A new theory framework for the electroweak radiative corrections in K l3 decays
- PDF / 999,744 Bytes
- 31 Pages / 595.276 x 841.89 pts (A4) Page_size
- 17 Downloads / 149 Views
Springer
Received: November 12, Revised: January 6, Accepted: January 27, Published: February 11,
2019 2020 2020 2020
Chien-Yeah Seng,a Daniel Galviza and Ulf-G. Meißnera,b,c a
Helmholtz-Institut f¨ ur Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universit¨ at Bonn, 53115 Bonn, Germany b Institute for Advanced Simulation, Institut f¨ ur Kernphysik and J¨ ulich Center for Hadron Physics, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany c Tbilisi State University, 0186 Tbilisi, Georgia
E-mail: [email protected], [email protected], [email protected] Abstract: We propose a new theory framework to study the electroweak radiative corrections in Kl3 decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important O(GF α) radiative corrections are described by a single tensor T µν involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special 0 channel that it suffers the least impact from the poorly-constrained advantage in the Kl3 low-energy constants. This finding may serve as a basis for a more precise extraction of the matrix element Vus in the future. Keywords: Chiral Lagrangians, Kaon Physics, Precision QED ArXiv ePrint: 1910.13208
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP02(2020)069
JHEP02(2020)069
A new theory framework for the electroweak radiative corrections in Kl3 decays
Contents 1 Introduction
1
2 Kl3 decay at tree level
4
3 General formalism for radiative corrections in semi-leptonic beta decays, and its application to Kl3 6
9
5 On-mass-shell formula, Ward identity, and current algebra
13
6 Obtaining the large-logs and comparing with the pure EFT language
16
7 Diagrammatic approach to the three-point function
18
8 Two-point and three-point functions of Kπ form factors at O(e2 p2 )
21
9 Conclusions
24
A Extra loop functions
25
B An explicit example of the calculation of two- and three-point functions 26
1
Introduction
One of the high-precision tests of the Standard Model (SM) is the test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix [1, 2]. In particular, its first-row matrix elements are required to satisfy the following relation: ∆CKM = |Vud |2 + |Vus |2 + |Vub |2 − 1 = 0.
(1.1)
The contribution from Vub is negligible, so the test only concerns |Vud | and |Vus |. The quoted values of these two matrix elements in the “CKM quark-mixing matrix” section of the 2018 Particle Data Group (PDG) read [3]: |Vud | = 0.97420(21), |Vus | = 0.2243(5).
(1.2)
With the numbers above, the deviation from the unitarity reads: ∆ CKM =−0.0006(5), so unitarity requirement is well-satisfied, and it turns into stringent bounds on parameters of
–1–
JHEP02(2020)069
4 ChPT calculation of the electromagnetic radiative corrections to the Kπ form factors
and ∆CKM = −0.0
Data Loading...
