QCD anatomy of WIMP- nucleon interactions Mikhail Solon UCB/LBNL - PowerPoint PPT Presentation

QCD anatomy of WIMP- nucleon interactions Mikhail Solon UCB/LBNL MITP workshop on Effective Theories and Dark Matter 16 March 2015 based on work with R. Hill: 1409.8290 see also 1111.0016, 1309.4092, 1401.3339.

Ω M h 2 6 = Ω B h 2 0 . 1423 ± 0 . 0029 0 . 02207 ± 0 . 00033 theory dreamscape experimental searches signals, backgrounds model-dependent uncertainties model-independent uncertainties 2

Scrutiny of underlying astrophysics is important, but we’ll stick to Standard Model physics here. annihilation: sommerfeld enhancement, bound states, M thermal bath effects, Sudakov logs production: complementarity m W QCD and EW running m b , m c m N scattering: nucleon matrix elements, DM-nucleon EFT, multinucleon effects 3

Develop an effective theory framework to put a handle on model-dependent and -independent uncertainties calculability universality precision brown muck, factorization, O(1 - 10 %), QCD simple heavy quark symmetry control uncertainties DM O(10 2 - 10 4 %) unknown SM anatomy p 2 v · p n · p LHC is carving out parameter space, M M pushing to regions requiring precision m W m W m W s · p ¯ M m W n · p 4

Heavy electroweak charged WIMPs M v · p M annihilation: thermal, theoretical control of Sudakov logs, m W production: null results pushing to higher limits s · p n · p M XENON 10 S2 (2013) 10 � 39 CDMS-II Ge Low Threshold (2011) 10 � 3 m W CoGeNT PICO250-C3F8 (2012) SM 10 � 40 10 � 4 ¯ M m W n · p CDMS Si (2013) SIMPLE (2012) p 2 10 � 41 10 � 5 WIMP � nucleon cross section � cm 2 � COUPP (2012) WIMP � nucleon cross section � pb � DAMA ZEPLIN-III (2012) 10 � 42 CRESST 10 � 6 CDMS II Ge (2009) S u wino: dimensional estimate p SuperCDMS Soudan e r EDELWEISS (2011) C 10 � 43 D 10 � 7 M Xenon100 (2012) S Cirelli, Fornengo, Strumia (2005) SNOLAB m W N DarkSide 50 E U T 10 � 44 R I N 10 � 8 Essig (2009) LUX O C PICO250-CF3I 7 Be T C A T E O H T S E R R E N Neutrinos I N G 8 B 10 � 45 10 � 9 Xenon1T Neutrinos m W DEAP3600 DarkSide G2 10 � 46 10 � 10 higgsino: Snowmass CF1 (2013) LZ (MicrOMEGAs) 10 � 47 10 � 11 (Green&ovals)&Asymmetric&DM&& } (Violet&oval)&Magne7c&DM& C AT TERI N G (Blue&oval)&Extra&dimensions&& Atmospheric and DSNB Neutrinos S 10 � 48 R E N T 10 � 12 H E O (Red&circle)&SUSY&MSSM& C O N R I U T N E this work &&&&&MSSM:&Pure&Higgsino&& 10 � 49 10 � 13 &&&&&MSSM:&A&funnel& &&&&&MSSM:&BinoEstop&coannihila7on& &&&&&MSSM:&BinoEsquark&coannihila7on& 10 � 50 10 � 14 & 1 10 100 1000 10 4 m b , m c WIMP Mass � GeV � c 2 � u H 2 L 100 baryon spec. d H 2 L 50 g H 2 L 10 - 47 pa 22 M p H MeV L had 10 - 47 s H 2 L 0 pert O triplet u H 0 L + d H 0 L L σ SI (cm 2 ) N 10 - 48 N N - 50 s H 0 L 10 - 48 m N 10 - 49 O - 100 L g H 0 L m W 3 N N 10 - 49 - 150 10 - 50 NLO lattice - 200 doublet tri LO 10 - 51 10 - 50 110 115 120 125 130 135 - 250 90 100 110 120 130 140 0 100 200 300 400 500 m h (GeV) 5 S s H MeV L

In the rest of the talk, L DM + L SM c 1 h N | | N i h N | | N i and illustrate with phenomenological examples. 6

Zeroth order question: why bother with radiative corrections? X X d M phys L = c i ( µ ) O i ( µ ) M phys = c i ( µ ) h O i ( µ ) i = 0 dµ i i µ 1 ∼ α log µ 1 - get the LO (LL) result µ 2 - some matrix elements acessible only at a certain scale - use complementarity - (avoid certain uncertainties) µ 2 7

Currents: relativistic scalar or fermion � c ϕ 1 ;q qq þ c ϕ 2 ;q qi γ 5 q þ c ϕ 3 ;q q γ μ q þ c ϕ 4 ;q � X ϕ � i ∂ μ ϕ � i ∂ μ j ϕ j 2 m q ¯ j ϕ j 2 m q ¯ L ϕ ; SM ¼ − ϕ ¯ − ϕ ¯ q γ μ γ 5 q m 2 m 2 m 2 m 2 W W W W q ¼ u;d;s;c;b þ c ϕ 5 αβ G A αβ þ c ϕ 6 G A αβ þ � � � : αβ ~ j ϕ j 2 G A j ϕ j 2 G A for n ¼ 3 ; 4 . m 2 m 2 W W L ψ ; SM ¼ c ψ 1 ψσ μν ψ F μν þ c ψ 2 � c ψ 3 ;q q γ μ q þ c ψ 4 ;q q γ μ γ 5 q þ c ψ 5 ;q X ψσ μν ψ ~ ψγ μ γ 5 ψ ¯ ψγ μ γ 5 ψ ¯ ψγ μ ψ ¯ F μν þ ¯ ¯ ¯ ¯ ¯ q γ μ q m 2 m 2 m 2 m W m W W W W q ¼ u;d;s;c;b þ c ψ 6 ;q q γ μ γ 5 q þ c ψ 7 ;q qq þ c ψ 8 ;q qq þ c ψ 9 ;q qi γ 5 q þ c ψ 10 ;q ψγ μ ψ ¯ ¯ ψψ m q ¯ ¯ ψ i γ 5 ψ m q ¯ ¯ ψψ m q ¯ ¯ ψ i γ 5 ψ m q ¯ ¯ qi γ 5 q m 2 m 3 m 3 m 3 m 3 W W W W W þ c ψ 11 ;q q γ μ q þ c ψ 12 ;q q γ μ q þ c ψ 13 ;q q γ μ γ 5 q þ c ψ 14 ;q ψ i ∂ μ ψγ 5 ∂ μ ψ i ∂ μ ψγ 5 ∂ μ ¯ − ψ ¯ ¯ − ψ ¯ ¯ − ψ ¯ ¯ − ψ ¯ q γ μ γ 5 q m 3 m 3 m 3 m 3 W W W W þ c ψ 15 ;q q σ μν q þ c ψ 16 ;q � þ c ψ 17 ψσ μν ψ m q ¯ q σ ρσ q ψψ G A αβ G A αβ ψσ μν ψ m q ¯ ¯ ϵ μνρσ ¯ ¯ m 3 m 3 m 3 W W W þ c ψ 18 αβ G A αβ þ c ψ 19 G A αβ þ c ψ 20 G A αβ þ � � � ; with n ¼ 1 ; 2 ; 5 ; 6 ; 11 ; 12 ; 13 ; 14 ; 15 ; 16 αβ ~ αβ ~ ψ i γ 5 ψ G A ψψ G A ψ i γ 5 ψ G A ¯ ¯ ¯ m 3 m 3 m 3 ef. [17]. W W W 8

Currents: heavy particle field L χ v ; SM ¼ c χ 1 ⊥ χ v F μν þ c χ 2 � c χ 3 ;q χ v σ μν χ v σ μν X χ v σ νρ ⊥ χ v ~ ϵ μνρσ v μ ¯ q γ σ q ¯ ¯ F μν þ ⊥ χ v ¯ m 2 m W m W W q ¼ u;d;s;c;b þ c χ 4 ;q q γ σ γ 5 q þ c χ 5 ;q qvq þ c χ 6 ;q qv γ 5 q þ c χ 7 ;q χ v σ νρ ϵ μνρσ v μ ¯ χ v χ v m q ¯ qq ⊥ χ v ¯ χ v χ v ¯ ¯ χ v χ v ¯ ¯ ¯ m 2 m 2 m 2 m 3 W W W W þ c χ 8 ;q qviv · D − q þ c χ 9 ;q qi γ 5 q þ c χ 10 ;q χ v χ v m q ¯ qv γ 5 iv · D − q χ v χ v ¯ ¯ ¯ χ v χ v ¯ ¯ m 3 m 3 m 3 W W W þ c χ 11 ;q q γ ν q þ c χ 12 ;q q γ σ q þ c χ 13 ;q χ v σ μν χ v σ μν χ v σ μν ⊥ i ∂ ⊥ ⊥ i ∂ ⊥ ρ ⊥ i ∂ ⊥ ¯ − μ χ v ¯ ϵ μνρσ ¯ − χ v ¯ ¯ − μ χ v ¯ q γ ν γ 5 q m 3 m 3 m 3 W W W þ c χ 14 ;q q γ σ γ 5 q þ c χ 15 ;q χ v σ μν χ v σ νρ ⊥ i ∂ ⊥ ρ ϵ μνρσ v μ ¯ q ð viD σ − þ γ σ iv · D − Þ q ϵ μνρσ ¯ − χ v ¯ ⊥ χ v ¯ m 3 m 3 W W þ c χ 16 ;q − þ γ σ iv · D − Þ γ 5 q þ c χ 17 ;q χ v σ νρ χ v i ∂ ⊥ μ ϵ μνρσ v μ ¯ q ð viD σ ⊥ χ v ¯ ¯ − χ v ¯ q γ μ q m 3 m 3 W W þ c χ 18 ;q q γ ν q þ c χ 18 ;q q γ σ q þ c χ 20 ;q χ v σ μν χ v σ μν ⊥ ∂ ⊥ ρ ⊥ ∂ ⊥ χ v i ∂ ⊥ μ ¯ þ μ χ v ¯ ϵ μνρσ ¯ þ χ v ¯ ¯ − χ v ¯ q γ μ γ 5 q m 3 m 3 m 3 W W W þ c χ 21 ;q q γ ν γ 5 q þ c χ 22 ;q q γ σ γ 5 q þ c χ 23 ;q χ v σ μν χ v σ μν ⊥ ∂ ⊥ ρ χ v σ μν ⊥ ∂ ⊥ ¯ þ μ χ v ¯ ϵ μνρσ ¯ þ χ v ¯ ¯ ⊥ χ v m q ¯ q σ μν q m 3 m 3 m 3 W W W þ c χ 24 ;q � þ c χ 25 αβ G A αβ þ c χ 26 χ v σ μν αβ ~ G A αβ q σ ρσ q χ v χ v G A χ v χ v G A ⊥ χ v m q ¯ ϵ μνρσ ¯ ¯ ¯ m 3 m 3 m 3 W W W χ n þ c χ 27 χ v χ v v μ v ν G A μα G A να þ c χ 28 for n ¼ 1 ; 2 ; 5 ; 6 ; 15 ; 16 ; 17 ; 18 ; 19 ; 20 ; 21 ; 22 ; 23 ; 24 . χ v σ μν ⊥ χ v ϵ μναβ v α v γ G A βδ G A ¯ ¯ γδ þ � � � ; m 3 m 3 W W m W M c χ 3 þ 2 c χ 12 ¼ m W M c χ 4 þ 2 c χ 14 ¼ m W � � 1 þ iq · D ⊥ 1 4 M 2 σ αβ q α D β M c χ 5 − 2 c χ 17 χ v ð x Þ → e iq · x χ v ð B − 1 x Þ 2 M 2 þ ⊥ þ … ¼ m W ð 9 M c χ 6 − 2 c χ 20 ¼ c χ 11 ¼ c χ 13 ¼ 0 ; Heinonen, Hill, Solon 2012 9

Through dimension seven, there are seven operator classes closed under renormalization and transforming irreducibly under continuous and discrete Lorentz transformations. QCD operator basis V μ q γ μ q q ¼ ¯ A μ q γ μ γ 5 q q ¼ ¯ T μν q σ μν γ 5 q q ¼ im q ¯ O ð 0 Þ qq , O ð 0 Þ ¼ G A μν G A μν ¼ m q ¯ q g O ð 0 Þ qi γ 5 q , O ð 0 Þ 5 g ¼ ϵ μνρσ G A μν G A 5 q ¼ m q ¯ ρσ O ð 2 Þ μν − − g μν q ð γ f μ iD ν g ¼ 1 4 iD − Þ q , 2 ¯ q O ð 2 Þ μν ¼ − G A μλ G A νλ þ g μν 4 ð G A αβ Þ 2 g O ð 2 Þ μν q γ f μ iD ν g ¼ 1 2 ¯ − γ 5 q 5 q 10

Example: Weak-scale matching L DM + L SM m W ∼ m Z ∼ m h ∼ m t L φ , SM + L n f =5 QCD L ψ ; SM ¼ 1 ψ ð i ∂ − M 0 Þ ψ − 1 ψ ð c 0 ψ 1 þ ic 0 ψ 2 γ 5 Þ ψ H † H þ � � � 2 ¯ Λ ¯ . . = c (0) + 1 q 1BE � L ψ ; SM ¼ 1 ψ ð i ∂ − M Þ ψ þ 1 X ψ ð c ψ 7 þ ic ψ 8 γ 5 Þ ψ 2 ¯ ¯ m q ¯ qq m 3 W q c 0 ψ 2 v 2 � ψ ð c ψ 17 þ ic ψ 18 γ 5 Þ ψ G A μν G A μν ψ → e − i ϕγ 5 ψ ; þ ¯ þ ��� ; ð 13 Þ tan 2 ϕ ¼ ψ 1 v 2 þ M 0 Λ ; c 0 s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c 0 � c 0 ψ 1 v 2 ψ 2 v 2 � 2 � 2 � M 0 þ M ¼ þ ; Λ Λ W M 0 f c ψ 7 ; c ψ 8 g ¼ m 3 ψ 1 þ v 2 � � c 0 M 0 Λ ½ c 0 2 ψ 1 þ c 0 2 ψ 2 � ; c 0 ψ 2 m 2 h Λ M f c ψ 17 ; c ψ 18 g ¼ − α s ð m W Þ f c ψ 7 ; c ψ 8 g : 11 12 π