Oblique corrections when $m_W \neq m_Z \cos{θ_W}$ at tree level

Simonas Draukšas; Vytautas Dūdėnas; Luís Lavoura

doi:10.1007/s12043-024-02771-w

paper

Oblique corrections when $m_{W} \neq = m_{Z} cos θ_{W}$ at tree level

arXiv:2305.14050 · doi:10.1007/s12043-024-02771-w

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 $S U (2) \times U (1)$ gauge symmetry \emph{and} the tree-level relation $m_{W} = m_{Z} cos θ_{W}$ 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 $m_{W} \neq = m_{Z} cos θ_{W}$ 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 $m_{W} = m_{Z} cos θ_{W}$ , by performing a simple substitution for $T$ . We also discuss the difficulties in using oblique parameters when comparing a model with $m_{W} \neq = m_{Z} cos θ_{W}$ 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.

arXiv comment38 pages

Oblique corrections when $m_{W} \neq = m_{Z} cos θ_{W}$ at tree level

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Oblique corrections when mW​=mZ​cosθW​ at tree level

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Oblique corrections when $m_{W} \neq = m_{Z} cos θ_{W}$ at tree level