Two-body currents in WIMP nucleus scattering

Two-body currents in WIMP nucleus scattering Martin Hoferichter Institute for Nuclear Theory University of Washington INT program on Nuclear ab initio Theories and Neutrino Physics Seattle, March 16, 2018 PLB 746 (2015) 4, PRD 94 (2016) 063505, PRL 119 (2017) 181803, with P. Klos, J. Menéndez, A. Schwenk 1802.04294, with A. Fieguth, P. Klos, J. Menéndez, A. Schwenk, C. Weinheimer work in progress M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 1

How to search for dark matter? Search strategies: direct, indirect, collider Assume DM particle is WIMP Direct detection: search for WIMPs scattering off nuclei in the large-scale detectors Ingredients for interpretation: DM halo: velocity distribution Nucleon matrix elements: WIMP nucleon couplings Nuclear structure factors: embedding into indirect X X Planck 2013 collider target nucleus direct M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 2

Direct detection of dark matter: schematics ] 2 WIMP-nucleon Cross Section [cm 39 40 41 42 43 44 45 46 47 48 49 Nuclear recoil in WIMP nucleus scattering DAMA/Na Flux factor Φ: DM halo and velocity distribution WIMP nucleus cross section Spin-independent: coherent A 2 Spin-dependent: S p or S n CDMS-Si (2013) XENON (2013) DAMA/I SuperCDMS (2014) 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 (2015) Billard et al., Neutrino Discovery limit (2013) 6 20 30 0 200 00 2000 000 2 WIMP mass [GeV/c ] Information on BSM physics encoded in normalization at q = 0 for SI case: σ SI χn M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 3

Direct detection of dark matter: scales q,g X Λ BSM q,g Y X 1 BSM scale Λ BSM : L BSM q,g X 2 Effective Operators: L SM + i,k 1 Λ i BSMO i,k q,g X Λ EW 3 Integrate out EW physics N X π X 4 Hadronic scale: nucleons and pions Λ hadrons N X π X effective interaction Hamiltonian H I 5 Nuclear scale: N H I N Λ nuclei nuclear wave function M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 4

Direct detection of dark matter: scales Λ hadrons N π X 4 Hadronic scale: nucleons and pions N π X effective interaction Hamiltonian H I 5 Nuclear scale: N H I N Λ nuclei Typical WIMP nucleon momentum transfer nuclear wave function q max = 2µ Nχ v rel 200 MeV v rel 3 µ Nχ 0 GeV QCD constraints: spontaneous breaking of chiral symmetry Chiral effective field theory for WIMP nucleon scattering Prézeau et al. 2003, Cirigliano et al. 2012, 2013, Menéndez et al. 2012, Klos et al. 2013, MH et al. 2015, Bishara et al. 2017 In NREFT Fan et al. 20, Fitzpatrick et al. 2012, Anand et al. 2013 need to match to QCD to extract information on BSM physics the EFT approach not unique! M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 5

Outline 1 Chiral effective field theory and dark matter 2 Two-body currents in spin-dependent scattering 3 Coherently enhanced two-body currents 4 Limits on Higgs Portal dark matter 5 Low-energy neutrino nucleus scattering 6 Conclusions M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 6

Chiral EFT: a modern approach to nuclear forces 2N force 3N force 4N force Traditionally: meson-exchange potentials Chiral effective field theory Based on chiral symmetry of QCD Power counting Low-energy constants Hierarchy of multi-nucleon forces Consistency of NN and 3N modern theory of nuclear forces Long-range part related to pion nucleon scattering LO NLO 2 N LO 3 N LO Figure taken from 11.1343 M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 7

Chiral EFT: currents Coupling to external sourcesl(v µ, a µ, s, p) Same LECs appear in axial current β decay, neutrino interactions, dark matter Vast literature for v µ and a µ, up to one-loop level With unitary transformations: Kölling et al. 2009, 2011, Krebs et al. 2016 Without unitary transformations: Pastore et al. 2008, Park et al. 2003, Baroni et al. 2015 For dark matter further currents: s, p, tensor, spin-2, θ µ µ (a) (b) (c) (d) in this talk: concentrate on 2b effects (c)+(d) M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 8

Direct detection and chiral EFT (a) (b) (c) (d) Expansion around chiral limit of QCD simultaneous expansion in momenta and quark masses Three classes of corrections: Subleading 1b responses(a) Radius corrections (b) Two-body currents (c),(d) NREFT covers (a), but misses (b) (d) (b): modifies coefficient of O i by momentum-dependent factor (c),(d): do not match directly onto NREFT, need normal ordering N N N N O eff i (a)+(b) just ChPT for nucleon form factors, but (c)+(d) genuinely new effects M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 9

Chiral counting Starting point: effective WIMP Lagrangian Goodman et al. 20 L χ = 1 [ ] C SS Λ 3 q χχ m q qq + C PS q χiγ 5χ m q qq + C SP q χχ m q qiγ 5q + C PP q χiγ 5χ m q qiγ 5q q + 1 [ Λ 2 C VV q q + 1 [ ] C S Λ 3 g χχαsga µν Gµν a Chiral power counting χγ µ χ qγ µq + C AV q χγ µ γ 5χ qγ µq + C VA q = O ( p ), m q = O ( p 2) = O(M 2 π), aµ, v µ = O(p), ] χγµ χ qγ µγ 5q + C AA q χγ µ γ 5χ qγ µγ 5q construction of effective Lagrangian for nucleon and pion fields organize in terms of chiral order ν, M = O(p ν ) m N = O ( p 2) M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018

Chiral counting: summary Nucleon V A WIMP t x t x WIMP Nucleon S P 1b 0 1 + 2 2 0 + 2 V 2b 4 2 + 2 2 4 + 2 2b NLO 5 3 + 2 1b 0 + 2 1 2 + 2 0 A 2b 4 + 2 2 2 + 2 4 2b NLO 5 + 2 3 1b 2 1 S 2b 3 5 2b NLO 4 1b 2 + 2 1 + 2 P 2b 3 + 2 5 + 2 2b NLO 4 + 2 +2 from NR expansion of WIMP spinors, terms can be dropped if m χ m N Red: all terms up to ν = 3 Two-body currents: AA Menéndez et al. 2012, Klos et al. 2013, SS Prézeau et al. 2003, Cirigliano et al. 2012, but new currents in AV and VA channel 1503.04811 Worked out the matching to NREFT and BSM Wilson coefficients for spin-1/2 hierarchy predicted from chiral expansion M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 11

Two-body currents: SD case S i (u) 0.1 0.01 0.001 129 Xe S p (u) 1b currents S n (u) 1b currents S p (u) 1b + 2b currents S n (u) 1b + 2b currents Nuclear structure factors for spin-dependent interactions Klos et al. 2013 S i (u) 0.0001 0.1 0.01 0.001 0.0001 0 1 2 3 4 5 6 7 8 9 u 131 Xe S p (u) 1b currents S n (u) 1b currents S p (u) 1b + 2b currents S n (u) 1b + 2b currents Based on chiral EFT currents (1b+2b) Shell model, normal ordering over Fermi gas u = q 2 b 2 /2 related to momentum transfer 2b currents probe the same combination of BSM Wilson coefficients and hadronic couplings absorb into 1b current 0 1 2 3 4 5 6 7 8 9 u M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 12

Two-body currents: SD case ) 2 SD WIMP-proton cross-section (cm -34-35 -36-37 -38-39 -40-41 -42 SuperK (bb) SuperK (τ + τ ) - CDMS PICO-2L DAMA SuperK (W + W ) LZ Projected PICASSO - KIMS PICO-60 ZEPLIN-III XENON IceCube (bb) IceCube (τ + τ ) - XENON0 + IceCube (W - ) W LUX 90% C.L. -43 1 2 WIMP Mass (GeV/c 3 2 ) 4 5 Xenon becomes competitive for σ p thanks to 2b currents! M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 13

Coherence effects Six distinct nuclear responses Fitzpatrick et al. 2012, Anand et al. 2013 M O 1 SI Σ,Σ O 4,O 6 SD Φ O 3 quasi-coherent, spin-orbit operator, Φ : not coherent Quasi-coherence of Φ Spin-orbit splitting Coherence until mid-shell About 20 coherent nucleons in Xe j = l 1 2 j = l+ 1 2 Interference M Φ O 1 O 3 Coherent 2b currents: Scalar N + Z Vector N Z concentrate on scalar case M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 14

Spectra and shell-model calculation Energy (kev) 900 800 700 600 500 400 300 200 0 0 Th 1/2 + 7/2-3/2 + 7/2 + 3/2 + 5/2 + 9/2-11/2-1/2 + 3/2 + 131 Xe Exp 3/2 + 7/2-7/2 + (1/2,3/2) + 3/2 + 5/2 + 9/2-11/2-1/2 + 3/2 + Excitation energy (kev) 2500 2000 1500 00 500 0 Theory 6 + 4 + 0 + 2 + 3 + 4 + 2 + 2 + 0 + 5 + 132 Xe Exp 6 + 5-4 + 4 + 2 + 0 + 3 + & 2 + 4 + 2 + 2 + 0 + Shell-model diagonalization for Xe isotopes with 0 Sn core Uncertainty estimates: currently phenomenological shell-model interaction chiral-eft-based interactions in the future? ab-initio calculations for light nuclei? M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 15

Scalar two-body currents F π(q 2 ) = Mπ ( ) ga 2 d 3 p 1 d 3 p 2 d 3 p 1 d3 p 2 2 2F π n 1 l 1 n 2 l τ 2 1 τ (2π) 6 R n1 l ( p 1 1 )R n 2 l ( p 2 2 )R n 1 l ( p 1 1 )R n2 l ( p 2 2 ) 2 (2l 1 + 1)(2l 2 + 1) 16π 2 P l1 (ˆp 1 ˆp 1 ) Pl2 (ˆp 2 ˆp 2 ) (2π) 3 δ (3) ( p 1 + p 2 p 1 p 2 q) ( ) q ex 1 3 τ 1 τ qex 2 2 ( (q ex 1 )2 + Mπ 2 )( (q ex 2 )2 + Mπ 2 ) Two-body current defines genuinely new structure factor Checked the oscillator model for 1b case reproduces perfectly the L = 0 multipole Another structure factor related to trace anomaly θ µ µ F M + (q 2 ) 0 1 0.1 129 Xe non-interacting, nlj basis non-interacting, nl basis interacting shell model 0 0.05 0.1 0.15 0.2 0.25 0.3 q [GeV] M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 16

Full set of coherent contributions structure factors 000 0 1 0.01 132 Xe F+ M 2 [O1] 2 F+ M Fπ θ [O1 2b θ] 2 F+ M F M [O1 IS IV] 2 F+ M Fπ [O1 2b scalar] Fπ θ 2 [2b θ] F M 2 [O1 IV] Fπ 2 [2b scalar] 2q 2 /m 2 N FM + 2 [O1 radius] q 2 /m 2 N FM + F Φ + [O1 O3] 0 0.05 0.1 0.15 0.2 0.25 0.3 q [GeV] Parameterize cross section as dσχn SI dq 2 = 1 4πv 2 (c + M q2 ) F+(q M 2 )+ (c M q2 ) mn 2 ċ M F (q M 2 ) mn 2 ċ+ M + c πf π(q 2 )+cπf θ π(q θ 2 )+ q2 ] [c Φ 2mN 2 + F+ Φ (q 2 )+c Φ F Φ (q 2 2 ) Single-nucleon cross section: σ SI χn = µ 2 N c M + 2 /π c related to Wilson coefficients and nucleon form factors M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 17

Discriminating different response functions structure factors 000 0 1 0.01 0.0001 m χ =GeV 132 Xe F M + 2 F M 2 q 2 /m 2 N FM + 2 q 2 /m 2 N FM 2 Fπ 2 q 4 /m 4 N FM + 2 q 4 /m 4 N FM 2 q 4 /m 4 N FΦ + 2 q 4 /m 4 N FΦ 2 0 0.03 0.06 0.09 0.12 0.15 q [GeV] White region accessible to XENON-type experiment Can one tell these curves apart in a realistic experimental setting? Consider XENON1T-like, XENONnT-like, DARWIN-like settings M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 18

Discriminating different response functions discrimination power at 1.28 [%] 0 80 60 40 20 0 F M 2 F 2 q 2 /4m 2 F M + 2 2 6 14 18 exposure [ ton years] DARWIN-like setting, m χ = 0 GeV q-dependent responses more easily distinguishable If interaction not much weaker than current limits, DARWIN could discriminate most responses from standard SI structure factor M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 19

Higgs Portal dark matter Higgs Portal: WIMP interacts with SM via the Higgs Scalar: H H S 2 Vector: H H V µv µ Fermion: H H f f If m h > 2m χ, should happen at the LHC WIMP nucleon cross section [ cm 2] -39-40 -42-43 -44-45 -46-47 limits on invisible Higgs decays 1 0 00-41 Scalar Fermion Translation requires input for Higgs nucleon coupling Vector WIMP mass [GeV] f N = fq N = 2 9 + 7 fq N 9 +O(αs) m Nfq N = N mq qq N q=u,d,s,c,b,t q=u,d,s Issues: input for f N = 0.260...0.629 outdated, 2b currents missing PandaX-II LUX XENON1T SuperCDMS M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 20

Higgs nucleon coupling (a) (b) (c) (d) One-body contribution f 1b N = 0.307(9) ud (15) s(5) pert = 0.307(18) Limits on WIMP nucleon cross section subsume 2b effects have to be included for meaningful comparison Two-body contribution Need s and θ µ µ currents Treatment of θ µ µ tricky: several ill-defined terms combine to Ψ T + V NN Ψ = E b A cancellation makes the final result anomalously small f 2b N = [ 3.2(0.2) A (2.1) ChEFT + 5.0(0.4) A ] 3 = 1.8(2.1) 3 M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 21

Improved limits for Higgs Portal dark matter WIMP nucleon cross section [ cm 2] -39-40 -41-42 -43-44 -45-46 -47 Scalar Fermion Vector 1 0 00 WIMP mass [GeV] PandaX-II LUX XENON1T SuperCDMS M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 22

Chiral counting for neutrino nucleus scattering Nucleon V A WIMP t x t x WIMP Nucleon S P 1b 0 1 + 2 2 0 + 2 V 2b 4 2 + 2 2 4 + 2 2b NLO 5 3 + 2 1b 0 + 2 1 2 + 2 0 A 2b 4 + 2 2 2 + 2 4 2b NLO 5 + 2 3 1b 2 1 S 2b 3 5 2b NLO 4 1b 2 + 2 1 + 2 P 2b 3 + 2 5 + 2 2b NLO 4 + 2 M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 23

Chiral counting for neutrino nucleus scattering Nucleon V A WIMP t x t x WIMP Nucleon S P 1b 0 1 2 0 V 2b 4 2 2 4 2b NLO 5 3 1b 0 1 2 0 A 2b 4 2 2 4 2b NLO 5 3 1b 2 1 S 2b 3 5 2b NLO 4 1b 2 1 P 2b 3 5 2b NLO 4 M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 23

Chiral counting for neutrino nucleus scattering Nucleon V A WIMP t x t x WIMP Nucleon S P 1b 0 1 2 0 V 2b 4 2 2 4 2b NLO 5 3 1b 0 1 2 0 A 2b 4 2 2 4 2b NLO 5 3 1b 2 1 S 2b 3 5 2b NLO 4 1b 2 1 P 2b 3 5 2b NLO 4 Standard interactions: coherent 2b currents scale with N Z, but Cu VV G ( F = 2 1 8 ) 2 cos 2 θ w 3 sin2 θ w proton coupling 2C VV u + C VV d 1b only scales with N 2, not (N + Z) 2 Cd VV G ( F = 2 1+ 4 ) 2 cos 2 θ w 3 sin2 θ w 1 4 sin 2 θ w suppressed Non-standard interactions: potentially large corrections from scalar 2b currents M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 23

Conclusions (a) (b) (c) (d) Chiral EFT for WIMP nucleon scattering Predicts hierarchy for corrections to leading coupling Connects nuclear and hadronic scales Ingredients: nuclear matrix elements and structure factors Applications: σ SD p limits from xenon via two-body currents Discriminating nuclear responses Improved limits on Higgs Portal dark matter from LHC searches Outlook: same formalism applies to low-energy neutrino scattering M. Hoferichter (Institute for Nuclear Theory) Two-body currents in WIMP nucleus scattering Seattle, March 16, 2018 24