Download Ab initio nuclear response functions for dark matter searches

Ab initio nuclear response functions for dark matter searches
Daniel Gazda
Chalmers University of Technology
Progress in Ab Initio Techniques in Nuclear Physics
TRIUMF, Feb 28 – Mar 3, 2017
Collaborators:
C. Forssén, R. Catena (Chalmers)
Funded by the Knut and Alice Wallenberg foundation
Outline:
Introduction
Motivation
Direct detection and dark matter–nucleon/nucleus interaction
Methodology
Nonrelativistic EFT for dark matter–nucleus interaction
Ab initio no-core shell model
Results
Nuclear response functions
Physical observables
Conclusions & outlook
Introduction
Methodology
Results
Conclusions
Motivation
Dark matter makes up about 5/6 of the total matter in the Universe.
Evidence for dark matter
rotational curves of galaxies
cosmic microwave background, large
structure formation
gravitational lensing, the Bullet Cluster
...
New type of particle provides simple
explanation. WIMP is a well motivated
candidate.
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
3 / 15
Introduction
Methodology
Results
Conclusions
Motivation
WIMP dark matter searches
χ
χ
SM
SM
χ
SM
SM
SM
χ
χ
χ
SM
production
collider searches
D. Gazda (Chalmers)
annihilation
indirect searches
γ, ν, CR telescopes
scattering
direct detection
deep underground detectors
Ab initio nuclear response functions for DM searches
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Introduction
Methodology
Results
Conclusions
10−39
XENON1T Sensitivity in 2 t ⋅y
DAMA/Na
10−40
CDMS-Si (2013)
−41
Expected limit (90% CL)
± 1 σ expected
± 2 σ expected
DAMA/I
10
XENON10 (2013)
10−42
10
PandaX
SuperCDMS (2014)
−43
10−44
DarkS
10−46
013)
2017
XE
T (2 t
NON1
10−47
⋅y)
⋅y)
T (20 t
Nn
XENO
covery
ino Dis
−48
Billard
10−49
6
10
20 30
100
(2015)
LUX (2
012)
N100 (2
XENO
10−45
10
ide-50
(2014)
2019
LZ 2019+
013)
limit (2
eutr
et al., N
200
1000 2000
10000
WIMP mass [GeV/c2]
taken from:
XENON
JCAP 1604,WIMP-nucleon
027 (2016) interaction: the
Figure 15. XENON1T
sensitivity
(90%collaboration,
C.L.) to spin-independent
solid blue line represents the median value, while the 1σ and 2σ sensitivity bands are indicated in green
and yellow respectively. The dotted blue line, visible at low WIMP masses, shows the XENON1T
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
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JCAP04(20
WIMP-nucleon Cross Section [cm 2]
Current status
Introduction
Methodology
Results
Conclusions
Dark matter direct detection & nuclear physics
new physics ΛUV – heavy mediators
SM + DM EFT
vEW – EW symmetry breaking
5-flavor QCD + DM EFT
mb
mc
3-flavor QCD + DM EFT
ΛQCD – chiral symmetry breaking
heavy baryon chiral EFT + DM
mπ
direct detection NREFT
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
6 / 15
Introduction
Methodology
Results
Conclusions
Dark matter direct detection & nuclear physics
new physics ΛUV – heavy mediators
SM + DM EFT
vEW – EW symmetry breaking
5-flavor QCD + DM EFT
Cirigliano et al.
(JHEP 1210, 25 (2012))
mb
mc
Darmstadt group:
Menéndez, Gazit,
Schwenk, Klos et al.
3-flavor QCD + DM EFT
(e.g. PRD 94, 063505 (2016))
ΛQCD – chiral symmetry breaking
heavy baryon chiral EFT + DM
mπ
direct detection NREFT
Fitzpatrick, Haxton et al.
(JCAP 1302, 4 (2013))
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
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Introduction
Methodology
Results
Conclusions
Nonrelativistic EFT for χ − N/nucleus interaction
Construct the most general form of dark matter–nucleon interaction.
(Fitzpatrick et al., JCAP 1302, 4 (2013))
momentum conservation together with the requirement of Galilean
invariance identifies 4 basic operators:
iq̂, v̂⊥ = v̂ + 2µq̂χN , Ŝχ , ŜN
all possible χ − N interaction terms (up to q 2 ): Ô1 = 1χN
Ô3 = iŜN ·
q̂
mN
×
v̂⊥
Ô9 = iŜχ · ŜN ×
Ô4 = Ŝχ · ŜN
Ô5 = iŜχ · mq̂ × v̂⊥
N Ô6 = Ŝχ · mq̂
ŜN · mq̂
N
Ô7 = ŜN · v̂⊥
Ô8 = Ŝχ · v̂⊥
N
Ô10 =
Ô11 =
q̂
mN
iŜN · mq̂
N
iŜχ · mq̂
N
Ô12 = Ŝχ · ŜN × v̂⊥
Ô13 = i Ŝχ · v̂⊥
ŜN · mq̂
N
Ô14 = i Ŝχ · mq̂
ŜN · v̂⊥
N h
Ô15 = − Ŝχ · mq̂
ŜN × v̂⊥ ·
N
q̂
mN
i
→ χ−nucleus Hamiltonian:
A X X
X
(i) τ
cjτ Ôj t(i)
ĤχA =
i=1 τ =0,1
D. Gazda (Chalmers)
j
Ab initio nuclear response functions for DM searches
7 / 15
Introduction
Methodology
Results
Conclusions
Nonrelativistic EFT for χ − N/nucleus interaction
Rate of nuclear scattering events in direct detection experiments:
dR
ρχ
=
2
dq
mA mχ
Z
d3 ~v f (~v + ~ve )v
dσ
dq 2
mχ , ρχ , f : dark matter mass, density, velocity distributions ← astrophysics
dσ
dq 2 : scattering cross section ← particle and nuclear physics
"
#
X
X
X
dσ
1
q2
ττ0
ττ0
ττ0
ττ0
=
R` W` + 2
R` W`
dq 2
(2J + 1)v 2 0
mN
0
00
00
00
τ,τ
`=Φ ,Φ M,
Φ̃0 ,∆,∆Σ0
`=M,Σ ,Σ
dark matter response functions Rmτ τ
nuclear response functions
D. Gazda (Chalmers)
0
W`τ τ
q
2
0
2
vT⊥2 , mq 2 , ciτ cjτ
0
N
Ab initio nuclear response functions for DM searches
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Introduction
Methodology
Results
Conclusions
Nonrelativistic EFT for χ − N/nucleus interaction
nuclear response functions:
0
ττ
WAB
(q 2 ) =
X
L≤2J
hJ, T , MT || ÂL;τ (q) ||J, T , MT ihJ, T , MT || B̂L;τ 0 (q) ||J, T , MT i
ÂL;τ , B̂L;τ – nuclear response operators:
MLM;τ (q) =
A
X
τ
MLM (qρi )t(i) ,
i=1
A X
1→
−
M
τ
∇ ρi × MLL (qρi ) · ~
σ(i) t(i) ,
q
i=1
A X
1→
−
τ
00
∇ ρi MLM (qρi ) · ~
σ(i) t(i) ,
ΣLM;τ (q) =
q
i=1
0
ΣLM;τ (q) = −i
∆LM;τ (q) =
A
X
M
MLL (qρi )
i=1
A X
·
1→
−
τ
∇ ρi t(i) ,
q
1→
1→
1 M
−
−
M
τ
∇ ρi × MLL (qρi ) · ~
σ(i) × ∇ ρi
+ MLL (qρi ) · ~
σ(i) t(i) ,
q
2
i=1
A X
1→
1→
−
−
00
τ
ΦLM;τ (q) = i
∇ ρi MLM (qρi ) · ~
σ(i) × ∇ ρi t(i)
q
q
i=1
0
Φ̃LM;τ (q) =
q
nuclear ground-state wave functions |J, T , MT i
calculated within no-core shell model (focus on 3 He and 4 He first)
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
9 / 15
Introduction
Methodology
Results
Conclusions
No-core shell model
Ab initio
all particles are active (no rigid core)
exact Pauli principle
realistic internucleon interactions
controllable approximations
Hamiltonian is diagonalized in a finite A-particle harmonic
oscillator basis
NCSM results converge to exact results
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
10 / 15
Introduction
Methodology
Results
Conclusions
Input Hamiltonians
VNN and VNNN potentials derived from chiral EFT
long-range part of the interaction, π-exchange, predicted by
chiral perturbation theory
short-range part parametrized by contact interactions, LECs
fitted to experimental data
N2LOsim Hamiltonian family
(Carlsson et al., PRX 6, 011019 (2016))
parameters fitted to reproduce simultaneously πN, NN, and
NNN low-energy observables
lab,max
TNN
≤ 125, . . . , 290 MeV
→ 42 Hamiltonians
ΛEFT ≤ 450, . . . , 600 MeV
all Hamiltonians give equally good description on the fit data
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
11 / 15
Introduction
Methodology
Results
Conclusions
Results
Aim
quantify the impact of nuclear structure uncertainties on the
interpretation of data from dark matter searches
focus on 3 He and 4 He nuclei – converged (exact) NCSM
calculations of ground-state wave functions possible
calculate all relevant nuclear response functions using the
complete N2LOsim Hamiltonian family
study the impact of systematical uncertainties of nuclear
response functions on the rate of nuclear recoil events in
directional dark matter detection
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
12 / 15
Introduction
Results
Conclusions
He nuclear response functions and recoil rates
1.4
7
00
WM
1.2
×10−21
Ô5
00 × 102
WΦ
00
Ô15
6
00
WΦ
00 M × 10
1.0
dR/d cos θ (kg−1 day−1 )
00 SM
WM
0.8
W 00
4
Methodology
0.6
0.4
0.2
5
4
3
2
1
0.0
−0.2
0.0
0.1
0.2
0.3 0.4
q (GeV)
0.5
0.6
Figure: Isoscalar nuclear response
functions of 4 He as functions of the recoil
momentum q calculated within ab initio
NCSM and SM.
D. Gazda (Chalmers)
0
−1.0
−0.5
0.0
cos θ
0.5
1.0
Figure: Differential rate of nuclear recoil
events as a function of the recoil
direction.
Ab initio nuclear response functions for DM searches
13 / 15
Introduction
Results
Conclusions
He nuclear response functions and recoil rates
1.4
7
00
WM
1.2
×10−21
Ô5
00 × 102
WΦ
00
Ô15
6
00
WΦ
00 M × 10
1.0
dR/d cos θ (kg−1 day−1 )
00 SM
WM
0.8
W 00
4
Methodology
0.6
0.4
0.2
5
4
3
2
1
0.0
−0.2
0.0
0.1
0.2
0.3 0.4
q (GeV)
0.5
0.6
Figure: Isoscalar nuclear response
functions of 4 He as functions of the recoil
momentum q calculated within ab initio
NCSM and SM.
D. Gazda (Chalmers)
0
−1.0
−0.5
0.0
cos θ
0.5
1.0
Figure: Differential rate of nuclear recoil
events as a function of the recoil
direction.
Ab initio nuclear response functions for DM searches
13 / 15
Introduction
3
Methodology
Results
Conclusions
He nuclear response functions and recoil rates
1.6
3.0
1.4
τ, τ 0 = 0, 0
τ, τ 0 = 0, 0 SM
1.2
τ, τ 0 = 1, 1
2.0
0
τ, τ 0 = 0, 1(1, 0)
τ, τ 0 = 0, 1(1, 0) SM
0.8
WΦτ 00τ
0
τ, τ 0 = 0, 0
τ, τ 0 = 0, 1 (1, 0)
2.5
1.0
ττ
WM
×10−3
0.6
1.2
×10−6
1.5
Ô4
1.0
Ô5
1.0
Ô15
0.5
0.2
0.0
0.0
−0.2
0.0
4
τ, τ 0 = 0, 1(1, 0)
τ, τ 0 = 0, 1(1, 0) SM
0.1
0.2
0.3
0.4
q (GeV)
0.5
−0.5
0.0
0.6
×10−1
1.4
3
τ, τ 0 = 0, 0
τ, τ 0 = 0, 1 (1, 0)
1.2
2
τ, τ 0 = 1, 1
τ, τ 0 = 0, 0 (1, 1) SM
1.0
0.2
0.3
0.4
q (GeV)
0.5
0.6
τ, τ 0 = 0, 0
τ, τ 0 = 0, 1 (1, 0)
τ, τ 0 = 1, 1
τ, τ 0 = 0, 1 (1, 0) SM
0.8
0.6
0.4
0.2
ττ
W∆
0
0.8
0
1
WΣτ 0τ
0.1
×10−3
dR/d cos θ (kg−1 day−1 )
0.4
0
0.6
−1
0.4
−2
0.2
−3
−4
0.0
0.0
−1.0
0.0
0.1
0.2
0.3
q (GeV)
0.4
0.5
0.6
−0.2
0.0
0.1
0.2
0.3
0.4
q (GeV)
0.5
0.6
−0.5
0.0
cos θ
0.5
1.0
Figure: Differential rate of nuclear recoil
events as a function of the recoil
direction.
Figure: Nuclear response functions of 3 He as functions of the recoil
momentum q calculated within ab initio NCSM and SM.
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
14 / 15
Introduction
Methodology
Results
Conclusions
Conclusions
Ab initio framework for computation of nuclear response
functions for dark matter scattering off nuclei have been
developed.
Certain nuclear response functions suffer from large
uncertainties which propagate into physical observables.
Ab initio nuclear structure calculations result in additional
response functions not appearing in SM calculations.
arXiv:1612.09165 [hep-ph]
Outlook:
response functions of
16 O
(CRESST-II),
19 F
(PICO), Xe, . . .
inelastic scattering, two-body meson-exchange currents, . . .
D. Gazda (Chalmers)
Ab initio nuclear response functions for DM searches
15 / 15