B→χc1(1P,2P)Kdecays in QCD factorization andX

Abstract

B → χc1(1P, 2P )K decays are studied in QCD factorization by treating charmonia as nonrelativistic bound states. No infrared divergences exist in the vertex corrections, while the logarithmic end-point singularities in the hard spectator corrections can be regularized by a momentum cutoff. Within certain uncertainties we find that the B → χc1(2P )K decay rate can be comparable to B → χc1(1P )K, and get Br(B 0 → χ. This might imply a possible interpretation for the newly discovered X(3872) that this state has a dominant J P C = 1 ++ (2P ) cc component but mixed with a substantial D 0D * 0 + D * 0D0 continuum component. The naively factorizable decay [1] B → χ c1 K was studied [2] in the QCD factorization approach [3] in which the nonfactorizable vertex and spectator corrections were also estimated, but the numerical results were four times smaller than experimental data. Recently, these decays were also studied in the PQCD approach [4]. In both the above approaches, light-cone distribution amplitudes(LCDAs) were used to describe χ c1 . As argued in Ref.[5], a more appropriate description of charmonium is the nonrelativistic (NR) wave functions which can be expanded in terms of the relative momentum q between charm and anticharm quarks. This argument is based on the nonrelativistic nature of heavy quarkonium [7]. With careful studies, we find that the two descriptions (i.e.LCDAs and NR) are equivalent for the S-wave charmonium states (see,e.g. [6]), but in the case of P-wave states the light-cone descriptions lose some important contributions in the leading-twist approximation. This is not surprising since q can be neglected in S-wave states, but cannot be neglected for P-wave states even in leading order approximation.On the phenomenological hand, the study of B → χ c1 (2P )K may help clarify the nature of the recently discovered resonance X(3872) [8], since the measurements for X(3872) favor J P C = 1 ++ [9] and hence χ c1 (2P ) becomes one of the possible assignments for it. On the other hand, aside from the conventional charmonium [10,11], a loosely bound S-wave molecule of D 0D * 0 + D * 0D0 has been suggested for X(3872) [12,14].Motivated by the above considerations, in this paper we study the decays B → χ c1 (1P, 2P )K within the framework of QCD factorization by treating the charmonia χ c1 (1P, 2P ) as nonrelativistic bound states with m c /m b taken to be a fixed value in the heavy b quark limit. We will estimate the production rate of χ c1 (2P ) and argue that the X(3872) may be dominated by the χ c1 (2P ) charmonium but mixed with some D 0D * 0 + D * 0D0 continuum component. In the non-relativistic bound-state picture, charmonium can be described by the color-singlet NR wave function. Let p be the total momentum of the charmonium and 2q be the relative momentum between c andc quarks, then v 2 ∼ 4q 2 /p 2 ∼ 0.25 can be treated as a small expansion parameter [7]. For P-wave charmonium χ c1 , because the wave function at the origin R P (0)=0, which corresponds to the zeroth order in q, we must expand the a...

The hidden-charm pentaquark and tetraquark states

“…Hence, a pure χ c1 (2P) with J PC = 1 ++ can easily couple to the S -wave DD * scattering state if their masses are similar. Moreover, their mixture can result in a small mass [548,609], which value can be significantly lower than the mass of the pure χ c1 (2P) state predicted in the GI model [17], but close to the mass of the X(3872).…”

“…[609], Meng, Gao, and Chao treated charmonia as nonrelativistic bound states in QCD factorization and obtained B(B 0 → K 0 X(3872)) = B(B + → K + X(3872)) ≈ 2 × 10 −4 , which might imply that the X(3872) contains a dominant J PC = 1 ++ (2P) cc component and a substantial D 0D * 0 continuum component.…”

Refined analysis on theX(3872)resonance

“…Other works describe the Xð3872Þ as a D 0DÃ0 =D 0 D Ã0 virtual state [23], a tetraquark [24] or a hybrid state [25]. On the other hand, it has also been considered as a mixture of a charmonium χ 0 c1 ¼ χ c1 ð2PÞ with a D 0DÃ0 =D 0 D Ã0 component [26,27]. The mixing can be induced by the coupled-channel effects, and the S-wave χ 0 c1 − DD Ã =DD Ã coupling can also explain the closeness of m Xð3872Þ to the threshold of D 0DÃ0 naturally [28,29].…”

α s v 2 corrections to η c and χ cJ production recoiled with a photon at e + e − colliders

“…k = 0.018 ± 0.04 [49,78]. With the results up-to O(α s v 2 ), we revisit the cross sections for X(3872) shown in figure 13.…”

“…Quarkonia with even charge conjugation are associated to the XY Z particles [74][75][76]. X(3872), the well-known one of the XY Z particles [77], is supposed to χ ′ c1 state or the mixture of this state with other structure in some view [49,78]. Recently, X(3872) has been observed in photon-recoiled process with a statistical significance of 6.4σ at BESIII [79].…”