That which does not kill us makes us stronger

That which does not kill us

All particle physics models

Write down and analyze all possible WIMP interactions with ordinary matter

Effective operators

if mediator mass ≫ exchanged energy

χ χ

O

q,g q,g

Four-particle effective operator

Interference is important although often neglected.

There are many possible operators.

Long(ish) distance interactions are not included.

Effective operators: LHC & direct detection

Name Operator Coefficient D1 χχ¯¯ qq m_q/M_∗³ D2 χγ¯ ⁵χ¯qq im_q/M_∗³ D3 χχ¯¯ qγ⁵q im_q/M_∗³ D4 χγ¯ ⁵χ¯qγ⁵q m_q/M_∗³ D5 χγ¯ ^µχ¯qγ_µq 1/M_∗² D6 χγ¯ ^µγ⁵χ¯qγ_µq 1/M_∗² D7 χγ¯ ^µχ¯qγ_µγ⁵q 1/M_∗² D8 χγ¯ ^µγ⁵χ¯qγ_µγ⁵q 1/M_∗² D9 χσ¯ ^µνχ¯qσ_µνq 1/M_∗² D10 χσ¯ _µνγ⁵χ¯qσαβq i/M_∗² D11 χχG¯ _µνG^µν α_s/4M_∗³ D12 χγ¯ ⁵χG_µνG^µν iα_s/4M_∗³ D13 χχG¯ _µνG˜^µν iα_s/4M_∗³ D14 χγ¯ ⁵χG_µνG˜^µν α_s/4M_∗³

Name Operator Coefficient C1 χ^†χ¯qq m_q/M_∗² C2 χ^†χ¯qγ⁵q im_q/M_∗² C3 χ^†∂_µχ¯qγ^µq 1/M_∗² C4 χ^†∂_µχ¯qγ^µγ⁵q 1/M_∗² C5 χ^†χG_µνG^µν α_s/4M_∗² C6 χ^†χG_µνG˜^µν iα_s/4M_∗² R1 χ²qq¯ m_q/2M_∗² R2 χ²qγ¯ ⁵q im_q/2M_∗² R3 χ²G_µνG^µν α_s/8M_∗² R4 χ²G_µνG˜^µν iα_s/8M_∗²

Table of effective operators relevant for the collider/direct detection connection

Goodman, Ibe, Rajaraman, Shepherd, Tait, Yu 2010

Fox, Harnik, Primulando, Yu 2012

CoGeNT

CRESST CDMS

XENON - 100 DAMA

Hq ± 33 %L Hc g^mcL I q gmqM

monojet razor combined

Hc g^mcL IasGmnG^mnM Spin-independent

0.1 1 10 100 1000

10^-46 10^-44 10^-42 10^-40 10^-38 10^-36

m_c@GeVD sSI@cm2 D

Spin-independent

LHC limits on WIMP-quark and WIMP-gluon

interactions are competitive with direct searches

Beltran et al, Agrawal et al., Goodman et al., Bai et al., 2010; Goodman et al., Rajaraman et al.

Fox et al., 2011; Cheung et al., Fitzptrick et al., March-Russel et al., Fox et al., 2012...

These bounds do not apply to SUSY, etc.

Complete theories contain sums of operators (interference) and not-so-heavy mediators (Higgs)

Effective operators: LHC & direct detection

Response ⇥h

4π 2Ji+1

i−1

Leading Long-wavelength Response

Multipole Limit Type

1

X

J =0,2,...

|hJi||MJ M||Jii|² M₀₀(q~xi) ^p1_4π1(i) MJ M : Charge

1

X

J =1,3,...

|hJi||Σ⁰⁰_{J M}||Jii|² Σ⁰⁰_1M(q~xi) ₂^p1_3πσ_1M(i) L⁵_{J M} : Axial Longitudinal

1

X

J =1,3,...

|hJi||Σ⁰J M||Jii|² Σ⁰_1M(q~xi) ^p1_6πσ_1M(i) T_{J M}^el5 : Axial Transverse Electric

1

X

J =1,3,...

|hJi|| q mN

∆J M||Jii|² _m^q

N∆1M(q~xi) −_2m^q

N

p6π`_1M(i) T_{J M}^mag :

Transverse Magnetic

1

X

J =0,2,...

|hJi|| q mN

Φ⁰⁰J M||Jii|² _m^q_NΦ⁰⁰₀₀(q~xi) −_3m^q

N

p4π~σ(i) · ~`(i) LJ M : Longitudinal

q

mNΦ⁰⁰_2M(q~xi) −_m ^q

N

p30π[xi⌦ (~σ(i) ⇥¹_ir)~ 1]2M 1

X

J =2,4,...

|hJi|| q mN

Φ˜⁰_{J M}||Jii|² _m^q

N

Φ˜⁰_2M(q~xi) −_m ^q

N

p20π[xi⌦ (~σ(i) ⇥¹_ir)~ 1]2M

T_{J M}^el :

Transverse Electric

All short-distance operators classified

1, ~S_χ · ~S_N, v², i(~S_χ ⇥ ~q) · ~v, i~v · (~S_N ⇥ ~q), (~S_χ · ~q)(~S_N · ~q)

~v^⊥ · ~S_χ, ~v^⊥ · ~S_N, i~S_χ · (~S_N ⇥ ~q).

i~S_N · ~q, i~S_χ · ~q,

(i~S_N · ~q)(~v^⊥ · ~S_χ), (i~S_χ · ~q)(~v^⊥ · ~S_N).

All nuclear form factors classified

Fitzpatrick et al 2012

Fitzpatrick et al 2012

nuclear oscillator model

Effective operators: direct detection

Experimental limits on single operators… Schneck et al (SuperCDMS) 2015

Effective operators: direct detection

Combined analysis of short-distance operators Catena, Gondolo 2014

log10(x3)

−4 −2 0

−2 0 2 4

log10(x4)

−4 −2 0

−1 0 1 2 3

log10(x5)

−4 −2 0

−2 0 2 4

log10(x6)

−4 −2 0

−2 0 2 4

log10(x7)

−4 −2 0

−2 0 2 4

log10(x8)

−4 −2 0

−2 0 2 4

log10(x9)

−4 −2 0

−2 0 2 4

log10(x10)

−4 −2 0

−2 0 2 4

log₁₀(x₁) log10(x11)

−4 −2 0

−2 0 2 4

−2 0 2 4

−1 0 1 2 3

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₃)

−2 0 2 4

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

log₁₀(x₄)

−1 1 3

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₅)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₆)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₇)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₈)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₉)

−2 0 2 4

−2 0 2 4

log₁₀(x₁₀)

−2 0 2 4

−2 0 2 4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

O₁ = 1χ1N O₇ = S~_N · ~v_χN^⊥ O₃ = −iS~_N ·⇣

~ q

m_N × ~v^⊥

χN

⌘

O₈ = S~_χ· ~v^⊥

χN

O₄ = S~_χ· ~S_N O₉ = −iS~_χ·⇣ ~S_N × ^~q

m_N

⌘ O₅ = −iS~_χ·⇣

~ q

m_N × ~v^⊥

χN

⌘

O₁₀ = −iS~_N · ^~q

m_N

O₆ = ⇣ ~S_χ· ^~q

m_N

⌘ ⇣ ~S_N · ^~q

m_N

⌘

O₁₁ = −iS~_χ· ^~q

m_N -0.02 -0.01 0.00 0.01 0.02

-40 -20 0 20 40

c₁m_v² c3mv2

-5 0 5

-200 -100 0 100 200

c₄m_v² c5mv2

-10 -5 0 5 10

-200 -100 0 100 200

c₈m_v² c9mv2

-10 -5 0 5 10

-3000 -2000 -1000 0 1000 2000 3000

c₄m_v² c6mv2LUX m = 10 TeV

Profile-likelihood 
 global analysis

Effective operators: direct detection

Combined analysis of short-distance operators Catena, Gondolo 2014

log10(x3)

−4 −2 0

−2 0 2 4

log10(x4)

−4 −2 0

−1 0 1 2 3

log10(x5)

−4 −2 0

−2 0 2 4

log10(x6)

−4 −2 0

−2 0 2 4

log10(x7)

−4 −2 0

−2 0 2 4

log10(x8)

−4 −2 0

−2 0 2 4

log10(x9)

−4 −2 0

−2 0 2 4

log10(x10)

−4 −2 0

−2 0 2 4

log₁₀(x₁) log10(x11)

−4 −2 0

−2 0 2 4

−2 0 2 4

−1 0 1 2 3

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₃)

−2 0 2 4

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

−1 1 3

−2 0 2 4

log₁₀(x₄)

−1 1 3

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₅)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₆)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₇)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₈)

−2 0 2 4

−2 0 2 4

−2 0 2 4

−2 0 2 4

log₁₀(x₉)

−2 0 2 4

−2 0 2 4

log₁₀(x₁₀)

−2 0 2 4

−2 0 2 4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

O₁ = 1χ1N O₇ = S~_N · ~v_χN^⊥ O₃ = −iS~_N ·⇣

~ q

m_N × ~v^⊥

χN

⌘

O₈ = S~_χ· ~v^⊥

χN

O₄ = S~_χ· ~S_N O₉ = −iS~_χ·⇣ ~S_N × ^~q

m_N

⌘ O₅ = −iS~_χ·⇣

~ q

m_N × ~v^⊥

χN

⌘

O₁₀ = −iS~_N · ^~q

m_N

O₆ = ⇣ ~S_χ· ^~q

m_N

⌘ ⇣ ~S_N · ^~q

m_N

⌘

O₁₁ = −iS~_χ· ^~q

m_N -0.02 -0.01 0.00 0.01 0.02

-40 -20 0 20 40

c₁m_v² c3mv2

-5 0 5

-200 -100 0 100 200

c₄m_v² c5mv2

-10 -5 0 5 10

-200 -100 0 100 200

c₈m_v² c9mv2

-10 -5 0 5 10

-3000 -2000 -1000 0 1000 2000 3000

c₄m_v² c6mv2LUX m = 10 TeV

Profile-likelihood 
 global analysis

log 10(c0 3 m v2 )

log10(c

1 m

v 2)

−5 −3 −1 1

−3

−2

−1 0 1 2 3 4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Effective operators: direct detection

Do not assume any particular 
 WIMP density or velocity distribution

All astrophysics models

.

✓event rate

◆

= ✓ detector response

◆

× ✓particle physics

◆

× (astrophysics)

DM-nucleus elastic scattering

Dark matter particle

Nuclear recoil

Detector response model

Is a nuclear recoil detectable?

Probability of detecting an event with energy (or number of photoelectrons) E, given an event occurred with recoil energy ER.

Counting efficiency, energy resolution, scintillation response, etc.

.

✓event rate

◆

= ✓ detector response

◆

× ✓particle physics

◆

× (astrophysics)

. ✓ detector response

◆

= G(E, E^R)

Particle physics model

WIMP-nucleus cross section:

spin-independent, spin-dependent, electric, magnetic, ...

What force couples dark matter to nuclei?

Coupling to nucleon number density, nucleon spin density, ...

WIMP speed

WIMP mass Nucleus recoil energy

.

✓event rate

◆

= ✓ detector response

◆

× ✓particle physics

◆

× (astrophysics)

. ✓particle physics

◆

= v² m

dσ dE_R

. (astrophysics) = η(v^min, t) ≡ ρ^χ Z

v>v_min

f(v, t)

v d³v

Astrophysics model

How much dark matter comes to Earth?

Local halo density

Velocity distribution

Minimum WIMP speed to impart recoil energy ER 
 v_min = (M E^R/µ + δ)/√2M E^R

.

✓event rate

◆

= ✓ detector response

◆

× ✓particle physics

◆

× (astrophysics)

Astrophysics model: velocity distribution

Standard Halo Model

The spherical cow of direct WIMP searches f(v) =

( ₁

N^escπ^3/2v¯₀³ e^{−|v+vobs|/¯v02} |v| < vesc

0 otherwise

truncated Maxwellian

Cosmological N-Body simulations including baryons are challenging but underway

We know very little about the dark matter velocity distribution near the Sun

0 150 300 450 600

v [km s^-1] 0

1 2 3 4 5

f(v) × 10-3

Aq-A-1

Figure 2. Top four panels: Velocity distributions in a kpc box at the Solar

NO BARYONS!!!!

Maxwellian

Vogelsberger et al 2009 Median

68% 95%

Astrophysics model: velocity distribution

orbit

Pal 5 trailing tail

leading tail

Odenkirchen et al 2002 (SDSS)

SDSS, 2MASS, SEGUE,…….

Streams of stars have been observed in the galactic halo

.

✓event rate

◆

= ✓ detector response

◆

× ✓particle physics

◆

× (astrophysics)

Agnese et al (SuperCDMS) 2014

FIXED FIXED

Astrophysics model: velocity distribution

.

✓event rate

◆

= ✓ detector response

◆

× ✓particle physics

◆

× (astrophysics) ARBITRARY FIXED

Astrophysics-independent approach

vmin

η

Fox, Liu, Wiener 2011; Gondolo, Gelmini 2012; Del Nobile, Gelmini, Gondolo, Huh 2013-14

Claimed signal Upper bound

˜

η(vmin) = σχp

ρ_χ m_χ

Z ^∞

v_min

f(v)

v d³v Rescaled astrophysics factor

common to all experiments

Minimum WIMP speed
 to impart recoil energy ER

R =

Z ^∞

0

dv R(v) ˜η(v)

Astrophysics-independent approach

Response function

• Every experiment is sensitive to a “window in velocity space.”

Measured rate Rescaled astrophysics factor

• The measured rate is a “weighted average” of the astrophysical factor.

Gondolo Gelmini 2012

R^SIHv_minL RHv_minL RHv_minL ê v_min³ RHv_minL ê v_min¹⁰

DAMA H2.0-2.5 keVee L

100 200 300 400 500 600 700 800

v_min@kmêsD

ResponsefunctionHarbitraryunitL

R^SIHv_minL RHv_minL RHv_minL ê v_min³ RHv_minL ê v_min¹⁰ CDMS-II-Si

H7-9 keV L

100 200 300 400 500 600 700 800

v_min@kmêsD

ResponsefunctionHarbitraryunitL

Hv_minL Hv_minL

v_min³ v_min¹⁰ oGeNT

keVee L

100 200 300 400 500 600 700 800

kmêsD

raryunitL

m=9 GeV m=9 GeV

Spin-independent isoscalar interactions

Still depends on particle model

Halo modifications alone cannot save the SI signal regions from the Xe and Ge bounds

Astrophysics-independent approach

σ_χA = A²σ_χpµ²_χA/µ²_χp

Del Nobile, Gelmini, Gondolo, Huh 2014

CDMS-Si event rate is similar to yearly modulated rates

SuperCDMS CoGeNT₀ CoGeNT₁ DAMA₁ CRESST SIMPLE CDMSlite CDMS-II-Si CDMS-II-Ge CDMS mod. limit XENON10 XENON100 LUX

m=7GeVêc², f_nêf_p=1

200 400 600 800 1000

10-27 10-26 10-25 10-24

v_min @kmêsD hrspc2 êm@days-1 D

Excluded

In the next episodes

In the next episodes... Revenge

DAMA/LIBRA$phase2$?$running8

Mean value:

7.5%(0.6% RMS) 6.7%(0.5% RMS)

Previous PMTs: 5.5-7.5 ph.e./keV New PMTs: up to 10 ph.e./keV

Quantum$Efficiency$features8

The light responses

Energy$resolution8

Residual$

Contamination8

JINST 7(2012)03009

•  To study the nature of the particles and features of related astrophysical, nuclear and particle physics aspects, and to investigate second order effects

•  Special data taking for other rare processes σ/E @ 59.5 keV for each detector with new PMTs with higher quantum efficiency (blu points) and with previous PMT EMI-Electron Tube (red points).

Belli, IDM2014

DAMA/LIBRA$phas

Second upgrade on end of 2010:

all PMTs replaced with new ones of higher Q.E.

HEP community + NASA + many contractors

In the next episodes... Precision cosmic rays

AMS (Alpha Magnetic Spectrometer)

AMS-02 can measure isotopic ratios to ~1%

precision up to Fe and ~100 GeV/nucleon, and much better at lower energies.

p

e- e+

He Li C

In the next episodes... WIMP astronomy

•Directional direct detection

- measure direction of nuclear recoil

•Several R&D efforts

- ^DRIFT

- Dark Matter TPC

- ^NEWAGE - ^MIMAC - ^D3

- Emulsion Dark Matter Search

- Columnar recombination

Only ~10 events needed to confirm extraterrestrial signal

DMTPC example

recoil calibration

Counts Counts

x position y position

In the next episodes... WIMP astronomy

Aberration of WIMPs

Bradley 1725 Aberration

Parallax

May

May December

20 arcsec

10 degrees

Photon arrival direction

WIMP arrival direction

Bozorgnia, Gelmini, Gondolo 2012

γ Draconis

In document Dark Matter Theory (Page 55-80)