Custodial symmetry violation in the SMEFT

Graham D. Kribs (Institute for Fundamental Science and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA) ; Xiaochuan Lu (Institute for Fundamental Science and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA) ; Adam Martin (Department of Physics, University of Notre Dame, South Bend, Indiana 46556 USA) ; Tom Tong (Institute for Fundamental Science and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA; Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA)

We investigate precision observables sensitive to custodial-symmetric/-violating UV physics beyond the Standard Model. We use the Standard Model effective field theory (SMEFT) framework which in general includes nonoblique corrections that require a generalization of the Peskin-Takeuchi T parameter to unambiguously detect custodial symmetry/violation. We take a first step towards constructing a SMEFT reparametrization-invariant replacement, which we call 𝒯, valid at least for tree-level custodial-violating contributions. We utilize a new custodial basis of νSMEFT (SMEFT augmented by right-handed neutrinos) which explicitly identifies the global SU(2)R symmetries of the Higgs and fermion sectors, which 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 𝒯 parameter at tree level. We illustrate our results with several UV theory examples, demonstrating that 𝒯 faithfully identifies custodial symmetry violation, while T can fail.

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      "source": "APS", 
      "value": "We investigate precision observables sensitive to custodial-symmetric/-violating UV physics beyond the Standard Model. We use the Standard Model effective field theory (SMEFT) framework which in general includes nonoblique corrections that require a generalization of the Peskin-Takeuchi <math><mi>T</mi></math> parameter to unambiguously detect custodial symmetry/violation. We take a first step towards constructing a SMEFT reparametrization-invariant replacement, which we call <math><mi>\ud835\udcaf</mi></math>, valid at least for tree-level custodial-violating contributions. We utilize a new custodial basis of <math><mrow><mi>\u03bd</mi><mi>SMEFT</mi></mrow></math> (SMEFT augmented by right-handed neutrinos) which explicitly identifies the global <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>R</mi></msub></math> symmetries of the Higgs and fermion sectors, which 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 <math><mi>\ud835\udcaf</mi></math> parameter at tree level. We illustrate our results with several UV theory examples, demonstrating that <math><mi>\ud835\udcaf</mi></math> faithfully identifies custodial symmetry violation, while <math><mi>T</mi></math> can fail."
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Published on:
07 September 2021
Publisher:
APS
Published in:
Physical Review D , Volume 104 (2021)
Issue 5
DOI:
https://doi.org/10.1103/PhysRevD.104.056006
arXiv:
2009.10725
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: