95% CL experimental measurements except . We can see that the constrained couplings have very large effects on at whole regions, and the 95% CL experimental bound of give quite obvious constraints at middle and high regions. Fig. 5 (b) shows us that the constrained couplings have some effects on at the middle region. As displayed in Fig.