Stars as Laboratories for Fundamental Physics - MPP Theory Group

500 Chapter 13
c) Long-Range Forces
Speculating further one may imagine some sort of neutrino “fifth-force
charge.” If electrons, protons, or dark-matter particles also carry such
a charge the bending of the neutrino trajectory in the fifth-force field of
the galaxy would lead to an energy-dependent time delay. This and related
arguments were advanced by a number of authors (Pakvasa, Simmons,
and Weiler 1989; Grifols, Massó, and Peris 1988, 1994; Fiorentini
and Mezzorani 1989; Malaney, Starkman, and Tremaine 1995).
The most plausible form for such a long-range interaction is one mediated
by a massless vector boson, i.e. a new gauge interaction, perhaps
related to a novel leptonic charge (Sect. 3.6.4). In this case neutrinos
and antineutrinos would carry opposite charges so that the cosmic neutrino
background would be essentially a neutral plasma with regard to
the new interaction. The resulting screening effects then invalidate the
SN 1987A argument (Dolgov and Raffelt 1995).
Screening effects would not operate if the force were due to a spin-0
or spin-2 boson which always cause attractive forces. However, any
force mediated by a massless spin-2 boson must couple to the energymomentum
tensor and thus is identical with gravity. The force mediated
by a scalar boson between a static source and a relativistic neutrino
is suppressed by a Lorentz factor. Therefore, even if scalar-mediated
forces existed between macroscopic bodies, their effect would be weakened
for relativistic neutrinos.
In summary, the SN 1987A signal does not seem to carry any simple
information concerning putative nongravitational long-range forces.
d) Fundamental Length Scale
Fujiwara has proposed a quantum field theory where the velocity of particles
increases with energy, leading to an energy-dependent advance of
the arrival times by ∆t/t = − 1 2 (l 0E ν ) 2 . Here, l 0 is a fundamental length
scale. Whatever the merits of this theory, a value l 0 ∼ < 10 −18 cm would
not be in conflict with the SN 1987A neutrino signal (Fujiwara 1989).
e) Lorentz Addition of Velocities
If relativistic particles (photons, massless neutrinos) are emitted by a
moving source (velocity v S ) their velocity c ′ in the laboratory frame
should be equal to c (velocity in the frame of the source). The Galilean
addition of velocities, on the other hand, would give c ′ = c + v S . In
general one may assume that velocities add according to c ′ = c + Kv S