Breit-Wigner Enhancement in the Interactions of a Light Scalar Dark Matter - Rencontres ...
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Breit-Wigner Enhancement in the Interactions of a Light Scalar Dark Matter In collaboration with T. Binder, S. Matsumoto and Y. Watanabe Kavli IPMU, University of Tokyo Sreemanti Chakraborti LAPTh, Annecy January 26
Scalar dark matter
1
0.5
• Singlet scalar is the simplest Beyond Standard =
0.0
1
M
Model extension 0.0 /Ω D
ΩS
0.1
• For lifetime ą age of the Universe, a singlet scalar M
=
−0.5 /Ω D
log10 λhs
Ω S
can be a dark matter candidate 1
=
−1.0 DM
• Scalar singlet dark matter only has Higgs portal in Ω S
/Ω
order to interact with Standard Model −1.5
1 2 2 1
L “ µ S ` λhs S 2 |H|2 −2.0
2 S 2
• In scalar singlet dark matter model, all other mass
2.0 2.5 3.0 3.5
region is excluded by direct detection except for log10 (mS /GeV)
the Higgs resonance at mS „ mH {2
Cline et. al Phys. Rev. D 88, 055025 (2013)
BW Enhancement in Dark Matter phenomenology
2
• An ”exception” to Boltzmann eqn
• When the mediator mass approaches twice the DM mass, DM
Breit-Wigner
annihilation cross section becomes sensitive to DM velocity
• Most general expression
small v0
16π γ2
σ“ M 2 β̄i βi pδ`~ 2 {4q2 `γ 2 Bi Bf
vrel
32π γ2 large v0
xσvrel y » BB
M 2 β̄i pδ`ξ v02 q2 `γ 2 i f
−4 −2 0 2 4 6 8 10
vrel2/(10−3c2)
• A boost factor is obtained in DM annihilation near the reso-
nance region
• Temperature dependence of thermal averaged DM annihila- Ibe et. al, Phys.Rev.D79:095009,2009
tion cross-section in BW resonance region is widely studied in
DM phenomenologyWhat do we have here?
3
• scalar 1 : χ, Z2 odd Ñ dark matter 10-4 γγ 4π,ηη,ρρ
• scalar 2 : φ1 , charge neutral ee ss
-6
10 μμ gg
ττ cc
˜ ¸ ˜ ¸˜ ¸
h1
Γ (GeV)
h cos θ ´ sin θ ππ
• “ 10-8 bb
φ sin θ cos θ φ1 KK
10-10
ó
10-12
h,φ
χ ÝÝÑ SM
χ
10-14
10-2 10-1 100 101
φ Cφχχ
mϕ (GeV)
χ
Γ pφ Ñ SMsq “ sin2 θ ΓphSM Ñ SMsq|m2 2
Ñmφ
hSM
We focus on BW resonance facilitated by light mediator
ë 10 MeV-10 GeVDark matter relic density
4
Effect of BW resonance
Early kinetic decoupling
• Dark matter annihi-
DM SM
• Small DM-mediator coupling reduces scatter-
lates into SM particles med ing rate between DM and SM particles in the
through s-channel reso- thermal bath
nance from φ mediation. DM SM • Suppressed scattering rate causes DM to ki-
netically decouple much earlier than the stan-
• Enhanced cross-section keeps the dark sector coupling dard freeze-out case
down in order to match with the observed relic density
• Need to solve full BE ñ drastic drop in relic
2
32Cφχχ rΓ pφ Ñ fSM qsm2 Ñs density around resonance than standard case
φ
σv pχχ Ñ fSM q » 5
MDM =1 TeV, δ=10-5 , α=10-4
mφ 2
pv 2 ´ vR2 q2 ` 16Γ2φ psq{mφ YEQ
10-4
ÿ Y
Γφ psq ”rΓ pφ Ñ χχq ` Γ pφ Ñ fSM qsm2 Ñs YxKD =90
φ 10-7
YxKD =∞
fSM
Duch et. al,
Y
ż8
10-10
xσv pχχ Ñ fSM qyv0 » dv σv pχχ Ñ fSM qf pv , v0 q JHEP09(2017)159
0 10-13
2
s »mφ p1 ` v 2 {4q{p1 ` vR2 {8q2
1 1000 106 109
vR2 ”4pmφ {mχ ´ 2q, γ ” Γ2φ psq{mφ
2 xDark matter self-interaction
5
Why self-interaction?
A solution to small-scale structure problem
DM DM
med
DM DM
Direct detection of SIDM, S. Tulin Chu et. al, PRL 122, 071103 (2019)
BW resonance and self-interaction
• BW introduces a natural velocity de- xσv pχχ Ñ χχqyv0
pendence in self-scattering cross-section 4
2v0 1
ż8 v Cφχχ f pv , v0 q
• Resonance enhancement can match the » ? σ0 ` 6
dv
π 2πmφ 0 pv 2 ´ vR2 q2 ` 16Γ2φ psq{mφ
2
simulated xσv y{m even with very low
2 2 2
DM-mediator coupling. σ0 “pλχ ´ 2Cφχχ {mφ ´ 3Chχχ {mh2 q2 {p32πmφ
2
qCombining constraints
6
Self-interaction
/m (cm2 /g × km /s)
1000
2 /g
cm
10
100
mφ À 50 GeV. m
2 /g
1c
For mφ À 10 GeV,
For our model
vR „ 100 km/s 10 m = 5 GeV
at 95 % C.L ñ 0.1
cm
2 /g γ = 10-5
vR = 200 km/s
narrow resonance! σ0 = 0.05 cm2 /g
1
10 50 100 500 1000 5000 104
(km /s)
in order to match the simulations from dwarf galaxies, LSB spiral galaxies and clusters.Combining constraints
6
Self-interaction
/m (cm2 /g × km /s)
1000
2 /g
cm
10
100
mφ À 50 GeV. m
2 /g
1c
For mφ À 10 GeV,
For our model
vR „ 100 km/s 10 m = 5 GeV
at 95 % C.L ñ 0.1
cm
2 /g γ = 10-5
vR = 200 km/s
narrow resonance! σ0 = 0.05 cm2 /g
1
10 50 100 500 1000 5000 104
(km /s)
in order to match the simulations from dwarf galaxies, LSB spiral galaxies and clusters.
Relic density
• Since the freeze-out occurs around T„ O(GeV) in the allowed mediator mass region, QCD phase transition
has a significant impact on the scattering rate
• In early kinetic decoupling calculation, zero DM-SM scattering assumption produces up to 10 % difference
in the relic abundance calculation compared to the largest scattering scenario
• For χ2 calculation, setting 20 % of Ωh2 as the standard deviation excludes the region below the muon
threshold.Astrophysical constraints
7
CMB
• DM annihilation could inject electromagnetic particles into the primordial plasma at the recombination era
´ ¯´ ¯ ´ ´4 ¯1{2
Tγ
• DM velocity at recombination, vDM “ 2 ˆ 10´4 1 eV 1 MeV
m
10
x
χ kd
• we have vR Á 10´3 " vDM , DM annihilation is s-wave
• Since we have BW enhanced annihilation, the velocity dependence in the s-wave annihilation cross-section
at recombination allow some parameter space
• PLANCK data excludes the region above the b quark threshold. The resonance is restricted in the tiny
region vR „ 10´3Astrophysical constraints
7
CMB
• DM annihilation could inject electromagnetic particles into the primordial plasma at the recombination era
´ ¯´ ¯ ´ ´4 ¯1{2
Tγ
• DM velocity at recombination, vDM “ 2 ˆ 10´4 1 eV 1 MeV
m
10
x
χ kd
• we have vR Á 10´3 " vDM , DM annihilation is s-wave
• Since we have BW enhanced annihilation, the velocity dependence in the s-wave annihilation cross-section
at recombination allow some parameter space
• PLANCK data excludes the region above the b quark threshold. The resonance is restricted in the tiny
region vR „ 10´3
Indirect searches
• For DM annihilation in the present time, the higher moments add significantly in xσv y, because vR „ 10´3
is close to DM velocity in the Milky Way
• Photon spectra originating from DM annihilation into charged particles significantly constrains the model
• Tightest constraints from e ˘ flux observations by Voyager I and AMS-02
• Large uncertainties in the injection spectra for hadron channel around 2 GeV mediator
• Large uncertainty in local DM density
• Injection spectra for lepton channel favours 1 À mφ À 2 GeV, vR „ 10´3Viable parameter space 8
Further on..
9
Weaker constraints
• Direct search is possible through DM-nucleon scattering, although sensitivity is not promising for light DM
ˆ ˙2
fN2 mN
4 Cφχχ Chχχ
• σSI pχN Ñ χNq “ 4πv 2 pm `m q2 sin θ m 2 ` cos θ m 2 ñ suppressed by small mixing
H χ N φ h
• Detectable through searches for invisible decay of the mediator. Present NA64 bound is very weak for low
DM-mediator couplingFurther on..
9
Weaker constraints
• Direct search is possible through DM-nucleon scattering, although sensitivity is not promising for light DM
ˆ ˙2
fN2 mN
4 Cφχχ Chχχ
• σSI pχN Ñ χNq “ 4πv 2 pm `m q2 sin θ m 2 ` cos θ m 2 ñ suppressed by small mixing
H χ N φ h
• Detectable through searches for invisible decay of the mediator. Present NA64 bound is very weak for low
DM-mediator coupling
Room for improvement
• Future γ-ray telescopes such as AMEGO, GECCO as well as X-ray telescopes propose promising probe for
MeV-a few GeV DM
• Belle-II proposes better sensitivity for B ` Ñ K ` +invisible decay channel, which can be a nice tool for
constraining our model. At present the BaBar sensitivity for this channel is not promising.Take home
10
• We consider a scalar dark matter interacting with the SM through a light scalar mediatorTake home
10
• We consider a scalar dark matter interacting with the SM through a light scalar mediator
• We focus on the Breit-Wigner enhancement facilitated by s-channel resonance of the light scalar mediatorTake home
10
• We consider a scalar dark matter interacting with the SM through a light scalar mediator
• We focus on the Breit-Wigner enhancement facilitated by s-channel resonance of the light scalar mediator
• Early kinetic decoupling significantly affects DM relic densityTake home
10
• We consider a scalar dark matter interacting with the SM through a light scalar mediator
• We focus on the Breit-Wigner enhancement facilitated by s-channel resonance of the light scalar mediator
• Early kinetic decoupling significantly affects DM relic density
• Velocity dependence in s-channel self-scattering cross section provides a solution to the core-cusp problemTake home
10
• We consider a scalar dark matter interacting with the SM through a light scalar mediator
• We focus on the Breit-Wigner enhancement facilitated by s-channel resonance of the light scalar mediator
• Early kinetic decoupling significantly affects DM relic density
• Velocity dependence in s-channel self-scattering cross section provides a solution to the core-cusp problem
• A χ2 analysis is implemented and the best fit favours mediator mass „ 1-2 GeV, mixing angle „ 10´5 and
vR „ 10´3 surviving relic density, self-interaction, CMB and indirect detection boundsTake home
10
• We consider a scalar dark matter interacting with the SM through a light scalar mediator
• We focus on the Breit-Wigner enhancement facilitated by s-channel resonance of the light scalar mediator
• Early kinetic decoupling significantly affects DM relic density
• Velocity dependence in s-channel self-scattering cross section provides a solution to the core-cusp problem
• A χ2 analysis is implemented and the best fit favours mediator mass „ 1-2 GeV, mixing angle „ 10´5 and
vR „ 10´3 surviving relic density, self-interaction, CMB and indirect detection bounds
• The model can be further constrained in near future probes at B-factory and other beam-dump experi-
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