Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particles Interacting with Electrons and Baryons 99
The energy-loss rates for scalars and pseudoscalars in Eqs. (3.22)
and (3.23) are independent of density, and proportional to T 4 and T 6 ,
respectively. The averages over the core of a typical HB star are ⟨T 4 8 ⟩ =
0.40 and ⟨T 6 8 ⟩ = 0.37 (Fig. 2.24). With Y e = 0.5 appropriate for helium,
carbon, and oxygen the 10 erg g −1 s −1 limit yields
α ′ < { 0.9×10 −28 scalar,
∼
1.6×10 −26 pseudoscalar.
(3.25)
These bounds apply to bosons with a mass below a few times the temperature,
m ∼ < 20−30 keV. For larger masses the limits are significantly
degraded because only the high-energy tail of the blackbody photons
can produce the particles. For massive pseudoscalars this effect was
explicitly studied in Sect. 1.3.5 in the context of solar limits.
For vector bosons which interact by means of a Yukawa coupling,
the same limits to α ′ apply except that they are more restrictive by a
factor of 2 because of the two polarization states which increases the
emission rate.
For vector bosons which couple by means of a “magnetic moment”
as the “paraphotons” in Eq. (3.3), the bound on g is the same as for
pseudoscalars apart from an extra factor of 2 in the emission rate from
the two polarization states.
3.3 Pair Annihilation
Electron-positron pair annihilation can produce new bosons by the
“crossed” version of the Compton amplitude while the conversion into
neutrino pairs does not require the participation of a photon (Fig. 3.4).
For pseudoscalars the cross section for e + e − → γa is (Mikaelian 1978)
σ =
[ 2παα′ s
ln
s − 4m 2 e
4m 2 e
For e + e − → νν it is (’t Hooft 1971; Dicus 1972)
σ = G2 F
12π
( √
1 + 1 − 4me/s) ]
2 . (3.26)
(C 2 V + C 2 A) (s − m 2 e) + 3 (C 2 V − C 2 A) m 2 e
√
1 − 4m 2 e/s
. (3.27)
Because pair annihilation requires the presence of positrons it is important
only for relativistic plasmas.
In this limit σ ∝ s −1 ln(s) for the production of bosons (pseudoscalar,
scalar, vector) and σ ∝ s for neutrino pairs. Therefore, the