bbn and cmb !1 bounds on hidden sector vectors · pair creation on nuclei compton scattering...
TRANSCRIPT
!1BBN and CMB bounds on hidden sector vectorsGraham White, TRIUMF
JHEP 1901 (2019) 074 and arxiv 2002.xxxxwith John Coffey, Lindsey Forestell and David Morrissey
Where to look for hidden sectors!2
Collider builders
New physics Mass
Where to look for hidden sectors!3
Why bother with cosmo?!4
arXiv:1407.0993 Fradette et al arXiv1605.07195 Berger et al
Outline!5
1. Big Bang nucleosynthesis 2. Model independent BBN constraints 3. Ionization of the intergalactic medium during recombination 4. Spectral distortions to the cosmic microwave background 5. Model Dependent constraints
Big Bang nucleosynthesis
• Inverse beta decay
• n/p~ frozen out at ~0.8 MeV
• Deuterium bottleneck
• At T ~ 150 keV bottleneck is broken and abundances are frozen in
• Most in Hydrogen and
!6
p + e → n + νe
D + γ → p + n
4He
Big Bang nucleosynthesis!7
Takes only BAU as input
BAU from cmb Predicts observed light element abundances
Constrains energy injection from new long lived particles
Most focus has been on the injections >> GeV
Particle data group
Big Bang nucleosynthesis!8
Focus on EM injection < 1 GeV
Initial injection of photons, electrons, muons, pions or neutrinos
Neutrinos decouple, muons and pions decay
Electrons and photons interact with the background resulting in an EM cascade
EM cascade breaks up nuclei
Electromagnetic Cascade!9
γ + γBG → e+ + e−
γ + γBG → γ + γ
γ + NBG → NBG + e+ + e−
γ + e−BG → γ + e−
e∓ + γBG → e∓ + γ
X → e+ + e− + γ
Photon-photon pair production
Photon photon scattering
Pair creation on nuclei
Compton scattering
Inverse Compton
Final state radiation
New
Photon spectrum• Spectrum
• Rate of injection
• Distribution:
• Conventional wisdom: Universal spectrum
!10Ni
γ ≡dni
γ
dE→ Nf
γ
f̄(E) =1R
Nγ(E) −ξγ
Γγ(EX)δ(E − EX)
R = nX(t)/τx
dnγ
dE≈ R
pγ(Eγ)Γγ(Eγ)
Effective threshold for pair production
Photon spectrum• Problems with Universal spectrum for low E
injections:
•
• Nuclear thresholds
!11
EX < (EC, Em)
Electromagnetic Cascade!12
1028
1030
1032
1034
1036
1038
1040
0.001 0.01 0.1
f̄ γ(G
eV−2)
Eγ (GeV)
EX = 30MeV
Universal SpectrumPoulin+Serpico
T = 1 eVT = 10 eV
T = 100 eV
1028
1030
1032
1034
1036
1038
1040
0.001 0.01 0.1
f̄ γ(G
eV−2)
Eγ (GeV)
EX = 30MeV
Universal SpectrumT = 1 eVT = 10 eV
T = 100 eV
Light element abundances!13
Yp = 0.245 ± 0.004
nD
nH= (2.53 ± 0.05) × 10−5
n3He
nH= (1 ± 0.5) × 10−5
(Helium mass fraction)
Light element abundances!14
Yp = 0.245 ± 0.004
nD
nH= (2.53 ± 0.05) × 10−5
n3He
nH= (1 ± 0.5) × 10−5
Theory uncertainty (photon capture)
Emission lines from Metal poor extragalactic regions 1503.08146
Observations of solar winds etc To determine composition of proto-solar cloud
Boltzmann equations• Take BBN products as initial conditions
!15
dYA
dt= ∑
i
Yi ∫∞
0Nγ(Eγ)σy+i→A(Eγ) − YA ∑
f∫
∞
0Nγ(Eγ)σy+A→f(Eγ)
Nucleon-destruction!16
D + γ → p + n
3He + γ → D + p
4He + γ → 3He + n
First Deuteron destruction (2.2 MeV)
First Deuteron creation (5.5 MeV)
First (important) Helium destruction (20.6 MeV)
Benchmarks for photon injection!17
10 MeV 30 MeV 100 MeV
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
Benchmarks for electron injection!18
10 MeV 30 MeV 100 MeV
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
Benchmarks for electron injection!19
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
4 6 8 10 12-15
-14
-13
-12
-11
-10
-9
log10τ(s)
EXYX(GeV
)
D
3He
4He
10 MeV 30 MeV 100 MeV
Monochromatic injection!20
-14.0-13.5-13.0-12.5-12.0-11.5-11.0-10.5-10.0-9.5-9.0
�EV = Ec(τV)
�EICγ ≤ 2MeV
ExYx(GeV)
Electrons Photons
Other model independent constraints!21
Monochromatic Injection into
1. Muons 2. � 3. � 4. �
π+π−
π0γπ+π−π0
Other model independent constraints!22
dNdEγ
=dNdEγ
rad
+dNdEγ
FSR
+dNdEγ
dir
dNdEe
=dNdEe rad
+dNdEγ
dir
All unstable —calculate the final photon and electron spectrum .
Some energy lost into neutrinos
Monochromatic Injection into
1. Muons 2. � 3. � 4. �
π+π−
π0γπ+π−π0
Other model independent constraints!23
Can calculate spectrum from decays of SM particles in the rest frame and boosting
γ = mV /2mSM = 1/ 1 − β2
dNx
dE=
24π ∫ dΩ′ �
1γ(1 + β cos θ′�E′ �/p′�)
dNx
dE′�
Other model independent constraints!24
Radiative contributions for muons
Other model independent constraints!25
Radiative contributions for charged pions
Note: take polarization into account
π− μ−
ν̄μ
νμe−
ν̄e
Other model independent constraints!26
Radiative contributions for charged pions
dNdEγ
= ∑l∈e,μ
BR(π+ → l, μ)dNdEγ
π+→l+νl
+ BR(π+ → μ+νμ)dNdEγ
μ
See also 1) HAZMA 2) Plehn et al 1911.11147
Other model independent constraints!27
FSR contributions for charged pions
Vπ+
π−γ
dNdE
∼αmπ+
π2(1 − x)
xlog ( m2
V(1 − x)m2
π+ )
Typically subdominant!
Other model independent constraints!28
FSR contributions for muons
Vμ+
μ−γ
dNdE
∼αmπ+
π1 + (1 − x)2
xlog ( m2
V(1 − x)m2
μ )
Typically dominant!
Note: Leading log becomes a poor approximation for light dark matter! We use the full FSR spectrum
Other model independent constraints!29
-14.0-13.5-13.0-12.5-12.0-11.5-11.0-10.5-10.0-9.5-9.0
μ π+π−π0
π+π−π0γExYx(GeV)
Model dependent constraints!30
Vector mediators: Dark Photons Gauged lepton family numbers �U(1)B−L
Model dependent constraints!31
Vector mediators: Dark Photons Gauged lepton family numbers �U(1)B−L
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
DP
BR
mV (GeV)
e+e�
µ+µ�
⇡+⇡�
⇡+⇡�⇡0
⇡0�inv
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
(B�L)
BR
mV (GeV)
e+e�
µ+µ�
⇡+⇡�
⇡+⇡�⇡0
⇡0�inv
VMD to estimate � decaysωData driven calculation of � meson decaysρ
Model dependent constraints!32
DP B − L
-14.0-13.5-13.0-12.5-12.0-11.5-11.0-10.5-10.0-9.5-9.0
ExYx(GeV)
Model dependent constraints!33
-14.0-13.5-13.0-12.5-12.0-11.5-11.0-10.5-10.0-9.5-9.0
Lμ − Le Lτ − Le Lμ − Lτ
ExYx(GeV)
CMB ionization constraints!34
Energy injected at very late times can affect the ionization history of the Universe, modifying the CMB
Constraints on the dark matter fraction from �1012s ≲ τ ≲ 1025s
CMB ionization constraints!35
Not all energy injected is deposited into the intergalactic medium
�( dρdt )
dep
= f(z)( dρdt )
inj
fion(z) =H(z)∑species ∫ ∞
zd log(1 + zin)
H(zin)∫ T(zin, z, E)E dN
dEdEe−t(z)/τχ
∑species ∫ E dNdE
dE
Only care about energy deposited into ionization
Energy is not deposited immediately
Depletion of initial abundance
CMB ionization constraints!36
Principal components
Tracy Slatyer 1109.6322 See also her work in 2015/2016 (project epsilon)
Most important
PC 1 PC 2 PC 3
Constraints � ∼ ei(z)∫dzz ∑
i
PCi(z)f(z)
CMB ionization constraints!37
-20.5
-20.0
-19.5
-19.0
-18.5
-18.0
-17.5
-17.0
DP B − L
ExYx(GeV)
CMB ionization constraints!38
-20.5
-20.0
-19.5
-19.0
-18.5
-18.0
-17.5
-17.0Lμ − Le Lτ − Le
Lμ − Lτ
ExYx(GeV)
CMB spectral distortion constraints!39Cobe/FIRAS and PIXIE can detect departures from a black body spectrum
Decays occurring between the decoupling of double Compton scattering and Compton scattering � change the photon chemical potential
Decays after decoupling of Compton scattering and recombination � change the Compton y parameter
2 × 106 ≳ z ≳ 5.2 × 104
(5.2 × 104 ≳ z ≳ 1090)
CMB spectral distortion constraints!40
μγ ∼ 1.4∫ dt𝒥μ(t)(Δ ·ργ
ργ ) y ∼ 4∫ dt𝒥y(t)(Δ ·ργ
ργ )Δ ·ργ = femmV
n0V
τVe−t/τv
𝒥μ𝒥y
1000 5000 1 ×104 5 ×104 1 ×105 5 ×105 1 ×106
0.001
0.010
0.100
1
zC zDC
Cobe and Pixie Limits!41
COBE : μ < 9 × 10−5 , |y | < 1.5 × 10−5
PIXIE : μ < 1 × 10−8 , |y | < 2 × 10−9
Freeze in abundances!42
sdYV
dt= ⟨
1γ
⟩neqV ΓV
YV = (YV)I+ (YV)II
(YV)I=
32π2
m3VΓ̃V ∫
xQCD
0dx
K1(x)x2sH
(YV)II=
32π2
m3VΓV ∫
∞
xQCD
dxK1(x)x2sH
Freeze in abundances!43
1 5 10 50 100 500 1000
5.×10-19
1.×10-18
2.×10-18
mV
mVYV(GeV
)
B − L
DP
∼ 5/2
Parameter constraints!44
DP B − L
Le − LτLe − Lμ
ϵeff = g 1/4παem
DP B − L
Le − LμLe − Lτ
Conclusions!45
We are motivated to look for light hidden sectors Cosmological constraints become very interesting in this region Between Spectral distortion, ionization history and BBN, an enormous parameter space can be probed! We demonstrated this for several well motivated hidden sector vector mediators
Back up slides!46
Extra details on Tracy’s code!47
Used functions from 2015 code to get f_ion
Used functions from 2012 code to do the PCA, rescaling f by the assumed ionization fraction and using f_ion generated by the 2015 code