Decay widths of Di-mesonic molecular states as candidates for Z c and Z b

Transcription

1 Decay widths of Di-mesonic molecular states as candidates for Z c and Z Smruti Patel Department of physics, Sardar Patel University, Vallah Vidyanagar fizix.smriti@gmail.com Manan Shah Department of physics, Sardar Patel University, Vallah Vidyanagar mnshah09@gmail.com Kaushal Thakkar Department of physics, Sardar Patel University, Vallah Vidyanagar kaushal2physics@gmail.com Departmecnt of physics, Sardar Patel University, Vallah Vidyanagar p.c.vinodkumar@gmail.com Recently significant progress in experimental investigations of tetraquark states has een achieved in a series of exciting experiments BELLE, BES-III, CLEO etc. which provides challenge to theory due to puzzling internal structure of tetraquark states. It is argued that it would e possile to solve this puzzle y examining their decay rates and therey knowing the working of strong force that confines quarks together inside the hadronic state. The exotic tetraquark states with charm and ottom flavor may open a new approach to study the finite density QCD matter ecause of the mass scales of charm and ottom hadrons. In this work, we compute the inding energy of the Di-mesons y considering a residual strong interaction of the Coulom plus Woods-Saxon type. Further, we predict the two ody strong decay widths, Z c ψns)+ π, Z c ρ+ η c of Z c + and Z ϒns)+ π of Z + ased on the phenomenological lagrangian field theory. XV International Conference on Hadron Spectroscopy-Hadron Novemer 2013 Nara, Japan Speaker. c Copyright owned y the authors) under the terms of the Creative Commons Attriution-NonCommercial-ShareAlike Licence.

2 1. Introduction Many theoretical works have focused on the issue of resolving the status as tetraquarks or dimesonic molecular states of the the recently discovered Z + c 3900) state y BES III [1] and BELLE Collaaration [2] and the Z 10610), Z 10650) resonances y BELLE [3, 4]. The interpretations of these new states have triggered considerale amount of theoretical work, especially due to the controversies related their internal structure. In this paper, we consider these exotic hadrons as D + D, B B and B B Di-mesonic molecular states. 2. Methodology We use a Lagrangian approach y considering these newly found states as Di-mesonic molecules. To calculate hadron molecular inding energies BE) of these states, we employ the interaction potential etween two color singlet mesons of the Woods Saxon plus Coulom form given y V r) = V exp r R a ) B r The potential parameters employed here are as follows: a = fm; V 0 = 0.03 GeV; B = 0.04; R = fm. These parameters are fitted optimally to get minimum statistical deviations from the experimental inding energy results. The masses of the Di-mesonic molecular states D + D, B B, B B are expressed in terms of the masses of the interacting mesons and the inding energy as 2.1) M D + D = M D + + M D BE, M B B = M B + M B BE, M B B = M B + M B BE, 2.2) The inding energy is otained y solving the Schrödinger equation numerically with the molecular interaction potential defined in Eqn 2.1). The Di-mesonic molecular masses and inding energies thus computed are listed in Tale 1 elow. Tale 1: Binding energies and Di-mesonic molecular mass in GeV). System BE Di-mesonic mass D ) D 2.007) B5.279) B 5.325) B 5.325) B 5.325) Our approach for computing the decay widths of these Di-mesons is ased on an interaction Lagrangian descried y the coupling of Z c and Z to its constituents as shown in fig. 1 and 2 respectively. The corresponding Lagrangian is given y [5, 6] L Zc x) = g 2 Z c Z c µ x) d 4 y Φ Zc y 2 ) Dx + y 2 ) D µx y 2 ) + D µx + y 2 ) Dx y 2 ) ) 2.3) L Z x) = g 2 Z Z µ x) d 4 y Φ Z y 2 ) Bx + y 2 ) B µx y 2 ) + B µx + y 2 ) Bx y ) 2 ) 2.4) 2

3 Figure 1: Two ody decays of Z + c ψns)π +, Z + c η c ρ + Figure 2: Two ody decays of Z + ϒnS)π+ g Z L Z x) = iε µναβ µ Z ν x) 2 d 4 y Φ Z y 2 ) B α x + y 2 ) B β x y 2 ) 2.5) where y is a Jacoi coordinate, g Zc, g Z, g Z are the dimensionless coupling constants of Z c, Z, Z to the Di-mesonic molecules D + D, B B, B B, respectively. In this calculation, size parameter Λ characterizing the distriution of the two constituent mesons in the tetraquark systems is taken as Λ=0.5 GeV [5]. It leads to a regularization of the ultraviolet divergences in the feynman diagrams. In the present calculation, we have taken our results of inding energies BE) as an input parameter as shown in Tale 1, while in [5, 6] they have taken inding energy as variale quantity 5-20 MeV). 3. Numerical results The decay widths of the two ody decays ΓZ c + ψns)π + ), ΓZ c + η c ρ + ) are given y [5] and that for ΓZ + ϒnS)π) is given y [6]. ) Γ Zc ψns)π + = g Z c ψns)π + 96πM 3 Z c λ 3/2 M 2 Z c,m 2 ψns),m2 π) Γ Zc η c ρ + = g Z c ψns)π + 96πM 3 Z c λ 3/2 M 2 Z c,m 2 η c,m 2 ρ) 1 + M2 ψns) 2MZ 2 c ) 1 + M2 η c 2M 2 Z c 3.1) 3.2) Γ P ϒnS)π + = g PϒnS)π + 16πM Z λm 2 p,m 2 ϒns),M2 π) wherep = Z, Z ) 3.3) Here λx,y,z) = x 2 + y 2 + z 2 2xy 2yz 2xz, is the Källen function and the states ns) are considered upto 2S only. The four coupling constants in eq. 3.1)-3.3) are computed as per the descriptions given y [5, 6, 7, 8]. The Di-mesonic masses of Z c, Z, Z are taken as given in Tale 1. 3

4 Tale 2: Decay width of D + D di-mesonic molecular state in MeV). System B.E. Decay Mode g Zc J 1 λx,y,z) g Zc ψns)π Decay width Γ in MeV) GeV) GeV) 4 GeV) 1 Present [5] [9] [10] [11] D + D Z c ψ1s)+ π Z c ψ2s)+ π Z c ρ+ η c Tale 3: Decay width of B B and B B di-mesonic molecular states in MeV). System B.E. Decay Mode g Z J 1 or J 2 λx,y,z) g Z ϒns)π Decay width Γ in MeV) GeV) GeV) 2 Present [6] EXP. [3] B B Z ϒ1s)+ π ±7.3 Z ϒ2s)+ π ±4.0 B B Z ϒ1s)+ π ±10±3 ϒ2s)+ π ± Conclusions Z In this paper, we have presented the masses of the Di-mesonic molecular states of D + D, B B, B B. These molecular states are found to lie elow their resonance threshold. The present partial decay widths of the dimesonic molecular states in the charm sector decaying to c c)ns+ π and ρ+ η c are presented in Tale 2. While those in the eauty sector decaying to ϒ1s) + π are presented in Tale 3. For Z c + state, partial decay width of particular mode is not availale experimentally, so we rely on theoretical data for the partial decay mode studied here. The decay mode Z c ψ1s)+ π is indeed one of the dominating mode than other decay modes.present results in the charm sector are found to e in good agreement with results of [6] for Z c +. The results for Z partial decay widths are consistent with experimental data [3]. The contriution from the triangle diagrams [12] which are not included in the present study will e taken into account for a complete study of these molecular states. Finally, we conclude that more high precision experimental data for the partial width of these states [Z c ), Z 10610) and Z 10650)], particularly in the case of Z c ) are required for resolving their status on firm footing. 5. Acknowledgements The work is part of a Major research project NO. F /2011SR) funded y UGC, INDIA. One of the our authors SP) would like to thank to Prof. Yuing Dong for fruitful discussions. References [1] M. Alikim et al. BESIII Collaoration), Phys. Rev. Lett. 110, ). [2] Z. Q. Liu et al. Belle Collaoration),Phys. Rev. Lett. 110, ). 4

5 [3] I. Adachi et al. Belle Collaoration), arxiv:hep-ex/ [4] A. Bondar et al. Belle Collaoration), Phys. Rev. Lett. 108, ). [5] Y. Dong et al., Phys. Rev. D 88, ). [6] Y. Dong et al., J. Phys. G 40, ). [7] Z. W. Lin et al., Phys. Rev. C 62, ). [8] Lin Z W and Ko C M, Phys. Lett. B 503, ); Oh Y S, Song T and Lee S H 2001 Phys. Rev. C 63, [9] Hong-Wei Ke, Zheng-Tao Wei and Xue-Qian Li,arxiv: ). [10] J. M. Dias, F. S. Navarra, and M. Nielsen, Phys. Rev. D 80, ). [11] L Maiani et al., Phys. Rev. D 87, ). [12] S. Ohkoda, S. Yasui and A. Hosaka, arxiv: ). 5