Prog. Theor. Phys. Vol. 89 No. 4 (1993) pp. 881-893
Scattering with Baryon Number Violation
— The Case of Higgs Particle Production
Department of Physics, Saga University, Saga 840
*Department of Physics, Kyushu University 33, Fukuoka 812
**Department of Liberal Arts, Kinki University in Kyushu, Iizuka 820
(Received October 30, 1992)
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 ΔB = 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.
DOI : 10.1143/PTP.89.881
G.'t Hooft, Phys. Rev. Lett. 37 (1976), 8[APS];
Phys. Rev. D14 (1976), 3432[APS]; D18 (1978), 2199(E).
N. S. Manton, Phys. Rev. D28 (1983), 2019[APS].
F. R. Klinkhamer and N. S. Manton, Phys. Rev. D30 (1984), 2212[APS].
- V. A. Kuzumin, V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B155 (1985), 36.
- A. Ringwald, Nucl. Phys. B330 (1990), 1.
- O. Espinosa, Nucl. Phys. B343 (1990), 310.
- H. Aoyama and H. Goldberg, Phys. Lett. B188 (1987), 506.
- See, for example, M. P. Mattis, LA-UR-91-2926 (1991).
- K. Funakubo, S. Otsuki, K. Takenaga and F. Toyoda, Prog. Theor. Phys. 87 (1992), 633[PTP]. This paper is referred to as I.
C. G. Callan, Jr. and S. Coleman, Phys. Rev. D16 (1977), 1762[APS].
T. Banks, C. M. Bender and T. T. Wu, Phys. Rev. D8 (1973), 3346[APS].
J.-L. Gervais and B. Sakita, Phys. Rev. D16 (1977), 3507[APS].
H. Aoyama, H. Goldberg and Z. Ryzak, Phys. Rev. Lett. 60 (1988), 1902[APS].
J. R. Klauder, Phys. Rev. Lett. 56 (1986), 897[APS].
A. Voros, Phys. Rev. A40 (1989), 6814[APS].
- M. E. Shaposhnikov, Phys. Lett. B242 (1990), 493.
- T. Banks, G. Farrar, M. Dine, D. Karabali and B. Sakita, Nucl. Phys. B347 (1990), 581.
- S. Yu. Klhebnikov, V. A. Rubakov and P. G. Tinyakov, Nucl. Phys. B367 (1991), 334.
- K. Cahill, Phys. Lett. B53 (1974), 174.
D. W. McLaughlin, J. Math. Phys. 13 (1972), 1099[CrossRef].
- T. Kugo and I. Ojima, Prog. Theor. Phys. Suppl. No. 66 (1979), 1[PTP].
- B. Ratra and L. G. Yaffe, Phys. Lett. B205 (1988), 57.
- K. Funakubo, S. Otsuki and F. Toyoda, Prog. Theor. Phys. 84 (1990), 1196[PTP].
L. G. Yaffe, Phys. Rev. D40 (1989), 3463[APS].
- J. Zadrozny, Phys. Lett. B284 (1992), 88.
Citing Article(s) :
Progress of Theoretical Physics Vol. 90 No. 4 (1993) pp. 885-893
The Improved Bounce Solution of SU(2)-Higgs Model