11 December 2014 GDR Terascale@Heidelberg New Directions in Direct DM Searches Paolo Panci the first part is based on: P . Panci, Review in Adv.High Energy.Phys. [arXiv: 1402.1507] the second on: C. Arina, E. Del Nobile, P . Panci, Published in PRL [arXiv: 1406.5542]
Direct Detection: Overview Direct searches aim at detecting the nuclear recoil possibly induced by: DM - elastic scattering: χ + N ( A, Z ) rest → χ + N ( A, Z ) recoil - inelastic scattering: r e c o i l χ + N ( A, Z ) rest → χ 0 + N ( A, Z ) recoil DM signals are very rare events (less then one cpd/kg/keV) Experimental priorities for DM Direct Detection the detectors must work deeply underground in order to reduce the com background of cosmic rays they use active shields and very clean materials against the residual com radioactivity in the tunnel ( and neutrons) γ , α they must discriminate multiple scattering (DM particles do not com scatter twice in the detector)
Direct Detection: Overview DM local velocity the collision between v 0 ∼ 10 − 3 c χ & N ⇒ occurs in deeply non relativistic regime ( v t = 0 q 0 1 @ 1 � v 2 1 � v 2 v 2 cos θ elastic 2 v 2 � t t E R = 1 4 m χ m N 2 m χ v 2 A , q inelastic 2 δ v t = µ χ N 6 = 0 ( m χ + m N ) 2 2 scatter angle DM kinetic energy Kinematics factor threshold velocity Theoretical differential rate of nuclear recoil in a given detector Z v esc d R N v ) d ⇥ � � d 3 v | ⇤ = N N v | f ( ⇤ d E R d E R m χ v min ( E R ) s ✓ ◆ 1 + µ χ N δ m N E R : Number of target : Minimal velocity com com v min ( E R ) = N N = N a /A N 2 µ 2 m N E R χ N : DM number density : DM escape velocity (450 - 650 km/s) com com ρ � /m χ v esc
Differential Cross Section d σ 1 1 1 Matrix Element (ME) for the v 2 |M N | 2 ( v, E R ) = DM-nucleus scattering d E R 32 π m 2 χ m N the framework of relativistic quantum field theory is not appropriate v ⌧ c )
Differential Cross Section d σ 1 1 1 Matrix Element (ME) for the v 2 |M N | 2 ( v, E R ) = DM-nucleus scattering d E R 32 π m 2 χ m N the framework of relativistic quantum field theory is not appropriate v ⌧ c ) Non relativistic (NR) operators framework NR d.o.f. for elastic scattering DM-nucleon relative velocity � v : exchanged momentum � q : nucleon spin ( ) � N = ( p, n ) s N : DM spin � s χ : The DM-nucleon ME can be constructed from Galileian invariant combination of d.o.f. 12 X c N i ( λ , m χ ) O NR |M N | = i i =1 functions of the parameters of your favorite theory (e.g. couplings, mixing angles, mediator masses), expressed in terms of NR operators
Differential Cross Section d σ 1 1 1 Matrix Element (ME) for the v 2 |M N | 2 ( v, E R ) = DM-nucleus scattering d E R 32 π m 2 χ m N the framework of relativistic quantum field theory is not appropriate v ⌧ c ) Non relativistic (NR) operators framework Contact interaction (q << Λ ) NR d.o.f. for elastic scattering O NR = , DM-nucleon relative velocity � v : 1 O NR v ⊥ ) , O NR exchanged momentum = i ⇣ s N · ( ⇣ q × ⇣ = ⇣ s χ · ⇣ s N , � q : 3 4 nucleon spin ( ) O NR v ⊥ ) , O NR � = i ⇣ s χ · ( ⇣ q × ⇣ = ( ⇣ s χ · ⇣ q )( ⇣ s N · ⇣ q ) , N = ( p, n ) s N : 5 6 v ⊥ , v ⊥ , DM spin � O NR O NR = ⇣ s N · ⇣ = ⇣ s χ · ⇣ s χ : 7 8 O NR O NR = i ⇣ s χ · ( ⇣ s N × ⇣ q ) , 10 = i ⇣ s N · ⇣ q , 9 The DM-nucleon ME can be constructed from v ⊥ · ( ⇣ O NR O NR 11 = i ⇣ s χ · ⇣ q , 12 = ⇣ s χ × ⇣ s N ) . Galileian invariant combination of d.o.f. 12 Long-range interaction (q >> Λ ) X c N i ( λ , m χ ) O NR |M N | = i 1 = 1 5 = 1 O lr q 2 O NR O lr q 2 O NR i =1 , , 1 5 functions of the parameters of your favorite 6 = 1 11 = 1 O lr q 2 O NR O lr q 2 O NR , 11 . theory (e.g. couplings, mixing angles, mediator 6 masses), expressed in terms of NR operators
Differential Cross Section 12 Nucleus is not point-like |M N | 2 = m 2 j F ( N,N 0 ) i c N 0 N X X ( v, q 2 ) c N m 2 i,j There are different Nuclear Responses N i,j =1 N,N 0 = p,n for any pairs of nucleons & pairs of NR pairs of Nuclear response any pairs of NR Operators operators nucleons of the target nuclei Nuclear responses for some common target nuclei in Direct Searches fluorine iodine Contact interaction (q << Λ ) A 2 N 10 5 10 5 A 2 10 4 Total 10 4 Total N O NR = , 10 3 H p , p L 10 3 H p , p L 1 H N , N' L H N , N' L F 1,1 F 1,1 O NR v ⊥ ) , O NR 10 2 H n , n L 10 2 H n , n L = i ⇣ s N · ( ⇣ q × ⇣ = ⇣ s χ · ⇣ s N , 3 4 10 H p , n L 10 H p , n L O NR v ⊥ ) , O NR = i ⇣ s χ · ( ⇣ q × ⇣ = ( ⇣ s χ · ⇣ q )( ⇣ s N · ⇣ q ) , 1 1 5 6 Nuclear Responses Nuclear Responses 10 - 1 10 - 1 v ⊥ , v ⊥ , O NR O NR = ⇣ s N · ⇣ = ⇣ s χ · ⇣ 10 - 2 10 - 2 7 8 10 - 3 10 - 3 O NR O NR = i ⇣ s χ · ( ⇣ s N × ⇣ q ) , 10 = i ⇣ s N · ⇣ q , 10 - 4 H N , N' L 10 - 4 9 F 6,6 H N , N' L F 6,6 v ⊥ · ( ⇣ 10 - 5 10 - 5 O NR O NR 11 = i ⇣ s χ · ⇣ q , 12 = ⇣ s χ × ⇣ s N ) . 10 - 6 10 - 6 10 - 7 10 - 7 10 - 8 10 - 8 Long-Range interaction (q >> Λ ) 10 - 9 10 - 9 10 - 10 10 - 10 10 - 11 10 - 11 1 1 O lr q 2 O NR O lr q 2 O NR 10 - 12 10 - 12 1 = , 5 = , 1 5 10 - 13 10 - 13 10 - 14 10 - 14 1 1 O lr q 2 O NR O lr q 2 O NR 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 6 = , 11 = 11 . 6 Exchanged Momentum q @ GeV D Exchanged Momentum q @ GeV D “The Effective Field Theory of Dark Matter Direct Detection”, JCAP 1302 (2013) 004
Rate of Nuclear Recoil Z v esc 12 d R N 1 d 3 v 1 m N ρ ⇥ v f � ( v ) F ( N,N 0 ) i c N 0 X X ( v, q 2 ) c N = N N j χ m 2 i,j m 2 d E R 32 π m χ v min ( E R ) N i,j =1 N,N 0 = p,n Comparison with the Experimental data exposure Z ∞ K N ( q N E R , E det )d R N Z X N th k = w k d E det ✏ ( E det ) d E R ( E R ) d E R ∆ E k 0 N =Nucleus takes into account the runs over the different species quenching factor: accounts for response and energy resolution in the detector (e.g. DAMA and the partial recollection of the of the detector CRESST are multiple-target) released energy Uncertainties in Direct DM Searches Local DM energy Density & Geometry of the Halo (e.g: spherically symmetric halos with com isotropic or not velocity dispersion, triaxial models, co-rotating dark disk and so on......) Nature of the interaction & Nuclear Responses (e.g: SI & SD scattering, long-range or point com like character of the interaction and so on......) Experimental uncertainties (e.g: detection efficiency close to the lower threshold, energy com dependence of the quenching factors, channeling in crystals and so on......)
II° Part: Model Dependent Contact interaction (q << Λ ) NR spin-independent Operators O NR = , O NR O NR v ⊥ ) , = 1 , = i ~ s χ · ( ~ q × ~ 1 1 5 O NR v ⊥ ) , O NR v ⊥ , = i ⇣ s N · ( ⇣ q × ⇣ = ⇣ s χ · ⇣ s N , O NR O NR = ~ 11 = i ~ s χ · ~ s χ · ~ q , 3 4 8 O NR v ⊥ ) , O NR = i ⇣ s χ · ( ⇣ q × ⇣ = ( ⇣ s χ · ⇣ q )( ⇣ s N · ⇣ q ) , 5 6 v ⊥ , v ⊥ , O NR O NR = ⇣ s N · ⇣ = ⇣ s χ · ⇣ 7 8 O NR O NR = i ⇣ s χ · ( ⇣ s N × ⇣ q ) , 10 = i ⇣ s N · ⇣ q , 9 v ⊥ · ( ⇣ O NR O NR 11 = i ⇣ s χ · ⇣ q , 12 = ⇣ s χ × ⇣ s N ) . NR spin-dependent Operators DM-nucleon Matrix Element O NR O NR v ⊥ ) , = ~ = i ~ s N · ( ~ s χ · ~ q × ~ s N , 12 4 3 v ⊥ , X c N i ( λ , m χ ) O NR O NR O NR |M N | = = ~ = ( ~ q )( ~ q ) , s N · ~ s χ · ~ s N · ~ 7 6 i O NR O NR 10 = i ~ = i ~ s χ · ( ~ q ) , s N · ~ s N × ~ i =1 q , 9 v ⊥ · ( ~ O NR 12 = ~ s N ) . s χ × ~
II° Part: Model Dependent Contact interaction (q << Λ ) NR spin-independent Operators O NR = , O NR O NR v ⊥ ) , = 1 , = i ~ s χ · ( ~ q × ~ 1 1 5 O NR v ⊥ ) , O NR v ⊥ , = i ⇣ s N · ( ⇣ q × ⇣ = ⇣ s χ · ⇣ s N , O NR O NR = ~ 11 = i ~ s χ · ~ s χ · ~ q , 3 4 8 O NR v ⊥ ) , O NR = i ⇣ s χ · ( ⇣ q × ⇣ = ( ⇣ s χ · ⇣ q )( ⇣ s N · ⇣ q ) , The coefficients of the spin independent operators 5 6 v ⊥ , v ⊥ , O NR O NR = ⇣ s N · ⇣ = ⇣ s χ · ⇣ are severely constrained by the double-phase xenon 7 8 experiments (xenon nuclei have a large factor) A 2 O NR O NR = i ⇣ s χ · ( ⇣ s N × ⇣ q ) , 10 = i ⇣ s N · ⇣ q , 9 v ⊥ · ( ⇣ O NR O NR 11 = i ⇣ s χ · ⇣ q , 12 = ⇣ s χ × ⇣ s N ) . NR spin-dependent Operators DM-nucleon Matrix Element O NR O NR v ⊥ ) , = ~ = i ~ s N · ( ~ s χ · ~ q × ~ s N , 12 4 3 v ⊥ , X c N i ( λ , m χ ) O NR O NR O NR |M N | = = ~ = ( ~ q )( ~ q ) , s N · ~ s χ · ~ s N · ~ 7 6 i O NR O NR 10 = i ~ = i ~ s χ · ( ~ q ) , s N · ~ s N × ~ i =1 q , 9 v ⊥ · ( ~ O NR 12 = ~ s N ) . s χ × ~
Recommend
More recommend
