Advances in High Energy Physics

Volume 2016, Article ID 2352041, 10 pages

http://dx.doi.org/10.1155/2016/2352041

## Semileptonic Decays of to Light Tensor Mesons

Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran

Received 23 June 2016; Revised 21 August 2016; Accepted 6 September 2016

Academic Editor: Juan José Sanz-Cillero

Copyright © 2016 Reza Khosravi and S. Sadeghi. 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

The semileptonic , , transitions are investigated in the frame work of the three-point QCD sum rules. Considering the quark condensate contributions, the relevant form factors of these transitions are estimated. The branching ratios of these channel modes are also calculated at different values of the continuum thresholds of the tensor mesons and compared with the obtained data for other approaches.

#### 1. Introduction

Investigation of the meson decays into tensor mesons is useful in several aspects such as CP asymmetries, isospin symmetries, and the longitudinal and transverse polarization fractions. A large isospin violation has already been experimentally detected in mode [1]. Also, the decay mode is mainly dominated by the longitudinal polarization [2, 3], in contrast with , where the transverse polarization is comparable with the longitudinal one [4]. Therefore, nonleptonic and semileptonic decays of meson can play an important role in the study of the particle physics.

In the flavor symmetry, the light -wave tensor mesons with containing isovector mesons , isodoublet states , and two isosinglet mesons and are building the ground state nonet which has been experimentally established [5, 6]. The quark content for the isovector and isodoublet tensor resonances is obvious. The isoscalar tensor states, and , have mixing wave functions where mixing angle should be small [7, 8]. Therefore, is primarily a state, while is dominantly [9].

As a nonperturbative method, the QCD sum rules is a well established technique in the hadron physics since it is based on the fundamental QCD Lagrangian [10]. The semileptonic decays of to the light mesons involving , , and have been studied via the three-point QCD sum rules (3PSR), for instance, [11], , [12–14], [15], [16], and [17]. The determination of the form factor value relevant for the and [14, 18] decays allowed prediction of the ratio , which agrees with the experimental measurements [19–21]. The obtained results of the decay [11] and simulations on the lattice [22–24] are in a reasonable agreement.

In this work, we investigate decays within the 3PSR method. For analysis of these decays, the form factors and their branching ratio values are calculated. So far, the form factors of the semileptonic decays have been studied via different approaches such as the LCSR [25], the perturbative QCD (PQCD) [5], the large energy effective theory (LEET) [26–28], and the ISGW II model [29]. A comparison of our results for the form factor values in and branching ratio data with predictions obtained from other approaches, especially the LCSR, is also made.

The plan of the present paper is as follows: the 3PSR approach for calculation of the relevant form factors of decays is presented in Section 2. In the final section, the value of the form factors in and the branching ratio of the considered decays are reported. For a better analysis, the form factors and differential branching ratios related to these semileptonic decays are plotted with respect to the momentum transfer squared .

#### 2. Theoretical Framework

In order to study decays, we focus on the exclusive decay via the 3PSR. The decay governed by the tree level transition (see Figure 1). In the framework of the 3PSR, the first step is appropriate definition of correlation function. In this work, the correlation function should be taken aswhere and are four-momentum of the initial and final mesons, respectively. is the squared momentum transfer and is the time ordering operator. is the transition current. and are also the interpolating currents of and the tensor meson , respectively. With considering all quantum numbers, their interpolating currents can be written as follows [33]:where is the four-derivative vector with respect to acting at the same time on the left and right. It is given as where and are the Gell-Mann matrices and the external gluon fields, respectively. It should be noted that the second current in (2) interpolates a spin particle for massless quarks. In the general case, to describe a spin state one has to use a current such that the trace of vanishes.