Distinguishing WIMP-nucleon interactions with directional dark - PowerPoint PPT Presentation

Distinguishing WIMP-nucleon interactions with directional dark matter experiments Bradley J. Kavanagh (LPTHE - Paris 06 & IPhT - CEA/Saclay) TeV Particle Astrophysics, Kashiwa - 27th Oct. 2015 Based on arXiv:1505.07406 NewDark

Possible WIMP-nucleon operators N N Direct detection: m χ & 1 GeV v ∼ 10 − 3 χ χ q . 100 MeV ∼ (2 fm) − 1 Relevant non-relativistic (NR) degrees of freedom: ~ ~ q q ~ ~ ~ v ⊥ = ~ v + S χ S N 2 µ χ N 2 m N Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Non-relativistic effective field theory (NREFT) Require Hermitian, Galilean invariant and time-translation invariant combinations: O 1 = 1 SI O 4 = ~ S χ · ~ S N SD [1008.1591, 1203.3542, 1308.6288, 1505.03117] Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Non-relativistic effective field theory (NREFT) Require Hermitian, Galilean invariant and time-translation invariant combinations: O 12 = ~ S χ · ( ~ O 1 = 1 v ⊥ ) S N × ~ SI O 3 = i ~ v ⊥ ) /m N O 13 = i ( ~ v ⊥ )( ~ S N · ( ~ q × ~ S χ · ~ S N · ~ q ) /m N O 4 = ~ S χ · ~ O 14 = i ( ~ q )( ~ S N v ⊥ ) /m N S χ · ~ S N · ~ O 5 = i ~ v ⊥ ) /m N SD O 15 = − ( ~ q )(( ~ S χ · ( ~ q × ~ v ⊥ ) · ~ q/m 2 S χ · ~ S N × ~ N O 6 = ( ~ q )( ~ q ) /m 2 S χ · ~ S N · ~ N . . O 7 = ~ v ⊥ . S N · ~ O 8 = ~ v ⊥ S χ · ~ O 9 = i ~ S χ · ( ~ S N × ~ q ) /m N O 10 = i ~ S N · ~ q/m N O 11 = i ~ S χ · ~ q/m N [1008.1591, 1203.3542, 1308.6288, 1505.03117] Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Calculating the cross section ‘Dictionaries’ are available which allow us to translate from relativistic interactions to NREFT operators: [e.g. 1211.2818, 1307.5955, 1505.03117] N γ µ γ 5 N χγ µ χ ¯ 8 m N ( m N O 9 − m χ O 7 ) E.g. ¯ Then calculating the scattering cross section is straightforward: d σ i 1 1 m A i F ( N,N 0 ) i c N 0 X c N ( v 2 ⊥ , q 2 ) = i χ m 2 m 2 v 2 d E R 32 π N N,N 0 = p,n Nuclear response functions: F i ( v 2 ⊥ , q 2 ) So how can we distinguish these different cross sections? Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Distinguishing operators: approaches • Materials signal - compare rates obtained in different experiments [1405.2637, 1406.0524, 1504.06554, 1506.04454] May require a large number of experiments • Annual modulation - due to different v-dependence annual modulation rate and phase can be different [1504.06772] Annual modulation is a small effect • Energy spectrum - look for an energy spectrum which differs from the standard SI case in a single experiment [1503.03379] Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Distinguishing operators: Energy-only Consider three different operators: O 1 , O 5 , O 7 SI operator F 1 ∼ q 0 v 0 F 5 ∼ q 2 ( v 2 ⊥ + q 2 ) ‘Non-standard’ F 7 ∼ v 2 operators ⊥ Generate mock data assuming either or . O 5 O 7 Assume the data is a mixture of events due to and the ‘non- O 1 standard’ operator (either or ). O 5 O 7 Fit values of and , fraction of events due to ‘non- A m χ standard’ interactions. With what significance can we reject the SI-only scenario? Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Distinguishing operators: Energy-only With what significance can we reject ‘standard’ ‘Perfect’ CF 4 SI/SD interactions in 95% of experiments? detector E R ∈ [20 , 50] keV Input WIMP mass: m χ = 50 GeV SHM velocity distribution F 1 ∼ q 0 v 0 F 5 ∼ q 2 ( v 2 ⊥ + q 2 ) F 7 ∼ v 2 ⊥ Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Comparing energy spectra F 1 ∼ q 0 v 0 F 5 ∼ q 2 ( v 2 ⊥ + q 2 ) F 7 ∼ v 2 ⊥ Energy spectrum differences between and are O 1 O 7 smoothed out once we integrate over (smooth) DM velocity distribution. v 2 True of any operators whose cross-sections differ only by . ⊥ Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Directional detection Different v-dependence could impact directional signal. Mean recoil direction is h ~ v i ⇠ � ~ Detector v e parallel to incoming WIMP direction (due to Earth’s motion). h ~ q i Convolve cross section with velocity distribution to obtain directional spectrum, as a function of , the angle between θ the recoil and the peak direction. So, what does the directional spectrum look like? Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Directional spectra of NREFT operators Total distribution of recoils as a function small θ , small v ⊥ of : θ ~ v || ~ ~ q v ⊥ ~ F 1 ∼ v 0 v large θ , large v ⊥ F 7 ∼ v 2 ⊥ ~ q ~ v || ~ v ~ v ⊥ Spectra of all operators given in [1505.07406, 1505.06441]. Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Distinguishing operators: Energy + Directionality With what significance can we reject ‘standard’ ‘Perfect’ CF 4 SI/SD interactions in 95% of experiments? detector E R ∈ [20 , 50] keV Input WIMP mass: m χ = 50 GeV SHM velocity distribution F 1 ∼ q 0 v 0 F 5 ∼ q 2 ( v 2 ⊥ + q 2 ) F 7 ∼ v 2 ⊥ Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Summary: a final example NREFT framework allows us to compare the different possible direct detection signals. Some operators can be distinguished in a single experiment from their energy spectra alone (e.g. if the form factor goes as ) F ∼ q n But , this is not true for all operators. Consider: F ∼ v 0 χχ ¯ L 1 = ¯ NN χγ µ γ 5 χ ¯ F ∼ v 2 L 6 = ¯ N γ µ N ⊥ These operators cannot be distinguished in a single non- directional experiment. Directional detection will be powerful and crucial tool for determining how DM interacts with the Standard Model! Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Backup Slides Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

The Directional Spectrum Recoil distribution for WIMP-nucleus recoils in direction with ˆ q ~ fixed WIMP speed : v m χ m N µ χ N = m χ + m N m χ m N s m N E R v min = 2 µ 2 χ N h |M| 2 i d R v � ( ~ v · ˆ q � v min ) = ⇢ 0 v 32 ⇡ m 2 N m 2 χ v 2 d E R d Ω q 2 ⇡ m χ WIMP flux Cross section Kinematics For standard SI and SD interactions: h | M | 2 i ⇠ v 0 q 0 Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

NREFT event rate The matrix element for operator i can now be written as: h |M i | 2 i = | h c i O i i nucleus | 2 = c 2 i F i,i ( v 2 ⊥ , q 2 ) c p = c n [Assuming for now: ] F i,i ( v 2 ⊥ , q 2 ) The nuclear response functions are the expectation values of the operators summed over all nucleons in the nucleus. ( v ⊥ ) 0 ( v ⊥ ) 2 They are proportional to or . d R i ⇢ 0 Z c 2 R 3 F i,i ( v 2 ⊥ , q 2 ) f ( ~ q − v min ) d 3 ~ = v ) � ( ~ v · ˆ v i 64 ⇡ 2 m 2 N m 3 d E R d Ω q χ Framework previously applied to non-directional direct detection and solar capture [1211.2818, 1406.0524, 1503.03379, 1503.04109 and others] . Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Direct detection m χ Zoom in m N (slightly) ~ v ~ q Look for interactions of DM particles from the halo with nuclei in a detector - measure energy of the recoiling nucleus. Expect lots of low energy backgrounds —> background discrimination can be… problematic… Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

The WIMP Wind WIMP: Weakly Interacting In the halo: Massive Particle v sun ∼ 220 km s − 1 Cygnus constellation v DM ∼ 220 km s − 1 Detector In the lab: ‘WIMP wind from Cygnus’ Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015

Radon Transform d R For standard SI/SD, for ∝ � ( ~ v · ˆ q − v min ) d E R d Ω q fixed DM speed: So integrating over all DM speeds: d R Z v ≡ ˆ q − v min ) d 3 ~ R 3 f ( ~ v ) � ( ~ v · ˆ f ( v min , ˆ q ) ∝ d E R d Ω q ‘Radon Transform’ (RT) For the SHM: v lag ) 2  � 1 − ( ~ v − ~ f ( ~ v ) = (2 ⇡� 2 ) 3 / 2 exp 2 � 2 v q ) 2  � 1 − ( v min − ~ v lag · ˆ ˆ f ( v min , ˆ q ) = exp p 2 � 2 2 ⇡� 2 v v Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Tokyo - 27th Oct. 2015

Directional Spectra ‘Perfect’ CF 4 detector E R ∈ [20 , 50] keV Standard SI/SD int. m χ = 100 GeV Recoils away Recoils towards from Cygnus Cygnus Bradley J Kavanagh (LPTHE & IPhT) Distinguishing WIMP operators TeVPA, Kashiwa - 27th Oct. 2015