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Can we determine the particle/antiparticle nature of Dark Matter? - - PowerPoint PPT Presentation

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Can we determine the particle/antiparticle nature of Dark Matter? Bradley J. Kavanagh GRAPPA, University of Amsterdam LAW Physics - 17th January 2018 b.j.kavanagh@uva.nl @BradleyKavanagh 1 Dark Matter on all scales Hradecky et al.

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@BradleyKavanagh b.j.kavanagh@uva.nl

Bradley J. Kavanagh GRAPPA, University of Amsterdam LAW Physics - 17th January 2018

Can we determine the particle/antiparticle nature of Dark Matter?

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Dark Matter on all scales

Planck [1502.01589] Rubin, Ford & Thonnard (1980) Hradecky et al. [astro-ph/0006397]

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Dark Matter near the Earth

NOT TO SCALE

Global and local estimates of DM at Solar radius give:

E.g. Iocco et al. [1502.03821], Garbari et al. [1206.0015], Read [1404.1938]

8.5 kpc

ρχ ∼ 0.2 − 0.8 GeV cm−3

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Direct detection of Dark Matter

Detector Target nucleus

χ mχ 1 GeV v ∼ 10−3 c

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Direct detection of Dark Matter

Detector

mχ 1 GeV v ∼ 10−3 c

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Direct detection of Dark Matter

Detector

Charge (ionisation) Heat (phonons) Light (scintillation)

Measure rate of recoils and energy of recoiling nuclei Reconstruct the properties of DM (mass, cross section, etc.) mχ 1 GeV v ∼ 10−3 c

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Direct detection of Dark Matter

Detector

Charge (ionisation) Heat (phonons) Light (scintillation)

In practise, need to worry about backgrounds, background rejection, detection efficiencies, energy resolutions, validation across multiple detectors, …

mχ 1 GeV v ∼ 10−3 c Measure rate of recoils and energy of recoiling nuclei Reconstruct the properties of DM (mass, cross section, etc.)

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Measuring the DM mass

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Peter, Gluscevic, Green, BJK, Lee [1310.7039] Green [0805.1704]

Characteristic recoil energy in keV Ge Xe

DM mass can be extracted from the slope of the recoil spectrum

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Measuring the local DM speed distribution

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With multiple experiments and more precise data, you could extract the DM mass and DM speed distribution simultaneously

Using Xe, Ar and Ge targets:

BJK, Green [1303.6868], but see also BJK, Fornasa,Green [1410.8051] and others

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Distinguishing Dirac from Majorana Dark Matter

Cross sections for Dirac and Majorana DM should scale differently with number of protons and neutrons

Queiroz, Rodejohann & Yaguna [arXiv:1610.06581]

What are the prospects for distinguishing Dirac vs. Majorana DM in upcoming experiments

BJK, Queiroz, Rodejohann & Yaguna [arXiv:1706.07819]

Which experiments should we build to get the most out of a DM discovery?

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

3 highlights of this work

1) It may be possible to determine whether DM is its own antiparticle: using multiple ton-scale direct detection experiments!
 2) To maximise our chances, we have to use particular combinations of detectors: should pursue Silicon detectors!
 3) This work is 100% reproducible: check it, make fun of it, reuse it, whatever!

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Dirac vs. Majorana DM

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

L ⊃ λN,1 χχ NN + λN,2 χγµχ NγµN + λN,3 χγµγ5χ Nγµγ5N + λN,4 χγ5χ NN + λN,5 χγµχ Nγµγ5N + ... DM-nucleon contact interactions

Start thinking about how DM can interact with nucleons : χ N = (p, n)

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

L ⊃ λN,1 χχ NN + λN,2 χγµχ NγµN + λN,3 χγµγ5χ Nγµγ5N + λN,4 χγ5χ NN + λN,5 χγµχ Nγµγ5N + ... DM-nucleon contact interactions

Start thinking about how DM can interact with nucleons : χ N = (p, n) Spin-dependent interaction

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

L ⊃ λN,1 χχ NN + λN,2 χγµχ NγµN + λN,3 χγµγ5χ Nγµγ5N + λN,4 χγ5χ NN + λN,5 χγµχ Nγµγ5N + ... DM-nucleon contact interactions

Start thinking about how DM can interact with nucleons : χ N = (p, n) Spin-dependent interaction Velocity suppressed

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

L ⊃ λN,e χχ NN + λN,o χγµχ NγµN DM-nucleon contact interactions

Start thinking about how DM can interact with nucleons : χ N = (p, n) Standard spin-independent DM-nucleon couplings typically dominate. These operators couple to the number of nucleons in the target - expect a coherent enhancement of the cross section:

σ ∼ [λpNp + λnNn]2

But note that the scalar current operator is even under the exchange of particle and antiparticle , while the vector current operator is

  • dd under the particle-antiparticle exchange.

χ ↔ χ

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2 L ⊃ λN,e χχ NN + λN,o χγµχ NγµN Majorana DM

Start thinking about how DM can interact with nucleons : χ N = (p, n)

Vanishes for Majorana DM

≡ λM

N χχ NN

Cross section for scattering with a nucleus A (in the zero-momentum transfer limit) is then:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

σD = 4µ2

χA

π 1 2

  • λD

p Np + λD n Nn

2 +

  • λD

p Np + λD n Nn

2 L ⊃ λN,e χχ NN + λN,o χγµχ NγµN Dirac DM

Start thinking about how DM can interact with nucleons : χ N = (p, n)

Both interactions are allowed

Cross section for scattering with a nucleus A (in the zero-momentum transfer limit) is then: Same as Majorana case, with .

λN,e → λN,e ± λN,o λD

N = (λN,e − λN,o)/2

λD

N = (λN,e + λN,o)/2

Cross section for DM particles Cross section for DM antiparticles Half of DM is particles, half is antiparticles

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

σD = 4µ2

χN

π 1 2

  • λD

p Np + λD n Nn

2 +

  • λD

p Np + λD n Nn

2 = 2µ2

χN

π

  • (λD 2

p

+ λD 2

p

)N 2

p + (λD 2 n

+ λD 2

n )N 2 n + 2(λD p λD n + λD p λD n )NpNn

  • σD =

4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Dirac DM (continued)

We can try to manipulate the Dirac cross section, to get it into the same form as the Majorana cross section, . σM ∼

  • λM

p Np + λM n Nn

2 λN =

  • 1

2(λD 2

N

+ λD 2

N )

f = (λD

p λD n + λD p λD n )/(2λpλn)

where and The DM-nucleus cross section scales differently with number of protons and neutrons for Dirac and Majorana DM! f ∈ [−1, 1]

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Generalising to other spins

We have discussed only spin-1/2 DM particles. However, similar logic applies for DM candidates of other spins. For example, in the case of scalar DM , the couplings leading to spin- independent scattering are: φ

L ⊃ 2λN,emφ φ†φ NN + iλN,o

  • φ†(∂µφ) − (∂µφ†)φ
  • NγµN

The second interaction is absent in the case of real scalar DM, so real and complex DM lead to different DM-nucleus cross sections! For vector DM, see e.g. [arXiv:0803.2360].

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

A visual example

  • λ [- -]

λ [- -]

Xe

∆ = 20% (λD

p , λD p , λD n , λD n ) = (6.7, 2.0, −5.6, −1.0) × 10−9 GeV−2

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Calculate DM-nucleus cross section for Dirac DM. Here, assume the following couplings: Attempt to fit assuming Majorana DM:

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2

Assume DM-nucleus cross section is measured to 20% precision.

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

  • λ [- -]

λ [- -]

A visual example

Xe

∆ = 20% (λD

p , λD p , λD n , λD n ) = (6.7, 2.0, −5.6, −1.0) × 10−9 GeV−2

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Calculate DM-nucleus cross section for Dirac DM. Here, assume the following couplings: Ar Attempt to fit assuming Majorana DM:

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2

Assume DM-nucleus cross section is measured to 20% precision.

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

  • λ [- -]

λ [- -]

A visual example

Xe

∆ = 20% (λD

p , λD p , λD n , λD n ) = (6.7, 2.0, −5.6, −1.0) × 10−9 GeV−2

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Calculate DM-nucleus cross section for Dirac DM. Here, assume the following couplings: Ar Si Attempt to fit assuming Majorana DM:

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2

Assume DM-nucleus cross section is measured to 20% precision.

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

  • λ [- -]

λ [- -]

∆ = 60%

A visual example

Xe

(λD

p , λD p , λD n , λD n ) = (6.7, 2.0, −5.6, −1.0) × 10−9 GeV−2

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Calculate DM-nucleus cross section for Dirac DM. Here, assume the following couplings: Ar Si Attempt to fit assuming Majorana DM:

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2

Assume DM-nucleus cross section is measured to 60% precision.

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Prospects for future experiments

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Future Experiments (2020-2025)

Assume constant efficiency for nuclear recoils in range ER ∈ [Emin, Emax] No backgrounds, perfect energy resolution “Best-case scenario”

XENONnT

[arXiv:1706.07819]

DEAP-50T EURECA-2

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Future Experiments (2020-2025)

Assume constant efficiency for nuclear recoils in range ER ∈ [Emin, Emax] No backgrounds, perfect energy resolution “Best-case scenario”

XENONnT

[arXiv:1706.07819]

DEAP-50T EURECA-2 ???

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Ensembles

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NB: Fix the overall cross section normalisation to give ~300 Xenon events (just below current bounds from LUX/Xenon1T)

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Statistical procedure

σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Recall that in the Dirac case, the DM-nucleus cross section can be written as:

For a given set of couplings and a given experimental ensemble:

  • 1. Generate mock data for the experiments
  • 2. Calculate the maximum likelihood under two hypotheses:



 


  • 3. Calculate the discrimination significance from the log-likelihood ratio

HM - the DM is Majorana-like, with free parameters: (mχ, λp, λn, f = ±1) HD - the DM is Dirac-like, with free parameters: (mχ, λp, λn, f ∈ [−1, 1])

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Repeat 100 times to estimate the median significance with which Dirac DM can be distinguished from Majorana.

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Code

All code for generating mock data, calculating likelihoods and producing plots is available online (and archived on Zenodo)

https://github.com/bradkav/AntiparticleDM http://doi.org/10.5281/zenodo.815457

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Code

All code for generating mock data, calculating likelihoods and producing plots is available online (and archived on Zenodo)

https://github.com/bradkav/AntiparticleDM http://doi.org/10.5281/zenodo.815457

  • Finding the maximum likelihood needed to be fast and the method we

used couldn’t be described in enough detail in the paper. Luckily, the code is an explanation of itself!

  • If people want to use this method to test their favourite model, now they

can, without having to re-do any of the work we did!

  • While making the code public, we found several mistakes. In explaining

and checking the code, we made it better!

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Discrimination significance: Dirac vs Majorana

Ensemble A: Xe + Ar + Si σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Discrimination significance: Dirac vs Majorana

Ensemble A: Xe + Ar + Si σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

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where for Xe

λn/λp ∼ Np/Nn

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Discrimination significance: Dirac vs Majorana

Ensemble A: Xe + Ar + Si σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

  • λ [- -]

λ [- -]

A visual example

Xe

∆ = 20% (λD

p , λD p , λD n , λD n ) = (6.7, 2.0, −5.6, −1.0) × 10−9 GeV−2

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Calculate DM-nucleus cross section for Dirac DM. Here, assume the following couplings: Ar Attempt to fit assuming Majorana DM:

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2

Assume DM-nucleus cross section is measured to 20% precision.

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Discrimination significance: Dirac vs Majorana

Ensemble A: Xe + Ar + Si σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Ensemble B: Xe + Ar + Ge

Discrimination significance: Dirac vs Majorana

σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

  • λ [- -]

λ [- -]

A visual example

Xe

∆ = 20% (λD

p , λD p , λD n , λD n ) = (6.7, 2.0, −5.6, −1.0) × 10−9 GeV−2

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Calculate DM-nucleus cross section for Dirac DM. Here, assume the following couplings: Ar Attempt to fit assuming Majorana DM:

σM = 4µ2

χA

π

  • λM

p Np + λM n Nn

2

Assume DM-nucleus cross section is measured to 20% precision. Ge

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Discrimination significance: Dirac vs Majorana

σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

Ensemble C: Xe + Ar + CaWO4

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Ensemble D: Xe + Ar + 50% Ge + 50% CaWO4

Discrimination significance: Dirac vs Majorana

σD = 4µ2

χA

π

  • [λpNp + λnNn]2 + 2λpλn(f − 1)NpNn
  • Reminder:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Xe + Ar + 50% Ge + 50% CaWO4

Comparing Ensembles

Ensemble D: Xe + Ar + Si Ensemble A:

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Comparing Ensembles

In some cases, you need more than 10x the exposure to achieve the same significance, when using Ge + CaWO4 vs. using Si

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Fundamental couplings L ⊃ λN,e χχ NN + λN,o χγµχ NγµN

Good discrimination is possible without a substantial hierarchy between the nucleon-level couplings (although isospin violation is needed) Need to start off with some high-scale theory with couplings to quarks and determine the nucleon-level couplings But isospin-violating Dirac DM is feasible (need, for example, new scalar and vector mediators) and has been studied Need to map individual models onto to see whether Dirac nature can be determined (λp, λn, f)

[1311.0022,1403.0324,1503.01780,1510.07053]

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Understanding Dark Matter

DM particle/antiparticle nature? [This Work] What are the best detectors to use to learn the most about Dark Matter?

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Understanding Dark Matter

Dark Matter mass?
 [0805.1704, 1310.7039] Mediator mass? [1707.08571] DM-nucleon interactions? [1505.07406, 1506.04454] DM particle/antiparticle nature? [This Work] Dark Matter distribution? [1303.6868, 1410.8051] Dark Matter relic density? [1712.04793,1712.07969] Number of DM species? [1709.01945] What are the best detectors to use to learn the most about Dark Matter?

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Conclusions

[arXiv:1706.07819] Depending on the model/couplings, 2020-2025 era detectors could determine the Dirac nature of DM at the 3-5σ level There are no current plans for a Silicon detector, but this would greatly improve prospects for Dirac/Majorana discrimination (in general, more variety is better!) The entire analysis is 100% reproducible, so you can see what we did, check it or apply it on your own favourite model! Models with isospin-violation lead to cancellations in the DM- nucleus cross section and are easiest to discriminate

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Dirac and Majorana DM-nucleus cross sections should scale differently across different detectors

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Bradley J Kavanagh (GRAPPA) LAW Physics - 17th Jan. 2018 DM Particle/Antiparticle

Conclusions

[arXiv:1706.07819] Depending on the model/couplings, 2020-2025 era detectors could determine the Dirac nature of DM at the 3-5σ level There are no current plans for a Silicon detector, but this would greatly improve prospects for Dirac/Majorana discrimination (in general, more variety is better!) The entire analysis is 100% reproducible, so you can see what we did, check it or apply it on your own favourite model! Models with isospin-violation lead to cancellations in the DM- nucleus cross section and are easiest to discriminate

Thank you!

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Dirac and Majorana DM-nucleus cross sections should scale differently across different detectors