Neutralino WIMP dark matter Varun Vaidya Dept. of Physics, CMU - - PowerPoint PPT Presentation

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Neutralino WIMP dark matter Varun Vaidya Dept. of Physics, CMU - - PowerPoint PPT Presentation

Jul 17, 2023 210 likes •565 views

Neutralino WIMP dark matter Varun Vaidya Dept. of Physics, CMU Los Alamos Natl. Lab Based on the work with M. Baumgart and I.Z. Rothstein, (PRL:114 (2015) 211301), M. Baumgart, I.Z. Rothstein, V.V (JHEP:1504(2015) 106), M. Baumgart, I.Z.

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SLIDE 1

Neutralino WIMP dark matter

Varun Vaidya

  • Dept. of Physics, CMU

Los Alamos Natl. Lab

Based on the work with M. Baumgart and I.Z. Rothstein,

(PRL:114 (2015) 211301), M. Baumgart, I.Z. Rothstein, V.V (JHEP:1504(2015) 106), M. Baumgart, I.Z. Rothstein, V.V (ArXiv: 1510.02470), M. Baumgart and V.V

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SLIDE 2

Outline

  • Introduction to dark matter
  • What are we calculating
  • Why are we calculating what we are

calculating

  • How are we calculating it
  • What do the calculations imply
  • Summary and future work
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SLIDE 3

Evidence for dark matter

  • Rotation curves of

galaxies

  • Gravitational lensing

from galactic clusters

  • MACHO's?
  • Cosmological evidence :

Anisotropies in CMB are too small for observed structure

  • Collision of Bullet cluster

with cluster 1E 0657-56

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SLIDE 4

Dark Matter Candidates

  • Massive particle that interacts gravitationally but
  • nly very weakly or not at all with SM particles

(WIMP's)

  • Neutrinos, Axions?
  • Along came SUSY : naturalness problem, gauge coupling

unification, natural dark matter candidate ->neutralino, sneutrino, gravitino?

  • Neutralino : Massive cold dark matter, lightest super-

symmetric partner(LSP) is stable by R parity conservation

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SLIDE 5

The WIMP Miracle

Thermal Equilibrium

  • 1. Expanding

Universe

  • 2. Net annihilation

Freeze -out, Γ ~ H Thermal Relic density

  • Relic Abundance

calculation using Boltzmann equation for a weakly interacting particle ~ TeV scale WIMP Assuming <σv> ~ Cα2/Mχ2

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SLIDE 6

Indirect Detection

  • Air Cherenkov Telescope :

HESS - High energy stereoscopic system , Namibia Goal: Detect Gamma Ray lines at WIMP mass

Direct detection

  • Production at Colliders :LHC?
  • Radioactively clean nuclei recoiling against a

scatterd DM particle: XENON, LUX ..

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SLIDE 7

What are we calculating

  • Cold neutral dark matter at galactic center, v ~10-3

interacting weakly.

  • Assuming that fermionic WIMP constitute the dark matter
  • f the universe , Mass ~ TeV
  • We want: annihilation cross section of the dark matter

to monochromatic gamma rays at the WIMP mass

  • A semi-inclusive cross section to a single high

energy photon

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SLIDE 8

WINO Dark matter

  • SUL(2) triplet fermion χ, superpartner of weak

gauge bosons, free mass parameter M2 ~ TeV

  • Mass eigenstates after electroweak breaking:

Neutralino : Majorana fermion Chargino

  • Mass splitting of 170 MeV from electroweak

radiative corrections

  • Neutral state χ0 is the LSP -> Dark matter WINO
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SLIDE 9

factor of 4 reduction

  • Expt. bounds

Wino Under Siege

  • Previous results- fixed order, excludes the wino

completely

  • A suggestion that an NLO calculation can have

a drastic impact on the cross section

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SLIDE 10

Astronomical uncertainties

  • Dark matter density ρ subject to large

uncertainties

  • A longstanding debate : Is the galactic DM halo

cusped or cored?

  • Flux of photons coming from Galactic center proportional

to ρ2

  • A cored profile reduces

the photon flux and hence can save the WINO

NFW Imperative to have a good handle on theoretical errors

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SLIDE 11

Exclusive vs Semi-inclusive

  • Other complementary calculations : two body exclusive process

χχ → γγ + 1/2γZ, an observed photon recoiling against an unseen photon or Z

  • Missing channels in exclusive calculation :
  • 1. There is no restriction on the nature of recoil particles.
  • 2. The observed photon can be accompanied by soft radiation

which lies below the detector energy resolution.

  • Current detector resolution (HESS) ~ 15% of WIMP mass from 1-

19 TeV. => ∆E > 150 GeV

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SLIDE 12

Annihilation to photon

  • Semi- inclusive cross section of annihilation

to a hard photon .

  • The wino's are non relativistic , v ~ 10-3
  • Interaction has two contributions :

Phase 1 : Well separated (r ~ 1/Mw), slow moving fermions interact via gauge boson exchange

χ0 χ0 χ0 χ0

  • r

χ+ χ- each rung ~ αMχ/Mw

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SLIDE 13
  • Hard scattering at short distance (r~ 1/MX): Two

channels available for semi -inclusive cross section

χ0 χ0 γ γ χ+ χ- γ γ / Z χ+ χ- W+ γ χ0 χ0 W+ χ- W- χ+ χ- γ W+ W-

Chargino contribution begins at tree level Neutralino only begins at one loop

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SLIDE 14

Bloch Nordsieck violation

  • IR safe observable -> final state should be a sum
  • ver indistinguishable (dangerous) states
  • In Unbroken Electroweak theory, IR divergences

due to semi-inclusive nature of cross section

  • Gauge boson masses turn IR divergences to

sudakov logs αw ln2(Mχ/MW)

  • Resummation becomes important to save

perturbation theory.

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SLIDE 15
  • Factorize the long distance non perturbative

physics from short distance annihilation process.

EFT for WIMP Annihilation

Neutralino, Chargino two body wavefunction

ψ00(0) , ψ+- (0) → enhancement factor due to long range gauge boson exchange

F00 , F±, F0± → Short range hard annihilation to photon

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SLIDE 16

Sommerfeld enhancement

  • Effect captured by solving Schrodinger equation with

effective potential

  • Sommerfeld enhancement for two channels

, ψ =

ψ+- ψ00

ψ+- ψ00

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SLIDE 17

EFT for annihilation

  • Hybrid "NRQCD" - SCET II theory with expansion

parameter λ = Mw/MX WIMP's ~ ( E ~ λ2 , p ~ λ) → Initial state Potential ~ (E ~ λ2, p ~ λ) → Long range Gauge boson exchange Collinear ~ (k+ ~ 1, k- ~ λ2, k┴ ~ λ) → Final state photon + jet Soft ~ (k+ ~ λ, k- ~ λ, k┴ ~ λ)

}

NRQCD

}

SCET

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SLIDE 18

recoil radiation with large invariant mass Off-shell heavy fermion propagator 6-field

  • perator basis
  • Soft gauge invariance fixes the position of soft wilson

lines required to reproduce IR physics

  • Majorana condition reduces the operator basis to 4
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SLIDE 19

Color-singlet collinear sector , Trivial soft sector SCET building blocks

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SLIDE 20

}

Soft Operators

}

Collinear Operators Cross section :

}

Fragmentation functions

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SLIDE 21

Rapidity renormalization group

New divergences due to Factorization: usually regulated by dim. reg. Rapidity divergences due to separation of the soft and collinear regions: a new regulator is needed that breaks residual boost invariance Rapidity renormalization group equations

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SLIDE 22

Anomalous Dimensions

  • v anomalous dimension

cancels between soft and collinear sectors.

  • Operator mixing

in each sector for μ and ν anomalous dimensions.

One loop Cusp One loop non-cusp

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SLIDE 23

Resummation at LL'

Resummation of logs by choosing a path in μ, ν space Power counting at LL' :

αw ln2(Mχ/MW) ~ 1 resummed to all orders, αw ln(Mχ/MW) << 1, included only at leading order

Net result: All terms of the form αwn+1 ln2n+1(Mχ/MW)

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SLIDE 24
  • Resummed cross section

Total rate

Sudakov factors

ψ00 , ψ+-

Sommerfeld enhancement factors photon self energy at Mw

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SLIDE 25
  • Sudakov factors as a function of WIMP mass
  • ~ 5 % effect for 3 TeV thermal WINO from the

dominant (χ+χ-) channel

Effect of resummation is small due to semi-inclusive nature of cross section

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SLIDE 26

Total Rate : Sommerfeld + Sudakov Exclusion plot using HESS with NFW profile

Thermal Wino in a lot of trouble !

The Wino-ing

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SLIDE 27

End point effects

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SLIDE 28

Viability of the Wino fraction of DM for different galactic profiles Coring needed for the Wino to avoid exclusion

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SLIDE 29

Higgsino Dark matter

Higgsino basis Two SU(2) doublets instead of a single triplet State charged under hypercharge

Hypercharge SU(2) gauge bosons

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SLIDE 30

Mass Eigenstates Neutralino majorana fermions Charged Dirac fermion LSP Three new operators due to the hypercharge field Remarkably we have exactly the SAME operators in the collinear and soft sectors as in the case of the WINO despite the different representation.

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SLIDE 31

Sommerfeld factors

=

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SLIDE 32

Total Rate

Rate at LL

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SLIDE 33

Higgsino bounds at LL'

Unstable at low mass

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SLIDE 34

Summary

  • A complete EFT calculation for semi-inclusive

annihilation cross section to a photon of Wino/Higsino dark matter at LL'

  • Sommerfeld enhancement- a huge non-perturbative

effect, puts the neutralino in trouble

  • Impact of resumming Sudakov logs is minimal due to

semi-inclusive nature of calculation

  • Either we need enough coring~ 1.5 kpc to save the

thermal Wino or look for non-thermal history

  • Reciprocally, the discovery of such a particle would

impact astrophysical observations End point corrections are important at low masses, needs further analysis

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SLIDE 35

Evidence for dark matter

  • Rotation curves of galaxies
  • Gravitational lensing from galactic clusters
  • Cosmological evidence : Anisotropies in CMB
  • Collision of Bullet cluster with cluster 1E 0657-56

Dark Matter Candidates

Massive particle that interacts gravitationally and (possibly) weakly with SM particles (WIMP's):

  • Neutrinos, Axions
  • SUSY :sneutrino, gravitino,

neutralino

Cold dark matter, (LSP) is stable by R parity conservation