K → μ + μ − as a clean probe of short-distance physics

Avital Dery (Department of Physics, LEPP, Cornell University, Ithaca, NY, 14853, USA) ; Mitrajyoti Ghosh (Department of Physics, LEPP, Cornell University, Ithaca, NY, 14853, USA) ; Yuval Grossman (Department of Physics, LEPP, Cornell University, Ithaca, NY, 14853, USA) ; Stefan Schacht (Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, U.K.)

The K → μ + μ − decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, ℬ(K S → μ + μ − ) ℓ=0 can be experimentally determined without the need to separate the ℓ = 0 and ℓ = 1 final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination V ts V td sin β + β s A 2 λ 5 η ¯ $$ \mid {V}_{ts}{V}_{td}\sin \left(\beta +{\beta}_s\right)\mid \approx \mid {A}^2{\lambda}^5\overline{\eta}\mid $$ with hadronic uncertainties below 1%.

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      "surname": "Grossman", 
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      "surname": "Schacht", 
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      "title": "K \u2192 \u03bc + \u03bc  \u2212  as a clean probe of short-distance physics"
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      "source": "Springer", 
      "value": "The K \u2192 \u03bc + \u03bc  \u2212  decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, \u212c(K  S  \u2192 \u03bc + \u03bc  \u2212 ) \u2113=0 can be experimentally determined without the need to separate the \u2113 = 0 and \u2113 = 1 final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination   <math> <mo>\u2223</mo> <msub> <mi>V</mi> <mi>ts</mi> </msub> <msub> <mi>V</mi> <mi>td</mi> </msub> <mo>sin</mo> <mfenced> <mrow> <mi>\u03b2</mi> <mo>+</mo> <msub> <mi>\u03b2</mi> <mi>s</mi> </msub> </mrow> </mfenced> <mo>\u2223</mo> <mo>\u2248</mo> <mo>\u2223</mo> <msup> <mi>A</mi> <mn>2</mn> </msup> <msup> <mi>\u03bb</mi> <mn>5</mn> </msup> <mover> <mi>\u03b7</mi> <mo>\u00af</mo> </mover> <mo>\u2223</mo> </math>  $$ \\mid {V}_{ts}{V}_{td}\\sin \\left(\\beta +{\\beta}_s\\right)\\mid \\approx \\mid {A}^2{\\lambda}^5\\overline{\\eta}\\mid $$  with hadronic uncertainties below 1%."
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Published on:
15 July 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 7
Pages 1-26
DOI:
https://doi.org/10.1007/JHEP07(2021)103
arXiv:
2104.06427
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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