New directional signatures from the non-relativistic EFT of dark matter or ‘Who ordered all these operators?’ Bradley J. Kavanagh (LPTHE - Paris 06 & IPhT - CEA/Saclay) RPP 2016, Annecy - 25th Jan. 2016 Based on arXiv:1505.07406 NewDark
Direct detection of Dark Matter χ Zoom in (slightly) Zoom in (a bit more) m χ & 1 GeV m χ m A v ∼ 10 − 3 ~ v ~ q Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
DM-nucleon interactions 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 ⊥ = ~ S χ v + S N 2 µ χ N m N ~ q ~ v || Fitzpatrick et al. [arXiv:1203.3542] ~ v ~ v ⊥ Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Non-relativistic effective field theory (NREFT) O 1 = 1 SI O 4 = ~ S χ · ~ S N SD [arXiv:1008.1591, arXiv:1203.3542, arXiv:1308.6288, arXiv:1505.03117] Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Non-relativistic effective field theory (NREFT) O 12 = ~ S χ · ( ~ O 1 = 1 v ⊥ ) O 1 = 1 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 [arXiv:1008.1591, arXiv:1203.3542, arXiv:1308.6288, arXiv:1505.03117] Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Non-relativistic effective field theory (NREFT) O 12 = ~ S χ · ( ~ O 1 = 1 v ⊥ ) O 1 = 1 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 d σ i ∼ 1 v 2 F i ( v 2 ⊥ , q 2 ) O 10 = i ~ S N · ~ q/m N d E R O 11 = i ~ S χ · ~ q/m N [arXiv:1008.1591, arXiv:1203.3542, arXiv:1308.6288, arXiv:1505.03117] Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Standard energy spectrum ‘Perfect’ CF 4 detector Standard SI/SD int. E R ∈ [20 , 50] keV Input WIMP mass: m χ = 100 GeV SHM velocity distribution Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
NREFT energy spectrum ‘Perfect’ CF 4 F ∼ v 2 detector ⊥ E R ∈ [20 , 50] keV Input WIMP mass: m χ = 100 GeV SHM velocity distribution F ∼ q 2 Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
NREFT energy spectrum ‘Perfect’ CF 4 detector E R ∈ [20 , 50] keV Input WIMP mass: m χ = 100 GeV SHM velocity distribution F 15 ∼ q 2 ( q 2 + v 2 F 7 ∼ v 2 ⊥ ) F 4 ∼ 1 ⊥ Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Distinguishing operators: Energy-only How many events are required to detect the effect of a ‘non-standard’ operator? F 4 ∼ 1 F 7 ∼ v 2 ⊥ F 15 ∼ q 2 ( q 2 + v 2 ⊥ ) Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Directional Detection Different v-dependence could impact directional signal. e.g. Drift-IId [arXiv:1010.3027] Mean recoil direction should point away from constellation Cygnus, due to Earth’s motion. h ~ v i ⇠ � ~ Detector v e h ~ q i Look at recoil rate, as a function of , the angle between θ the recoil and the mean recoil direction. Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Standard directional spectrum ‘Perfect’ CF 4 Standard SI/SD int. detector E R ∈ [20 , 50] keV Input WIMP mass: m χ = 100 GeV SHM velocity distribution Recoils away Recoils towards from Cygnus Cygnus Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
NREFT directional spectrum small θ , small v ⊥ F ∼ q 2 ~ v || ~ ~ q v ⊥ ~ v large θ , large v ⊥ F ∼ v 2 ⊥ ~ q ~ v || ~ v ~ v ⊥ Recoils away Recoils towards from Cygnus Cygnus q = 2 µ χ N ~ Also note: v · ˆ q = 2 µ χ N v cos ✓ Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
NREFT directional spectrum F ∼ q 2 O 4 Most isotropic: O 7 F 7 ∼ v 2 ⊥ Most anisotropic: O 15 F ∼ v 2 F 15 ∼ q 2 ( q 2 + v 2 ⊥ ⊥ ) Recoils away Recoils towards from Cygnus Cygnus Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Distinguishing operators: Energy and direction How many events are required to detect the effect of a ‘non-standard’ operator? F 4 ∼ 1 F 7 ∼ v 2 ⊥ F 15 ∼ q 2 ( q 2 + v 2 ⊥ ) Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Conclusions Direct detection is a unique probe of the different possible interactions between DM and nucleons. However, not all operators can be distinguished in an energy- only experiment. E.g.: F ∼ v 0 χχ ¯ L 1 = ¯ NN χγ µ γ 5 χ ¯ F ∼ v 2 L 6 = ¯ N γ µ N ⊥ But, many operators have interesting directional signatures and directional sensitivity may allow us to detect the effects of ‘non-standard’ operators with only a few hundred events. Directional detection allows us to probe otherwise inaccessible particle physics of Dark Matter! Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Conclusions Direct detection is a unique probe of the different possible interactions between DM and nucleons. However, not all operators can be distinguished in an energy- only experiment. E.g.: F ∼ v 0 χχ ¯ L 1 = ¯ NN χγ µ γ 5 χ ¯ F ∼ v 2 L 6 = ¯ N γ µ N ⊥ But, many operators have interesting directional signatures and directional sensitivity may allow us to detect the effects of ‘non-standard’ operators with only a few hundred events. Directional detection allows us to probe otherwise inaccessible particle physics of Dark Matter! Thank you Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Backup Slides Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Directional Spectra h |M| 2 i ⇠ q 2 q = 2 µ χ N ~ Note: v · ˆ q = 2 µ χ N v cos ✓ h |M| 2 i ⇠ v 2 ⊥ Most isotropic: 1 : O 1 , O 4 , O 7 = ~ S n · ~ v ⊥ v 2 : O 7 , O 8 , ⊥ q 2 : O 9 , O 10 , O 11 , O 12 , h |M| 2 i ⇠ Least isotropic: v 2 ⊥ q 2 : O 5 , O 13 , O 14 , q ~ q ~ q 4 : O 3 , O 6 , O 15 = ( ~ )(( ~ v ⊥ ) · ) S χ · S n × ~ m n m n q 4 ( q 2 + v 2 ⊥ ) : O 15 . Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
A (new) ring-like feature h |M| 2 i ⇠ ( v ⊥ ) 2 Operators with lead to a ‘ring’ in the directional rate. Contours : ring opening angle in degrees Shading : ring amplitude (ratio of ring to centre) A ring in the standard rate has been previously studied [Bozorgnia et al. - 1111.6361], but this ring occurs for lower WIMP masses and higher threshold energies. Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Statistical tests F 4 , 4 ∼ 1 Calculate the number of signal events F 7 , 7 ∼ v 2 required to… ⊥ F 15 , 15 ∼ q 4 ( q 2 + v 2 ⊥ ) …reject isotropy… …confirm the median recoil dir… [astro-ph/0408047] [1002.2717] …at the level in 95% of experiment. 2 σ Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
Distinguishing operators Generate data assuming an NREFT operator ( or ). O 15 O 7 Assume data is a combination of standard SI/SD interaction and non-standard NREFT operator. Fit to data with two free parameters and . A m χ : fraction of events which are due to non-standard NREFT A interaction. Perform likelihood ratio test (in 10000 pseudo-experiments) to determine the significance with which we can reject SD-only interactions: Null hypothesis, H 0 : all events are due to SD interactions, A = 0 Alt. hypothesis, H 1 : there is some contribution from NREFT ops, A 0 6 = Bradley J Kavanagh (LPTHE - Paris) Directional signatures in NREFT RPP 2016 - 25th Jan. 2016
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