Aug 2, 2007 ... two key review articles: ... R.J. Gaitskell (experiment review) in Ann. Rev. Nucl. ....
Emax. Emin. dR(Ei). Ei r. For Emax use ∞ or vesc (later. . . ) .... e−v2 esc/v2. 0. ]
Fortunately, average value well approximated by numerical fit.
Direct Detection of WIMP Dark Matter: Part 1 - a primer Dan Akerib Case Western Reserve University CDMS Collaboration SLAC Summer Institute Aug 2, 2007
Standard Cosmology Colley, Turner & Tyson
from Perlmutter, Phys. Today (units of critical density)
WMAP
WMAP Dan Akerib
SSI 2007
Tytler & Burles Case Western Reserve University
Non-Baryonic Dark Matter Matter = 0.30 ± 0.04
•
Nature of dark matter Non-baryonic Large scale structure predicts DM is ‘cold’
WIMPs – Weakly Interacting Massive Particle
Freeze out: H > A~ n A v
Baryons = 0.05 ± 0.005
•
Production suppressed (T= OmegaCDMmin) Guidice and Romanino, 2004, mu < 0 A. Pierce, Finely Tuned MSSM Guidice and Romanino, 2004, mu > 0 Chattopadhyay et. al Theory results - post WMAP Baltz and Gondolo, 2004, Markov Chain Monte Carlos (1 sigma) Baer et. al 2003 Kim/Nihei/Roszkowski/de Austri 2002 JHEP Ellis et. al Theory region post-LEP benchmark points Baltz and Gondolo 2003 Baltz and Gondolo, 2004, Markov Chain Monte Carlos 060227062601
Dan Akerib
10
Case Western Reserve University
WIMPs in the Galactic Halo detector
Exploit movements of Earth/ Sun through WIMP halo
Direction of recoil -- most events should be opposite Earth/Sun direction (Spergel 1988) Annual modulation -- harder spectrum when Earth travels with sun (Drukier, Freese, & Spergel 1986)
galactic center Sun 230 km/s
June Dec.
energy transferred appears in ‘wake’ of recoiling nucleus
WIMP-Nucleus Scattering
Scatter from a Nucleus in a Terrestrial Particle Detector
Log(rate)
•
WIMP
~2% seasonal effect
Dec
June
Erecoil Dan Akerib
SSI 2007
Case Western Reserve University
Defining the Signal
•
Kinematics
•
Rate
• •
n(v ) MW
halo density cross section
• •
SD/SI coherence & form factors
ER
dR log dER
annual modulation of rate diurnal modulation of direction
ER
Backgrounds Experimental methods & results Dan Akerib
vE
MN
σW N
Primary signal Secondary features
• •
halo potential WIMP mass target mass & velocity
} mostly tomorrow
SSI 2007
Case Western Reserve University
References and further reading
•
References and notation - generally following the treatment of two key review articles:
•
A very nice pedagogic reference
•
J.D. Lewin and P.F. Smith, Astroparticle Physics 6 (1996) G. Jungman, M. Kamionkowski and K. Griest, Physics Reports 267 (1996) S. Golwala, Ph.D. thesis, UC Berkeley (2000) (http://cdms.berkeley.edu)
• •
10th CDMS dissertation - first astrophysics results! winner of first APS Tanaka dissertation prize!
See also
Dan Akerib
R.J. Gaitskell (experiment review) in Ann. Rev. Nucl. Part. Sci. 54 (2004) G. Heusser (low background techniques) in Ann. Rev. Nucl. Part. Sci. 45 (1995)
SSI 2007
Case Western Reserve University
Differential energy spectrum (simplified) dR R0 −ER /E0 r = e dER E0 r R ER R0 E0 r MW MN
dR log dER ER
= = = =
event rate per unit mass recoil energy ∞ total event rate dR dER = R0 dER most probable incident 0 energy (Maxwellian) ∞ 4MW MN dR = ER = ER dER (MW + MN )2 dER 0 = mass of WIMP = E0 r = mass of target nucleus
Dan Akerib
SSI 2007
Case Western Reserve University
WIMP search - c.1988 Germanium ionization detector (UCSB/UCB/LBL) http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini
log cross section (arb. units)
•
070802080001
0
1
2
10 WIMP Mass [GeV]
10
from Jungman et al. (D.O. Caldwell et al.)
Dan Akerib
SSI 2007
Case Western Reserve University
3
Typical numbers For: MW
β ER
Dan Akerib
=
E0
= MN = 100 GeV/c ⇒r=1
2
∼ 0.75 × 10−3 = 220 km/s MW β02 c2 GeV 1 = 2 100 2 (0.75 × 10−3 )2 c2 c = 30 keV =
1 2
SSI 2007
Case Western Reserve University
Refinements dR = R0 S(ER ) F 2 (ER ) I dER OBS S(ER ) = spectral function — masses and kinematics F 2 (ER ) = form factor correction, with ER = q 2 /2MW I = interaction type
Dan Akerib
SSI 2007
Case Western Reserve University
Kinematics DM particle with velocity v and incident KE Ei = 12 MW v 2 scattered at angle θ in CM frame gives recoil energy in lab frame θ θ
where
(1 − cos θ) E R = Ei r 2 4 M W MN 4m2r = r= MW MN (MW + MN )2
and
MW MN mr = MW + MN
is the reduced mass Dan Akerib
SSI 2007
Case Western Reserve University
Kinematics Isotropic scattering: uniform in cos θ Incident WIMP with energy Ei gives recoil energies uniformly in ER = 0 → Ei r
log
dR dER
Recall “familiar” case for equal masses (r = 1), target at rest, head-on collision ER = Ei dR(Ei) Overall spectrum? —sample incident spectrum In each interval Ei → Ei + dEi contribution to spectrum in ER → ER + dER at rate dR(Ei ) of ER dR(E ) dR Ei r i (ER ) = d dER Ei r Dan Akerib
SSI 2007
Case Western Reserve University
Kinematics Need to integrate over range of incident energies dR (ER ) = dER
Emax
Emin
dR(Ei ) Ei r
For Emax use ∞ or vesc (later. . . )
ER Ei ≥ ≡ Emin r
dR dER
dR(Ei) log
For Emin , to get recoil of energy ER need incident energy
ER
Ei r and also need differential rate. . . Dan Akerib
SSI 2007
Case Western Reserve University
Differential rate In a kilogram of detector of nuclear mass number A N0 dR = σ v dn A where the differential density dn is taken as a function v n0 dn = f (v , vE ) d3v k
volume v swept per unit time contains dn(v) particles with velocity v
with n0 = ρDM /MW and normalization k = f d3v
Dan Akerib
SSI 2007
Case Western Reserve University
Coordinate system collision kinematics
v
=
vW,E vE,G vW,G
= = =
WIMP velocity in the target/Earth frame Earth velocity in the Galaxy frame WIMP velocity in the Galaxy frame
galaxy dynamics
vW,G
vE,G
galaxy
vW,G
= vW,E + vE,G = v + vE
−( v + vE )2 /v02
f (v , vE ) = e
Maxwellian velocity distribution Dan Akerib
SSI 2007
Case Western Reserve University
Differential rate For simplified case of vE = 0 and vesc = ∞ 1 3 v f (v, 0) d v dR = R0 4 2πv0 with R0 =
− 12 N0 ρDM 2π A MW
σ0 v0 −v 2 /v02
For Maxwellian f (v, 0) = e , isotropic d3 v → 4πv 2 dv, Ei = 12 MW v 2 and E0 = 12 MW v02 : dR (ER ) = dER = Dan Akerib
∞ ER r
dR(Ei ) R0 = 1 Ei r r( 2 MW v02 )2
R0 −ER /E0 r e E0 r SSI 2007
∞
vmin
vmin
−v 2 /v02
e
v dv
= 2ER /rMW
Case Western Reserve University
Corrections: escape velocity
For finite vesc 2 dR k0 R0 −ER /E0 r −vesc /v02 = −e ) (e dER k1 (vesc , 0) E0 r
but
k0 k1
= 0.9965 for vesc = 600 km/s,
and for MW = MN = 100 GeV/c2 , maximum ER = 200 keV ⇒ cutoff energy ER = 30 keV
Dan Akerib
SSI 2007
Case Western Reserve University
Corrections: earth velocity Clearly vE = 0 — but ∼ v0 = 230 km/s. Full calculation yields: √
2 2 vmin + vE vmin − vE π v0 k0 R0 dR(vesc , vE ) erf −erf −e−vesc /v0 = dER k1 E0 r 4 vE v0 v0 x −t2 3 2 where erf(x) = √π 0 e dt, vmin = v0 ER /E0 r, k0 = (πv02 ) 2 and
2 2 vesc 2 vesc k1 = k0 erf −√ − e−vesc /v0 v0 π v0 Fortunately, average value well approximated by numerical fit R0 −c2 ER /E0 r dR(vesc = ∞, vE ) = c1 e dER E0 r
~30% increase in integrated rate = c1/c2 = 0.751/0.561 and harder spectrum Dan Akerib
SSI 2007
Case Western Reserve University
Signal modulations: annual effect June
June Dec
Dec
Dec
WIMP Signal
±2%
June
Dec
June
Background Dec
Dec
t − 152.5 vE (t)[km/s] = 232 + 15 cos 2π 365.25 galactic center Sun 230 km/s Dan Akerib
Log(rate)
t in days after January 1 June Dec. SSI 2007
Dec
~2% seasonal effect need ~1000 events June
Erecoil
Case Western Reserve University
Signal modulations: recoil direction
•
Differential angular spectrum:
d2 R 1 R0 −(vE cos ψ−vmin )2 /v02 = e dER d(cos ψ) 2 E0 r
• •
Asymmetry more recoils in forward direction by 5x: ~10 events Orientation of lab frame rotates relative to forward direction
eg, definition of forward/backward in lab frame changes as earth rotates ⊥ versus reduces asymmetry to 20% effect: ~300 events
ψ galactic center Sun 230 km/s Dan Akerib
me a r f g n rotati SSI 2007
θ
Case Western Reserve University
Refinements dR = R0 S(ER ) F 2 (ER ) I dER OBS S(ER ) = spectral function — masses and kinematics time dependence
F 2 (ER ) = form factor correction, with ER = q 2 /2MW I = interaction type in zero-velocity limit (v
