QCD方法下的D→ππ与D→KK CP不对称性计算

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本文主要探讨了基于量子色动力学（Quantum Chromodynamics, QCD）的方法在计算 charm (D) 衰变为 pion-pion (π-π+) 和 kaon-kaon (K-K+) 的非轻子衰变过程中直接CP违反（Direct CP Asymmetry）的不对称性。QCD 视锥规则和轻锥积分规则被应用于计算强子矩阵元素，这是一种创新性的计算策略，它避免了依赖于模型激发的幅度分解，而是直接利用夸克-强子对偶这一物理原理。 QCD 是描述强相互作用的理论，特别是对于强子内部夸克的相互作用。在这个研究中，作者亚历山大·霍德贾米里安和阿列克谢·A·彼得罗夫提出了一种基于QCD的第一手计算方法，这种方法强调了在理解这些衰变过程中的CP违反现象时，不依赖于特定模型假设的重要性。直接CP违反是指在基本粒子衰变过程中，如果弱相互作用不遵守CP对称性，即粒子与其反粒子的衰变概率不相等，就会观察到这种不对称性。论文中，作者对D0介子衰变为π-π+和K-K+的过程进行了深入分析，通过企鹅图（Penguin Diagrams）这一特定的QCD拓扑结构来确定CP违反的来源。企鹅图在粒子物理学中指的是某些涉及W玻色子交换的高阶弱相互作用过程，它们在CP违反机制中起着重要作用。作者提供的是标准模型下的估计值，这些估计是通过对QCD基本原理的计算得出的，而不是通过实验数据拟合得到的模型参数。此外，文章还讨论了目前计算的局限性和可能的改进方向，这表明研究者们正在努力提高理论精度，以便更好地理解和预测CP违反现象在D介子衰变中的表现。这种QCD基础的计算方法为未来的实验测量提供了理论支持，也为深入探索CP违反、夸克动力学和粒子物理学的其他未解问题提供了新的计算工具。这篇论文不仅展示了QCD在描述CP违反物理现象中的应用，而且标志着理论物理学家在探索强相互作用中的一个关键步骤，为未来在实验上验证这些理论预测以及进一步测试标准模型奠定了基础。

Physics Letters B 774 (2017) 235–242

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Direct CP asymmetry in D → π

−

and D → K

−

in QCD-based

approach

Alexander Khodjamirian

, Alexey A. Petrov

a,b,c,∗

Theoretische Physik 1, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, D-57068 Siegen, Germany

Department of Physics and Astronomy, Wayne State University, Detroit, MI 48201, USA

Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48196, USA

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

Article history:

Received

19 July 2017

Received

in revised form 12 September

2017

Accepted

25 September 2017

Available

online 28 September 2017

Editor: B. Grinstein

We present the ﬁrst QCD-based calculation of hadronic matrix elements with penguin topology

determining direct CP-violating asymmetries in D

→ π

−

and D

→ K

−

nonleptonic decays. The

method is based on the QCD light-cone sum rules and does not rely on any model-inspired amplitude

decomposition, instead leaning heavily on quark–hadron duality. We provide a Standard Model estimate

of the direct CP-violating asymmetries in both pion and kaon modes and their difference and comment

on further improvements of the presented computation.

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

1. Introduction

Despite years of intense experimental efforts, CP-violation has

never been unambiguously observed in the decays of up-type

quarks. In the Standard Model (SM) this fact can be explained

by the suppression of all CP-violating amplitudes resulting from

the smallness of relevant Cabibbo–Kobayashi–Maskawa (CKM) ma-

trix

elements. To make matters worst, accurate predictions of up-

type

CP-violating observables are hard to obtain, since the nec-

essary

hadronic matrix elements are dominated by long-distance

contributions. In order to calculate these matrix elements one

needs to employ a QCD-based method that deals with nonpertur-

bative

effects in a model-independent manner. In this letter we

shall calculate CP-violating observables in exclusive singly Cabibbo-

suppressed

(SCS) decays of D-mesons using a variant of light-cone

QCD sum rules (LCSRs).

Observables

that are sensitive to CP-violation are most often

written in terms of asymmetries [1],

( f ) =

(D → f ) − (D → f )

(D → f ) + (D → f )

(1)

formed from the partial rates of a D-meson decay to a ﬁnal state

f and of its CP-conjugated counterpart. Depending on the initial

state, the asymmetry in Eq. (1) could be a function of time, if

-mixing is taken into account.

Corresponding author.

E-mail

address: apetrov@wayne.edu (A.A. Petrov).

The measured time-integrated asymmetry contains a direct

component

(see, e.g., [2]), which will be the main focus of this pa-

per.

Direct CP asymmetry occurs when the absolute values of the

D → f decay amplitude, which we denote by A

≡ A(D → f ), and

of the corresponding CP-conjugated amplitude A

≡ A(D → f ) are

different. This can be realized if the decay amplitude A

can be

separated into at least two different parts,

= A

(1)

iδ

iφ

+ A

(2)

iδ

iφ

, (2)

where φ

= φ

are the weak phases (odd under CP), and δ

= δ

are the strong phases (even under CP). The CP-violating asymme-

try

is then given by

dir

( f ) ∝

(1)

(2)

sin(δ

−δ

) sin(φ

−φ

). (3)

The amplitude pattern of Eq. (2) naturally emerges in the SCS non-

leptonic

decays such as D

→ K

−

and D

→ π

−

model-independent computation of the amplitude ratio and

the strong phase difference in Eq. (3) is a daunting task in charm

physics (for reviews see e.g., [3]). In SM, the sizes of direct CP-

violating

asymmetries for any ﬁnal state are always proportional

to a small combination of the CKM factors V

∗

, which ensures

that a

dir

( f ) is small even if the maximal strong phase difference

is assumed. Hence, if a larger value of CP-violating asymmetry is

observed, it would provide a “smoking gun” signal of new physics

in the charm sector of quark–ﬂavor transitions. However, due to a

very uncertain hadronic input, the available estimates of a

dir

( f )

https://doi.org/10.1016/j.physletb.2017.09.070

0370-2693/

SCOAP

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