Abstract
We investigate precision observables sensitive to custodial symmetric/violating UV physics beyond the Standard Model. We use the SMEFT framework which in general includes non-oblique corrections that requires a generalization of the Peskin-Takeuchi $T$ parameter to unambiguously detect custodial symmetry/violation. We take a first step towards constructing a SMEFT reparameterization-invariant replacement, that we call $\mathscr{T}$, valid at least for tree-level custodial violating contributions. We utilize a new custodial basis of $\nu$SMEFT (SMEFT augmented by right-handed neutrinos) which explicitly identifies the global $SU(2)_R$ symmetries of the Higgs and fermion sectors, that in turn permits easy identification of higher-dimensional operators that are custodial preserving or violating. We carefully consider equation-of-motion redundancies that cause custodial symmetric operators in one basis to be equivalent to a set of custodial symmetric and/or violating operators in another basis. Utilizing known results about tree/loop operator generation, we demonstrate that the basis-dependent appearance of custodial-violating operators does not invalidate our $\mathscr{T}$ parameter at tree-level. We illustrate our results with several UV theory examples, demonstrating that $\mathscr{T}$ faithfully identifies custodial symmetry violation, while $T$ can fail.
Highlights
It is widely anticipated that there is new physics beyond the Standard Model (SM)
We show that T l can be constructed from Z-pole observables and mW, faithfully determining at tree level if the UV sector contains “hard” custodial violation, independent of whether the UV sector contributes only obliquely
From known results about tree/loop operator generation [47,48,49], we find that restricting to treelevel-generated operators, our set of observables, and our T l parameter, remain faithful in identifying hard custodial violation of UV physics
Summary
It is widely anticipated that there is new physics beyond the Standard Model (SM). In the absence of directly producing the new particles of the beyond-the-SM (BSM) sector, we would like to maximize the information we can glean about the UV physics from indirect probes. In the SMEFT framework, one works with effective operators whose constituents have manifest transformation properties under the global SUð2ÞR symmetries in the SM Higgs and/or fermion sectors In this sense, the Wilson coefficients are superior to the S, T, U parameters, as they can directly indicate SUð2ÞR symmetries or their violation. From known results about tree/loop operator generation [47,48,49], we find that restricting to treelevel-generated operators, our set of observables, and our T l parameter, remain faithful in identifying hard custodial violation of UV physics This is the main result of this paper.
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