Taming astrophysics and particle physics in the direct detection of - PowerPoint PPT Presentation

Taming astrophysics and particle physics in the direct detection of dark matter Bradley J. Kavanagh LPTHE & IPhT (CEA/Saclay) LPTHE seminar - 12th Jan. 2016 bradley.kavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark

Based on… arXiv:1207.2039 arXiv:1303.6868 arXiv:1312.1852 arXiv:1410.8051 in collaboration with Anne Green and Mattia Fornasa, and… arXiv:1505.07406 as well as ongoing work with Chris Kouvaris, Riccardo Catena and Ciaran O’Hare. Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Direct detection of dark matter DM m χ & 1 GeV N N v ∼ 10 − 3 χ χ Measure energy (and possibly direction) of recoiling nucleus Reconstruct the mass and cross section of DM However, we don’t know what speed the DM particles have v and we don’t know how they interact with nucleons! Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Overview Direct detection event rate Astro uncertainties: Particle uncertainties: N-body simulations Non-relativistic operators What can go wrong? Different signals How to solve it How to distinguish them Combining uncertainties Future work Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Particle physics Astrophysics Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Particle physics Astrophysics Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Direct detection event rate Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Event rate v m A m χ ✓ ρ χ ◆ • Flux of DM particles with speed is f 1 ( v ) d v v v m χ • Minimum speed required to excite a recoil of energy in a E R nucleus of mass is: m A s m A E R v min = v min ( E R ) = 2 µ 2 χ A • Event rate per unit detector mass is then Z ∞ d R vf 1 ( v ) d σ ρ χ = d v d E R d E R m χ m A v min Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Event rate v m A m χ ✓ ρ χ ◆ • Flux of DM particles with speed is f 1 ( v ) d v v v m χ • Minimum speed required to excite a recoil of energy in a E R nucleus of mass is: m A s m A E R v min = v min ( E R ) = 2 µ 2 ρ χ ∼ 0 . 2 − 0 . 6 GeV cm − 3 χ A Read (2014) • Event rate per unit detector mass is then [arXiv:1404.1938] Z ∞ d R vf 1 ( v ) d σ ρ χ = d v d E R d E R m χ m A v min Particle and nuclear physics Astrophysics Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Standard Halo Model (SHM) Speed distribution obtained for a spherical, isotropic and ρ ( r ) ∝ r − 2 isothermal Galactic halo, with density profile . Leads to Maxwell-Boltzmann distribution: − ( v − v e ) 2 ✓ ◆ f ( v ) ∝ exp Θ ( v esc − | v − v e | ) 2 σ 2 v I → f 1 ( v ) = v 2 f ( v ) d Ω v √ 2 σ v ≈ 220 km s − 1 with . v e ≈ v e ∼ 220 − 250 km s − 1 σ v ∼ 155 − 175 km s − 1 E.g. Feast et al. (1997) [astro-ph/9706293], Bovy et al. (2012) [arXiv:1209.0759] 
 − 41 km s − 1 v esc = 533 +54 Piffl et al. (RAVE, 2013) [arXiv:1309.4293] Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Cross section Typically assume contact interactions (heavy mediators) In the non-relativistic limit, obtain two main contributions. Write in terms of DM-proton cross section : σ p Spin-independent (SI) σ p d σ A SI χ p v 2 A 2 F 2 SI χχ ¯ SI ( E R ) NN ¯ ∝ µ 2 d E R Nuclear physics Spin-dependent (SD) ∝ σ p d σ A J + 1 SD SD F 2 χγ 5 γ µ χ ¯ N γ 5 γ µ N SD ( E R ) ¯ µ 2 χ p v 2 d E R J We’ll look at more general interactions in the second half of the talk… Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

The final event rate ρ χ σ p d R i C i F 2 = i ( E R ) η ( v min ) i = SI , SD d E R m χ µ 2 χ p SI interactions, SHM distribution Enhancement factor, C i F 2 Form factor, i ( E R ) Mean inverse speed, Z ∞ f 1 ( v ) η ( v min ) = d v v v min Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Astrophysical uncertainties Z ∞ d R vf 1 ( v ) d σ ρ χ = d v d E R d E R m χ m A v min Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

N-body simulations High resolution N-body simulations can be used to extract the DM speed distribution Non-Maxwellian Debris flows Dark disk structure 6 5 5 f 1 ( v ) [10 − 3 km − 1 s] Aq-A-1 5 4 4 4 3 3 f H v L * 10 3 f(v) × 10 -3 L 10 3 2 2 2 1 1 1 0 0 0 0 100 200 300 400 500 0 100 200 300 400 500 600 700 0 150 300 450 600 ê s L v H km ê s L v [km s -1 ] Vogelsberger et al. (2009) Kuhlen et al. (2012) Pillepich et al. (2014) 10 4 10 4 [arXiv:0812.0362] [arXiv:1202.0007] [arXiv:1308.1703] 10 4 10 4 However, N-body simulations cannot probe down to the 5000 5000 Counts Counts sub-milliparsec scales probes by direct detection… 1000 1000 500 500 Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016 100 100 0 100 200 300 400 500 0 100 200 300 400 500 600 700 ê s L ê s L

Local substructure May want to worry about ultra-local substructure - subhalos and streams which are not completely phase-mixed. Analysis of N-body simulations indicate that it is unlikely for a single stream to dominate the local density - lots of different ‘streams’ contribute to make a smooth halo. Helmi et al. (2002) [astro-ph/0201289] Vogelsberger et al. (2007) [arXiv:0711.1105] However, this does not exclude www.cosmotography.com the possibility of a stream - e.g. due to the ongoing tidal disruption of the Sagittarius dwarf galaxy. Freese et al. (2004) [astro-ph/0309279] Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Examples Z 1 f 1 ( v 0 ) I f 1 ( v ) = v 2 f ( v ) d v 0 f ( v ) = f ( v ) d Ω v η ( v ) = v 0 v What happens if we assume the wrong speed distribution? Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

What could possibly go wrong? Generate mock data for 3 future experiments - Xe, Ar, Ge - for a ( m χ , σ p SI ) given assuming a stream distribution function. Then construct confidence contours for these parameters, assuming: (correct) stream distribution (incorrect) SHM distribution Benchmark Best fit Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

A solution Many previous attempts to tackle this problem Strigari & Trotta [arXiv:0906.5361]; Fox, Liu & Weiner [arXiv:1011.915]; Frandsen et al. [arXiv:1111.0292]; Feldstein & Kahlhoefer [arXiv:1403.4606] Write a general parametrisation for the speed distribution: Peter [arXiv:1103.5145] N − 1 ! X a k v k f ( v ) = exp − k =0 BJK & Green [arXiv:1303.6868] This form guarantees a positive distribution function. Now we attempt to fit the particle ( m χ , σ p ) physics parameters , as well as the astrophysics parameters . { a k } f 1 ( v ) = v 2 f ( v ) Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Results Using our parametrisation 2 σ 1 σ Best fit m χ = m rec Assuming incorrect distribution But , there is now a strong degeneracy in the reconstructed cross section… Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Cross section degeneracy Z ∞ d R f 1 ( v ) d v ∝ σ d E R v v min Minimum DM speed probed by a typical Xe experiment This is a problem for any astrophysics-independent method! Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Incorporating IceCube B IceCube can detect neutrinos from DM annihilation in the Sun A Rate driven by solar capture of DM, which depends on the DM-nucleus scattering cross section Crucially, only low energy DM particles are captured: Z v max d C f 1 ( v ) d v d V ∼ σ v 0 But Sun is mainly spin-1/2 Hydrogen - so we need to include SD interactions… Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016

Direct detection only Consider a single benchmark: SI = 10 − 45 cm 2 ; σ p SD = 2 × 10 − 40 cm 2 m χ = 30 GeV; σ p ν µ ¯ annihilation to , SHM+DD distribution ν µ Benchmark Bradley J Kavanagh (LPTHE & IPhT) Direct detection uncertainties LPTHE seminar - 12th Jan. 2016