Can the CNB be detected by a torsion balance?
B. Heckel, Univ. of Washington
vacuum can
prehanger
HH coils
fiber
autocollimator
()
compensation
masses
thermal
shield
magnetic
shielding
pendulum
feet
turntable ()
 U
   

 10 eV
 ~  q~   q~   r /  

V (r )  VN (r )1       e

  1    2


q~  B  L
Can the CNB be detected by a torsion balance?
Hagmann, astro-ph/9902102
Ringwald, arXiv:0901.1529
Stodolsky, MPI-PAE/PTh 1/90
Braginsky, Klapdov, et al,
, 
F   f p
4
Relic Neutrinos
T= 1.95 K
<n> = 56 / cm3
N= S n = 300 /cm3
p = 5 x 10-4 eV ; at least 2 species non-relativistic; assume all non-relativistic
Gravitational clustering provides a density enhancement of 1.5-20; assume 10
Isotropically distributed in galaxy; Earth’s motion has v/c = 10-3
Flux = 300 x 10 x 10-3 c = 1011 /cm2-s
  h / p  0.25 cm
F   f p
f  N v rel  1011 / cm 2  s
G F2 m2 2
57
2
2  m 

N n  2 10 N n cm  
8
 eV 
2
4    t
Nn 
 
3  2  mn
3
p  m v rel  h /   5 10 4 eV
N
a  F mt   t
v rel
3



N
10
c   t
 27
2
 10 cm / s 

3  
3 
v
10
g
cm
3000
cm


 rel  
Smaller by (v/c)2 for Majorana neutrinos ?
N     mr a
3 cm

.03 10 10 rad
a 

 3 10 14 cm / s 2
mr
30 g  3cm
30 g
30 g
a  1015 cm / s 2
(a  10 27 cm / s 2 )
is possible, but still too large by 1012
If all of the neutrons in 30g target scattered neutrinos coherently,
a would be 10-19 cm/s2
If all of the neutrinos incident on the 30g target scattered
coherently, a would be 10-16 cm/s2
Conclusions
The coherent scattering of relic neutrinos leads to a large
enhancement of the scattering cross section.
Current torsion balance test masses scatter roughly 1 relic
neutrino per second. But the momentum transfer is too small
to be observable.
I wouldn’t fund this experiment.