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## Chiral perturbation theory

### Author

Céline Degrande

- Université catholique de Louvain
- celine.degrande@…

### Description of the model and references

Most of the processes involving the pseudoscalar mesons happen at scales at which pertubative QCD cannot be trusted anymore. Despite our resulting incapacity to compute their properties directly from the fundamental Lagrangian, the shape of the effective Lagrangian can be inferred using the global approximate chiral symmetry of QCD.

The model describe the strong interaction of the nonet of pseudoscalars at leading order in 1/N and p2. The isospin limit is assumed and the mass matrix of the light quarks is assumed to be real. The Lagrangian contains up to the 6th order in the pseudoscalar meson and the expansion parameters (b and c) are not fixed.

- Annals Phys.128:363,1980: E. Witten,
*Large N Chiral Dynamics.* - Phys.Rev.161:1483-1494,1967: J. A. Cronin,
*Phenomenological model of strong and weak interactions in chiral**U(3) x U(3).* - Phys.Rev.177:2239-2247,1969: S. R. Coleman, J. Wess, B. Zumino,
*Structure of phenomenological Lagrangians. 1.* - Phys.Rev.177:2247-2250,1969: C. G. Callan, S. R. Coleman, J. Wess, B. Zumino,
*Structure of phenomenological Lagrangians. 2.*

### Model File and an example of notebook

### Interfaces

Here is the output file for FeynArts 3.4 for Chiral perturbation theory (ChiPT) : ChiPT.mod

### Validation

The ChiPT model was checked analytically. Namely, the expressions of the amplitudes computed in JHEP05(2009)043 have been compared to the one obtained using FeynRules and FeynArts. Finally, the FeynArts amplitudes have been integrated by cutoff and simplified using the mass relation of the model.

- FromFA.m: Simplification package for ChiPT
- ValidationChiPT.nb: Validation notebook for ChiPT