10-th International Workshop on H.E.S.P. September 16-21, 2003, Dubna, Russia Bradyons and Tachyons S.B. Nurushev Institute for High Energy Physics

Contents Introduction Classification of particles Causality Problem Generalized Galilean Transformation Where may we look for tachyons? Charged Tachyons Cherenkov Radiation Spectrum Summary

Introduction The first discussions of the particles moving with the superluminal velocities were traced back to J.J. Thompson [1], O. Heavyside [2], and A. Sommerfeld [3].. For a long time it was generally believed that the special theory of relativity precludes the possibility of transmitting energy from point to point in space-time at velocities greater than c, the speed of light in a vacuum.

Introduction Such belief stems out from the Einstein conclusion “… velocities greater than that of light … have no possibilities of existence,” [4]. Other versions of this statement are presented in the standard textbooks on relativity [5]. At the beginning of the 60’s the interest to the superluminal particles surged among theoreticians [6], [7], [8]. The major theoretical efforts were directed toward a justification of existence of such a particle named as tachyon [9].

Classification of particles Three Classes of Particles Based on SR, three classes of particles were proposed by Bilaniuk et al [7]. The Class III particles, i.e. tachyons, would be created in nuclear interactions at superluminal velocities. The sign of 4-D line element, ds 2, is associated with three classes of particles. For simplicity, let us put dy = dz = 0, then > 0 Class I (subluminal particles) ds 2 = c 2 dt 2 - dx 2 = 0 Class II (photon) (3) < 0 Class III (tachyon)

Classification of particles Figure 1, Energy vs. velocity for three classes of particles

Causality Problem Figure 2, A 2-D diagram for Lorentz transformation

Generelized Galileen Transformation x = r(X - vT) t = r - -1 T (6) Figure 3, A 2-D diagram of GGT r=[1-(v/c) 2]-1/2

Figure 4a,4b 2-D diagram of E vs. p for three classes of particles P E P E E=

Experimental data on the neutrino mass m 2 (ν e ) = -2.5±3.3 eV 2 This is from Tritium decay experiment m 2 (ν μ ) = ±0.023 MeV 2 This is from pion decay experiment

Charged Tachyons The next important item is a way by which tachyon looses its energy. The charged stable tachyon may emit the Cherenkov radiation. The Lorenz - invariant formulation of the Cherenkov radiation by tachyon was given in paper [10]. Tachyon behaving as the deformed sphere looses energy per unit path length in the following way

Charged Tachyons where e – electron charge (assuming that tachyon carries a single electron charge), a 0 -radius of sphere, s is the traveling distance. The range of tachyon considered as the distance from the production point to the point of inevitable annihilation with anti-tachyon is defined by a relation R =

Charged Tachyons For numerical estimate it was assumed in paper [10], that tachyon has the same charge and mass as the electron has and the tachyon size is of order of the electron Compton wave length. Then we have R=5.5  (E/  ), (In centimeter).

Charged Tachyons Numerically for E   it follows R = 5.5  cm. This estimate immediately leads to two important conclusions: 1.No way to detect tachyon through its ionization 2.The only accessable way to detect tachyon is its Cherenkov radiation

Cherenkov Radiation Spectrum For simplicity the Gaussian-like charge distribution was used which gives the following spectral distribution of the tachyons Cherenkov radiation [V.F.P]

Where is a frequency of the emitted Cherenkov radiation, - wavelength, c - speed of light. The maximum of the spectral distribution occurs at frequency Cherenkov Radiation Spectrum

Assuming p= √2 μ and a 0 =λ c = hc/mc= 3.8· cm, one gets

Cherenkov Radiation Spectrum This corresponds to photon energy E = 11 MeV

Table 1. Where may we look for tachyons? Inter.BradyonsTachyonsComments Gravit.graviton u s >>c 1. T.V. Flandern, Phys. Lett. A250 (1998) 1. Weakν e, ν μ, ν זּ M 2 (ν e ),<0, M 2 (νμ ),<0 2. G-j. Ni and T. Chang, hep-ph/ E-Mγ u s >cPhotons with mass-? StrongFermions Bosons ++++ Stable or resonanse, pole Quantum optics J.W. Pan et al.Phys. Rev. Lett. 86 (2001)

Cherenkov Radiation As resume one can list the following important measurements of the Cherenkov radiation which should be done: The Cherenkov radiation ring should be measured. Tachyon velocity can be extracted from such measurements. The spectral distribution of the Cherenkov radiation should be measured including its maximum. The size of tachyon can be extracted from such measurement and from point 1 The Cherenkov radiation absolute intensity should be also measured. Assuming that we can restore a whole tachyon energy by such measurements we can extract the tachyon mass from all listed above measurements.