Generalized positivity bounds on chiral perturbation theory
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Springer
Received: April 19, Revised: June 22, Accepted: July 6, Published: July 29,
2020 2020 2020 2020
Yu-Jia Wang,a,b Feng-Kun Guo,c,d Cen Zhange,d and Shuang-Yong Zhoua,b a
Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026, China b Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China c CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China d School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China e Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Recently, a new set of positivity bounds with t derivatives have been discovered. We explore the generic features of these generalized positivity bounds with loop amplitudes and apply these bounds to constrain the parameters in chiral perturbation theory up to the next-to-next-to-leading order. We show that the generalized positivity bounds give rise to stronger constraints on the ¯li constants, compared to the existing axiomatic bounds. The parameter space of the bi constants is constrained by the generalized positivity bounds to be a convex region that is enclosed for many sections of the total space. We also show that the improved version of these positivity bounds can further enhance the constraints on the parameters. The often used Pad´e unitarization method however does not improve the analyticity of the amplitudes in the chiral perturbation theory at low energies. Keywords: Chiral Lagrangians, Effective Field Theories ArXiv ePrint: 2004.03992
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)214
JHEP07(2020)214
Generalized positivity bounds on chiral perturbation theory
Contents 1
2 Chiral perturbation theory
3
3 Generalized positivity bounds 3.1 The Y bounds 3.2 The improved Y bounds
5 5 6
4 Y bounds on ChPT 4.1 Structure of the bounds 4.2 Bounds on ¯l1 and ¯l2 4.3 Bounds on the bi constants
7 7 9 12
5 Improved Y bounds on ChPT 5.1 Structure of the bounds 5.2 Bounds on ¯l1 and ¯l2 5.3 Bounds on the bi constants 5.4 Pad´e approximation
14 14 17 19 19
6 Summary
22
A Loop functions and bi constants
23
B 3D sections of the constrained bi space
25
1
Introduction
Chiral perturbation theory (ChPT) is one of the oldest and most widely studied effective field theories (EFTs) [1–7]. It is the low energy description of quantum chromodynamics (QCD), which is perturbative at high energies but strongly coupled at low energies, giving rise to the vast richness of hadron physics. The essential feature of the theory is that a chiral symmetry group, a product of two groups of the same structure, is spontaneously (and often mildly explicitly) broken down to the diagonal subgroup, which generates a nonlinear realization of the chiral symmetry. The structure of ChPT thus is largely determ
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