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arXiv 2403.14331hep-phhep-th
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通过非重整化SO(10)模型中的质子衰变约束16_H的标量

Constraining scalars of $16_H$ through proton decays in non-renormalisable $SO(10)$ models

Saurabh K. Shukla

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28 Pages, 1 figure and 3 tables. version 2: References added, Published in Nuclear Physics B
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AI总结：

本文通过计算非重整化SO(10)模型中16_H标量对质子衰变的贡献，发现仅三对标量可在树级诱导质子衰变，并约束了B-L破缺尺度及标量质量范围。

摘要：

基于自由度较少的不可约表示的非重整化版本SO(10)，与具有许多自由度张量的重整化版本相比，不会遇到标准模型规范耦合非微扰性的灾难。16_H是最小的表示，在非重整化层次上参与Yukawa拉氏量，对带电和中性费米子质量有贡献，并且具有六个具有不同B-L电荷的不同标量。我们计算了由16_H与SO(10)的16维费米子多重态耦合所产生的项的所有可能分解中不同标量对的轻子夸克和双夸克耦合，即16 16 16_H 16_H/Λ。计算不同对标量对有效的六维B-L守恒算符的树级和圈级贡献，结果表明只有三对标量，即σ(1,1,0)-T(3,1,1/3)、H(1,2,-1/2)-Δ(3,2,1/6)和H-T，能在树级诱导质子衰变。假设16_H的Yukawa耦合与一个现实SO(10)模型中126_H的Yukawa耦合相当，并将截断尺度设为Planck尺度，通常会将B-L破缺尺度约束为比截断尺度(Λ)低4到5个数量级。此外，分析质子主要两体衰变道的分支模式，我们观察到由于Yukawa耦合的层次性质，质子倾向于衰变成第二代介子。在一个现实的SO(10)情景中，我们发现M_T > 10^8 TeV，而M_Δ可以轻至几个TeV。

英文摘要：

Non-renormalisable versions of $SO(10)$\, based on irreducible representations with lesser degrees of freedom, are free of running into the catastrophe of non-perturbativity of standard model gauge couplings in contrast to the renormalisable versions having tensors with many degrees of freedom. $16_H$ is the smallest representation, participates in Yukawa Lagrangian at the non-renormalisable level, contributing to the charged and neutral fermion masses, and has six distinct scalars with different $B-L$ charges. We computed the leptoquark and diquark couplings of different pairs of scalars stemming from all possible decomposition of the term resulting from the coupling of $16_{H}$ with the ${\mathbf{16}}$ dimensional fermion multiplet of $SO(10)$,\, i.e. $\frac{\mathbf{16}\,{\mathbf{16}}\,16_{H}\,16_{H}}Λ$. Computing the tree and loop level contribution of different pairs to the effective dimension six, $B-L$ conserving operators, it turns out only three pairs, viz $σ\big(1,1,0\big)- T\big(3,1,\frac{1}{3}\big)$, and $H\big(1,2,-\frac{1}{2}\big)-Δ\big(3,2,\frac{1}{6}\big)$, and $H-T$ can induce proton decay at tree level. Assuming that the Yukawa couplings of the $16_{H}$ are comparable to those of the $\overline{126}_{H}$ of a realistic $SO(10)$ model and setting the cutoff scale to the Planck scale typically constrains the $B-L$ breaking scale to be $4\sim 5$ orders of magnitude less than the cutoff scale $(Λ)$. Moreover, analysing the branching pattern of the leading two-body decay modes of the proton, we observed a preference for the proton to decay into second-generation mesons due to the hierarchical nature of Yukawa couplings. In a realistic $SO(10)$\, scenario, we find that $M_T >10^{8}$ TeV, while $M_Δ$ could be as light as a few TeV$s$.

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