Abstract
This is the first paper of our systematic efforts on lepton number violating (LNV) hadronic decays in the effective field theory approach. These decays provide information complementary to popular nuclear neutrinoless double-β (0νββ) decay in that they can probe LNV interactions involving heavier quarks and charged leptons. We may call them hadronic 0νββ decays in short, though β refers to all charged leptons. In this work we investigate the decays K±→ π∓l±l± that arise from short-distance or contact interactions involving four quark fields and two charged lepton fields, which have canonical dimension nine (dim-9) at leading order in low energy effective field theory (LEFT). We make a complete analysis on the basis of all dim-9 operators that violate lepton number by two units, and compute their one-loop QCD renormalization effects. We match these effective interactions in LEFT to those in chiral perturbation theory (χPT) for pseudoscalar mesons, and determine the resulting hadronic low energy constants (LECs) by chiral symmetry and lattice results in the literature. The obtained decay rate is general in that all physics at and above the electroweak scale is completely parameterized by the relevant Wilson coefficients in LEFT and hadronic LECs in χPT. Assuming the standard model effective field theory (SMEFT) is the appropriate effective field theory between some new physics scale and the electroweak scale, we match our LEFT results to SMEFT whose leading effective interactions arise from LNV dim-7 operators. This connection to SMEFT simplifies significantly the interaction structures entering in the kaon decays, and we employ the current experimental bounds to set constraints on the relevant Wilson coefficients in SMEFT.
Highlights
Appear in nuclear 0νββ decays, and can at least provide new information on lepton number violation that cannot be extracted from nuclear 0νββ decays
The result obtained is general in the sense that it depends only on the Wilson coefficients of effective interactions in low energy effective field theory (LEFT) based on the QCD and QED gauge symmetries, and on the hadronic low energy constants (LECs) in χPT parameterizing nonperturbative QCD physics
If there are no new particles with a mass at or below the electroweak scale ΛEW ≈ mW, SM serves as a good starting point for an effective field theory, namely, the standard model effective field theory (SMEFT) [29,30,31,32,33,34,35,36,37], between some new physics scale ΛNP and the scale ΛEW
Summary
Low energy effective field theory (LEFT) is an effective field theory for quarks and leptons that respects the QCD and QED gauge symmetries SU(3)C × U(1)EM. The short-distance contribution to the meson decays under consideration originates at leading order in LEFT from dim-9 LNV operators that involve four quark fields and two lepton fields. Our basis of operators shown in table 1 is responsible for all leading-order shortdistance mechanisms of low energy processes that violate lepton number by two units: L|L∆ELF|T=2 =. Where the subscript i covers all indices appearing in the operators These processes include in particular the popular nuclear 0νββ decays and the three- and four-body decays of the charged mesons K, D, Ds, B and the τ lepton. For the decay K− → π+e−μ− with different leptons in the final state, the antisymmetric lepton bilinears in equation (2.3) enter This will bring about a total of 70 dim-9 operators in LEFT, making their matching to χPT much more complicated. We defer its study to a separate work [19] in which we will include the long-distance contribution to the decays
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