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Cosmological Constraints! on !
Very Dark Photons
Anthony Fradette
work presented in AF, Maxim Pospelov, Josef Pradler, Adam Ritz : PRD Aug 2014 (arXiv:1407.0993)
Cosmo 2014 - Chicago, IL
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 2
Plan
•Dark Photon review and motivation
•Very Dark Photon (VDP) thermal production
•VDP and Big Bang Nucleosynthesis
•VDP and Cosmic Microwave Background
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 3
MotivationStandard
ModelDark
Sector
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 4
Motivation
OsH†H LHNR Bµ⌫V
µ⌫
Leading SM coupling to Neutral Hidden SectorScalar Right-Handed neutrino U(1)
Portals
Standard Model
Dark Sector
Hello?
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 5
Motivation
OsH†H LHNR Bµ⌫V
µ⌫
Leading SM coupling to Neutral Hidden SectorScalar Right-Handed neutrino U(1)
Portals
Standard Model
Dark Sector
Hello?
Dark PhotonmV ⌧ mZFor , only mixes kinetically with photons
e0 = e
↵e↵ = ↵2B. Holdom, Phys. Lett. B 166, 196 (1986)
LVint = �
2Fµ⌫V
µ⌫ = eVµJµem
LVmass
Stueckelberg
Higgs’
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 6
Dark Photon Landscape aµ,favae
aµ
BABARMAMIAPEX/
KLOEWASA
E141
U70
CHARM
E137LSND
SN
�2
10�4
10�6
10�8
10�10
�2
10�4
10�6
10�8
10�10
�
mV (M eV )104103102101
mV (M eV )104103102101
mV (M eV )104103102101
10�2
10�4
10�6
10�8
10�10
1
Sun
mwLSWCoulomb Rydberg
Jupiter Earth
CMB
HBRG
DPB
LSW
Cosmology
ThermalDM
non-Thermal DM
Haloscopes
AGN, SNR
ALPS-II
UWAADMX
Dish Antenna
ADMX-HFADMX
Stückelberganisotropic
Non-zero FI-term
Hidden Higgs HmHhªm˝ 'LStückelb
erg isotropic HlineL
-18 -15 -12 -9 -6 -3 0 3 6
-15
-12
-9
-6
-3
0
-15
-12
-9
-6
-3
0
Log10mA'@eVD
Log 10e
See Review from: Essig et al., Snowmass 2013
mV < 2me
mV > 2me
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 7
Very Dark Photon ? aµ,favae
aµ
BABARMAMIAPEX/
KLOEWASA
E141
U70
CHARM
E137LSND
SN
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
Can we use the Universe as a detector?
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 8
Very Dark Photon ?Can we use the Universe as a detector?
⌧V ' 3
↵e↵mV= 6⇥ 105 yr⇥ 10 MeV
mV⇥ 10�35
↵e↵
aµ,favae
aµ
BABARMAMIAPEX/
KLOEWASA
E141
U70
CHARM
E137LSND
SN
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
10
10
10
10
-2
-6
-10
-14
Recombination Very Dark!
⌧V [s]
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 9
Very Dark Photon ?Can we use the Universe as a detector?
⌧V ' 3
↵e↵mV= 6⇥ 105 yr⇥ 10 MeV
mV⇥ 10�35
↵e↵
aµ,favae
aµ
BABARMAMIAPEX/
KLOEWASA
E141
U70
CHARM
E137LSND
SN
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
10
10
10
10
-2
-6
-10
-14
Recombination Very Dark!
⌧V [s]
BBN?
CMB?
Can it been seen on Earth?
�prod
⇠ ⇡↵↵e↵
E2
c.m.
⇠ 10�66 � 10�52 cm2
e+e� ! V �
Postma and Redondo, 2008 No explicit bounds derived
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 10
VDP Thermal Production
l
l
Aµ Vµ
κ
time
Dominant contribution from coalescence
sY =Y
i=l,l,V
Z ✓d3pi
(2⇡)32Ei
◆(NlNl �NV )(2⇡)
4�(4)(pl + pl � pV )X
|Mll|2
The Boltzmann equation
is modified because of darkness
⇣Y =
nV
s
⌘
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette -
Cosmological Constraints on Very Dark Photons
Anthony Fradette
1 Maxim Pospelov 1,2 Josef Pradler 3 Adam Ritz 1
1University of Victoria, Canada 2Perimeter Institute, Canada 3Johns Hopkins University, USA
Dark Photons
⌅ A Standard Model Extension
⌅ Neutral hidden sectors, weaklycoupled to the SM, arewell-motivated for New Physics(eg. dark matter, right-handedneutrinos, ...)
⌅ A marginal operator that couldprovide leading coupling to theSM is a new U(1) kineticallymixed with the photon
LV = ≠Ÿ
2Fµ‹V
µ‹ = eŸVµJ
µem.
Aµ Vµ
e+
e�
Figure 1: Illustration ofthe coalescence produc-tion of the dark photonthrough an o�-shell pho-ton.
⌅ The parameter space
Helioscopelongitudinal
SolarLifetime
Cold Dark Matter
CoulombCoulombin atoms
Jupiter Earth
LSW
FIRAS+hCMBCMB
EW
BRHp0Æge+e-L
HB
Fixed target
ThermalC
osmology
ae,m
Haloscopes
e+e-Æm+m-g LHC
-15 -12 -9 -6 -3 0 3 6 9 12
-15
-12
-9
-6
-3
0
Log10mX@eVD
Log 10c
Figure 2: Current contraints on kinetic mixing of dark pho-tons (DP). Pink area is where DP could be cold dark matter.From [1].For m
V
> 2m
e
, we have
·V
ƒ 3–e�m
V
= 6 ◊ 105 yr ◊ 10 MeVm
V
◊ 10≠35
–e�
recombination very dark!
References
[1] J. Jaeckel, Frascati Phys. Ser. 56, 172 [arXiv:1303.1821 [hep-ph]]. 383-399.
[2] J. Redondo and M. Postma, JCAP 0902, 005 (2009) [arXiv:0811.0326 [hep-ph]].
[3] L. Zhang, X. Chen, M. Kamionkowski, Z. -g. Si and Z. Zheng, Phys. Rev. D 76, 061301 (2007)[arXiv:0704.2444 [astro-ph]].
[4] T. R. Slatyer, arXiv:1211.0283 [astro-ph.CO].
[5] M. Pospelov and J. Pradler, Ann. Rev. Nucl. Part. Sci. 60, 539 (2010) [arXiv:1011.1054 [hep-ph]].
Acknowledgement
The Goal
Explore the sensitivity of Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN) datato Very Dark Photons (VDP) with mass m
v
> 2m
e
.
Freeze-in abundance
⌅ Abundance found by integrating the Boltzmann equation forthe reaction in fig 1.
⌅ Thermal bath induces a resonant production through thephoton self-energy⌅ Tranverse and longitudinal modes behave di�erently
d
2�proddÊdT
à 13
m
4v
|m2v
≠ ⇧L
|2+ 2
3m
4v
|m2v
≠ ⇧T
|2
⌅ Subleading due to T
r ,T (L) & 8.1m
v
, parametrically higherthan bulk production [2]
10-28
10-26
10-24
10-22
10-20
10-18
1 10 100
dY
v/d
ωd
T (
Me
V-2
)
T (MeV)
mv = 10 MeVmv = 20 MeV
Figure 3: Di�erential produc-tion rate illustrating the bulkproduction with the T and L res-onance at higher temperature.Showing w = 2m
V
.
15
20
30
50
70
10
100
2 5 20 30 1 10
Lo
g(T
r/m
v)
Log(ω/mv)
transverselongitudinal
Figure 4: Resonant temperaturefor T and L propagation modesfor 1 massless fermion contribu-tion to self-energy.
⌅ We use a crude model for hadronic contribution with freequarks for T > T
c
and a charged pion gas for T < T
c
0.001
0.01
0.1
1
10
50 100 150 200 250 300 350 400 450 500
Ep.b
. (e
V)
mV (MeV)
ΓV-1 = 1014 s
0.1
1
10
Ep.b
. (e
V)
αeff = 10-35
totale+e-
µ+µ
-
π+π
-
u+u-
d+d-
s+s-
Figure 5: Total energy stored per baryons along the leptonicand maximal hadronic contributions for –e� = 10≠35 and�≠1
V
= 1014s. The quark and pion curves are for T
c
= 150MeV and T
c
= Œ respectively. Neglects resonant production.
Cosmic Microwave Background
⌅ Precision measurement of damping tail in temperature powerspectrum provide strong constraints on energy injection atrecombination.
⌅ Generic constraints for decaying particledE
dtdV
= 3’mp�e
≠�t
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-17 10-16 10-15 10-14 10-13 10-12
ζ
Γ [sec]
WMAP 7 + SPTWMAP 3
Planck
Figure 6: CMB constraints on energy injection parameters ’and �. The WMAP 3 curve also includes large scale structureand together with the Planck forecast are reproduced fromRef. [3].
⌅ Not all energy is deposited (eg. heating, neutrinos escape,not on-the-spot deposition, etc.)
13 æ ionization 2
3 æ heating
’ = f
3⌦
V
⌦b
= f
3Ep.b.m
p
.
⌅ The authors of [4] provide transfer functions T (zinj, zdep, E )⌅ We find fe� for a dark photon with decays
V æ {e
+e
≠, µ+µ≠, fi+fi≠} by averaging the E
dep
E
inj
over therange zdep œ [800, 1000]
0
0.2
0.4
0.6
0.8
1
f eff
e+e-
µ+µ
-
π+π
-
total
00.250.5
0.751
50 100 150 200 250 300 350 400 450 500
Br
mV (MeV)
Figure 7: E�ective deposition e�ciency of each decay channelwith the sum weighted by their branching ratios for �≠1
V
=1014s.
Big Bang Nucleosynthesis
⌅ Injection of energetic e
+e
≠ quickly transfers energy tophotons via inverse compton scattering
⌅ “ + “bgd æ e
+e
≠ allowed for E“ & m
2e
/22T
⌅ For smaller E“, the energy is dissipated throughphotodestruction of nuclei
⌅ Photodisintegration start at temperatures
Tph ƒ
8>><
>>:
7 keV, 7Be + “ æ 3He + 4He (1.59 MeV),5 keV, D + “ æ n + p (2.22 MeV),0.6 keV, 4He + “ æ 3He/T + n/p (20 MeV),
which a�ect final BBN abundances [5]
Main Results
Region of the parameter space ruled out by
experiments
Figure 8: CMB constraints on VDP. Does not include reso-nant production.
Coming up
⌅ For m
V
≥ few GeV, V æ nn is allowed⌅ Increase of neutrons around 7Be synthesis can help 7Li
problem [5]⌅ We expect N
new neutrons
N
baryons
ƒ 10≠3 which will suppress 7Li
11
VDP Thermal Production
l
l
Aµ Vµ
κ
time
Dominant contribution from coalescence
sY =Y
i=l,l,V
Z ✓d3pi
(2⇡)32Ei
◆(NlNl �NV )(2⇡)
4�(4)(pl + pl � pV )X
|Mll|2
The Boltzmann equation
is modified because of darkness V not in equilibrium Freeze-in production
0
⇣Y =
nV
s
⌘
d2�prod
d!dT/ 1
3
m4
V
|m2
V �⇧L|2
+2
3
m4
V
|m2
V �⇧T |2
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 12
VDP Thermal Production
0.0001
0.001
0.01
0.1
1
10
1 10 100 1000 10000
Ep
.b. (
eV
)
mV (MeV)
ΓV-1 = 1014 s
0.1
1
10
Ep
.b. (
eV
)
αeff = 10-35
totale+e-
µ+µ
-
τ+τ-
π+π
-
K+K-
u/d+u/d-
s+s-
c+c-
aµ,favae
aµ
BABARMAMIAPEX/
KLOEWASA
E141
U70
CHARM
E137LSND
SN
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�
mV (M eV )
�
1041031021011
10�2
10�4
10�6
10�8
10�10
10�12
10�14
10�16
10�18
10
10
10
10
-2
-6
-10
-14
1
10
10
10
-4
-8
4
Basic QCD transition model
Free meson gas Free quarks
Tc = 157 MeV
nV
nb
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 13
VDP and Big Bang NucleosynthesisBBN is a good probe for New Physics
6Li/H
N
7Li/H
7Be/H
3He/HT/H
D/H
Yp
H
SBBN f.o.
D b.n.
e± ann.n/p dec.ν dec.
t/sec
T/keV
0.1 1 10 100 1000 104 105 106
1000 100 10 1
1
10−2
10−4
10−6
10−8
10−10
10−12
10−14
SBBN f.o.
D b.n.
e± ann.n/p dec.ν dec.
T/keV1000 100 10 1
1
10−2
10−4
10−6
10−8
10−10
10−12
10−14 23
p − n D
3He
T
4He
7Be
7Li
p n
D p
DD
1
T D
3 He 4 H
e
DD
2
3H
e D
7Li p
4He T
3He n 7Be n
Figure 4.1: Main reactions in BBN. Each line is labeled by the reactants. DD1corresponds to D +D →3 He+ n and DD2 to D +D → T + p. Inspired by [2].
which is highly suppressed due to the low number density of the reactants, thus
dwarfing the 3-body cross section. The heavier elements will be created in stars,
where the density formed by gravitational collapse become high enough to allow 4.4
at a decent rate.
This system has been solved numerically in ref. [60] and is shown in figure 4.2a. It
is standard to state the abundance of 4He as Yp, the mass fraction relative to the total
mass of baryons. Its actual relative number density by nuclei is fHe ≡n4HenH
= Yp
4−Yp≃
0.07. All other species abundances are quoted as their relative number density to the
hydrogen nuclei. BBN has only one free parameter ηB = nBnγ, which is determined by
the WMAP satellite. In particular, with a baryon to photon ratio of ηB = 6.2×10−10
from WMAP5 [61], the abundance of 3He and T are
3He
H
∣
∣
∣
∣
p
= 1.00× 10−5,T
H
∣
∣
∣
∣
p
= 7.8× 10−8. (4.5)
4.1.1 The Tritium Decay Scenario in BBN
Ultimately, we want to analyze the effects of the TDS on the CMB radiation. Since the
Universe is opaque at the BBN epoch, the outcome of the primordial nucleosynthesis
serves as initial conditions on CMB physics. Therefore, for the TDS to be viable,
we must verify that it does not spoil BBN. We consider the three variation channels
proposed in section 3.3.
The fundamental constants enter everywhere in the network of differential equa-
Pospelov and Pradler, 2010
• Minimal assumptions • 1 parameter : (Planck, WMAP)⌘b
Provides constraints on any modification to nuclear reaction network!!e.g. energy injection from non-SM particle decays !
mV < 2m⇡
mV > 2m⇡
Electromagnetic energy injection
Hadronic energy injection
Opposing trends in YV � ⌧V
mV � Localized constraints in
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 14
VDP and Big Bang Nucleosynthesis
• Injection of quickly transfers energy to photons via inverse Compton scattering
• allowed for • For smaller , the energy is dissipated
through photodestruction of nuclei
e+e� (µ+µ�)
� + �bgd ! e+e� E� & m2e/22T
tph '
8<
:
2⇥ 104s, 7Be + � ! 3He + 4He (1.59MeV),5⇥ 104s, D+ � ! n+ p (2.22MeV),4⇥ 106s, 4He + � ! 3He/T+ n/p (20MeV),
E�
Region Ia
• Reduction of 7Li (3-4 x 10-10)!!• Underproduction of D!
D/H = (2.53± 0.04)⇥ 10�5
3He/D < 1Cooke et al., 2013
Region Ib• Increase of 6Li by !
Not a constraintO(100)
Region Ic• Creation of 3He ruled out by
3He/D < 1
108
105
102
1
103
106
Ic
Ib
Ia
mV (M eV )
�
1041031021011
10�10
10�11
10�12
10�13
10�14
10�15
nV /nb�V / sec6Li/H
7Li/HD/H
3He/D
4He
mV (M eV )
�
1041031021011
10�10
10�11
10�12
10�13
10�14
10�15
mV < 2m⇡ : EM energy injection
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 15
VDP and Big Bang Nucleosynthesis: Hadronic energy injection
• Simplified by considering long-lived mesons , , and (anti-)nucleons
!• Important reactions
mV > 2m⇡
108
105
102
1
103
106
III
II
Ic
Ib
Ia
mV (MeV)
κ
1041031021011
10−10
10−11
10−12
10−13
10−14
10−15
nV /nb
τV / sec
6Li/H
7Li/HD/H
3He/D
4He
mV (MeV)
κ
1041031021011
10−10
10−11
10−12
10−13
10−14
10−15
Region II• Short lifetime !!• Additional , rises !!!
Region III
⇡± K± K0L
⇡� + p ! ⇡0 + n
p $ n n/p
Yp 0.26D/H 3⇥ 10�5
Charge exchange
(before D-bottleneck)• Extra neutrons from
or indirect production !• Lithium depletion !• Extra neutrons yield more D!
V ! nn
D/H 3⇥ 10�5
7Be + n ! 7Li + p7Li + p ! 4He + 4He
Lithium depletion
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 16
VDP and Cosmic Microwave Background
Planck, 2013
The CMB is an integrated image over the recombination epoch
0.0001
0.001
0.01
0.1
1
0 200 400 600 800 1000 1200 1400
X e
z
RCDMmV = 10 MeV, g = 2x10-17
0 1e-10 2e-10 3e-10 4e-10 5e-10 6e-10 7e-10 8e-10 9e-10 1e-09
10 100 1000
CTT
l(l+
1)/2/
l
mV = 10 MeV, g = 2x10-17
RCDM
Provides constraints on any modification to visibility function!!e.g. energy injection from non-SM particle decays !
Partial reionization enhances late scatterings of CMB photons
Washes out small scale TT correlation
Chen and Kamionkowski, 2004eg.:Slatyer et al., 2009
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 17
VDP and Cosmic Microwave Background
0
0.2
0.4
0.6
0.8
1
f eff
e+e-
µ+µ
-
π+π
-
total
00.250.5
0.751
50 100 150 200 250 300 350 400 450 500
Br
mV (MeV)
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-17 10-16 10-15 10-14 10-13 10-12
c
K [sec-1]
Planck + WMAP 9 PolWMAP 7 + SPT
WMAP 3Planck forecast (2007)
κ
mV (MeV)
Planck
WMAP7
τV
nv/nb
10-17
10-16
10-15
1 10 100
1015
1013
1011
10-8
10-6
10-4
dE
dtdV= 3⇣mp�e
��t
1
3
2
3
Generic constraints on decaying particle
⇣ Energy output ionization
heating
Energy is not deposited right away
For eg. Zhang et al., 2007
Slatyer, 2012
Cosmo 2014 - Chicago, IL Cosmological Constraints on Very Dark Photons - Anthony Fradette - 18
Summary
BBN
CMB
aµ,fav
ae
aµ
BABARMAMIAPEX/
KLOEWASA
E141
U70
CHARM
E137LSND
SN
mV (MeV)
κ
1041031021011
10−2
10−4
10−6
10−8
10−10
10−12
10−14
10−16
10−18
mV (MeV)
κ
1041031021011
10−2
10−4
10−6
10−8
10−10
10−12
10−14
10−16
10−18
7Li/HD/H
3He/D
4HePlanck
mV (MeV)
κ
1041031021011
10−2
10−4
10−6
10−8
10−10
10−12
10−14
10−16
10−18
• The Universe is a great particle detector !!• Minimal assumptions !!!• Additional contributions can only strengthen
constraints !!!• Present-day decays ? Abundance falls short
by many orders of magnitude (antimatter, gamma-ray, neutrino signals…)
V �! ��
T ⇠ O(1� 1000 MeV)