Oblique corrections when \(m_W \ne m_Z \cos {\theta _W}\) at tree level

IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pramana Pub Date : 2024-07-08 DOI:10.1007/s12043-024-02771-w
Simonas Draukšas, Vytautas Dūdėnas, Luís Lavoura
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Abstract

The parametrization of the oblique corrections through S, T, and U – later extended by V, W and X – is a convenient way of comparing the predictions for various electroweak observables at the one-loop level between the Standard Model and its extensions. That parametrization assumes that the extensions under consideration have \({SU(2)\times U(1)}\) gauge symmetry and the tree-level relation \(m_W = m_Z \cos {\theta _W}\) between the Weinberg angle and the gauge-boson masses. In models where that relation does not hold at the Lagrangian level, the parameter T is not ultraviolet-finite, making the parametrization inadequate. We present expressions that parametrize the difference of the various predictions of two models with \(m_W \ne m_Z \cos {\theta _W}\) in terms of oblique parameters. The parameter T does not play a role in those expressions. Conveniently, they may be reached from the ones that were derived for models with tree-level \(m_W = m_Z \cos {\theta _W}\), by performing a simple substitution for T. We also discuss the difficulties in using oblique parameters when comparing a model with \(m_W \ne m_Z \cos {\theta _W}\) to the Standard Model. Finally, we compute the relevant five oblique parameters S, U, V, W and X in the SM extended by both, hypercharge \(Y=0\) and \(Y=1\), triplet scalars.

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当 $$m_W \ne m_Z \cos {\theta _W}$ 在树级时的斜向修正
通过S、T和U--后来扩展为V、W和X--对斜校正进行参数化,是比较标准模型及其扩展在一回路水平上对各种电弱观测指标的预测的一种方便方法。这种参数化假定所考虑的扩展具有({SU(2)\times U(1)}\)规对称性,以及温伯格角和规玻质量之间的树级关系(m_W = m_Z \cos {\theta _W}\)。在该关系在拉格朗日层面不成立的模型中,参数T不是紫外无限的,使得参数化不充分。我们提出了一些表达式,用斜参数来参数化两个模型的\(m_W \ne m_Z \cos {\theta _W}/)的各种预测的差异。参数 T 在这些表达式中不起作用。我们还讨论了在将\(m_W \ne m_Z \cos {\theta _W}\)模型与标准模型进行比较时使用斜参数的困难。最后,我们计算了由超电荷\(Y=0\)和\(Y=1\)、三重标量扩展的SM中相关的五个斜参数S、U、V、W和X。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Pramana
Pramana 物理-物理:综合
CiteScore
3.60
自引率
7.10%
发文量
206
审稿时长
3 months
期刊介绍: Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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