Daniel Gazda. Chalmers University of Technology. Progress in Ab Initio Techniques in Nuclear Physics TRIUMF, Feb 28 Mar 3, 2017

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1 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

2 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

3 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

4 Motivation WIMP dark matter searches χ χ SM SM χ SM SM SM production collider searches χ χ annihilation indirect searches γ, ν, CR telescopes χ SM scattering direct detection deep underground detectors D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 4 / 15

5 Current status ] 2 WIMP-nucleon Cross Section [cm DAMA/Na CDMS-Si (2013) XENON (2013) SuperCDMS (2014) DAMA/I XENON0 (2012) PandaX (2014) XENON1T (2 t y) XENON1T Sensitivity in 2 t y Expected limit (90% CL) ± 1 σ expected ± 2 σ expected XENONnT (20 t y) DarkSide-50 (2015) LUX (2013) Billard et al., Neutrino Discovery limit (2013) WIMP mass [GeV/c ] Figure 15. XENON1T taken from: sensitivity XENON (90% collaboration, C.L.) to spin-independent JCAP 1604, WIMP-nucleon 027 (2016) interaction: the 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 5 / LZ JCAP04(20

6 Dark matter direct detection & nuclear physics new physics Λ UV heavy mediators SM + DM EFT v EW EW symmetry breaking 5-flavor QCD + DM EFT m b m c 3-flavor QCD + DM EFT Λ QCD chiral symmetry breaking heavy baryon chiral EFT + DM direct detection m π NREFT D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 6 / 15

7 Dark matter direct detection & nuclear physics new physics direct detection Λ UV heavy mediators SM + DM EFT v EW EW symmetry breaking 5-flavor QCD + DM EFT m b m c 3-flavor QCD + DM EFT Λ QCD chiral symmetry breaking heavy baryon chiral EFT + DM m π NREFT Cirigliano et al. (JHEP 12, 25 (2012)) Darmstadt group: Menéndez, Gazit, Schwenk, Klos et al. (e.g. PRD 94, (2016)) Fitzpatrick, Haxton et al. (JCAP 1302, 4 (2013)) D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 6 / 15

8 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: iˆq, ˆv = ˆv + ˆq 2µ χn, Ŝ χ, Ŝ N all possible χ N interaction terms (up to q 2 ): ) Ô 1 = 1 χn Ô 9 = iŝ χ (ŜN ˆq ( ) m N Ô 3 = iŝ N ˆq ˆv m ˆq Ô = iŝ N N m N ˆq Ô 4 = Ŝ χ Ŝ N Ô 11 = iŝ χ ( ) m N ) Ô 5 = iŝ χ ˆq ˆv m Ô 12 = Ŝ χ (ŜN ˆv N ) ) ) ˆq ˆq Ô 6 = (Ŝχ (ŜN Ô m N m 13 = i (Ŝχ ˆv (ŜN N ) ˆq m N ) ) Ô 7 = Ŝ N ˆv Ô ˆq 14 = i (Ŝχ (ŜN ˆv m N Ô 8 = Ŝ χ ˆv Ô 15 = (Ŝχ χ nucleus Hamiltonian: A Ĥ χa = cj τ Ô (i) j t(i) τ i=1 τ=0,1 j ) ) ˆq [(ŜN ˆv m N ] ˆq m N D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 7 / 15

9 Nonrelativistic EFT for χ N/nucleus interaction Rate of nuclear scattering events in direct detection experiments: dr dq 2 = ρ χ d 3 v f ( v + v e )v dσ m A m χ dq 2 m χ, ρ χ, f : dark matter mass, density, velocity distributions astrophysics dσ dq : scattering cross section particle and nuclear physics 2 dσ dq 2 = 1 (2J + 1)v 2 τ,τ [ R ττ l l=m,σ,σ W ττ l dark matter response functions Rm ττ ( nuclear response functions W ) l ττ q 2 + q2 m 2 N ( v 2 T l=φ,φ M, Φ,, Σ, q2 mn 2 ), ci τ c τ j Rl ττ Wl ττ ] D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 8 / 15

10 Nonrelativistic EFT for χ N/nucleus interaction nuclear response functions: WAB ττ (q2 ) = J, T, M T Â L;τ (q) J, T, M T J, T, M T ˆB L;τ (q) J, T, M T L 2J Â L;τ, ˆB L;τ nuclear response operators: M LM;τ (q) = A M LM (qρ i )t τ (i), i=1 Σ A LM;τ (q) = i [ ] 1 ρi M M LL q (qρ i ) σ (i) t τ (i), i=1 Σ A LM;τ (q) = [ ] 1 ρi M LM (qρ i ) σ (i) t τ (i) q, i=1 A LM;τ (q) = M M LL (qρ i ) 1 ρi t τ (i) q, i=1 Φ A LM;τ (q) = [( )( 1 ρi M M LL q (qρ i ) σ (i) 1 ) ρi + 1 ] q 2 MM LL (qρ i ) σ (i) t τ (i), i=1 Φ A LM;τ (q) = i ( )( 1 ρi M LM (qρ i ) σ (i) 1 ) ρi t τ (i) q q i=1 nuclear ground-state wave functions J, T, M T 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

11 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 / 15

12 Input Hamiltonians V NN and V NNN 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 N2LO sim Hamiltonian family (Carlsson et al., PRX 6, 0119 (2016)) parameters fitted to reproduce simultaneously πn, NN, and NNN low-energy observables } T lab,max NN 125,..., 290 MeV 42 Hamiltonians Λ EFT 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

13 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 N2LO sim 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

14 4 He nuclear response functions and recoil rates W WM 00 WΦ 00 2 W 00 Φ M WM 00 SM dr/d cos θ (kg 1 day 1 ) Ô5 Ô q (GeV) Figure: Isoscalar nuclear response functions of 4 He as functions of the recoil momentum q calculated within ab initio NCSM and SM cos θ Figure: Differential rate of nuclear recoil events as a function of the recoil direction. D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 13 / 15

15 4 He nuclear response functions and recoil rates W WM 00 WΦ 00 2 W 00 Φ M WM 00 SM dr/d cos θ (kg 1 day 1 ) Ô5 Ô q (GeV) Figure: Isoscalar nuclear response functions of 4 He as functions of the recoil momentum q calculated within ab initio NCSM and SM cos θ Figure: Differential rate of nuclear recoil events as a function of the recoil direction. D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 13 / 15

16 3 He nuclear response functions and recoil rates W M ττ τ, τ = 0, 0 τ, τ = 0, 0 SM τ, τ = 0, 1(1, 0) τ, τ = 0, 1(1, 0) SM 0.0 τ, τ = 0, 1(1, 0) τ, τ = 0, 1(1, 0) SM q (GeV) τ, τ = 0, 0 τ, τ = 0, 1 (1, 0) τ, τ = 1, 1 τ, τ = 0, 0 (1, 1) SM τ, τ = 0, 1 (1, 0) SM W Φ ττ q (GeV) τ, τ = 0, 0 τ, τ = 0, 1 (1, 0) τ, τ = 1, 1 τ, τ = 0, 0 τ, τ = 0, 1 (1, 0) τ, τ = 1, 1 dr/d cos θ (kg 1 day 1 ) Ô4 Ô5 Ô15 W Σ ττ q (GeV) W ττ q (GeV) Figure: Nuclear response functions of 3 He as functions of the recoil momentum q calculated within ab initio NCSM and SM cos θ Figure: Differential rate of nuclear recoil events as a function of the recoil direction. D. Gazda (Chalmers) Ab initio nuclear response functions for DM searches 14 / 15

17 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. Outlook: arxiv: [hep-ph] 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