Is a WIMP explanation of the DAMA modulation effect still viable? - - PowerPoint PPT Presentation
Is a WIMP explanation of the DAMA modulation effect still viable? Gaurav Tomar Based on Phys.Rev. D99 (2019) no.2, 023017 and JCAP 1906 (2019) no.06, 048 In collaboration with S. Scopel, S. Kang, and J. H. Yoon Sogang University, Seoul
Gaurav Tomar Based on Phys.Rev. D99 (2019) no.2, 023017 and JCAP 1906 (2019) no.06, 048 In collaboration with S. Scopel, S. Kang, and J. H. Yoon Sogang University, Seoul
Search of Dark Matter
Dark matter can be searched by many ways:
Status of Dark Matter Detection: 1707.06277
1 / 39
WIMP direct detection
Elastic recoil of non relativistic halo WIMPs off the nuclei of an underground detector.
Recoil energy of the nucleus lies in the keV range. Expected signal is very low. large exposure and extremely low background is required.
2 / 39
The DAMA signal
First result published 20 years ago. In strong tension with experiments using different target material for standard spin-independent, spin-dependent interactions and Maxwellian velocity distribution. Modulation detectors sharing the similar NaI target (ANAIS(?), COSINE-100) are not yet sensitive enough. Limits extended to specific generalizations: inelastic scattering, non-relativistic models, halo-independent approaches etc.
3 / 39
Theoretical predictions for the WIMP direct detection depend on two main ingredients:
with different targets Spin-independent interaction: σχN ∝ [cpZ + (A − Z)cn]2 Spin-dependent WIMP–nucleon interaction: σχN ∝
p + cnSA n
2
Generally, a Maxwellian distribution
4 / 39
Nuclear response functions at vanishing momentum transfer
S.Kang, S.Scopel, GT, J.H. Yoon, “Present and projected sensitivities of Dark Matter direct detection experiments to effective WIMP-nucleus couplings” Astropart.Phys. 109 (2019) 50-68
Nuclear response function W ′s is normalized such as 16π (2jT + 1)×W p
TM(y = 0) = Z 2 T ,
16π (2jT + 1)×W n
TM(y = 0) = (AT−ZT)2 5 / 39
Reduction of sensitivity
cn cp ≃ Z Z − A ≃ −0.7
sensitivity of Xenon detector.
Lint ∋ cp Sχ · Sp + cn Sχ · Sn,
reducing the sensitivity of Xenon detector.
We will use DAMA as a benchmark to explore these scenarios and what about other non-standard interactions?
6 / 39
Hamiltonian density of WIMP-nucleus interaction, H(r) =
15
(c0
j + c1 j τ3)Oj(r)
cp
j = (c0 j + c1 j )/2 (proton) and cn j = (c0 j − c1 j )/2 (neutron)
All operators is guaranteed to be Hermitian if built out of the following four 3-vectors, i q mN , v ⊥, Sχ, SN with v ⊥ = v + q/2µN ⇒ v ⊥ · q = 0. A.L.Fitzpatrick, W.Haxton, E.Katz, N.Lubbers and Y.Xu, JCAP1302, 004 (2013),1203.3542.
8 / 39
Possible operators
N.Anand, A.L.Fitzpatrick and W.C.Haxton, Phys.Rev.C89, 065501 (2014),1308.6288. O1 = 1χ1N; O2 = (v ⊥)2; O3 = i SN · ( q mN × v ⊥) O4 =
SN; O5 = i Sχ · ( q mN × v ⊥); O6 = ( Sχ · q mN )( SN · q mN ) O7 =
v ⊥; O8 = Sχ · v ⊥; O9 = i Sχ · ( SN × q mN ) O10 = i SN · q mN ; O11 = i Sχ · q mN ; O12 = Sχ · ( SN × v ⊥) O13 = i( Sχ · v ⊥)( SN · q mN ); O14 = i( Sχ · q mN )( SN · v ⊥) O15 = −( Sχ · q mN )(( SN × v ⊥) · q mN ).
9 / 39
Factorization of WIMP physics and nuclear physics
The expected rate, dRχT dER (t) =
NT ρWIMP mWIMP
d3vTf ( vT, t)vT dσT dER , with, dσT dER = 2mT 4πv2
T
2jχ + 1 1 2jT + 1|MT|2
Besides usual spin-dependent and spin-independent interactions, new contributions arise with explicit dependence
q and WIMP incoming velocity.
10 / 39
WIMP model for DAMA which complies with other experiments. How? Xe, Ge are neutron odd targets. Spin-dependent WIMP-proton cross-section by choosing, cn/cp = −0.028 F is proton odd target. v∗Na,I
min
< vlab
esc < v∗F min
v∗
min =
12 / 39
In Inelastic scenario δ = 0 mχ′ − mχ = δ The minimal velocity to deposit a recoil vmin = 1 √2mNER
µχN + δ
S.Kang, S.Scopel, GT, J.H. Yoon, “Proton-philic spin-dependent inelastic dark matter as a viable explanation of DAMA/LIBRA-phase2” Phys.Rev. D99 (2019) no.2, 023017
1 2 3 4 5 6 7 8 E′ (keVee) 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Sm (cpd/kg/keVee) total sodium iodine DAMA mχ=12.1 (GeV) χ2=13.1937 δ=18.3 (keV) σ0=7.95e-35 (cm2) 9 10 11 12 13 14 15 16
mχ (GeV)
10−38 10−36 10−34 10−32 10−30
σ0 (cm2)
XENON1T CDMSLite DAMA0 COUPP PICO60(C3F8) PICASSO PANDAX-II SuperCDMS CDEX KIMS CRESST-II PICO60(CF3I) COSINE-100 DAMA
Maxwellian velocity distribution
14 / 39
S.Kang, S.Scopel, GT, J.H. Yoon, “Proton-philic spin-dependent inelastic dark matter as a viable explanation of DAMA/LIBRA-phase2” Phys.Rev. D99 (2019) no.2, 023017
640 660 680 700 720 740 760 780
vmin (km/s)
10−22 10−20 10−18 10−16 10−14
̃ η (days−1)
XENON1T CDMSLite DAMA0 PANDAX-II SuperCDMS CDEX KIMS CRESST-II COSINE-100 DAMA
˜ η(vmin, t) = ˜ η0(vmin)+ ˜ η1(vmin) cos[ω(t − t0)] ˜ ηi [vmin,1,vmin,2] = ∞
0 dvmin ˜
ηiR[E ′
1,E ′ 2]
∞
0 dvminR[E ′
1,E ′ 2]
= Ri
[E ′
1,E ′ 2]
∞
0 dvminR[E ′
1,E ′ 2]
Halo independent case.
15 / 39
6 8 10 12 14 16 18
mχ (GeV)
18 20 22 24 26 28 30 32
δ (KeV)
mχ = 11.4 GeV, δ = 23.7 KeV ′, ξ = 1.0 ′, ξ = 0.8 ′, ξ = 0.6 ′, ξ = 0.4 ′, ξ = 0.2 ′, ξ = 0.1
ξ: modulation fraction; D: compatibility factor ∗ pSIDM is still viable for 18 keV < δ < 29 keV, 8 GeV < mχ < 17 GeV.
16 / 39
COSINE-100 Collaboration, G. Adhikariet al., Nature 564 (2018) 83-86
Exclude DAMA at low mass using similar target, NaI Spin-independent interaction Maxwellian velocity distribution
17 / 39
Important point: DAMA measures modulation SDAMA
m
while COSINE-100 constraints time average SCOSINE . SDAMA
m
/SCOSINE is model dependent SDAMA
m
≃ 0.02 events/kg/day/keVee, SCOSINE ≤ 0.13 events/kg/day/keVee SDAMA
m
SDAMA = SDAMA
m
SCOSINE × SCOSINE SDAMA ≥ 0.12 In Spin-independent case: SDAMA
m
SDAMA
< 0.12, for pSIDM scenario:
SDAMA
m
SDAMA
> 0.12
S.Kang, S.Scopel, GT, J.H. Yoon, “Proton-philic spin-dependent inelastic dark matter as a viable explanation of DAMA/LIBRA-phase2” Phys.Rev. D99 (2019) no.2, 023017 18 / 39
Assumptions and Inputs
One coupling is dominant at a time. Sensitivity is expressed in terms of 90% C.L. bounds on effective cross-section, σN,lim = max(σp, σn) σp = (cp
j )2 µ2 χN
π , σn = (cn
j )2 µ2 χN
π
20 / 39
COSINE-100 Collaboration, S.Kang, S.Scopel, GT, J.H. Yoon, “COSINE-100 and DAMA/LIBRA-phase2 in WIMP effective models” JCAP 1906 (2019) no.06, 048 21 / 39
COSINE-100 Collaboration, S.Kang, S.Scopel, GT, J.H. Yoon, “COSINE-100 and DAMA/LIBRA-phase2 in WIMP effective models” JCAP 1906 (2019) no.06, 048 22 / 39
NR EFT couplings besides standard SI and SD interactions have larger modulation fraction Average rate less sensitive to modulation. no exclusion for most of them.
23 / 39
106 kg of NaI, 97.7 kg yr Phys.Rev.Lett. 123 (2019) no.3, 031301 “consistent with both a null hypothesis and DAMA/LIBRA’s 2-6 keV best fit value“ Need more statistics. ANAIS shares the same threshold of DAMA-phase-2 (1 keV), COSINE-100 threshold is 2 keV 112.5 kg of NaI, 157.55 kg yr Phys.Rev.Lett. 123 (2019) no.3, 031302 ”best fits in [2-6] Kev and [1-6] keV energy intervals incompatible at 2.5 σ and 1.9 σ“
24 / 39
Based on Python. 14 existing experiments included: XENON1T, PandaX-II, KIMS, CDMSLite, SuperCDMS, COUPP, PICASSO, PICO-60 (CF3I and C3F8 targets), CRESST-II, DAMA (modulation data), DAMA0 (average count rate), CDEX, and DarkSide-50 Allows to implement experiments by providing energy resolution, exposure, efficiency, quenching etc in different forms. Flexible to easily implement any new experiment and/or update new information. Efficient to calculate and handle a large number of response functions. Tabulates the response functions as a function of the recoil energy.
25 / 39
Includes WIMPs of spin 0,1/2 and 1, all NR couplings including interferences for each energy bin, isotope and velocity dependence. Valid for any velocity distribution of WIMPs. More involved analysis e.g. including optimal interval method, background subtraction. Development with rigorous testing is in progress. Plan to eventually make it publicly available. Interface with some existing codes (runDM, DirectDM) is tested but more has to be worked. A python routine named NRDD-constraints has been released by our group. https://github.com/NRDD-constraints/NRDD
26 / 39
The rate can be written as Particularly suitable for numerical calculations. Response functions R are tabulated as a function of ER. No need to calculate for each mχ or mass-splitting δ. Interpolation is used ¯ Rττ ′
0,1,1E,1E −1(ER) at ER = E ± R (vk, mχ, δ),
k = 1, ..., N.
27 / 39
We have calculated 75768 response functions for 19 experiments and 14 couplings. If include interferences then 37884 more response functions.
28 / 39
S.Kang, S.Scopel, GT, J.H. Yoon, “Present and projected sensitivities of Dark Matter direct detection experiments to effective WIMP-nucleus couplings” Astropart.Phys. 109 (2019) 50-68 29 / 39
30 / 39
Effective models provide a useful tool to fully exploit experimental data In all cases strong complementarity between Xenon, Germanium, Iodine and Fluorine targets Loopholes still exist, even DAMA (!) still allowed example, pSIDM scenario COSINE-100 bound is naturally evaded in pSIDM and many Effective models due to large modulation fractions WimPyDD: a flexible, user-friendly object-oriented Python code for direct detection analysis (stay tuned)
32 / 39
33 / 39
Connection to relativistic effective theory: 1203.3542
34 / 39
WIMPs response funtions: 1203.3542
35 / 39
Maxwellian velocity distribution: f ( vT, t) = N
2πv2
rms
3/2 e
− 3|
vT + vE |2 2v2 rms
Θ(uesc − | vT + vE(t)|) N =
2 √πze−z2−1 , with z = 3u2
esc/(2v2 rms). In the isothermal sphere model
hydrothermal equilibrium between the WIMP gas pressure and gravity is assumed, leading to vrms=
rotational velocity.
36 / 39
Six distinct nuclear response functions are defined as,
M : vector-charge (spin-independent part, non-zero for all nuclei) Φ′′ : vector-longitudinal, related to spin-orbit coupling σ · l (also spin-independent, non-zero for all nuclei) Σ′, Σ′′ : longitudinal and transverse components of nuclear spin, their sum is the usual spin-dependent interaction, require j > 0 ∆ : associated to orbital angular momentum operator l, requires j > 0 ˜ Φ′ : related to the vector-longitudinal operator, transforms as a tensor under rotation, require j > 1/2
37 / 39
38 / 39
39 / 39