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Renormalizable and unitary nonlocal quantum field theory with CPT violation and its implication

Moshe M. Chaichian, Markku A. Oksanen, Anca Tureanu

TL;DR

This work challenges the prevailing view that relativistic nonlocal QFTs cannot be simultaneously renormalizable and unitary by presenting a Lorentz-invariant, CPT-violating nonlocal model with a nonlocal fermion mass term and a nonlocal Yukawa interaction. Using a causality-preserving kernel $F(x,y)$ and Schwinger’s action principle for quantization, the authors show that the UV behavior at one loop matches the local theory and that perturbative unitarity holds, even with CPT violation. They demonstrate that nonlocal contributions vanish at high energies, preserving standard unitarity bounds, and discuss mass splitting between particles and antiparticles through a CP-violating, gauge-generalizable framework with potential implications for baryogenesis. The results open a path to extending the Standard Model with CPT-violating nonlocal interactions and CP-violating phases, potentially contributing to explanations of baryon asymmetry; further work is needed to realize gauge theories and baryon-number-violating mechanisms within this framework.

Abstract

It is a common belief that any relativistic nonlocal quantum field theory encounters either the problem of renormalizability or unitarity or both of them. It is also known that any local relativistic quantum field theory (QFT) possesses the CPT symmetry. In this Letter we show that a previously proposed nonlocal Lorentz invariant QFT, which violates the CPT theorem, is both renormalizable and unitary, thus being a first presented example in the literature of such a nonlocal theory. The theory satisfies the requirement of causality as well. A further generalization of such a nonlocal QFT to include the gauge theories is also envisaged. In particular, dressing such a Standard Model with a CP violating phase, will make the theory satisfying most of the necessary criteria to finally explain the baryon asymmetry of the universe by a viable QFT. As for the necessity of baryon number violation, there are hopefully several possibilities such as by GUT and electroweak baryogenesis, leptogenesis or sphalerons.

Renormalizable and unitary nonlocal quantum field theory with CPT violation and its implication

TL;DR

This work challenges the prevailing view that relativistic nonlocal QFTs cannot be simultaneously renormalizable and unitary by presenting a Lorentz-invariant, CPT-violating nonlocal model with a nonlocal fermion mass term and a nonlocal Yukawa interaction. Using a causality-preserving kernel and Schwinger’s action principle for quantization, the authors show that the UV behavior at one loop matches the local theory and that perturbative unitarity holds, even with CPT violation. They demonstrate that nonlocal contributions vanish at high energies, preserving standard unitarity bounds, and discuss mass splitting between particles and antiparticles through a CP-violating, gauge-generalizable framework with potential implications for baryogenesis. The results open a path to extending the Standard Model with CPT-violating nonlocal interactions and CP-violating phases, potentially contributing to explanations of baryon asymmetry; further work is needed to realize gauge theories and baryon-number-violating mechanisms within this framework.

Abstract

It is a common belief that any relativistic nonlocal quantum field theory encounters either the problem of renormalizability or unitarity or both of them. It is also known that any local relativistic quantum field theory (QFT) possesses the CPT symmetry. In this Letter we show that a previously proposed nonlocal Lorentz invariant QFT, which violates the CPT theorem, is both renormalizable and unitary, thus being a first presented example in the literature of such a nonlocal theory. The theory satisfies the requirement of causality as well. A further generalization of such a nonlocal QFT to include the gauge theories is also envisaged. In particular, dressing such a Standard Model with a CP violating phase, will make the theory satisfying most of the necessary criteria to finally explain the baryon asymmetry of the universe by a viable QFT. As for the necessity of baryon number violation, there are hopefully several possibilities such as by GUT and electroweak baryogenesis, leptogenesis or sphalerons.
Paper Structure (5 sections, 41 equations, 2 figures)

This paper contains 5 sections, 41 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The model
  3. Renormalizability
  4. Unitarity
  5. Appendix concerning perturbative unitarity

Figures (2)

  • Figure 1: Feynman rules for the fermion-scalar vertex of the nonlocal Yukawa interaction \ref{['Lagrangian.int']}: (a) absorption of a scalar particle, (b) creation of a scalar particle.
  • Figure 2: Diagrams of one-loop corrections for Yukawa interaction: (a) the fermion self-energy correction, (b) the scalar self-energy correction, (c) the fermion-scalar vertex correction, and (d) the vertex correction to interaction of four scalar fields; only one diagram is drawn, while the other box diagrams are obtained by permutations of the momenta $p_1,p_2,p_3,p_4$. The diagrams with external scalar legs have different version for incoming and outgoing scalar particles due to Fig. \ref{['fig:treediagrams']}.