The rare semi-leptonic B c decays involving orbitally excited final mesons

et al. 2019

Phys. Rev. D

Self Cite

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...

Section: Resonances Mass Expmentioning

confidence: 99%

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

et al. 2019

Phys. Rev. D

Self Cite

“…BS equation [33] is the relativistic two-body bound states formula. Based on our previous studies [34][35][36][37], the relativistic corrections for transitions of higher excited states are larger and more important than that for the ground states, so the relativistic method is more reliable for the processes involved the high excited states. In the instantaneous approximation of the interaction kernel, we can achieve the Salpeter equation.…”

mentioning

confidence: 99%

“…In the instantaneous approximation of the interaction kernel, we can achieve the Salpeter equation. The Salpeter method has been widely used to deal with heavy mesons' decay constants calculation [38,39], annihilation rate [40,41], and hadronic transition [34][35][36][37]. This paper is organized as follows: first we present the general formalism of semi-leptonic and non-leptonic decay forB (s) meson, including decay width, forward-backward asymmetry, and lepton spectra.…”

mentioning

confidence: 99%

Decays of B, $$B_s$$ B s and $$B_c$$ B c to D-wave heavy–light mesons

et al. 2017

Eur. Phys. J. C

Self Cite

“…We take μ = m b for the b decays and a 1 = 1.14, a 2 = −0.2 [9] are used in this work. To estimate the systematic uncertainties from non-factorizable contributions, we treat the N c as an adjustable parameter varying from 2 to +∞ [40], and then we calculate the deviation to the central values. We stress that the factorization method used here is just taken as a preliminary study for the nonleptonic decays.…”

Section: Nonleptonic Decay Formalismmentioning

confidence: 99%

D-wave charmonia $$\eta _{c2}(1^1\!D_2)$$ η c 2 ( 1 1 D 2 ) , $$\psi _2(1^3\!D_2)$$ ψ 2 ( 1 3 D 2 ) , and $$\psi _3(1^3\!D_3)$$ ψ 3 ( 1 3 D 3 ) in $$B_c$$ B c decays

et al. 2016

Eur. Phys. J. C

Self Cite

We study the semileptonic and nonleptonic decays of B c meson to D-wave charmonia, namely,, and ψ 3 (1 3 D 3 ). In our calculations, the instantaneous Bethe-Salpeter method is applied to obtain the hadronic matrix elements. This method includes relativistic corrections which are important especially for the higher orbital excited states. For the semileptonic decay channels with electron as the final lepton, we get the branching ratios