Timothy Cohen with Daniel Phalen and Aaron Pierce arXiv:1001.3408 - - PowerPoint PPT Presentation

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

On the Correlation Between the Spin-Independent and Spin-Dependent Direct Detection of Dark Matter

Timothy Cohen

with Daniel Phalen and Aaron Pierce arXiv:1001.3408

Michigan Center for Theoretical Physics (MCTP) University of Michigan, Ann Arbor

PHENO Symposium May 10, 2010

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 1/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

Outline

1

Introduction

2

Direct Detection Preliminaries

3

Spin Dependent Cross Sections for Mixed Dark Matter

4

Spin Independent versus Spin Dependent

5

Conclusions and Optimism

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 2/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ WMAP has given us a very precise measurement of the relic

density of dark matter: ΩDM ℎ2 = 0.1131 ± 0.0034.

∙ Now we just have to figure out what it is.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 3/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ WMAP has given us a very precise measurement of the relic

density of dark matter: ΩDM ℎ2 = 0.1131 ± 0.0034.

∙ Now we just have to figure out what it is. ∙ For this work we will assume that dark matter is a weakly

interacting massive particle (WIMP).

∙ We would like to explore the near term prospects for the

direct detection of WIMP dark matter.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 3/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The simplest weak interaction is

풪vector = (¯ 휒D 훾휇 휒D) 푍0

휇

∙ With a weak scale coefficient, this operator implies a direct

detection signal that has been excluded for 푚DM ≳ 50 TeV.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 4/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The simplest weak interaction is

풪vector = (¯ 휒D 훾휇 휒D) 푍0

휇

∙ With a weak scale coefficient, this operator implies a direct

detection signal that has been excluded for 푚DM ≳ 50 TeV.

∙ If the dark matter is Majorana, this operator trivially vanishes.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 4/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The simplest weak interaction is

풪vector = (¯ 휒D 훾휇 휒D) 푍0

휇

∙ With a weak scale coefficient, this operator implies a direct

detection signal that has been excluded for 푚DM ≳ 50 TeV.

∙ If the dark matter is Majorana, this operator trivially vanishes. ∙ If we still wish to couple to the 푍0, this requires mass mixing

between an 푆푈(2) charged state and a singlet.

∙ This in turn must be proportional to electroweak symmetry

breaking.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 4/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The simplest weak interaction is

풪vector = (¯ 휒D 훾휇 휒D) 푍0

휇

∙ With a weak scale coefficient, this operator implies a direct

detection signal that has been excluded for 푚DM ≳ 50 TeV.

∙ If the dark matter is Majorana, this operator trivially vanishes. ∙ If we still wish to couple to the 푍0, this requires mass mixing

between an 푆푈(2) charged state and a singlet.

∙ This in turn must be proportional to electroweak symmetry

breaking.

∙ Hence, the following operators will naively be non-vanishing:

풪Higgs = (¯ 휒 휒) ℎ 풪푍0 = (¯ 휒 훾휇훾5 휒) 푍0

휇

∙ 풪Higgs and 풪푍0 lead to spin-independent and spin-dependent

scattering off of nuclei respectively.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 4/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ A canonical example of a Majorana dark matter candidate

which interacts with the 푍0 and ℎ is the MSSM neutralino.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 5/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ A canonical example of a Majorana dark matter candidate

which interacts with the 푍0 and ℎ is the MSSM neutralino.

∙ Many neutralino studies focus on the pure Bino. ∙ Then, in order to reproduce the relic density thermally, one

also requires a light slepton.

∙ This is in tension is with LEP due to bounds on the slepton

masses.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 5/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ A canonical example of a Majorana dark matter candidate

which interacts with the 푍0 and ℎ is the MSSM neutralino.

∙ Many neutralino studies focus on the pure Bino. ∙ Then, in order to reproduce the relic density thermally, one

also requires a light slepton.

∙ This is in tension is with LEP due to bounds on the slepton

masses.

∙ However, this tension is alleviated if one considers a mixed

(well-tempered) neutralino with 푚DM > 푚푊 .

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 5/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ A canonical example of a Majorana dark matter candidate

which interacts with the 푍0 and ℎ is the MSSM neutralino.

∙ Many neutralino studies focus on the pure Bino. ∙ Then, in order to reproduce the relic density thermally, one

also requires a light slepton.

∙ This is in tension is with LEP due to bounds on the slepton

masses.

∙ However, this tension is alleviated if one considers a mixed

(well-tempered) neutralino with 푚DM > 푚푊 .

∙ We will show that well-tempering can naturally imply

spin-independent and spin-dependent signals for the next generation of experiments.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 5/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

Outline

1

Introduction

2

Direct Detection Preliminaries

3

Spin Dependent Cross Sections for Mixed Dark Matter

4

Spin Independent versus Spin Dependent

5

Conclusions and Optimism

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 6/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The best limits on dark matter with 푚DM > 푚푊 are given by ∙ Define “large” cross sections as 휎large

SI

> 5 × 10−9 pb and 휎large

SD

> 10−4 pb, motivated by the near term projections of currently running experiments.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 7/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The following operator leads to spin-independent scattering:

풪SI

푞 = 푐푞 (¯

휒 휒) (¯ 푞 푞),

∙ In the MSSM (with heavy squarks) the coefficients of the

spin-independent operator in the decoupling and large tan 훽 limits is: 푐푢 ∼ (푍푊 − 푡푤 푍퐵)푍퐻푢 푚2

ℎ

푐푑 ∼ 푐푢 ( 1 − 푡훽 푚2

ℎ

푚2

퐻

푍퐻푑 푍퐻푢 )

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 8/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The following operator leads to spin-independent scattering:

풪SI

푞 = 푐푞 (¯

휒 휒) (¯ 푞 푞),

∙ In the MSSM (with heavy squarks) the coefficients of the

spin-independent operator in the decoupling and large tan 훽 limits is: 푐푢 ∼ (푍푊 − 푡푤 푍퐵)푍퐻푢 푚2

ℎ

푐푑 ∼ 푐푢 ( 1 − 푡훽 푚2

ℎ

푚2

퐻

푍퐻푑 푍퐻푢 )

∙ with typical size

휎MSSM

SI

(휒 푁 → 휒 푁) ≈ 5 × 10−9 pb ((푍푊 − 푡푤 푍퐵) 푍퐻푢 0.1 )2

∙ Note that this requires neutralino mixing to be non-vanishing.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 8/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The following operator leads to spin-dependent scattering:

풪SD

푞

= 푑푞 (¯ 휒 훾휇훾5 휒)(¯ 푞 훾휇훾5 푞).

∙ In the MSSM (with heavy squarks) the coefficients of the

spin-dependent operator is: 푑푞 ∼ ( ∣푍퐻푑∣2 − ∣푍퐻푢∣2)

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 9/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The following operator leads to spin-dependent scattering:

풪SD

푞

= 푑푞 (¯ 휒 훾휇훾5 휒)(¯ 푞 훾휇훾5 푞).

∙ In the MSSM (with heavy squarks) the coefficients of the

spin-dependent operator is: 푑푞 ∼ ( ∣푍퐻푑∣2 − ∣푍퐻푢∣2)

∙ with typical size

휎MSSM

SD

(휒 푝 → 휒 푝) ≈ 4 × 10−4 pb (∣푍퐻푑∣2 − ∣푍퐻푢∣2 0.1 )2

∙ Note that this also requires neutralino mixing to be

non-vanishing.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 9/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

Outline

1

Introduction

2

Direct Detection Preliminaries

3

Spin Dependent Cross Sections for Mixed Dark Matter

4

Spin Independent versus Spin Dependent

5

Conclusions and Optimism

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 10/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The spin-dependent cross section is proportional to

∣푍퐻푑∣2 − ∣푍퐻푢∣2.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 11/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The spin-dependent cross section is proportional to

∣푍퐻푑∣2 − ∣푍퐻푢∣2.

∙ In the limit of Mostly Bino (or Wino) with some Higgsino one

can approximate this value by

푐2훽 푠2

푤 푚2 푍

휇2−푀2

1

for ∣푀1∣, ∣휇∣, ∣휇∣ − ∣푀1∣ > 푚푍, 푀2 → ∞

푐2훽 푐2

푤 푚2 푍

휇2−푀2

2

for ∣푀2∣, ∣휇∣, ∣휇∣ − ∣푀2∣ > 푚푍, 푀1 → ∞

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 11/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The spin-dependent cross section is proportional to

∣푍퐻푑∣2 − ∣푍퐻푢∣2.

∙ In the limit of Mostly Bino (or Wino) with some Higgsino one

can approximate this value by

푐2훽 푠2

푤 푚2 푍

휇2−푀2

1

for ∣푀1∣, ∣휇∣, ∣휇∣ − ∣푀1∣ > 푚푍, 푀2 → ∞

푐2훽 푐2

푤 푚2 푍

휇2−푀2

2

for ∣푀2∣, ∣휇∣, ∣휇∣ − ∣푀2∣ > 푚푍, 푀1 → ∞

∙ In the limit of a very mixed Bino-Higgsino or Wino-Higgsino

• ne can approximate this value by

(푠훽−푐훽) 푠푤 푚푍 2 √ 2 ∣휇∣

for ∣푀1∣ = ∣휇∣ > 푚푍, 푀2 → ∞

(푠훽−푐훽) 푐푤 푚푍 2 √ 2 ∣휇∣

for ∣푀2∣ = ∣휇∣ > 푚푍, 푀1 → ∞

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 11/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The spin-dependent cross section is proportional to

∣푍퐻푑∣2 − ∣푍퐻푢∣2.

∙ In the limit of Mostly Bino (or Wino) with some Higgsino one

can approximate this value by

푐2훽 푠2

푤 푚2 푍

휇2−푀2

1

for ∣푀1∣, ∣휇∣, ∣휇∣ − ∣푀1∣ > 푚푍, 푀2 → ∞

푐2훽 푐2

푤 푚2 푍

휇2−푀2

2

for ∣푀2∣, ∣휇∣, ∣휇∣ − ∣푀2∣ > 푚푍, 푀1 → ∞

∙ In the limit of a very mixed Bino-Higgsino or Wino-Higgsino

• ne can approximate this value by

(푠훽−푐훽) 푠푤 푚푍 2 √ 2 ∣휇∣

for ∣푀1∣ = ∣휇∣ > 푚푍, 푀2 → ∞

(푠훽−푐훽) 푐푤 푚푍 2 √ 2 ∣휇∣

for ∣푀2∣ = ∣휇∣ > 푚푍, 푀1 → ∞

∙ It is the limit of Wino-Higgsino which leads to the largest

spin-dependent cross sections for the neutralino.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 11/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The largest obtainable spin-dependent cross section in the

MSSM is given by ∣푍퐻푑∣2 − ∣푍퐻푢∣2 < 0.4 ⇒ (휎SUSY

SD

) < 6 × 10−3 pb

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 12/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The largest obtainable spin-dependent cross section in the

MSSM is given by ∣푍퐻푑∣2 − ∣푍퐻푢∣2 < 0.4 ⇒ (휎SUSY

SD

) < 6 × 10−3 pb

∙ In models with gaugino mass unification (푀1 ∼ 2푀2) the

largest spin-dependent cross section is ∣푍퐻푑∣2 − ∣푍퐻푢∣2 < 0.32 ⇒ (휎SUSY

SD

) < 4 × 10−3 pb

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 12/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The largest obtainable spin-dependent cross section in the

MSSM is given by ∣푍퐻푑∣2 − ∣푍퐻푢∣2 < 0.4 ⇒ (휎SUSY

SD

) < 6 × 10−3 pb

∙ In models with gaugino mass unification (푀1 ∼ 2푀2) the

largest spin-dependent cross section is ∣푍퐻푑∣2 − ∣푍퐻푢∣2 < 0.32 ⇒ (휎SUSY

SD

) < 4 × 10−3 pb

∙ If one imposes that the relic density is thermal

∣푍퐻푑∣2 − ∣푍퐻푢∣2 < 0.24 ⇒ (휎SUSY

SD

)thermal < 2 × 10−3 pb

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 12/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ The points are for gaugino mass unification.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 13/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

Outline

1

Introduction

2

Direct Detection Preliminaries

3

Spin Dependent Cross Sections for Mixed Dark Matter

4

Spin Independent versus Spin Dependent

5

Conclusions and Optimism

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 14/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ Recall that

푚2

푍

2 = −∣휇∣2 + 푚2

퐻푑 − 푚2 퐻푢푡2 훽

푡2

훽 − 1

∙ Hence, small 휇 implies less fine-tuning in the 푍0 mass.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 15/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ Recall that

푚2

푍

2 = −∣휇∣2 + 푚2

퐻푑 − 푚2 퐻푢푡2 훽

푡2

훽 − 1

∙ Hence, small 휇 implies less fine-tuning in the 푍0 mass. ∙ In the plots that follow, the shaded region is “large:” much of

the region with low fine-tuning will be probed in the near-term.

∙ Points with small spin-independent cross sections require

either a pure neutralino or some sort of conspiracy, e.g. a cancellation between the contributions from the light and heavy Higgs.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 15/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ Here we make no assumptions about the thermal relic density. ∙ We still assume the neutralinos constitute the majority of the

dark matter.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 16/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ Here we impose that the thermal relic density matches

• bservation to within 3 휎.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 17/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ Here we impose a thermal relic density, gaugino mass

unification and the decoupling limit.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 18/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

Outline

1

Introduction

2

Direct Detection Preliminaries

3

Spin Dependent Cross Sections for Mixed Dark Matter

4

Spin Independent versus Spin Dependent

5

Conclusions and Optimism

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 19/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ If dark matter is a WIMP with interactions with the 푍0, it

should also have interactions with the Higgs to result in a vanishing vector operator to avoid direct detection bounds.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 20/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ If dark matter is a WIMP with interactions with the 푍0, it

should also have interactions with the Higgs to result in a vanishing vector operator to avoid direct detection bounds.

∙ A canonical example is the MSSM neutralino. ∙ Tension with LEP bounds points toward a mixed neutralino. ∙ This naively implies large spin-independent and large

spin-dependent cross sections.

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 20/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

∙ If dark matter is a WIMP with interactions with the 푍0, it

should also have interactions with the Higgs to result in a vanishing vector operator to avoid direct detection bounds.

∙ A canonical example is the MSSM neutralino. ∙ Tension with LEP bounds points toward a mixed neutralino. ∙ This naively implies large spin-independent and large

spin-dependent cross sections.

∙ Hence, dark matter direct detection experiments are beginning

to probe a very interesting region of the parameter space.

∙ Maybe the detection of neutralino dark matter is right around

the corner!!

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 20/21

Introduction Direct Detection Preliminaries Spin Dependent Cross Sections for Mixed Dark Matter Spin Independent versus Spin Dependent Conclusions and Optimism

Thank You

Are there any questions?

Correlation Between SI and SD Direct Detection Timothy Cohen (University of Michigan) 21/21