利用pQCD方法研究ϒ（nS）→BcDs，BcDd弱衰变

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"这篇论文详细探讨了使用扰动量子色动力学(pQCD)方法研究ϒ(nS)→BcDs和ϒ(nS)→BcDd的弱衰变过程。作者发现这两个衰变的分支比分别为Br(ϒ(nS)→BcDs)约为O(10^-10)和Br(ϒ(nS)→BcDd)约为O(10^-11)，这些值在未来的实验中有可能被测量到。该研究由中国河南师范大学和南阳师范学院的物理与电子工程学院的学者共同完成，并发表在Physics Letters B期刊上。文章强调，这是首次运用pQCD方法来分析这些衰变，且该研究结果对粒子物理学领域的理论与实验研究具有重要意义。" 这篇论文属于高能物理学领域，专注于弱相互作用过程的研究，特别是涉及底夸克的衰变。其中的ϒ(nS)代表Υ态的底onium，这是一种由一个底夸克和其对应的反夸克组成的束缚态。Bc则指的是包含一个粲夸克和一个底夸克的重子，而Ds和Dd是包含奇异夸克的D介子的不同同位素。扰动量子色动力学(pQCD)是理论物理学家用来处理强相互作用的一种工具，尤其是在高能量尺度下，它能够提供对粒子衰变和散射过程的精确描述。在本文中，研究人员使用pQCD方法来计算ϒ(nS)衰变为BcDs和BcDd的几率，即它们的分支比。他们发现这两个衰变的概率相当小，但并非完全无法探测。分支比的估计值表明，尽管这些衰变过程极其罕见，但在未来的技术进步和更精确的实验条件下，如大型强子对撞机(LHC)的相关实验，可能会有机会观测到这些现象。弱衰变是粒子物理学标准模型中的基本过程，由W和Z玻色子作为媒介。在ϒ(nS)的弱衰变中，底夸克通过交换W玻色子转变成其他夸克，这一过程涉及到量子数如电荷、颜色和味的改变。通过pQCD方法，可以估算出这些变化过程的概率，为理解基本粒子的性质和相互作用提供了重要的理论依据。这篇论文的贡献在于首次采用pQCD方法研究ϒ(nS)的特定衰变模式，提供了实验探测这些衰变可能性的理论预测，从而对粒子物理学的理论框架进行了扩展和完善。未来，这些研究结果可能有助于粒子物理学家更好地理解基本粒子的行为，以及在宇宙早期状态下物质的形成和演化。

Physics Letters B 752 (2016) 322–328

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

The ϒ(nS) → B

, B

decays with perturbative QCD approach

Junfeng Sun

, Yueling Yang

a,∗

, Qingxia Li

, Haiyan Li

, Qin Chang

, Jinshu Huang

Institute of Particle and Nuclear Physics, College of Physics and Electronic Engineering, Henan Normal University, Xinxiang 453007, China

College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China

a r t i c l e i n f oa b s t r a c t

Article history:

Received

1 November 2015

Accepted

19 November 2015

Available

online 26 November 2015

Editor:

B. Grinstein

The ϒ(nS) → B

, B

weak decays are studied with the pQCD approach ﬁrstly. It is found that

branching ratios Br(ϒ(nS) → B

) ∼ O(10

−10

) and Br(ϒ (nS) → B

) ∼ O(10

−11

), which might be

measurable in the future experiments.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Since the discovery of bottomonium (the bound states of the

bottom quark b and the corresponding antiquark

b, i.e., b

b) at Fer-

milab

in 1977 [1,2], remarkable achievements have been made in

the understanding of the properties of bottomonium, thanks to the

endeavor from the experiment groups of CLEO, BaBar, Belle, CDF,

D0, LHCb, ATLAS, and so on [3]. The upsilon, ϒ(nS), is the S-wave

spin-triplet state, n

, of bottomonium with the well established

quantum number of I

−

−−

[4]. The typical total widths of

the upsilons below the kinematical open-bottom threshold (where

the radial quantum number n = 1, 2 and 3) are a few tens of keV

(see Table 1), at least two orders of magnitude less than those

of bottomonium above the B

B threshold. (Note that for simplicity,

ϒ(nS) will denote the ϒ(1S), ϒ(2S) and ϒ(3S) mesons in the fol-

lowing

content if not speciﬁed explicitly.) As it is well known, the

ϒ(nS) meson decays primarily through the annihilation of the b

pairs

into three gluons, which are suppressed by the phenomeno-

logical

Okubo–Zweig–Iizuka rule [5–7]. The allowed G-parity con-

serving

transitions, ϒ(nS) → ππϒ(mS) and ϒ(nS) → ηϒ(mS)

where 3 ≥ n > m ≥ 1, are greatly limited by the compact phase

spaces, because the mass difference m

ϒ(3S)

−m

ϒ(2S)

is just slightly

larger than 2m

, and m

ϒ(2S)

−m

ϒ(1S)

is just slightly larger than

. The coupling strengths of the electromagnetic and radiative

interactions are proportional to the electric charge of the bottom

quark, Q

=−1/3in the unit of |e|. Besides, the ϒ(nS ) meson can

also decay via the weak interactions within the standard model, al-

though

the branching ratio is small, about 2/τ



∼O(10

−8

) [4],

where τ

and 

are the lifetime of the B

u,d,s

meson and the to-

tal

width of the ϒ(nS) meson, respectively. In this paper, we will

Corresponding author.

E-mail

address: yangyueling@htu.cn (Y. Yang).

study the ϒ(nS) → B

, B

weak decays with the perturbative

QCD (pQCD) approach [8–10]. The motivation is listed as follows.

From

the experimental point of view, (1) over 10

ϒ(nS) data

samples have been accumulated by the Belle detector at the KEKB

and the BaBar detector at the PEP-II e

−

asymmetric energy col-

liders

[11] (see Table 1). It is hopefully expected that more and

more upsilons will be collected with great precision at the running

upgraded LHC and the forthcoming SuperKEKB. An abundant data

samples offer a realistic possibility to search for the ϒ(nS) weak

decays which in some cases might be detectable. (2) The signals

for the ϒ(nS) → B

s,d

weak decays should be clear and easily

distinguishable from background, because the back-to-back ﬁnal

states with opposite electric charges have deﬁnite momentums and

energies in the center-of-mass frame of the ϒ(nS) meson. In addi-

tion,

the identiﬁcation of either a single ﬂavored D

s,d

or B

meson

can be used not only to avoid the low double-tagging eﬃciency

[12], but also to provide an unambiguous evidence of the ϒ(nS)

weak decay. It should be noticed that on one hand, the ϒ(nS)

weak decays are very challenging to be observed experimentally

due to their small branching ratios, on the other hand, any evi-

dences

of an abnormally large production rate of either a single

charmed or bottomed meson might be a hint of new physics be-

yond

the standard model [12].

From

the theoretical point of view, the ϒ(nS) weak decays per-

mit

one to cross check parameters obtained from the B meson

decays, to further explore the underlying dynamical mechanism

of the heavy quark weak decay, to test various theoretical ap-

proaches

and to improve our understanding on the factorization

properties. Phenomenologically, the ϒ(nS) → B

, B

weak

decays are favored by the color factor due to the external W emis-

sion

topological structure, and by the Cabibbo–Kabayashi–Maskawa

(CKM) elements |V

| due to the b →c transition, so usually their

branching ratio should not be too small. In addition, these two de-

cay

modes are the U -spin partners with each other, so the ﬂavor

http://dx.doi.org/10.1016/j.physletb.2015.11.053

0370-2693/

SCOAP

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