Stars as Laboratories for Fundamental Physics - MPP Theory Group

114 Chapter 3
3.6.4 Leptonic and Baryonic Gauge Interactions
The physical motivation for considering long-range interactions mediated
by vector bosons, besides the fifth-force episode, is the hypothesis
that baryon number or lepton number could play the role of physical
charges similar to the electric one (Lee and Yang 1955; Okun 1969).
Their association with a gauge symmetry would provide one explanation
for the strict conservation of baryon and lepton number which so
far has been observed in nature. In the framework of this hypothesis
one predicts the existence of baryonic or leptonic photons which couple
to baryons or leptons by a charge e B or e L , respectively. The novel
gauge bosons would be massless like the ordinary photon.
Therefore, the limits established in the previous sections on the dimensionless
couplings of vector bosons can be readily restated as limits
on the values of putative baryonic or leptonic charges. The energy-loss
argument applied to helium-burning stars yields
e L ∼ < 1×10 −14 ,
e B ∼ < 3×10 −11 , (3.50)
according to Eqs. (3.43) and (3.47), respectively. Tests of the equivalence
principle (i.e. of a composition-dependent fifth force) on solarsystem
scales yield β ∼ < 10 −9 (Sect. 3.6.3) so that
e B ∼ < 1×10 −23 . (3.51)
Apparently this is the most restrictive limit on e B that is currently
available.
One may be tempted to apply the limits from the equivalence principle
also to a leptonic charge e L . However, in this case one has to worry
about the fact that even neutrinos would carry leptonic charges. The
universe is probably filled with a background neutrino sea in the same
way as it is filled with a background of microwave photons. This neutrino
medium would constitute a leptonic plasma which screens sources
of the leptonic force just as an electronic plasma screens electric charges
(Zisman 1971; Goldman, Zisman, and Shaulov 1972; Çiftçi, Sultansoi,
and Türköz 1994; Dolgov and Raffelt 1995).
Debye screening will be studied in Sect. 6.4.1. For the screening
wave number one finds the expression
∫ ∞
kS 2 = 2 (e L /π) 2 dp f p p (v + v −1 ), (3.52)
0
where p = |p| is the momentum (isotropy was assumed), v = p/E
the velocity of the charged particles, and f p the occupation number of