Advances in High Energy Physics

Volume 2016, Article ID 4957236, 8 pages

http://dx.doi.org/10.1155/2016/4957236

## Study of Strange Charmed Meson Family Using HQET

School of Physics and Material Science, Thapar University, Patiala, Punjab 147004, India

Received 7 January 2016; Revised 11 March 2016; Accepted 13 March 2016

Academic Editor: Sally Seidel

Copyright © 2016 Pallavi Gupta and A. Upadhyay. 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

Recently LHCb predicted spin 1 and spin 3 states and which are studied through their strong decays and are assigned to fit the and states in the charm spectroscopy. In this paper, using the heavy quark effective theory, we state that assigning as the mixing of states is rather a better justification to its observed experimental values than a pure state. We study its decay modes variation with hadronic coupling constant and the mixing angle . We appoint spin 3 state as the missing state and also study its decay channel behavior with coupling constant . To appreciate the above results, we check the variation of decay modes for their spin partners states, that is, and , with their masses and strong coupling constant, that is, and . Our calculation using HQET approach gives mixing angle of the state for to lie in the range ( radians radians). Our calculation for coupling constant values gives to lie within value range of and to be 0.40. We expect from experiments to observe this mixing angle to verify our results.

#### 1. Introduction

Over the last decade many new heavy-light mesons have been observed by various experimental collaborations. The state was first observed by the BaBar Collaboration in with mass and width [1]. It was supposed to have natural parity states, that is, , , , , and so forth. But the assignment of as the state was ruled out after the observation of [2]. Along with the channel [2] BaBar also gives the ratio measured as . Along with this , BaBar Collaboration also observed state in the invariant mass spectrum with mass MeV and decay width [1]. In [2], BaBar Collaboration reported the branching ratio for this state as . The and state had went through extensive discussions by various theoretical models, to find a place in strange charm spectrum. Various discussions suggest to be suitable as state or as a radial excitation of -wave, that is, state. Zhang et al. have assigned as or states using the model [3], Colangelo et al. assign to be state using the heavy meson effective theory [4, 5], and Li et al. favor as the or state using Regge phenomenology [6]. All these different approaches calculated different value of the ratio . Heavy quark effective theory predicts to be ≈ 0.39 [4], while model calculated it to be ; both of the predicted values of are far from the experimental value . All these references favored as state due to observed narrow decay width, at the cost of mismatch of with experiments.

Recently LHCb Collaboration predicted a new resonance around 2.86 GeV in the invariant mass spectrum from decay channel , containing the mixture of spin 1 and spin 3 states components corresponding to and [7, 8] where the mass and width parameters are Here the first error is statistical error, the second is the experimental systematic effects, and the last one is due to model variations. Thus LHCb observed two states with spin 1 and spin 3. From the previous study it can be speculated that it is the spin 3 resonance of that belongs to state, with a narrow width . Theoretically, value can be matched with the experimental value, considering its contribution coming from the spin 1 state of resonance. Comparing with earlier theoretical mass predictions, LHCb spin 1 resonance can be assumed to fit in state of family or can be a mixture of and states since both these states have the same orbital angular momentum. Assigning as a mixing state of may give a better justification than assigning it as a pure state, because the value calculated by taking to be a mixed state of now depends on the mixing angle of these mixed states. By choosing suitable mixing angle , the calculated value can be better justified with the experimental value. Li and Ma assign to be mixing state of and to be its orthogonal partner [9] and obtained , nearly close to the experimental value. Zhong and Zhao by chiral quark model [10, 11] studied the state as the state with some mixing. Wang [12] tried to reproduce the experimental value with some suitable hadronic coupling constants, by including chiral symmetry breaking corrections in heavy quark effective theory. Besides these studies, Vijande et al. also assign to be the multiquark exotic state as [13]. Godfrey and Jardine by adopting the pseudoscalar emission decay model [14] and Song et al. by adopting QPC model [15] studied as . Various predictions are made to study the mixing effects in state [16–19].

In Particle Data Group [20] and strange charmed states are nicely described, but information for other states is still missing. The strange meson states with their states predicted by various theoretical model are gathered in Table 1. From the mass predicted by various theoretical models, that is, from second, third, and fourth columns of Table 1, and can be fitted as spin 1 and spin 3 state of family.