Leading Chiral Logarithms of $K_S\to \gamma \gamma$ and $K_S\to \gamma l^{+}{l}^{-}$ at two Loops

Abstract

We obtain the leading divergences at two-loop order for the decays $K_S\to \gamma \gamma$ and $K_S\to \gamma {ł}^{+}{ł}^{-}$ using only one-loop diagrams. We then find the double chiral logarithmic corrections to the decay branching ratio of $K_S\to \gamma \gamma$ and to the decay rate for $K_S\to \gamma {ł}^{+}{ł}^{-}$. It turns out that these effects are numerically small and therefore make a very small enhancement on the branching ratio and decay rate. We also derive an expression for the corrections of type $\log \mu \times$ LEC. Numerical analysis done for the process $K_S\to \gamma \gamma$ shows that these single logarithmic effects can be sizable but come with opposite signs with respect to the double chiral logarithms.

v3: more references, typos corrected, version accepted for publication

References in corpus (3)

• Implications of LHCb measurements and future prospects
• The Massive O(N) Non-linear Sigma Model at High Orders
• Standard Model and New Physics contributions to $K_L$ and $K_S$ into four leptons

Cited by in corpus (1)

• Leading logarithms for mesons and nucleons