V. A. Gusseinov

The goal of this paper is the analysis of the processes of high-energy muon production in scattering of low-energy neutrinos (antineutrinos) by ultrarelativistic electrons

, (1)

(2)

in a constant uniform magnetic field. The analyses show that these scatterings permit to register low-energy neutrinos experimentally. The reaction (1) is called the inverse muon decay (IMD) [ 1] . The reaction (2) is cross-symmetrical to the process IMD. These are pure lepton processes. IMD has been investigating since 1979 experimentally [ 2] . One loop electroweak radiation corrections to the cross section of the process IMD have been found in [ 3] in the framework of the standard model. IMD has been investigated in [ 4,5] in a constant crossed field (E× H=E²-H²=0). In [ 4] the general expression for the cross section of IMD has been studied with helping of numerical methods. In [ 5] the asymptotic formulae for the cross section have been found in various limit cases. The cross section of IMD has been investigated in [ 6] in a constant uniform magnetic field for the initial electron being on the ground Landau level. The cross sections of the processes of high-energy muon production in scattering of low-energy neutrinos (antineutrinos) by ultrarelativistic electrons ( and ) in a constant uniform magnetic field with account of transverse and longitudinal polarization states of electrons and muons have been calculated in [ 7] . The work [ 8] has been devoted to the new results of precise measurement of the cross section of IMD.

Let us suppose that the electron has a great transverse momentum (, where e is the charge of an electron, is the mass of a muon) in the magnetic field , i.e. the motion of the electron is quasi-classical: . is the principal quantum number. For the muon it is also . We have to note that we use the system of units where and the signature of the metrics is

(+ - - - ). Let the initial neutrino (antineutrino) fly along the magnetic field H||Oz:

. (3)

The gauge of the potential of the constant uniform magnetic field H has been chosen as follows

. (4)

Let z- component of the momentum of the electron is P z =0. We choose the energy of the initial neutrino (antineutrino) in the following interval

. (5)

All these accepted restrictions mean that the total cross sections of the considered processes will only depend on the field parameter

(6)

and the kinematic parameter (compare with [ 9] )

, (7)

where is the tensor of the external field, w is the energy of the initial neutrino, is the energy of the electron.

The conditions (3), (5) and can be written in the following relativistic forms

, , , , (8)

where

. (9)

In accordance with the general theory [ 5,10] the influence of the external field on the process (1) and (2) is determined with the parameter

, (10)

where corresponds to the threshold of the free process [ 7] .

For the very small values at the influence of the external field can be neglected. In this case the process in the external field turns into the free process.

The effects of the external fields become especially substantial in that case when , i.e. . To achieve the condition either we have to increase or we have to decrease . The intensities of the modern strong impulse magnetic fields and the effective internal magnetic fields of the monocrystals are H=10⁸ Gs [ 11] . But these values are much more less than the characteristic (Schwinger) field intensity Gs and . Therefore the parameter (and ) . If the tranverse momentum of the charged particle taking part in the process (), then can be relatively large. So a great increase of the field parameter is caused by a great increase of the external field intensity H and the transverse momentum . If we take into account that the maximum energy of the beams in - collider LEP 2 achieved in 1996 is e =86 GeV [ 12] and H=10⁸ Gs then we obtain the estimate which is very small.

The other possibility of increasing h is connected with a great decrease of , i.e. . In principle can be made too small. But it is connected with some technical difficulties. Because it requires the precise trimming of the kinematic parameter k so that . We do not discuss technical aspects of this problem believing that all of them may be overcome.

When , we have

, (11)

where GeV is the threshold energy of the free process. If we put e = 11 GeV, then we obtain w = 0.511 MeV which is in the boundary of the detectable region. For the e = 1 GeV we obtain w = 5.6 MeV. Neutrinos of such energy are met in solar and reactor neutrinos. It shows that in principle it is possible to register low-energy neutrinos. The nearer is to the stronger is the effects of the external field. We can show it in the following estimations using the parameters e = 86 GeV and H=10⁸ Gs:

; ;

; ;

; ,

I would like to thank Professors A.V.Borisov, V.Ch. Zhukovskii, I.G. Jafarov and O.S.Pavlova for many helpful discussions on this work.

References

[1] L.B. Okun, Leptons and quarks ( Nauka, Moscow, 1990) p.152.

[2] N. Armenise et al., Phys. Lett. B84 (1979) 137.

[3] D.Yu. Bardin and V.A. Dokuchaeva, Nucl. Phys. B287 (1987) 839.

[4] V. A. Lyulka, Yad. Fiz. 39 (1984) 680.

[5] A.V.Borisov, L.V.Morozova and M.K.Nanaa. Izv.vuzov. Fizika. 12 (1992) 106.

[6] A. V. Borisov and V. A. Gusseinov, Yad. Fiz 57 (1994) 496.

[7] A. V. Borisov, V. A. Gusseinov and O.S. Pavlova, Yad. Fiz. 61 (1998) 103.

[8] Vilain P. et al. Preprint CERN- PPE / 96- 01.Geneva. 1996.

[9] V.Ch. Zhukovskii and P.A. Eminov, Izv. vuzov. Fiz. 8 (1980) 47.

[10] I.M. Ternov, V.Ch.Zhukovskii and A.V. Borisov, Quantum processes in an intense external field (Publishing house of MSU, Moscow, 1989) p.78, p. 83, p. 84

[11] V. N. Bayer, V. M. Katkov and V. M. Strakhovenko, Results of a science and engineering. In ser. Beams of the charged particles and solid

(VINITI, Moscow, 1992) Vol. 4, p. 57.

[12] CERN Courier. 37 [ 1] (1997) p. 2.