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arXiv 2302.03051hep-phhep-exhep-lat
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$Z^\prime$模型中FCNC在单圈水平上的自然抑制及其对K、D和B衰变的影响

Natural Suppression of FCNCs at the One-Loop Level in $Z^\prime$ Models with Implications for K, D and B Decays

Andrzej J. Buras

摘要:

我们分析$Z^\prime$的贡献,FCNC过程中的一个循环的水平。类似于CKM矩阵,我们引入了两个$3\times3$酉矩阵$\hatΔ_d(Z^\prime)$和$\hatΔ_u(Z^\prime)$,它们也是厄米特的。由于$\text{SU(2)}_L$规范对称性未破缺,它们分别控制了下夸克和上夸克之间由$Z^\prime$介导的味相互作用,其中$\hatΔ_d(Z^\prime)=\hatΔ_u(Z^\prime)\equiv \hatΔ_L(Z^\prime)$用于左手电流。这确保了在单环水平抑制这些对所有$Z^\prime$介导的FCNC过程的贡献。与GIM机制相反,$Z^\prime$对$K$和$B_{s,d}$系统中味观测量的贡献由下夸克质量决定,它们是${\cal O}(m^2_b/M^2_{Z^\prime})$并且可以忽略。在${\cal O}(m^2_t/M^2_{Z^\prime})$抑制的情况下,它们在$D$系统中可能也可以忽略不计。我们提出了一个明确的参数化的$\hatΔ_L(Z^\prime)$在两个混合角和两个复杂的阶段,区别于CKM矩阵深刻。有趣的是,在前两代和第三代之间,夸克和轻子与$Z^\prime$的耦合的味普适性的破裂被认为是$\hatΔ_L(Z^\prime)$是厄米的结果。强调了在Cabibbo异常光中$\hatΔ_L(Z^\prime)$和CKM矩阵的么正性的重要性。

英文摘要:

We analyse $Z^\prime$ contributions to FCNC processes at the one-loop level. In analogy to the CKM matrix we introduce two $3\times3$ unitary matrices $\hatΔ_d(Z^\prime)$ and $\hatΔ_u(Z^\prime)$ which are also hermitian. They govern the flavour interactions mediated by $Z^\prime$ between down-quarks and up-quarks, respectively, with $\hatΔ_d(Z^\prime)=\hatΔ_u(Z^\prime)\equiv \hatΔ_L(Z^\prime)$ for left-handed currents due to the unbroken $\text{SU(2)}_L$ gauge symmetry. This assures the suppression of these contributions to all $Z^\prime$ mediated FCNC processes at the one-loop level. As, in contrast to the GIM mechanism, one-loop $Z^\prime$ contributions to flavour observables in $K$ and $B_{s,d}$ systems are governed by down-quark masses, they are ${\cal O}(m^2_b/M^2_{Z^\prime})$ and negligible. With the ${\cal O}(m^2_t/M^2_{Z^\prime})$ suppression they are likely negligible also in the $D$ system. We present an explicit parametrization of $\hatΔ_L(Z^\prime)$ in terms of two mixing angles and two complex phases that distinguishes it profoundly from the CKM matrix. This framework can be generalized to purely leptonic decays with matrices analogous to the PMNS matrix but profoundly different from it. Interestingly, the breakdown of flavour universality between the first two generations and the third one, both for quark and lepton couplings to $Z^\prime$, is identified as a consequence of $\hatΔ_L(Z^\prime)$ being hermitian. The importance of the unitarity for both $\hatΔ_L(Z^\prime)$ and the CKM matrix in the light of the Cabibbo anomaly is emphasized.

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