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

= Πrespectively. 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)