Semiclassical approach to the decay of protons in circular motion under the influence of gravitational fields

Abstract

We investigate the possible decay of protons in geodesic circular motion around neutral compact objects. Weak and strong decay rates and the associated emitted powers are calculated using a semiclassical approach. Our results are discussed with respect to distinct ones in the literature, which consider the decay of accelerated protons in electromagnetic fields. A number of consistency checks are presented along the paper.

Massive particle production from accelerated sources in high magnetic fields

“…where p 1 and p 2 are the source particles, described by a classical current corresponding to the states of a two level system following a prescribed classical trajectory with proper acceleration a, and q i are the emitted particles, described by quantized fields. (For further details, see [5,6], for instance.) We assume that the respective masses m qi of the emitted particles q i obeys m qi < m p1,2 , where m p1 and m p2 stands for, respectively, the masses of the source particles p 1 and p 2 .…”

“…If m p1 < m p2 + i m qi , the process is known to be forbidden for inertial trajectories (a = 0). It is intuitive to expect that, if the source is supposed to follow a prescribed trajectory, the momentum k i of the emitted particle q i , measured in the rest frame of the source, must be constrained to |k i | ≪ m 1,2 [5,6]. Moreover, the mean energyω i of the emitted particles (also measured in the proton's reference frame) is of the order of the source proper acceleration [5], i.e.,ω…”

“…Following the same procedure employed in the Refs. [5,6], one obtains the differential decay rate as function of the energy of the emitted pion…”

“…For the physical relevant case of protons in circular motion, one has also exactly the same threshold (10). For such case, the formulas for the neutral pion production (5) can be obtained from the previously one calculated in [6] for scalar emissions…”

Can a charged decaying particle serve as an ideal clock in the presence of a magnetic field?

“…This experiment is cited in standard textbooks, see for example [2], as the evidence for the ideal clock hypothesis. Even if clocks can be considered ideal under the regime in which particle accelerators normally operate, more generally, it has been proven by several authors that this is not the case [3][4][5][6]. They have studied the decay law of different particles, in rectilinear and circular motion, as a function of the proper acceleration a and they have shown that the rate depends on the particle trajectory.…”