Simple Gradient Flow Equation for the Bounce Solution

Abstract

Motivated by the recent work of Chigusa, Moroi, and Shoji, we propose a new simple gradient flow equation to derive the bounce solution which contributes to the decay of the false vacuum. Our discussion utilizes the discussion of Coleman, Glaser, and Martin and we solve a minimization problem of the kinetic energy while fixing the potential energy. The bounce solution is derived as a scale-transformed of the solution of this problem. We also show that the convergence of our method is robust against a choice of the initial configuration.

6 pages, 8 figures; corrected a typo in Eq. (15)

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• Obtaining the sphaleron field configurations with gradient flow
• $Z_3$ meta-stable states in PNJL model
• Perturbative analysis of the Wess-Zumino flow
• Higgs Field-Induced Triboluminescence in Binary Black Hole Mergers
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• Upper bound on the smuon mass from vacuum stability in the light of muon $g-2$ anomaly