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Real-time simulation of asymmetry generation in fermion-bubble collisions

Marcela Carena1,2,3,4,5,*, Ying-Ying Li6,†, Tong Ou3,5,‡, and Hersh Singh2,§

  • *Contact author: mcarena@perimeterinstitute.ca
  • †Contact author: liyingying@ihep.ac.cn
  • ‡Contact author: tongou@uchicago.edu
  • §Contact author: hershs@fnal.gov
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Phys. Rev. D 113, 014502 – Published 5 January, 2026

DOI: https://doi.org/10.1103/nphy-2y8q

Abstract

Motivated by the out-of-equilibrium dynamics during an early-Universe first-order phase transition, we perform real-time simulations of fermion-bubble scattering in 1+1 dimensions. This nonequilibrium process can generate a charge-conjugation C asymmetry outside the bubble wall, induced by the complex fermion mass profile. The resulting C asymmetry is the 1+1-dimensional analog of the CP asymmetry in 3+1 dimensions, a key ingredient in baryon asymmetry generation at the electroweak scale. Using tensor network methods, we track the real-time evolution of the C asymmetry in the charge density as the fermion interacts with the bubble wall, a regime inaccessible to analytic calculations. We further introduce two observables to quantify the asymmetry in the asymptotic region where reflected particles are well separated from the scattering point: one based on the net charge outside the bubble wall, and the other on the spatial displacement between the reflected particle and antiparticle wave packets. Our study represents a first step toward nonperturbative, real-time computations of CP asymmetry in 3+1 dimensions for electroweak baryogenesis.

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Phys. Rev. D 113, 014502– Published 5 January, 2026
  • Received 24 August 2025
  • Accepted 17 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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