Advances in High Energy Physics

Volume 2016 (2016), Article ID 5796131, 7 pages

http://dx.doi.org/10.1155/2016/5796131

## Analysis of Decay in Scalar Leptoquark Model

^{1}Institute of Particle Physics, Central China Normal University, Wuhan, Hubei 430079, China^{2}Department of Physics, Nanyang Normal University, Nanyang, Henan 473061, China

Received 20 April 2016; Revised 27 June 2016; Accepted 10 July 2016

Academic Editor: Enrico Lunghi

Copyright © 2016 Shuai-Wei Wang and Ya-Dong Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We analyze the baryonic semilepton decay in the scalar leptoquark models with and states, respectively. We also discuss the effects of these two NP models on some physical observables. For some measured observables, like the differential decay width, the longitudinal polarization of the dilepton system, the lepton-side forward-backward asymmetry, and the baryon-side forward-backward asymmetry, we find that the prediction values of SM are consistent with the current data in most ranges, where the prediction values of these two NP models can also keep consistent with the current data with . However, in some ranges, the prediction values of SM are difficult to meet the current data, but the contributions of these two NP models can meet them or keep close to them. For the double-lepton polarization asymmetries, , , , and are sensitive to the scalar leptoquark model but not to . However, , , , and are not sensitive to these two NP models.

#### 1. Introduction

The current data have hinted at several anomalies in decays induced by the flavor-changing neutral current (FCNC) processes , which have been recognized as very important probes of the Standard Model (SM) and new physics (NP). For the baryonic semilepton decays, experimentally, decay has been observed by the CDF collaboration [1] and measured by the LHCb collaboration at CERN [2]. Theoretically, studies on the decay have been investigated in the SM and beyond the SM [3–16]. Their results showed that some observables of these processes are sensitive to the contributions of NP.

The leptoquark models have many kinds of states, not only vector ones, but also scalar ones. In regard to different decay processes, the different leptoquark states may produce different effects. For processes, model independent constrains on leptoquarks are obtained in [17], where scalar leptoquark states with and have visible effects on the processes of B meson decays. For decay, their quark level transitions are also ; therefore, in this paper, we try to examine the effects of scalar leptoquark models on some observables of decay, such as the differential decay width, the longitudinal polarization of the dilepton system, the lepton-side forward-backward asymmetry, and the baryon-side forward-backward asymmetry and double-lepton polarization asymmetries.

The outline of this paper is as follows. In the next section we present the SM theoretical framework for transitions. In Section 3, we introduce the employed scalar leptoquark models; the transition form factors are given in Section 4. In Section 5, we present the physical observables and numerical analyses. Finally, we will have a concluding section.

#### 2. Transitions

At quark level, the rare decay is governed by the transition; its effective Hamiltonian in the SM can be written aswhere is the Fermi constant, is the fine-structure constant, and denote the CKM matrix elements.

Following [18], the effective Wilson coefficients in the high region are given bywhere the explicit expressions of these functions , , , and can be found in [19–21]. However, in the low region, nonfactorizable hadronic effects are expected to have the sizeable corrections; these have not been calculated for the baryonic decay [21, 22]. According to [18], we use the effective Wilson coefficients and in (2) both in the low region and in the high region by increasing the uncertainty.

#### 3. Scalar Leptoquark Models

Here we consider two kinds of the minimal renormalizable scalar leptoquark models [17], containing one single additional representation of where baryon number violation cannot be allowed in perturbation theory. There are only two such models which are represented as and under the gauge group.

The interaction Lagrangian for the scalar leptoquark couplings to the fermion bilinear can be written aswhere are the generation indices, the couplings are in general complex parameters, is the right-hand up-type quark (charged lepton) singlet, is the scalar leptoquark doublet, is a matrix, and is the left-hand quark (lepton) doublet.

After performing Fierz transformation, the contribution to the interaction Hamiltonian for iswhich can be written in the style of the SM effective Hamiltonian asThen we obtain the new Wilson coefficients

The interaction Lagrangian for the scalar leptoquark couplings to the fermion bilinear can be written as

After performing Fierz transformation, the contribution to the interaction Hamiltonian for the iswhere and are six-dimensional operators obtained from and by the replacement . Writing in the style of the SM effective Hamiltonian, we obtain the new Wilson coefficients:

In [23], comparing the bounds on NP coupling parameters obtained from , , and mixing, respectively, the authors obtain the following results:where the bounds will be used in the process of our calculations.

#### 4. Transition Form Factors

For decay, these form factors have been calculated in the framework of QCD light-cone sum rules (LCSR) in the low region [22] and lattice QCD in the high region [18], respectively. All of them use the helicity-based definition of the form factors [24]:where and . The fit functions of helicity-based form factors can be found in equations (133)–(135) of [22] and equation (49) of [18].

#### 5. Physical Observables and Numerical Analyses

##### 5.1. Some Measured Observables

According to [25], the polarization at the LHC has been measured to be small and compatible with zero, and polarization effects will average out for the symmetric ATLAS and CMS detectors, so we consider the initial baryon as unpolarized. The fourfold differential rate of the can be written as [26]where the angles and denote the polar directions of and , respectively. is the azimuthal angle between the and decay planes, and the explicit expressions of the coefficients can be found in [26].(a)The differential decay width is (b)The longitudinal polarization of the dilepton system is (c)The lepton-side forward-backward asymmetry is(d)The baryon-side forward-backward asymmetry is

In the process of numerical analyses, we consider the theoretical uncertainties of all input parameters. For the form factors, we use the results of QCD light-cone sum rules (LCSR) in the low region [22] and lattice QCD in the high region [18]. Comparing to the current data which have been measured by LHCb collaboration [27], we plot the dependence of four observables mentioned above on the full physical region except the intermediate region of in Figure 1.