小S-D波混合增强重夸克自旋对称性破坏：ϒ(10860)衰变比率的理论预测

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本文主要探讨了"增强重夸克自旋对称性的破坏"这一主题，它在量子色动力学（QCD）的框架下具有重要意义。重夸克自旋对称性是一种假设，它预测了包含重夸克系统的衰变比率或生产率时，具有一定的对称性。然而，这种对称性实际上并不完美，因为存在着自然的破缺，通常表现在自旋对称性破坏的大小上，约为QCD尺度因子ΛQCD与重夸克质量mQ的比值O(ΛQCD/mQ)。研究者们注意到，特别是在高能物理实验中，如Belle Collaboration最近观测到的ϒ(10860)衰变为χbJω的过程，这些衰变显示出显著的自旋对称性破坏。ϒ(10860)被认为是一个主要由5S态构成的纯态，但实测结果却显示其衰变宽度的比值与理论预期的自旋对称性明显不符。这提示可能存在一种新的机制，即S波和D波成分在ϒ(10860)的波函数中的混合可能起着关键作用。文章作者 Feng-Kun Guo、Ulf-G. Meißner 和 Cheng-Ping Shen 探索了这个现象，他们提出，如果D波成分的衰减受到耦合通道效应的影响，那么可以预测ϒ(10860)衰变为χb0ω和χb2ω的比率Γ(ϒ(10860)→χb0ω)/Γ(ϒ(10860)→χb2ω)可能会有所不同。他们的研究不仅挑战了传统的自旋对称性理论，也为理解重夸克系统的行为提供了新的见解。通过实验数据的比较和理论分析，该论文旨在深化我们对重夸克系统动态的理解，并为未来更精确的实验测量提供理论指导。这篇工作发表在《物理学 letters B》杂志上，是开放获取的，便于学术界进一步讨论和验证。研究历史显示，论文于2014年6月30日首次接收，经过修订后于同年9月19日接受，最终于9月26日在线发布。编辑A. Ringwald对本文进行了审阅。

Physics Letters B 738 (2014) 172–177

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Enhanced breaking of heavy quark spin symmetry

Feng-Kun Guo

a,∗

, Ulf-G. Meißner

a,b

, Cheng-Ping Shen

Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany

Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany

School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China

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

Article history:

Received

30 June 2014

Received

in revised form 16 July 2014

Accepted

19 September 2014

Available

online 26 September 2014

Editor: A.

Ringwald

Heavy quark spin symmetry is useful to make predictions on ratios of decay or production rates of

systems involving heavy quarks. The breaking of spin symmetry is generally of the order of O (Λ

QCD

with Λ

QCD

the scale of QCD and m

the heavy quark mass. In this paper, we will show that a small

S-and D-wave mixing in the wave function of the heavy quarkonium could induce a large breaking

in the ratios of partial decay widths. As an example, we consider the decays of the Υ(10 860) into the

ω ( J =0, 1, 2), which were recently measured by the Belle Collaboration. These decays exhibit a huge

breaking of the spin symmetry relation were the Υ(10 860) a pure 5S bottomonium state. We propose

that this could be a consequence of a mixing of the S-wave and D-wave components in the Υ(10 860).

Prediction on the ratio Γ(Υ(10 860) → χ

ω)/Γ (Υ (10 860) → χ

ω) is presented assuming that the

decay of the D-wave component is dominated by the coupled-channel effects.

(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP

A heavy quarkonium is a system consisting of a heavy quark

and a heavy antiquark. The ground states and low-lying excited

states below the open-ﬂavor thresholds were well described in

terms of potential quark models, e.g., the Godfrey–Isgur quark

model [1], while the higher excited states are more complicated.

The complexity comes from, e.g., the nearby strongly coupled

thresholds, the existence of many new quarkonium-like states dis-

covered

in the last decade and so on. Because the heavy quark

mass m

is much larger than the scale of quantum chromodynam-

ics

(QCD), Λ

QCD

, the amplitude of changing the spin orientation

of a heavy quark by interacting with soft gluons is small, sup-

pressed

by O(Λ

QCD

) relative to the spin-conserving case [2].

The resulting heavy quark spin symmetry (HQSS) [3] can lead

to important observable consequences. On the one hand, heavy

quarkonium states are organized into spin multiplets; on the other

hand, the decay or production rate involving one heavy quarko-

nium

can often be related to the one of its spin partners in the

leading approximation. Breaking of HQSS is typically of the order

of O(Λ

QCD

) or even higher. In this paper, we will argue that

the HQSS breaking could be much larger in certain processes. To

be speciﬁc, we will show that a small mixing of S- and D-wave

Corresponding author.

E-mail

addresses: fkguo@hiskp.uni-bonn.de (F.-K. Guo),

meissner@hiskp.uni-bonn.de (U.-G. Meißner), shencp@ihep.ac.cn (C.-P. Shen).

heavy quarkonia could result in a signiﬁcant breaking of the spin

symmetry relations when the decay amplitude of the D-wave com-

ponent

is enhanced. As an example, we will calculate the processes

Υ(10 860) → χ

ω ( J = 0, 1, 2). Measurements for these transi-

tions

were done by the Belle Collaboration very recently, and the

results for the branching fractions are [4]



Υ(

10 860) → χ



3.9 ×10

−3



Υ(

10 860) → χ



1.57 ±0.22

stat.

±0.21

sys.

) ×10

−3



Υ(

10 860) → χ



0.60 ±0.23

stat.

±0.15

sys.

) ×10

−3

. (1)

One sees that the branching fraction for the χ

ω mode is larger

than that for the χ

ω. Comparing the HQSS prediction on the

ratio B(Υ (5S) → χ

ω)/B(Υ (5S) → χ

ω) = 0.63 assuming the

Υ(10 860) to be the 5S bottomonium state, see Eq. (6) below, with

the observed value 2.62 ± 1.30, the breaking is more than 100%.

This is a very large spin symmetry breaking. As we will show later,

a small mixture of a D-wave

bb component in the Υ(10 860) is

able to cause the ratios of Γ(Υ(10 860) → χ

ω) to be very dif-

ferent

from the spin symmetry relations as observed.

Consequences

of HQSS can be easily analyzed using heavy me-

son

effective ﬁeld theory (for a review, see Ref. [5]). Let us take the

transitions from a vector heavy quarkonium into the χ

ω as an

example, where χ

is a P -wave heavy quarkonium with quantum

http://dx.doi.org/10.1016/j.physletb.2014.09.043

0370-2693/

SCOAP

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