Mixing angle and decay constants of JP=1+ heavy-light mesons

Abstract

The mass spectra, mixing angle and decay constants of the J P = 1 + heavy-light mesons are systematically studied within the framework of the Bethe-Salpeter equation (BSE). The full 1 + Salpeter wave function is given for the first time. The mixing between the 1 +− and 1 ++ in the 1 + heavylight systems are automatically determined by the dynamics in the equation without any man-made mixing. The results indicate that in a rigorous study there exists the phenomenon of mixing angle inversion or mass inversion within 1 + heavy-light doublet, which is sensitive to the s-quark mass for the charmed mesons and u-or d-quark masses for the bottomed mesons. This inversion phenomenon can answer the question of why we have confused mixing angles in the literature and partly explain the lower mass of D s1 (2460) compared to that of D s1 (2536). The decay constants are also presented and can behave as a good quantity to distinguish the 1 + doublet in heavy-light mesons. This study indicates that the light-quark mass may play an important role in deciding the mass order, mixing angle, and decay constant relation between the |j l = 3 2 and |j l = 1 2 heavy-light mesons. I. IntroductionGenerally, all the physical mesons have definite J P spin parity or J P C for quarkonia. The spin S and orbital angular momentum L are no longer the good quantum numbers in the relativistic situations, and usually the physical states are not located in the definite 2S+1 L J states. These situations become obvious in the 1 + and 1 − mesons; for the 1 − states, the 2 3 S 1 -1 3 D 1 mixing is needed to fit the experimental measurements for both quarknia [1, 2] and heavy-light mesons [3-9], while for the 1 + states, we always have to make the 1 P 1 -3 P 1 mixing fit the physical states [10][11][12]. So, to describe the bound states more effectively and appropriately, one should focus on the J P (C) , which are always the good quantum numbers. In the previous literature, the unnatural parity 1 + heavy-light mesons were usually studied by two methods, one is the heavy quark effective theory (HQET) [11,12], and another makes a man-made mixing between the 1 P 1 and 3 P 1 states. For the former one, which works in the approximation m Q → +∞, and it does not hold well when the light-quark mass is comparable with the heavy quark, such as in the (cs) and (bc) systems. While for the latter one, the mixing angle is always difficult to decide and usually treated as a free parameter. Neither of the two methods to deal with the unnatural parity states is satisfactory.On the other hand, the mass relation between the two 1 + states is also a problem. The mass of the broad state D 1 (2430) is little heavier than that of the narrow state D 1 (2420), while compared with the narrow state D s1 (2536), the broad state D s1 (2460) has a much lower mass. In the relativized Godfrey-Isgur (GI) model [13], the masses of the 1 + (cs) doublet are predicted to be 2.55 and 2.56 GeV [12,14], which correspond to the experimental D s1 (2535) and D s1 (2460) respectively in the * Corre...

Strong decays of excited $ 2^+ $ charmed mesons

“…Ref. [38], the Cornell potential has an free parameter V 0 fixed by the masses of corresponding mesons, an linear confinement item V s , and the one-gluon exchange Coulomb-type item…”

“…According to Ref [31,38,43,44],. we specify D 1 (2420)/D s1 (2536) as |j l = 3/2 and D 1 (2430)/D s1 (2460) as |j l = 1/2 for 1 + state, D 2 (2740) as |j l = 5/2 and D 2 (2780) as |j l = 3/2 for 2 − state within this paper.…”

Mass spectra, wave functions and mixing effects of the (bcq) baryons

“…In this work, we will deal with the doubly heavy baryons with (bcq) flavors within the framework of the instantaneous Bethe-Salpeter equation, which has already been successfully used to cope with the doubly heavy baryons with 1 + diquark cores [7], the recently observed pentaquark P c and fully heavy tetraquark [25,26], and also generally applied to the meson mass spectra [27][28][29], the hadronic transitions and decays [30][31][32][33][34][35][36]. The theoretical calculations from BS methods have achieved satisfactory consistences with the experimental measurements, which give us more confidence and thereby inspire us to apply the same methods in baryon bound problems.…”

Mass spectra and wave functions of $T_{QQ\bar Q\bar Q}$ tetraquarks

“…The constructed relativistic wave functions are based on the good quantum number J P (C) rather than the nonrelativistic characteristics spin and orbital angular momentum 2S+1 L J . The BSE framework has been successfully used in the mass spectra of mesons [27][28][29], traditional baryons and pentaquarks [23,30], hadronic transitions, electro-weak decays, and etc [31][32][33][34][35][36][37]. In this work we would try to push the BSE framework further to study the fully heavy QQ Q Q system and develop a precise and systematic approach to describe the compact tetraquark states.…”