Table Of ContentDetecting MeV Gauge Bosons With High-Energy Neutrino Telescopes
Dan Hooper
Fermi National Accelerator Laboratory, Theoretical Astrophysics, Batavia, IL 60510
(Dated: February 2, 2008)
IfannihilatingMeV-scaledarkmatterparticlesareresponsiblefortheobserved511keVemission
from theGalactic bulge, then new light gauge bosons which mediate thedark matter annihilations
may have other observable consequences. In particular, if such a gauge boson exists and has even
verysmallcouplingstoStandardModelneutrinos,cosmicneutrinoswith∼TeVenergieswillscatter
with thecosmic neutrinobackgroundthroughresonant exchange,resulting in adistinctivespectral
absorption line in the high-energy neutrinospectrum. Sucha feature could potentially be detected
byfuture high-energy neutrinotelescopes.
PACSnumbers: 95.85.Ry;95.30.Cq,95.35.+d;FERMILAB-PUB-07-017-A
7
0
0 I. INTRODUCTION tions of core-collapse supernovae [13].
2 In this letter, we present a new way in which a gauge
n Some years ago, it was suggested that the 511 keV bosonassociatedwithMeV-scaledarkmattermaybede-
a radiation observed from the Galactic bulge by the tected. In particular, neutrinos produced in cosmic ray
J
SPI/INTEGRALsatellite[1]maybetheproductofdark accelerators could interact with cosmic backgroundneu-
3 matter annihilations [2]. For dark matter particles to trinos via the resonant exchange of the new gauge bo-
2
generate the observed spectral line width of this signal, son, resulting in an absorption line in the high-energy
1 theirannihilationsmustinjectpositronswithenergiesbe- cosmic neutrino spectrum. This resembles, in some
v low a few MeV [3] and, therefore, such particles must be respects, the scattering of ultra-high energy neutrinos
4 much lighter than the range of masses typically associ- through resonant Z-exchange, known as Z-burst mech-
9 ated with dark matter. anism [14]. Similar ideas have also been explored for
1 very light gauge bosons associated with the generation
It has long been understood that weakly interacting
1 of neutrino masses [15]. We find that if the new gauge
particleswithmassessmallerthanafewGeV(butlarger
0
than ∼1 MeV) are expected to be overproduced in the boson’s coupling to neutrinos is larger than approxi-
07 earlyuniverserelativetothemeasureddarkmatterabun- mately gUνν >∼ 10−5(mU/MeV), then this process will
efficiently deplete the neutrino flux over a range of ener-
/ dance [4]. This conclusion can be modified, however,
h gies, m2/2m (1+z) < E < m2/2m , where z is the
p if new light mediators are introduced which make dark U ν ν U ν
redshiftofthe neutrinosourceandm isthemassofthe
- matterannihilationsmoreefficient[5]. Forexample,neu- U
p tralinoswithin the MSSM are requiredby this argument gaugeboson. Although challenging,sucha feature could
e to be heavier than ∼20 GeV [6]. Within extended su- potentially be observed by future high-energy neutrino
h telescopes.
persymmetric models with light Higgs bosons mediating
:
v neutralino annihilation, however, much smaller masses
i
X are possible [7].
II. NEUTRINO ABSORPTION VIA A LIGHT
For dark matter particles with 0.5-3 MeV masses to
r GAUGE BOSON RESONANCE
a generate the measured dark matter abundance, they
must annihilate during the freeze-out epoch with a cross
sectionofσv ∼pb. Toinjectthefluxofpositronsneeded If a new gauge boson exists which couples to neutri-
to generate the signal observed by SPI/INTEGRAL, nos, then propagating neutrinos will scatter with the
however, an annihilation cross section of σv ∼ 10−4 − cosmic neutrino background at a resonant energy of
10−5 pb is required. Together, these requirements lead E ≈m2/2m , where m is the mass of the new gauge
ν U ν U
us to consider dark matter particles with s-wave sup- boson. For a gauge boson with an MeV-scale mass, and
pressed annihilations (σv ∝ v2). Such behavior can be considering∼0.1eVneutrinos,this correspondstoares-
found,forexample,inthecaseoffermionicorscalardark onance at E ∼1-10 TeV.
ν
matter particles annihilating through a vector mediator. Although the couplings of a light gauge boson to
For such a dark matter particle to annihilate sufficiently neutrinos are quite tightly constrained by νe scatter-
in the early universe to not be overabundant today, the ing experiments [8, 9], over very long baselines, high-
mediating boson would also have to be quite light [8, 9]. energy neutrinos may interact efficiently with cosmic
The existence of a new gauge boson which couples to background neutrinos via the exchange of the new bo-
dark matter and (at least some of the) Standard Model son, even if the relevant couplings are very small. These
fermions would have a number of potentially observable resonantinteractions will be elastic in nature (νν¯→νν¯)
consequences. Constraints on such a scenario have been or, if m >2m , produce electron-positron pairs (νν¯→
U e
placedbycolliderexperiments[10],neutrinoexperiments e+e−). We first focus on the case in which m <2m .
U e
[8, 11], atomic physics experiments [12] and by observa- νν¯→νν¯processeswilldepletethenumberofneutrinos
2
inthe resonancerange,leadingtoanabsorptionline and
a slight “pile up” feature in the cosmic neutrino spec-
trum. Near resonance, the neutrino-antineutrino cross
section is well approximated by
g4 s
σνν¯ ≈ 16π[(m2 −Usν)ν2+m2Γ2], (1)
U U U
where g is the U’s coupling to neutrinos. The decay
Uνν
width of the gauge boson is given by:
g2 m
Γ ≈ Uνν U, (2)
U
12π
Xν
where the sum is over the three neutrino species. At the
resonant energy, this leads to a cross section of
π
σνν¯ ∼ m2 , (3)
U
and a corresponding mean free path for a neutrino of
FIG. 1: The suppression of the high-energy neutrino spec-
2 trum from a source at redshift z =3 for the case of mU =1
λ≈ 1 ∼pc mU , (4) MeV, and for three choices of the gauge boson’s coupling to
nνσνν¯ (cid:18)1MeV(cid:19) neutrinos: gUνν = 10−5 (solid), 5×10−5 (dashed) and 10−4
(dotted).
where n =3πΓ(3)ζ(3)T3 ≈56(1+z)3cm−3 is the num-
ν ν
ber density of cosmic background neutrinos (per flavor).
Although this mean free path is very short by the
standards of neutrino astronomy, the width of the cor-
responding resonance is also very narrow. For a 1 MeV
gauge boson and a 0.1 eV neutrino mass, a neutrino will
scatter on resonance only within a small range of en-
ergies: ∆E ∼ 1TeV × g2 . The neutrino’s energy
ν Uνν
moves relative to the resonance as a result of redshift
energy losses, however, effectively broadening the reso-
nance considerably [15]. The depth of such a resonance
will be sufficient to deplete the neutrino flux over an en-
ergy range m2/(2m (1+z)) < E < m2/(2m ) if the
U ν ν U ν
distancepropagatedwhileonresonanceislargerthanthe
mean free path:
c ∆E g2 c m2
∆D >∼λ=⇒ ν ≈ Uνν >∼ U , (5)
H E 4πH πn
ν ν
whereH is the rateofHubble expansion. This condition
is satisfied if the U −ν−ν coupling is larger than:
m 1
gUνν >∼4×10−5(cid:18)1MUeV(cid:19)(1+z)3/2, (6) FfoIrGt.h2e:cTasheeosfumppUre=ss1ioMnoefVt,hgeUhνiνgh=-e1n0e−rg5yanneduftorrinsoousprceecstrautma
redshift of z =0.1 (thicksolid), 1.0 (thin solid), 3.0 (dashed)
where z is the redshift at which the neutrino possesses and 5.0 (dotted).
the energy needed to scatter at resonance.
Even if the gauge boson is heavy enough to decay to
e+e−, the result of Eq. 6 is expected to remain largely
unchanged. Although the resonant cross section would In Figs. 1 and 2, these results are illustrated. For
be modified by a factor of ∼ (g /g )2 by allowing a gauge boson with a ∼1 MeV mass and couplings to
Uνν Uee
such decays, the change in the width of the resonance neutrinosoforder∼10−5, high-redshiftsourceswillhave
will counteract this effect. Considering the m > 2m their neutrino flux considerably suppressed within the
U e
case,therefore,makestheconditionofEq.6onlyslightly range E /(1+z) < E < E , where E = m2/2m is
R ν R R U ν
less restrictive. the resonant energy.
3
III. DISCUSSION
Inthebasicscenarioweareconsideringhere,thereare
a number of potentially free parameters, including the
gauge boson’s couplings to various fermions, the gauge
boson’s coupling to dark matter, and the masses of the
gauge boson and dark matter particle. These quantities
can be constrained by a number of considerations.
Firstly, the product of the gauge boson’s couplings
to neutrinos and electrons is constrained by νe scat-
tering experiments, such that gUννqgU2eReR +gU2eLeL <∼
m2G [8, 9]. To satisfy this constraint and at the same
U F
time generate the observed abundance of dark matter,
some care must be taken. The most simple solution
would be to set the U’s couplings to all left-handed
fermions(includingneutrinos)tozero. Inthiscase,there
willbe no observableconsequencesin νe experiments,or
for neutrino astronomy. On the other hand, if the U’s
couplings to left and right-handed fermions are similar
FIG. 3: The distribution of events observed in a high-
in magnitude (or the right-handed couplings are sub-
resolution (∆(logE) ≈ 0.1), high-energy neutrino telescope
dasomlairngaentasorgUzeνrνo)∼wgeUfieLnedLt<h∼at4t×he1se0−c6o(umpUlin/MgsecVa)n. bIef faotrrtehdeshciaftsezo≈f m5.U W=e1hMaveeVc,ognUsiνdνer=ed4a×fl1u0x−6ofamnduosnounrecues-
we consider the case of gUνν = gUeLeL, we can simul- trinos of Eν2µdNνµ/dEνµ =2×10−7 GeV cm−2 s−1, a cubic
taneously satisfy νe scattering andgeneratea significant kilometer detector volume and ten years of exposuretime.
degreeofneutrinoabsorption(ie. satisfytheconditionof
Eq. 6) for high-redshift sources (z >∼ 3). If the coupling
g issomewhatlargerthanthecorrespondingcoupling tionscouldbeused,whichproduceshowerscontainingall
Uνν
to electrons, less distant sources could also possess this of the neutrino’s energy. Such events could, however, be
feature. confusedwithshowersproducedthroughneutralcurrent
interactions.
Assuming good neutrino energy resolution (using well
IV. PROSPECTS AND CHALLENGES FOR reconstructed, contained events), it may be possible to
FUTURE HIGH-ENERGY NEUTRINO reliably detect (or exclude) the presence of an absorp-
TELESCOPES tion line. Even with a low threshold, kilometer-scale
experiment and an optimistic neutrino flux, such a de-
terminationwouldlikelyrequiremanyyearsofexposure,
Detectinganabsorptionfeatureinthehigh-energycos-
however. To convincingly resolve such a feature would
mic neutrino spectrum will be challenging for a number
requirean experimentalprogramwith a greatereffective
of reasons. Most importantly, a very large number of
volume and energy resolution than current or planned
neutrinoswouldneedtobedetectedbeforethespectrum
experiments.
could be adequately reconstructed. In the TeV energy
In Fig. 3, we illustrate what would be required of a
region, in which we have focused on in this letter, next
future high-energy neutrino telescope to observe an ab-
generation kilometer-scale neutrino telescopes, such as
IceCube, willdetect ∼10muoneventsper energydecade sorption feature by plotting the number of events aver-
aged in ∆(logE) ≈ 0.1 energy bins at energies around
(from charged-current muon neutrino interactions) per
anabsorptionfeature. Here,wehaveusedm =1MeV,
year if an optimistic neutrino flux is assumed (saturat- U
g = 4×10−6 and have considered sources at a red-
ing the Waxman-Bahcall bound [16], for example) [17]. Uνν
shift of z ≈ 5. We have used an optimistic high-redshift
Of these, only those events which can be identified (by
cosmic neutrino flux of E2 dN /dE = 2×10−7 GeV
timinganddirectionalconsiderations)tohaveoriginated νµ νµ νµ
from high-redshift sources will be of use in detecting an cm−2 s−1 and an experiment with a cubic kilometer in-
absorption feature. Furthermore, each muon track re- strumented volume, and ten years of observation time.
veals,atmost,theenergyofthemuonproduced,andnot
the total energy of the responsible neutrino. To measure
V. CONCLUSIONS
the cosmic neutrino spectrum with sufficient resolution
to detect an absorption feature would require a detec-
tor capable of measuring the energy of both the muon In this letter, we have pointed out that the existence
track and the accompanying hadronic shower. Alterna- of a new MeV-scale gauge boson coupled to neutrinos
tively, charged-current electron or tau neutrino interac- wouldleadtoabsorptionfeaturesinthe high-energycos-
4
mic neutrino spectrum. The very narrow resonance at photons from the galactic bulge, which could be gener-
a center-of-mass energy equal to the gauge boson’s mass atedby MeV-scaledark matter annihilating throughthe
will deplete the neutrino flux over an energyrange given exchange of the new gauge boson. If such scenario is
by E /(1 + z) < E < E , where E = m2/2m indeed found in nature, high-energy neutrino astronomy
R ν R R U ν
and z is the redshift of the source. The depletion of maybe ableto offercomplementaryinsightsinto the na-
the flux in this range will be efficient if the gauge bo- ture of dark matter.
son’s coupling to neutrinos is larger than approximately
gUνν >∼10−5(mU/MeV).
The possible existence of a light gauge boson has pre- This work has been supported by the US Department
viously been motivated by the observation of 511 keV of Energy and by NASA grant NAG5-10842.
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