A halo-independent lower bound on the DM capture rate in the Sun from a DD signal Juan Herrero-García Royal Institute of Technology (KTH), Stockholm JCAP 1505 (2015) 05, 036, arxiv [hep-ph]: 1502.03342 In collaboration with M. Blennow, S. Clementz and T. Schwetz TAUP 2015, Torino, 10 th of September Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 1 / 20
Outline 1 Motivation 2 DD and capture rate in the Sun (C Sun ) 3 A halo-independent (HI) lower bound on C Sun 4 Numerical analysis 5 Summary and concluding remarks Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 2 / 20
Motivation Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 3 / 20
Motivation: derive a new HI framework for DD and capture Uncertainties on f(v), ρ are crucial on interpretation of DM signals. 1 Many studies: For DD [McCabe, Frandsen, Drees, Savage... ]. Talk by N. Bozorgnia. For C Sun [Bruch, Choi...]. 2 Also halo-independent (HI) methods: For DD: for fixed m χ, compare η(v m, t) (detector independent) in same v m range [Fox, Del Nobile, Bozorgnia, Feldstein, JHG...]. Talk by P. Gondolo. HI upper bounds from DD and Γ Sun [Ferrer...]. Talks by S. Wild. New HI framework to compare DD with ρ χ, LHC, Ω χ, and indirect detection [Blennow, JHG, Ferrer]. Talk by S. Vogl. Here new HI framework for comparing a positive DD signal with Γ Sun : We use that both the DD signal and C Sun depend on σ SI/SD. However, the velocities probed by both are very different. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 4 / 20
Direct detection and the capture rate in the Sun Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 5 / 20
Direct detection: there is a minimum velocity v m Goodman, Drukier, Freese... For elastic SI interactions the event rate can be expressed as where η(v m, t) C R(E R, t) = A 2 F 2 A(E R ) η(v m, t), v > v m by kinematics, with: v m dvv f det (v, t), with C ρ χσ SI/SD 2m χ µ 2 χp. ma E R v m =. 2µ 2 χa Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 6 / 20
Capture: there is a maximum velocity v cross (shown H, SD) For the DM to be captured there is a minimal and maximal E R : E min = m χ 2 v2, E max = 2µ2 χa m A (v 2 + u 2 esc(r)). These define the maximum velocity to be trapped: vcross(r) A 4mA m χ = m χ m A u esc(r) Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 7 / 20
A halo-independent lower bound on the DM capture rate in the Sun JCAP 1505 (2015) 05, 036, arxiv [hep-ph]: 1502.03342 Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 8 / 20
Overlap in velocity (H, SD) and assumptions of the bound Gould, Edsjo, Kavanagh, Blennow... Overlap in v thr < v < v A cross(r): DD is sensitive to v > v thr. Capture for v < v A cross(r). We can derive a lower bound on the capture, assuming: 1 We use that v e 29 km/s v m so that: f det (v) = f Sun (v + v e ) f Sun (v) f(v). 2 f(v), ρ χ constant so they are equal for the capture and for DD. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 9 / 20
A lower bound on the capture C Sun = 4π C A A 2 RS 0 v A drr 2 cross ρ A (r) dv f(v) v F A (v, r) 0 4π C A A 2 RS 0 v A drr 2 cross ρ A (r) dv f(v) v F A (v, r). v thr From a perfectly measured DD spectrum one can extract: C f(v) = 1 ( ) d R(ER ) va 2 dv FA 2(E R) The bound on C Sun can be expressed in terms of DD quantities. It is independent of f(v), v esc, σ SI/SD and ρ χ. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 10 / 20
Equilibrium between capture and annihilations in the Sun DM obeys (A Sun annihilation rate, no evaporation for m χ 3.5 GeV): dn dt = C Sun A Sun N 2. Equilibrium (dn/dt = 0) occurs for t eq t Sun 4.5 Gyr, where: C Sun t eq = 1 CSun A Sun ( 10 21 s 1 ) 1/2 ( 3 10 26 cm 3 s 1 ) 1/2 ( 100 GeV ) 3/4 0.5 Gyr, σv ann m χ where σv ann is the thermally-averaged annihilation cross section. For C Sun 10 21 s 1, no equilibrium reached if σv ann < σv fo. If it is reached Γ Sun given solely in terms of C Sun : Γ eq Sun = N 2 2 A Sun = C Sun 2. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 11 / 20
Numerical analysis Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 12 / 20
Comparison with the SHM Our bounds are strongest: For Xe in 20 m χ 1000 GeV (SD) and m χ 50 GeV (SI). Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 13 / 20
C Sun and upper bounds on BR for Xe mock signal Results: For xenon, for SD, annihilations into ν would be constrained to BR at the few % level. ττ, W W at the 10% level. Strong dependence on m χ. Stronger bounds at the wrong m χ. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 14 / 20
DAMA (already strongly disfavored HI by DD) Using HI bounds on modulation: A η (v m ) v e s α dη dv m [Schwetz, Zupan, JHG]. DAMA in strong tension: Na: for SI annihilation into νν, ττ (bb) are strongly constrained for m χ 5 (15) GeV, while SD is excluded for all channels. I: for SI, strong bounds for m χ 10, 35 GeV for νν, ττ. For SD m χ 40 (80) GeV excluded for νν, ττ (bb). Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 15 / 20
Unknown couplings to n and p, and uncertainties in SD FF The extracted f(v) depends on couplings to n and p, and FF: C f extr (v) = C f(v) A 2 true Ftrue(E 2 R ) A 2 wrong Fwrong(E 2 R ) η(v) ( d A 2 true F 2 ) true(e R ) v dv A 2 wrong Fwrong(E 2. R ) Isospin violation (IV), κ f n /f p : SD Xe (n) & F (p), κ a n /a p : CSun(κ) [s 1 ] 10 22 10 20 10 18 10 16 Silicon Xenon κ true = 1 κ true = 1 κ true = 0.7 2 1 0 1 2 κ Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 16 / 20
Preliminary: inelastic (m χ m χ = δ), self-interactions Blennow, Clementz, JHG: in preparation. Left) C Sun for inelastic scattering (solid) and bounds (dashed) δ (kev) black: 0, red: 25, blue: 50. Right) C Sun for inelastic self-interactions (solid) [no bounds possible] m χ (GeV) red: 10, green: 50, blue: 100, yellow: 500, black: 1000. CSun [s 1 ] 10 26 10 25 10 24 10 23 C self (δ)/c self (δ=0) 1 0.8 0.6 0.4 0.2 10 22 10 100 1000 0 10 100 1000 m χ [GeV] δ [kev] Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 17 / 20
Summary and conclusions Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 18 / 20
Summary We derived a lower bound on C Sun in terms of a positive DD signal that is independent of f(v), v esc, σ SI/SD and ρ χ. We assumed f(v), ρ χ constant on t eq and equal in DD and C Sun. If equilibrium between capture-annihilations is reached (otherwise need σ ann ) one can derive upper bounds on BR from no ν signal. It is strong for SD and channels to νν, ττ and m χ 100 GeV. Extension to inelastic scattering, isospin-violation and self-interactions in preparation [Blennow, Clementz, JHG]. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 19 / 20
Concluding remarks: complementarity of the signals DD Γ Sun Lesson No No Keep trying... Axions? Eventually, does DM interact non-gravitationally? No Yes There is NO halo-independent lower bound on R from a ν signal Dark disk? [Bruch, Choi...] Self-interactions? [Zentner, JHG (in preparation)...] IV? Inelastic? [Nussinov, Menon, Shu, JHG (in preparation)...] Yes No HI upper bounds on BRs [this work]. SD dominated by neutrons? Asymmetric DM with suppressed Γ? [Kaplan, Nussinov...] p-wave suppressed σ ann? [Kappl...] Channels without ν (or not energetic enough)? IV? Inelastic? [Nussinov, Menon, Shu, JHG (in preparation)...] Yes Yes Check if the lower bounds here derived are fulfilled. If so, extract DM properties by a fit [Arina, Serpico, Kavanagh...]. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 20 / 20
Back-up slides Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 20 / 20
Capture rate in the Sun [Press, Griest, Gould, Bergstrom, Edsjo, Blennow...] The DM velocity inside the gravitational potential of the Sun w 2 = v 2 + u 2 esc(r), with u 2 esc(r) the escape velocity from the Sun. The capture rete is given by (notice that wdw = vdv) with C Sun = 4π ρ χ m χ A RS Ω A (w, r) = w ρ A m A 0 dr r 2 dv f(v) v w Ω A (w, r), 0 Emax(w) E min (w) where E R is the nuclear recoil energy. de R dσ A de R (w), If equilibrium between capture and annihilation is reached: Γ Sun = 1 2 C Sun Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 21 / 20
A lower bound on the capture C Sun 4π RS A 2 A 0 = 4π [ RS A 2 drr 2 ρ A (r) A 0 v A ( drr 2 cross ρ A (r) dv d η(v) ) F A (v, r) v thr dv v A cross ] η thr F A (v thr, r) + v thr dv η(v) F A(v, r), where in the last line we integrated by parts, with F A (v A cross, r) = 0. Features: Either the derivative or the function η(v), including its value at the threshold, have to be determined from DD. The bound is independent of the DM velocity distribution, the galactic escape velocity, the scattering cross section and the local DM density. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 22 / 20
Numerical examples We simulate mock data motivated by future experiments: Xenon, with σ SI = 10 45 cm 2 and σ SD = 2 10 40 cm 2. Assuming m χ = 100 GeV, for an exposure of 1 ton yr, about 154 (267) events in the range 5 45 kev for SI (SD) are predicted. Germanium, with E thr = 1 kev, focusing on low DM masses. Assuming m χ = 6 GeV and σ SI = 5 10 42 cm 2 and σ SD = 2 10 40 cm 2, 1.5 10 4 (2 3) events for SI (SD) predicted in the range 1 10 kev for an exposure of 100 kg yr with energy resolution of 30%. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 23 / 20
C Sun and BR assuming equilibrium (Γ Sun = C Sun /2) for Ge Results: For Ge, for both SD and SI direct annihilations into ν would be constrained to BR at the few % level. ττ are at wrong m χ. Strong dependence on m χ. Stronger bounds at the wrong m χ. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 24 / 20
Halo-independent bounds on annual modulation in DD Annual modulation [Freese et al]: Depending on the time of the year, we should receive more or less DM flux in our detectors. The annual modulation A η (v m ) can be constrained in terms of the constant rate η(v m ) (almost) halo-independently [JHG, Schwetz, Zupan], by expanding η(v, t) in v e /v 1, with v e 30 km/s. If there is a preferred direction in the DM velocity: A η (v m ) v e sin α halo dη dv m. Therefore there is also a lower bound on the capture for A η (v m ): C Sun 4π A RSun A 2 drr 2 ρ A (r) 0 v A cross v thr dv à η (v) sin α halo v e F A (v). Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 25 / 20
Expansion of η(v m, t) in v e /v v esc v > v m v e, so we can expand η(v m, t) to first order in v e : η(v m, t) = d 3 v f det( v) = d 3 v f Sun( v + v e (t)) = v m v v m v = d 3 v f Sun( v) v m v + d 3 v f Sun ( v) v v e(t) v 3 [Θ(v v m ) δ(v v m ) v m ] η(v m ) + A η (v m ) cos 2π(t t 0 ). η(v m ) is constant, A η is modulated, with observed rates: R CF 2 (E r ) η(v m ) and A R CF 2 (E r )A η Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 26 / 20
The general bound on the annual modulation 1 Halo smooth on v e 30 km/s. 2 Only time dependence in v e (t), not in f Sun (no change on months). [ vm2 dv m A η (v m ) v e η(v m1 ) + dv η(v) ] v m1 v v m1 3 If there is a constant ˆv HALO governing the modulation: where: vm2 in general sin α can be set to 1. v m1 dv m A η (v m ) sin α v e η(v m1 ) sin α 0.5 when ˆv HALO ˆv SUN (isotropic, SHM, DD...). And phase t 0 = June 2nd. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 27 / 20
DAMA results Na dominates for DM masses m χ 20 GeV. I is relevant for larger DM masses. Small overlap for I for H (SD). Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 28 / 20
Evidence for dark matter Rotation curves of spiral galaxies: Bullet cluster (X-rays + grav. lensing): CMB spectrum alone: Ω DE 0.69, Ω B 0.05, Ω DM 0.26 Combination of data from CMB, SN IA, BBN and clusters. M/L ratio in galaxy clusters (virial theorem to gas). Growth of structure (N-body simulations). Globular clusters in galaxies... Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 29 / 20
Properties of a DM particle (or particles) 1 Interacts gravitationally. 2 With the observed density (long-lived/ stable). 3 Neutral. 4 Cold (or warm), otherwise small scales would have been erased. 5 Collisionless: it does not dissipate, it forms haloes. We assume DM is a Weakly Interacting Massive Particle (WIMP): weak-scale cross-section with the SM. mass m χ O(1 10 3 ) GeV. which yield right relic abundance (WIMP miracle) and make DD possible. Juan Herrero-García (KTH) A HI lower bound on the DM capture rate TAUP, Torino, 10/09/2015 30 / 20