Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particles Interacting with Electrons and Baryons 113
different materials u 1 ≈ u 2 ≈ m u is the atomic mass unit, approximately
equal to a nucleon mass m N . For this force not to compete
with gravity one needs g < O(10 −19 ) or α = g 2 /4π < O(10 −37 ) so that
low-mass scalars, if they exist, need to have extremely feeble couplings
to matter. Their smallness implies that such particles would not have
any impact whatsoever on the energy loss of stars.
Therefore, for boson masses so small that the Compton wave length
λ is macroscopic, the most restrictive limits on g obtain from analyzing
the forces between macroscopic bodies, not from the energy-loss argument.
The existence of a composition-dependent “fifth force” in nature
with a strength of about 1% of gravity and a range λ of a few hundred
meters seemed indicated by a reanalysis of Eötvös’s original data
(Fischbach et al. 1986). Subsequently many experiments were carried
out to search for this effect, with no believable positive outcome (for
a review see Fischbach and Talmadge 1992). However, these investigations
produced extremely restrictive limits on β, depending on the
assumed range λ of the new force. The limits also depend on the presumed
coupling; if the new force couples to baryon number one finds
that β < ∼ 10 −3 for λ in the cm range, or β < ∼ 10 −9 for λ of order the
Earth-Sun distance and above. Thus, novel long-range forces must be
much weaker than gravity. No bounds on β seem to exist for λ below
the cm range, i.e. for boson masses of order 10 −3 eV and above, apart
from the stellar energy-loss argument.
The effect of a novel force with intermediate range on the equations
of stellar structure was discussed by Glass and Szamosi (1987,
1989). Solar models including such a force and the impact on the
solar oscillation frequencies were discussed by Gilliland and Däppen
(1987) and Kuhn (1988). For a force so weak or weaker than indicated
by the laboratory limits, no observable consequences for stellar
structure and evolution seem to obtain. Also, the impact of the
new field on the value of fundamental coupling constants even at compact
objects such as neutron stars is far below any observable limit
(Ellis et al. 1989).
A significant bound obtains from the orbital decay of the Hulse-
Taylor binary pulsar. In order for the energy loss in the new scalars to
remain below 1% of the gravitational wave emission the Yukawa coupling
to baryons must satisfy g < ∼ 3×10 −19 (Mohanty and Panda 1994).
This translates into β < ∼ 1 for scalar boson masses below the orbital pulsar
frequency of 2π/P = 2.251×10 −4 s −1 , i.e. for λ −1 < ∼ 1.5×10 −19 eV
or λ > ∼ 1.3×10 14 cm. This “fifth-force limit,” however, is weaker than
those derived by terrestrial laboratory methods.