PHY326/426:Lecture 16Direct Detection Searches for WIMPs

•Finish WIMP-nucleon collision kinematics•The background problem in WIMP detection •Sources of background•Passive shielding - going underground•Passive shielding - materials and purity

Signals and Background Rejection

Two remaining oversimplifications1. WIMPs do not all have the same velocity v!2. WIMP nucleon cross sections are NOT independent of energy.

Rate in energy range ER -> ER+dER

Incorporating WIMP velocities

Assuming the isothermal sphere model:

where

Evaluating the Integral

vmin is the minimum WIMP velocity that can result in a nuclearrecoil of kinetic energy ER.

or

Maximum recoil energy occurs when cos!=-1, in which case

Evaluating the Integral

vmin =

or

Maximum recoil energy occurs when cos!=-1, in which case

the minimum WIMP velocity that can result in a nuclear recoil of kinetic energy ER.

Substitute with

So that

Evaluating the Integral

Rate of WIMP Energy DepositionTherefore the rate of WIMP energy deposition into the detector( in events per second) from all incoming WIMP velocities is:

Substitute back in P and Q:

And we arrive at:

QED

F2 – FORM FACTOR correction

The Final Parts

!

dR

dEOBS

= R0S(E

R)F

2(E

R)I

for high A nuclei the spectrum is suppressed

I – SPIN FACTOR correction whether the nucleus has spin may determine the interaction strengthspin-dependent or spin-independent determines the rate

The Form Factor F2In reality, larger WIMP recoil energies require higher momentum transfer from the WIMP to the nucleus. The probability of a process is actually highly dependent on the momentum transfer. In fact, it falls rapidly with increasing transferred momentum, meaning a rapidly falling probability with increasing ER

Define the nuclear form factor for a scattering interaction asfollows:

Here, q is the magnitude of the momentum transferred fromthe WIMP to the nucleus through the interaction.

In practice this can be written in terms of the recoil of the nucleus:

Dependence of F2 on Recoil Energy

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0 200 400 600 800 1000

Coherent form factors (Fermi density)

19F; c = 2.77 fm23Na; c = 2.94 fm127I; c = 5.59 fm129Xe; c = 5.63 fm131Xe; c = 5.64 fm

F2

E(keV)

10000 200 400 600 800ER (keV)

10-1

10-2

10-3

10-4

10-5

10-6

10-7

1

F2(E

R)

Coherent Form Factors(Fermi Density)

(e.g. Ressell et al. Phys. Rev. C 56 No.1 (1997) 535).

Note the very rapiddrop-off in the formfactor, and consequentlythe cross section for scattering, with increasingnuclear recoil.

Example Expected Recoil Spectra

Predicted spectrum for an example 100 GeV WIMP for different target nuclei

Last Time - Signal RateLast time, we (finally) finished deriving the rate for WIMPnuclear interactions, assuming spin independence.

The quantities (other than constants) in this formula are:total mass of sensitive material in detector

atomic mass of target in atomic mass unitsWIMP, target nucleus, reduced rest energies

[GeV] width of energy bin used for event rate countdark matter rest energydensity in halo

WIMP nuclear form factor at recoil energy ERWIMP-nucleon cross section at zero recoil energy

virial velocity multiplied by divided by speed of lightevents per GeV of energy bandwidth per second

Summary So FarWIMP Properties

(1) Neutral - interact by nuclear recoil

(2) Energy of recoiling nucleus ~1-100 keV(3) Rate of interactions in normal matter << 1/day/kg

WIMP Detection(1) Ionisation Charge(2) Scintillation Light(3) Heat Phonons

either with whole nucleus or unpaired nucleon with spin

A WIMP detector consists of a sensitive volume which producessome kind of pulse when a collision in that detector produces a signal above threshold.

Here is a schematic of a detector readout:

Problem: ANYTHING that can make pulses can mimic a signal from WIMPs.

The Background Problem

Detector

(2) Cosmic Rays (especially Muons, that produce neutrons)

For each DM event there are a >106 events from other sources

(1) Radiation from surroundings (α, β, γ, neutrons)

Cosmic rays

The Background ProblemThere are two sources of background:

Gammas are a particular problem but in both cases it is NEUTRONS are the ultimate background problem

Produced in large numbers by radioactive decays of trace isotopes of common elements in target or surrounding materials.

Gamma interactions with target are different to WIMPs - gammas interact electromagnetically with electrons.

Gamma backgrounds can be reduced by use of pure materials, shielding, and discrimination by exploiting difference between gamma and WIMP interactions.

Neutrons are a problem! - no charge so interact via elastic collisions with target nuclei - producing signals potentially like WIMP interactions.

Sources of Neutrons:• Decays of U/Th deposits in target and surrounding materials. Need low background materials

• Cosmic Ray Muon induced neutrons - neutrons knocked out of surrounding materials (spallation) by highly penetrating muons.

The Background ProblemGamma Rays Neutrons

Cosmic ray muons

Neutrons from materialsSurrounding detector

Neutrons fromDetector materials

UPPERATMOSPHERE

ULTRAHIGH ENERGYPRIMARY CRPARTICLEFROMSPACE

DETECTORON EARTH

Muons collide with surrounding material releasing a neutron

Sources of Background Neutrons

NEUTRONS are the ultimate background problem and the PRIME REASON to go underground is to shield against NEUTRONS produced by cosmic ray muons

How to Reduce Background(1) Passive shielding - i.e. (a) surround your detector by material to absorb the background gammas and neutrons (b) make detector pure

(3) Active discrimination - identify and reject background events in the detector through measuring some property that identifies them as not due to WIMP interactions

(2) Active shielding - detect the background particle scattering in a “veto” detector around the main detector, reject coinicences

How to Identify a Real WIMP Signal(1) Observe different energy spectra - i.e. use the kinematics of earlier - should get different response from different target nuclei(2) Observe annual modulation - i.e. use the motion of the earth around the Sun to see an annual change in the spectra(3) Observe directionality of the recoils - i.e. use the motion of the earth through the galaxy to see a preferred direction of the recoils

NEXT LECTURE

Siting a detector UNDERGROUND allows you to reduce the background of CR-muon induced neutrons.

Overburden of Rock above your head attenuates cosmic ray muons.

Depth of site often quoted in Meters of Water Equivalent (MWE) - adjusting for variation in rock density. (Boulby mine = 1100m deep or 2805mwe).

Muo

n Fl

ux (c

m-2

s-1 )

Neu

tron

Prod

uctio

n (g

-1s-1

)

Depth (mwe)

10-13

10-11

10-9

10-7

10-5

10-3

10 -1

0 1000 2000 3000 4000 5000 6000 7000 8000

Muon FluxNeutron Production

BoulbySo

udan

Gra

n Sa

sso

Kam

ioka

Frej

us

Mon

t Bla

nc

Sudb

ury

Passive Shield (1) - Go UndergroundPlot of muon flux from cosmic rays vs. depth

neutron production

muon flux

Boulby Laboratory (UK)

Plymouth

London

Birmingham

Liverpool

Newcastle

Edinburgh

Inverness

Belfast

Dublin

Redcar

Hartlepool

Peterlee

Middlesbrough

Billingham

Newton Aycliffe

Stockton

Darlington

Middlesborou

Whitb

Staith

York

SHIELD your detector from external backgroundsGamma Shielding:High ʻZʼ material, e.g. Pb, CuNeutron Shielding:High hydrogen content e.g.Water, wax, plastics e.g (polypropylene)

Pb ‘Castle’

Gamma shielding for the NAIAD detector

Cu

NaI Target

Target

Shielding

Installing under-floor neutron shielding@ Boulby (Polypropylene pellets).

Passive Shielding (2a) - Material Around Detector

Select low-background materials (for detector and surroundings).

Choose materials with very LOW Uranium, Thorium, Potassium content.

Materials can be tested by mass spectrometry techniques - or through high sensitivity background activity monitoring.

U (ppb) Th (ppb) K (ppm)

Copper <0.1 <0.1 <0.01Stainless Steel ~1 ~1 <0.5 Perspex <1 <1 <1 NaI <1 <1 <1 Lead <0.1 <0.1 <0.1

Glass ~1000 ~800 ~300 Ceramic capacitor ~800 ~200 ~1300 Rock Salt ~10 ~220 ~1000Brazil Nuts ~2500 ~7000 ~24000

Passive Shielding (2b) - Minimise Background Radioactivity

Problem: Despite using low-background materials and shielding background radiation (principally gammas) will STILL dominate.

Action: Build a detector that can discriminate between gamma interactions (electron recoils) & WIMPs (nuclear recoils)

Even in the lowest background sites, gamma background event rates are of the order of 106 /kg/day

Mea

sure

able

par

amet

er

ER (recoil energy)

Detector energy threshold Electron

recoils

Nuclearrecoils

Here WIMPs can be CLEARLY

distinguished from backgrounds

Here background discrimination = ‘statistical’

Example discrimination techniques:

Experiment: TechniqueNAIAD Light pulse durationZEPLIN-II Scintillation / ionisation ratioCDMS Heat/ionisation

Background Discriminationmore next lecture

END