Scattering with Baryon Number Violation

Abstract

A formalism based on path-integral expression of time-evolution operator during tunneling at a finite energy proposed by the authors is applied to SU (2) gauge-Higgs system to produce Higgs particles with Δ B = 1. Instead of starting from instanton tunneling at the zero energy , a classical bounce solution giving sphaleron ( instanton ) action at high ( low ) energies is used as the tunneling configuration . Fourier transform of the bounce configuration in coherent state expression at the entrance and exit of the tunneling plays an important role . Numerical results at various energies for M_H/M_W = 1 ∼2 are given . Though the cross section with ΔB = 1 results from a severe cancellation of several large quantities in the leading order as occurred in the instanton calculus , it seems unlikely that the cross section grows as largely as to reach unitarity bound at energies E ≤E_sph. It is pointed out that the actual value g^2 = 0.418 of the SU(2) gauge coupling constant may be too large to take the weak coupling limit .