Closing in on the radiative weak chiral couplings

Luigi Cappiello; Oscar Catà; Giancarlo D’Ambrosio

doi:10.1140/epjc/s10052-018-5748-6

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2018) 78: 265
https://doi.org/10.1140/epjc/s10052-018-5748-6

Regular Article - Theoretical Physics

Closing in on the radiative weak chiral couplings

Luigi Cappiello¹^,2, Oscar Catà³^* and Giancarlo D’Ambrosio²

¹ Dipartimento di Scienze Fisiche, Universitá di Napoli ‘Federico II’, Via Cintia, 80126, Napoli, Italy
² INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Napoli, Italy
³ Theoretische Physik 1, Universität Siegen, Walter-Flex-Straße 3, 57068, Siegen, Germany

^* e-mail: oscar.cata@uni-siegen.de

Received: 13 February 2018
Accepted: 19 March 2018
Published online: 27 March 2018

Abstract

We point out that, given the current experimental status of radiative kaon decays, a subclass of the $\mathcal{O} (p^4)$ counterterms of the weak chiral lagrangian can be determined in closed form. This involves in a decisive way the decay $K^\pm \rightarrow \pi ^\pm \pi ^0 l^+ l^-$ , currently being measured at CERN by the NA48/2 and NA62 collaborations. We show that consistency with other radiative kaon decay measurements leads to a rather clean prediction for the $\mathcal{{O}}(p^4)$ weak couplings entering this decay mode. This results in a characteristic pattern for the interference Dalitz plot, susceptible to be tested already with the limited statistics available at NA48/2. We also provide the first analysis of $K_S\rightarrow \pi ^+\pi ^-\gamma ^*$ , which will be measured by LHCb and will help reduce (together with the related $$K_L$$ decay) the experimental uncertainty on the radiative weak chiral couplings. A precise experimental determination of the $\mathcal{{O}}(p^4)$ weak couplings is important in order to assess the validity of the existing theoretical models in a conclusive way. We briefly comment on the current theoretical situation and discuss the merits of the different theoretical approaches.