Interaction of ultra-high energy neutrinos with a thermal gas of relic neutrinos

1
Interaction of ultra-high energy neutrinos with a
thermal gas of relic neutrinos
astro-ph/0507333

• Introduction and motivations
• UHE ? damping and transmission probability
• ( in the framework of finite-temperature F.T.
  )
• Applications
• Conclusions

• Véronique Van Elewyck
• _at_ HEP 2005
• Work done in collaboration with
• J. C. DOlivo, L. Nellen and S.Sahu

2
Introduction and motivations
From Ringwald 2004

• Basic ingredients of the model
• UHE neutrino flux
• --- from astrophysical processes En 1022 eV
• (produced along with UHECR)
• --- from top-down mechanisms En 1023 - 1024
  eV
• Cosmic neutrino background (C?B)
• --- thermal distribution
• present temperature T0? 1.69 10-4 eV
  1.95 K
• (vs. T0? 2.73K)
• present density n0? 112 cm-3 per species
• (vs. n0? 410 cm-3)
• ?UHE travel unaffected and undeflected on
  cosmological distances except for their
  interaction with the C?B
• ? role in the production of UHECR beyond the
  GZK cutoff ?
• Z-burst mechanism Weiler 1998, Fargion
  et al., 1999

3
Introduction and motivations

• ?UHE ?relic interactions
• Dominant process ? - ? annihilation through
  Z-boson (s-channel)
• in the usual approximation of relic
  neutrinos at rest (P ltlt m?)
• absorption line at
  in UHE? spectrum

-
-
-
s(?? ? Z ? f f ) 10-31 cm2 resonance peak at
s 2mn EUHE MZ2
Roulet, 1993
(other relevant processes have s 10-35
10-34 cm2 )
4
Introduction and motivations

• position depth of the absorption line
• are also determined by the position
  (redshift) of the source
• Eres ? Eres /(1z), broadening effect
• good opportunity to detect the CnB
  experimentally
• test some features of UHE? source
  distribution
• possible determination of absolute
  neutrino masses
• (provided sufficient resolution and enough
  statistics)

z1
z5
z10
Eres (z0)
19 20 21 22
23 log(EeV)

• How does the thermal motion of the relic ?
  affect
• the ?relic ?UHE annihilation process, the
  transmission probability,
• the absorption dips ? possibly relevant for
• small neutrino masses
• nUHE coming from large redshifts ( hotter
  universe Tn (1z) T0n)
• neutrino clusters (higher densities, higher
  temperatures)

5
UHE? damping in finite-temperature field theory
(FTFT)
For an ultrarelativistic neutrino with 4-momentum

In medium
In vacuum
Z (q)
?UHE (k)
?UHE (k)
1,2
1,2
?r (p)
rest frame of the medium uµ(1,0,0,0)
damping factor
The damping is calculated from the imaginary part
of Seff using
the vertices of the theory are doubled
selects the (anti-) neutrino distribution function
6
UHE? damping in FTFT
one finally gets
the only kinematically allowed process is
?? annihilation
_
cross-section for the process ?? ? Z ? all
relic neutrino distribution
_
7
UHE? damping in FTFT
P eV
P eV
Folded with the thermal distribution
mn 0.1 eV
K eV
K eV
Prms 6 10-4 eV ltlt m? s(0 , K)
s(Prms , K) s(2 Prms , K) s(5 Prms , K)
the position of the resonance is not affected
by the thermal distribution of nr momenta
-
K eV
8
UHE? damping in FTFT
P eV
P eV
Folded with the thermal distribution
mn 0.001 eV
K eV
K eV
Prms 6 10-4 eV gt m? s(P , K) varies
significantly in the range of ?r momenta selected
by the thermal distribution the peak is broader,
lower, and shifted to lower values of K
s(0 , K)
-
s(Prms , K)
s(2 Prms , K)
s(5 Prms , K)
K eV
9
Transmission probability for the ?UHE

• Effect of the redshift
• For a neutrino travelling on cosmological
  distances in the expanding Universe

K ? K0 (1z) --- the nUHE was more
energetic Tn ? T0n (1z) --- the thermal bath of
?r was hotter
K0, T0? present quantities
(we take )
10
Transmission probability for the nUHE

• - thermal effects are relevant
• for mn 10-2 eV or smaller
• (m?/T? 102 or smaller)
• absorption dips get
• shallower and broader
• more difficult to evaluate mn from
  the position of the
• absorption line
• the dips are shifted to
• lower energies
• more accessible ?

z1
z1
z5
z5
z10
z10
mn 0.1 eV
z20
mn 0.01 eV
z20
z1
z1
z5
z5
z10
z10
mn 0.001 eV
mn 0.0001 eV
z20
z20
11
Application 1 realistic UHE? flux
Reasonable assumptions (see e.g. Eberle et
al., 2004)
distribution of the sources
activity
(Nsources per comoving

volume per time)
characteristics of the sources
injection spectrum
( neutrinos emitted per
energy bin)

• typical astrophysical sources have n 4, zmax
  10
• typical non-accelerator sources have n 1-2
• spectral index a 1-2
  (we take zmin0 everywhere)

12
Application 1 realistic UHE? flux
Typical top-down n a 0 zmax 10, 20
Thermal effects
Typical bottom-up n a 2 zmax 2,5,10
mn 0.01 eV
Small
mn 0.0001 eV
Important !
13
Application 2 nr clustering
Gravitational clustering of neutrinos can produce
local overdensities at different scales we
approximate the neutrino cluster density by a
constant ncluster an0n with a typical
extension Lcluster and take z0
a 103
a 109 a 1010 a 1011
a 104
mn 0.1 eV Lcluster 1 Mpc
mn 1 eV Lcluster 10 pc
On small scales (10-5 10 pc) neutrino
clouds with extremely high densities a 9-15
!! Stephenson et al. 1998 even for mn 1eV,
relic neutrinos would be relativistic
On large scales ( 50 kpc 1 Mpc) n clustering
limited by Pauli blocking limit on maximum
phase-space density mn 0.1 eV, a 102
104
14
Conclusions

• The effects of thermal motion in the CnB
  significantly affect the
• shape position of the absorption dip if (at
  least one) mn 10-2 eV
• absorption lines are shallower and broader
• the absorption dip in the flux is smeared
  out more difficult to detect, especially for
  source populations at small redshifts
• More difficult to estimate absolute mn
• shifting of the absorption dip to lower energies
• improve the possibility of detection for small m?
  ...?

• Thermal effects have only a marginal impact on
  clustered neutrinos
• in standard schemes as large mn are required
  and the overdensities
• achievable are limited
• BUT in alternative models allowing very high
  densities on small scales
• strong enhancement of absorption effects, even
  for large mn ,
• as soon as relic neutrinos can approach a
  relativistic regime