Universite Clermont Auvergne

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Field theory

The Theory Pole is active in two different topics, field theory on the light front and finite field theories based for instance on the recently proposed Taylor-Lagrange renormalization scheme.

Light front quantization can be used to solve relativistic QFTs, and study composite systems using Hamiltonian formalism. In this formalism, the evolution of the system is parametrised in terms of the light-front time \tau= t + z/c.

The state vector describing any bound state system is thus decomposed in Fock components, and physical observables can be calculated in a non-perturbative way order-by-order in the truncation of the Fock expansion. These components correspond to states with a well-defined number of particles at a given light-front time. In this form of dynamics, the N-body Fock components are boost-invariant, contrary to the standard formulation at constant ordinary time.

Among the most relevant results obtained regarding field theory on the light front, we have applied a successful covariant formulation of light front dynamics, allowing the control of the otherwise explicit violation of rotational invariance. Furthermore, a non-perturbative renormalization scheme was also developed to ensure that all divergences are renormalised at each step of the Fock truncation. As a concrete physical example, the calculation of the anomalous magnetic moment of a spin ½ fermion in the Yukawa model, taking into account 2- and 3-body contributions, has been done in 3+1 dimensions.

The motivation for Finite Field Theories is deeply related to the need to address the true origin of the divergences emerging in field theory, rather than dealing and overcoming their consequences. As it is already well known, but rarely taken into account in any practical calculation, quantum fields must be correctly treated as distributions acting on test functions with specific mathematical properties. True physical scales can thus be separated from spurious mathematical ones in order to analyse from a physical point of view all experimental results available. This is of particular interest in the present search for new physics at high energies. A study of the physical interpretation and applicability of the Taylor-Lagrange renormalization to light-front field theory has allowed verifying that this scheme is particularly suited for non-perturbative calculations, contrary to most of the “standard” regularization and renormalization schemes. The Taylor-Lagrange scheme has been also applied to the perturbative computation of the radiative corrections to the Higgs boson mass, suggesting that the fine-tuning arising in the “standard” computation might be an artefact of the chosen regularisation scheme.

The renormalization group equations arising in the Taylor-Lagrange scheme appear to have a similar structure to those arising in the DR+\bar{MS} scheme, albeit with an explicit mass dependence. Understanding these differences and physical consequences will be the next step in these studies.

Recent publications :

  • J.-F. Mathiot, "The renormalization group equations revisited", Int.J.Mod.Phys. A33 (2018) no.26, 1830024 [arXiv:1810.04933 [hep-th]]
  • O. Leitner, J.-F. Mathiot and N. A. Tsirova,“The Pion wave function in covariant light-front dynamics”, Eur. Phys. J. A 47 (2011) 17 [arXiv:1009.5484 [hep-ph]].
  • J.-F. Mathiot and N. A. Tsirova, “Light-front chiral effective field theory”, Phys. Atom. Nucl. 76 (2013) 1387.
  • N. A. Tsirova, V. A. Karmanov and J.-F. Mathiot, ”Chiral effective field theory on the light front in the nucleon sector”, Phys. Atom. Nucl. 73 (2010)1952.
  • J.-F. Mathiot, A. V. Smirnov, N. A. Tsirova and V. A. Karmanov, “Nonperturbative renormalization in light-front dynamics and applications”, Few Body Syst. 49 (2011) 183 [arXiv:1009.5269 [hep-th]].
  • V. A. Karmanov, J.-F. Mathiot and A. V. Smirnov, “Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space”, Phys. Rev. D 82 (2010) 056010 [arXiv:1006.5640 [hep-th]].
  • V. A. Karmanov, J.-F. Mathiot and A. V. Smirnov,” Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model”, Phys. Rev. D 86 (2012) 085006 [arXiv:1204.3257 [hep-th]].
  • P. Grangé, J.-F. Mathiot, B. Mutet and E. Werner, “Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics”, Phys. Rev. D 82 (2010) 025012 [arXiv:1006.5282 [hep-th]].
  • P. Grangé, J.-F. Mathiot, B. Mutet and E. Werner, “Aspects of fine-tuning of the Higgs mass within finite field theories”, Phys. Rev. D 88 (2013) 125015 [arXiv:1312.5278 [hep-ph]].