[论文解读] Addressing the strong CP problem with quark mass ratios

J. Lorenzo Díaz-Cruz, U. J. Saldaña-Salazar+1 more|arXiv (Cornell University)|May 12, 2016

Particle physics theoretical and experimental studies参考文献 45被引用 4

一句话总结

本文主张，在对夸克质量（Yukawa）矩阵结构作出最小假设的前提下，标准模型中并不存在强CP问题。通过分析使这些矩阵对角化的双酉变换，作者表明强相互作用中的CP破坏被自然抑制，从而无需引入如轴子或新对称性等新物理。

ABSTRACT

The strong CP problem is one of many puzzles in the theoretical description of elementary particles physics that still lacks an explanation. Solutions to that problem usually comprise new symmetries or fields or both. The main problem seems to be how to achieve small CP in the strong interactions despite large CP violation in weak interactions. Observation of CP violation is exclusively through the Higgs–Yukawa interactions. In this letter, we show that with minimal assumptions on the structure of mass (Yukawa) matrices the strong CP problem does not exist in the Standard Model and no extension to solve this is needed. However, to solve the flavor puzzle, models based on minimal SU(3) flavor groups leading to the proposed flavor matrices are favored. [e-mail] [e-mail] [e-mail] Introduction.—Problems are the nourishment of theoretical physics. Besides several other problems that still wait to be finally solved, the strong CP problem seems to be one of the simplest to be elucidated. The problem itself resides in the interplay of non-perturbative effects in Quantum Chromodynamics (QCD) and CP violation (CPV) in weak interactions (basically the Higgs–Yukawa sector in the Standard Model). Curiously, the majority of present day solutions to many of the problems in high energy physics obey the tendency of always going beyond the Standard Model (SM); the strong CP problem seems to share the same tendency. However, here we follow a different philosophy and carefully scrutinize the structure of the SM, offering an alternative solution to the strong CP problem. Our point of view might be defined as pragmatic as we only study the mass matrices along with the bi-unitary transformations diagonalizing them. Now, before moving to the details of our treatment let us first briefly discuss what the strong CP problem is. A comprehensive review of this problem can be found e. g. in [1] and similar references. The θ parameter of QCD parametrizes the non-equivalence of possible QCD vacua as for non-abelian gauge fields there can be non-vanishing winding numbers defined as

研究动机与目标

• 挑战主流观点，即强CP问题必然需要标准模型之外的新物理。
• 研究QCD中观测到的CP破坏缺失是否可由Yukawa矩阵的内在结构解释。
• 确定对夸克质量的味结构作出最小假设时，是否能自然抑制强CP参数θ。
• 评估味谜题与强CP问题是否相互关联，并可在最小SU(3)味对称性框架内同时解决。

提出的方法

• 分析在使夸克质量矩阵对角化的双酉变换下，夸克质量矩阵的结构。
• 对Yukawa矩阵的形式施加最小假设，以约束强相互作用中可能存在的CP破坏相位。
• 将Higgs–Yukawa相互作用作为CP破坏的唯一来源，与实验观测一致。
• 通过追踪夸克质量矩阵对角化过程中的CP奇数贡献，评估QCD中的有效θ参数。
• 假设存在最小SU(3)味群结构，以解释观测到的夸克质量和混合模式。
• 证明QCD拉格朗日量中产生的CP破坏相位自然地小至10^-10或更小，与实验限制一致。

实验结果

研究问题

• RQ1 是否仅通过标准模型Yukawa矩阵的结构，而无需引入新对称性或新场，即可解决强CP问题？
• RQ2 Higgs–Yukawa作用在生成CP破坏中扮演什么角色，它如何影响QCD的θ参数？
• RQ3 QCD强CP参数的观测极小值是否自然地源于夸克质量矩阵结构？
• RQ4 基于最小SU(3)味对称性的模型能否同时解释味谜题和QCD中CP破坏的缺失？
• RQ5 弱相互作用中观测到的CP破坏是否足以解释QCD θ参数的极小性？

主要发现

• 在对夸克质量矩阵结构作出最小假设的前提下，标准模型中并不存在强CP问题。
• 当Yukawa矩阵受最小味结构约束时，QCD中的有效θ参数自然被抑制至10^-10以下。
• 强相互作用中的CP破坏仅通过夸克质量与混合角的相互作用产生，而这些参数已由观测到的味结构所固定。
• 解决强CP问题无需引入新物理——如轴子或新的全局对称性。
• 基于最小SU(3)味群的模型提供了一个一致的框架，可同时解决味谜题与强CP问题。
• 通过Higgs–Yukawa作用在弱相互作用中观测到的CP破坏，不足以通过质量矩阵的特定结构在QCD中产生大CP破坏。