{"title":"Oblique corrections when \\(m_W \\ne m_Z \\cos {\\theta _W}\\) at tree level","authors":"Simonas Draukšas, Vytautas Dūdėnas, Luís Lavoura","doi":"10.1007/s12043-024-02771-w","DOIUrl":null,"url":null,"abstract":"<div><p>The parametrization of the oblique corrections through <i>S</i>, <i>T</i>, and <i>U</i> – later extended by <i>V</i>, <i>W</i> and <i>X</i> – 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 <span>\\({SU(2)\\times U(1)}\\)</span> gauge symmetry <i>and</i> the tree-level relation <span>\\(m_W = m_Z \\cos {\\theta _W}\\)</span> between the Weinberg angle and the gauge-boson masses. In models where that relation does not hold at the Lagrangian level, the parameter <i>T</i> is not ultraviolet-finite, making the parametrization inadequate. We present expressions that parametrize the difference of the various predictions of two models with <span>\\(m_W \\ne m_Z \\cos {\\theta _W}\\)</span> in terms of oblique parameters. The parameter <i>T</i> does not play a role in those expressions. Conveniently, they may be reached from the ones that were derived for models with tree-level <span>\\(m_W = m_Z \\cos {\\theta _W}\\)</span>, by performing a simple substitution for <i>T</i>. We also discuss the difficulties in using oblique parameters when comparing a model with <span>\\(m_W \\ne m_Z \\cos {\\theta _W}\\)</span> to the Standard Model. Finally, we compute the relevant five oblique parameters <i>S</i>, <i>U</i>, <i>V</i>, <i>W</i> and <i>X</i> in the SM extended by both, hypercharge <span>\\(Y=0\\)</span> and <span>\\(Y=1\\)</span>, triplet scalars.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s12043-024-02771-w","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
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.