Bounce Configuration Research Articles

Scattering with Baryon Number Violation

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 .

Scattering with Baryon Number Violation: The Case of Higgs Particle Production

\noindent 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 $\Delta B=1$. 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 \sim 2 $ are given. Though the cross section with $\Delta B=1$ results from a severe cancellation of several large quantities in the leading order as occured in the instanton calculus, it seems unlikely that the cross section grows as largely as to reach unitarity bound at energies $E \leq E_{sph}$. 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.}

The equivalent Schrodinger equation for the bounce solution

The authors study the equivalent Schrodinger equation for the bounce configuration. They get the lowest eigenvalue in the limit of small external currents using the Landau-Lifshitz approach.