EFFECTIVE FIELD THEORY OF WIMP DARK MATTER

Matthew Baumgart (Arizona State University)

25th International Summer Institute on Phenomenology…Gangneung, South Korea

8/19/2019

MB, I.Z. Rothstein, V. Vaidya: 1409.4415, PRL 114 (2015) 211301; MB, I.Z. Rothstein, V. Vaidya: 1412.8698, JHEP 1504 (2015) 106;

MB and V. Vaidya: 1510.02470, JHEP 1603 (2016) 213;MB, T. Cohen, I. Moult, N. Rodd, T. Slatyer, M. Solon, I, Stewart, V. Vaidya 1712.07656, JHEP 1803 (2018) 117;

MB, T. Cohen, I. Moult, N. Rodd, T. Slatyer, I, Stewart, V. Vaidya 1808.08956, JHEP 1901 (2019) 036

WHY DARK MATTER?

2

Vera Rubin 1928-2016Established Rotation Curve anomaly

Colliding Clusters:Gravitational wells

nowhere near visible peaks

“Not modified gravity”

Galactic Rotation curves:Stars move faster

than expected

Anomalies on 3 differentastrophysical scales!

DARK MATTER ABUNDANCE

3

Cosmic Microwave Background:

Fluctuations measure Dark Matteras 27% of Universe’s energy (Planck)

Animations from W. Hu

IT’S IN THERE SOMEWHERE

(After S. Rajendran)

We know some “dark” particles! Neutrinos!But they aren’t dark matter

10-43 GeVCompton

WavelengthVisible Universe

1019 GeVPlanck Mass

The Great Ruler of Particle Physics

10-22 GeVCompton

Wavelength tofit in Dwarf Galaxy

Boson excluded

100 eVTremaine-Gunn BoundStack fermions in galaxy

Fermion excluded

10-20-10-11 GeVQCD axion Dark Matter

102-104 GeVWeakly-Interacting

Massive Particle (WIMP) Dark Matter

4

Mass in GeV

WHY WIMPS?

5

Annihilation

Cosmic Expansion

No Annihilation

χ

χ

X

ψ

ψ

<σv>annihilation ~ C α2/Mχ2

DM density decreases:Annihilation & expansion

WIMP MIRACLE

6

M� ⇠ TeV⇣10

pC↵

⌘r⌦DM

0.27

⌦DM ⇠ 1

103h�vi1

TCMBMPlanck⇠ 1

103h�vi1

TeV2

See Dimopoulos PLB 246(1990):347-52

WIMP can be simple additionto known particles & forces.

WHY?

DM density decreases:Ω: Annihilation & expansion

Y: Annihilation

STARTING SIMPLE W/ WIMPS

7

χ

χ

X

ψ

ψ

<σv>annihilation ~ C α2/Mχ2

Maybe we already know everything here except χ?

X: Z-boson, Higgs?ψ: Elementary Fermion, Higgs?

α: αweak?

RELIC DENSITY

8

Simple Candidates! Dark Matter ↔ Weak Scale:

Weak Triplet: “Wino”Weak Doublet: “Higgsino”

Weak Quintuplet

Tying WIMP to Weak Scalee.g. SUSY & explaining elementary fermion masses

1403.6118: MB, D. Stolarski, T. Zorawski

Correct Dark MatterDensity fixes Mχ:

Wino: 3 TeVHiggsino: 1 TeV

Quintuplet: 9 TeV

ΩDM = 0.27Measured Dark Matter

DensityWeak Force“Charges”

ECHO OF THE WIMP MIRACLE

9 HESS event

Schematic of air shower observed by Cherenkov Telescope(spie.org)

O(TeV) γ leads to O(104m) light poolon ground

χ0

χ0

W+

W−

γ

χ0

χ0

γ

γ

Indirect Detection:Photons from Dark Matter Annihilation

HESS/VERITAS can probe Dark Matter Masses

up to 70 TeV

Successor CTA will start in 2023,will test up to 100 TeV

WINO SHOT DEAD BY HESS?

*1307.4082: Cohen, Lisanti, Pierce, and Slatyer ; see also “In Wino Veritas”, 1307.4400: Fan & Reece

From 1307.4082: Blue line: Wino annihilation rateBlue shade: Exclusion from HESS

Yellow shade: All DM is thermal wino

10

Ruled out

by 16x?

-10 -5 0 5 10 kpc

5

10

15

20rHGeVL

Cusp vs. Core

We are here ~ 8.5 kpc

Navarro-Frank-White (cusped) halo profile assumed

The Loophole

WHAT COULD SAVE THE WINO?

11

From Cohen et al.1307.4082

O(1-10) Factor at stake, need state of the art calculation

to determineSimulations with baryons show cusped profiles down to 1 kpc (1208.4844, 1305.5360,

1306.0898)

0.25x

Halo Model Quantum Corrections

Flatten distribution in galactic center (core)

Claim in literature of 75% reduction from

first quantum corrections

Core needed:1.5 kpc

Core needed:0.5 kpc

• 3 separate threats to perturbation theory!

• Mχ/mw >> 1 → Long range force

• Mχ/mw >> 1 → Electroweak shower

• Log(1-zcut) → Phase space restriction

• Proliferation of scales → Effective Field Theory

DIGITAL SIGNAL PROCESSING AND QUANTUM FIELD THEORY

1 min 10 MB

µ−

νµ

e−

νe

µ−

νµ

e−

νe

W−

Dropping high-frequencymodes can suffice

13Quantum relativist terminology:

Energy=Mass=Momentum=Frequency

Effective Field Theory: Systematically decouple

High-Energy Physics

MODERN EFFECTIVE FIELD THEORY

14

1 min 1 MB

q

g

qg

g

g

Eliminate modesMP3: PsychoacousticsEffective Field Theory:

Kinematics

1007.0758: MB, Marcantonini, C., Stewart, I.Freq.

Time

Shower of radiation: Less Low-energy and Collinear

enhancement

LONG-RANGE FORCES

• Sommerfeld Enhancement, generic for WIMP Dark Matter (v~10-3-6)

• Quantum-Mechanically Potential drags wavefunction to peak at origin

15

h�vi = | (0)|2 �pert.

R

In absence of gravitation, capture radius is geometric, R

Rb

Turning on gravity, cross section grows forslower projectile:

v

v

bcapture = R

r1 +

2GM

v2R

Wavefunction at the origin bcapture ⇠1

v

Classical Analogy

SOMMERFELD ENHANCEMENT

16

An ' ↵

✓↵WM�

mW

◆n

αWMχ/mW or αW/v>1 → Sum to all orders!

Reduce Relativistic WIMP QFT toQuantum Mechanics + Potential

[J. Hisano, S. Matsumoto, M. Nojiri, O. Saito, hep-ph/0412403MB, Rothstein, I., Vaidya, V.: 1412.8698]

| (0)|2 / min

↵W

v,↵WM�

mW

�Parametrically enhanced

wavefunction

NR“QCD” FOR WIMPS

17

Mχ

Mχv

Mχv2

Heavy Particle Mass

Heavy Particle Momentum

Heavy Particle Energy

(kinetic & binding)

Hierarchy of scales for nonrelativistic particles

*Classic treatment of NRQCD in Bodwin, Braaten, LePagehep-ph/9407339

WIMPχ (E,p)~(Mχv2,Mχv)

PotentialAμ→V(r) (E,p)~(Mχv2,Mχv)

UltrasoftS~Exp[i∫v.Aus] (E,p)~(Mχv2,Mχv2)

SoftAsμ

(E,p)~(Mχv,Mχv)

Multimodal Effective Field Theory

“Soft” Radiation appears as a Wilson Line

• 3 separate threats to perturbation theory!

• Mχ/mw >> 1 → Long range force

• Mχ/mw >> 1 → Electroweak shower

• Log(1-zcut) → Phase space restriction

• Proliferation of scales → Effective Field Theory

HUGE ACCELERATION → CLASSICAL RADIATION

19

↵W

⇡log(M2

wino

/m2

W )

2 ⇡ 0.6 Double log Large correction!

Charged particles in annihilation process radiate (γ, W, Z) from acceleration

�v = �v0

���exph� ↵

2⇡log(E

high

/Elow

) log(Ehigh

/Ecollinear

)

i���2

Above rate produces classical spectrum, but hard to see in quantum perturbation theory

Perturbative factorpicks up

kinematic enhancements“Sudakov double log”

(Radiation)

BLOCH-NORDSIECK THEOREM VIOLATION*

Electroweak physics has infrared divergences, even in fully inclusive observables

20

*hep-ph/0001142: Ciafaloni, Ciafaloni, & Comelli;

hep-ph/0103315: Ciafaloni

σe+e- ≠ σe+ν, virtual corrections only cancel

emission upon color averaging

A B A B

C

De+ e- e+ e-νe

W-

B-N VIOLATION IN EFT

21

S

a0b0ab12 =

⌧0

�����Y

3kn Y

dkn

�†(x)�(M� Ms )

⇣Y

3gn Y

dfn Y

agv Y

bfv

⌘(0)

���� 0��

a0b0,

! �

a0b0�(m2

X)h0|⇣Y

†n

⌘e3Y

aev Y

bfv Y

3fn |0i

Wilson lines collapse from measurement inclusivity, but identifying photon in final state precludes sum over degenerate states.

Yv: Soft radiation wrapping WIMPYn/nbar: Soft radiation wrapping final state

Y †Y = 1<latexit sha1_base64="SfFDyAZmRhVWr38N+qzn8psgcz8=">AAAB/HicbVDLSsNAFJ34rPUV7dLNYBFclaQKdiMU3LisYF80sUwmk3boZCbMTIQQ6q+4caGIWz/EnX/jtM1CWw9cOJxzL/feEySMKu0439ba+sbm1nZpp7y7t39waB8dd5RIJSZtLJiQvQApwignbU01I71EEhQHjHSDyc3M7z4Sqajg9zpLiB+jEacRxUgbaWhX+g9eiEawD6+hFwgW5u50aFedmjMHXCVuQaqgQGtof3mhwGlMuMYMKTVwnUT7OZKaYkamZS9VJEF4gkZkYChHMVF+Pj9+Cs+MEsJISFNcw7n6eyJHsVJZHJjOGOmxWvZm4n/eINVRw88pT1JNOF4silIGtYCzJGBIJcGaZYYgLKm5FeIxkghrk1fZhOAuv7xKOvWae1Gr311Wm40ijhI4AafgHLjgCjTBLWiBNsAgA8/gFbxZT9aL9W59LFrXrGKmAv7A+vwBGhqTvg==</latexit>

SOFT/COLLINEAR ENHANCEMENT

22

1

p2A=

1

2EbEc(1� cos ✓)

Keep modes with kinematic enhancement (soft, collinear)

/

*Originally developed for study of QCDhep-ph/0005275: Bauer, Fleming, Luke

hep-ph/0011336: Bauer et al.

SCET forDark Matter annihilation

[MB, Rothstein, I., Vaidya, V.: 1409.4415]

χ

χ

pa,W pb, γ

pc,W

Soft radiation: Time-scalesmuch longer than annihilation

χ

χ

pa,W pb, γ

pc,W

Collinear Radiation: Narrow splittingof one particle into 2

θ

SOFT-COLLINEAR EFFECTIVE THEORY

• Large scale-hierarchies can arise within one field

• We can use Renormalization Group to resum kinematic logs

23

Integrate out hard modes, keep those collinear to null directions and soft fields

Hard

Lightcone momentak+ = k0 + k3

k- = k0 - k3

Jet of energy Q

p⊥ << Q

Mjet2 ~ p⊥Q

ultrasoft

SCET OBSERVABLES

24

��Xi =��X

collinear

i��X

soft

iFactorized Hilbert Space:

d� = H(Q) J(Q, zcollinear

)⌦ S(zsoft

)

Squared Wilsoncoefficient

Jn = h0��Bn?�

⇥f(Q, z

collinear

)⇤��XnihXn

��Bn?��0i

S = h0��(Y Y )† �

⇥f(z

soft

)⇤(Y Y )

��0i

H

J

S

SEMI-INCLUSIVE ANNIHILATION

• HESS/VERITAS observes photons colliding with the atmosphere

• Therefore, we compute χχ→γ+(Whatever else)

• But we have introduced a new scale, Mχ(1-zcut)~ Bin size

25

From HESS collaboration 1301.1173at 3 TeV, energy resolution is ~400 GeV

mW = 80 GeV

Eγ (soft W)=Mχ-mW/2Eγ (collinear Ws) = Mχ-mW2/Mχ

χ0

χ0

γ

γ

χ0

χ0

W+

W−

γ

or ?or …

SCET WITH 2 EXPANSIONS

26

Mχ

Mχ√(1-zcut)

Mχ(1-zcut)

Center of MassEnergy

Measured Jet Mass

Soft radiationscale

MWElectroweak

scale

• 3 separate threats to perturbation theory!

• Mχ/mw >> 1 → Long range force

• Mχ/mw >> 1 → Electroweak shower

• Log(1-zcut) → Phase space restriction

If J(Mχ,(1-zcoll),mW)

Mχ Hard

Mχ√(1-zcut)~Mχ(1-zcut)~MW Jet ~ Soft ~ Electroweak

SOFT REFACTORIZATION

28

IncreasingVirtuality

H

Jn

Jn

H

S: Perform matching@ Mχ√(1-zcut)

S→HS(Mχ√(1-zcut))S(mW)???

Remaining soft:(p+,p-,p⊥)~M(λ,λ,λ)

λ = mW/Mχ

BUT…what about measurement

function?

(1� z) =1

4M2�

m2X =

1

4M2�

X

i2Xs

pµi +X

i2Xc

pµi

!2

⌘ (1� zs) + (1� zc) +O(�2)

FULLY FACTORIZED THEORY

29

Collinear soft modes account for radiationalong photon direction,

but contribute to recoil jet mass

d�

dz= H(m�, µ) ·HJn(m�, (1� z), µ) ·HS(m�, (1� z), µ)

· J�(mW , µ, ⌫) · S(mW , µ, ⌫) · CS(m�, (1� z),mW , µ, ⌫) · Jn(mW , µ, ⌫)

Alternate collinear-soft scaling:(p+,p-,p⊥)~M(1-zcut)(λ2,1,λ)

λ = mW/Mχ(1-zcut)

Factorization holds to NLL!MB et al.: 1808.08956

• 3 separate threats to perturbation theory!

• Mχ/mw >> 1 → Long range force

• Mχ/mw >> 1 → Electroweak shower

• Log(1-zcut) → Phase space restriction

• Proliferation of scales → Effective Field Theory

LL RESUMMED PHOTON SPECTRUM

31

d�

dz=

⇡↵2

W sin

2 ✓W2M2

�ve

h�2C2(W )

↵W⇡ log

2⇣

2M�M

⌘i((F

0

+ F1

)�(1� z)

+

0

B@C2

(W )

↵W

⇡log

4M2

�(1� z)

M2

!e

C2(W )

↵W2⇡ log

2

✓M2

4M2�(1�z)

◆�

1� z

1

CA

+

F0

+

" C

2

(W )

↵W

⇡log

4M2

�(1� z)

M2

!+ 3C

2

(W )

↵W

⇡log

✓M

2M�(1� z)

◆!

⇥

0

B@e

� 3

2C2(W )

↵W⇡ log

2⇣

M2M�(1�z)

⌘+C2(W )

↵W2⇡ log

2

✓M2

4M2�(1�z)

◆�

1� z

1

CA

#

+

F1

)

Squared WilsonCoefficient for

wino annihilation

Linear combinationof Sommerfeld

factors

MB et al.: 1712.07656

CUMULATIVE RESUMMED ANNIHILATION RATE

32

LL

NLL

0.5 0.6 0.7 0.8 0.9 1.0zcut

0

1

2

3

4

5

6

7

8

h�vi

⇥10

26[c

m3 /

s]

Thermal WinoCross Section

H.E

.S.S

.R

esol

utio

n

MB et al.: 1808.08956Thermal relic wino rate vs. Energy fraction

HESS WINO LIMITS

33

Update to HESS 2013 analysis projected to rule out by 30x,

halo loophole 1-1.5 kpc

More aggressive analysis with better galactic center understanding,

halo loophole closes, rc>2.5 kpc

Rinchiuso et al.: 1808.04388

Hooper: 1608.00003 limit of 2 kpc

CONCLUSION• Despite certain lore, WIMPs remain motivated, viable, simple

dark matter candidate.

• But…we have the wino on the run.

• Data already in the can will kill (or discover) it!

• Analysis easily extendable to other SU(2) reps, general SUSY LSP, Higgs Portal, Bound State effects

• Multi-TeV regime requires electroweak resummation even at qualitative level.

34

DISCOVERY AT THE LHC? NO

35

From Cirelli et al. 1407.7058

500 GeV, LHC Wino reach

1202.4847 (ATLAS)

Find Winos by their charged partner’s

disappearing trackMχ > 270 GeV

Higgsino reachmay not improve

over LEP: 110 GeV

Han et al.: 1401.1235

MINING FOR WINOS? NO

36

σwino~10-47 cm2

From Rick Gaitskell (LUX) talk

Higgsino limits even weaker

χ

χZ

q

q

Z portalexcluded

Example: Coupling Dark Matterto Nucleons through Z

Ruled Out

Wino: Simple Model,but not Simple Calculation

10-35cm2M. Goodman & E. Witten: PRD31 (1985)

J. Hisano et al.: 1104.0228R. Hill & M. Solon: 1309.4092

RG REGAINS CONTROL

37

Above high-frequencycutoff, Λ, remove but

change coupling

⇒λ λ

λ′

d�

d log(⇤)=

3�2

16⇡2

�(⇤) =�(⇤0

)

1� 316⇡2�(⇤0

) log(⇤/⇤0)

Included λ Log(Λ/Λ0) to all orders!

2→2 scattering in 2nd-order perturbation theory

V (�) =�

4!�4

SOMMERFELD RESONANCES

38

rBohr ~ 1/αMχ

rRange ~ 1/mW

rBohr >> rRangeNo bound state

rRange >> rBohrBound state forms

Transition from short to long-range force leads to resonance

For winomW = αWMχ @ Mχ = 2.4 TeV

WINO NR COMPUTATION

39

Zero-energy bound states → Peaks

n=1 n=2n=3

αWMχ = n2 mW

� � �� �� ����χ(���)���

�

��

���

����

���

�=|ψ(�) �

������� ψ+-����� ψ�

Thermal Relic

D0����3T

v i�2 �3v

�����0�0

�S

E= 4

p2M� s00 ;

D0����+T

v i�2 ��v

�����0�0

�S

E= 4M� s0±

Wavefunction at the origin

ELECTROWEAK RESUMMATION ERA

• Electroweak parton shower for colliders

• Interplay with QCD shower

• Factorization violation at LHC from Glauber modes*

• High-energy neutrinos (Eν>PeV) demanding resummation

e− e+ e− e+

W+

ν

Inclusive electroweak processes can havedouble-log IR sensitivity

(Bloch-Nordsieck Theorem Violation)

Log(PeV/mW)2 ~ 100[*MB, Erdogan, O., Rothstein, I., Vaidya, V.: 1811.04120]

HIGGSINO RATE AT LL´

41

ΔΜ0= 200 keV; ΔΜ+= 350 MeV

Minimally split

Higgsino.*Purest viable

doublet*Cheung et al:

hep-ph:0512192

ΔΜ0= 2 GeV; ΔΜ+= 480 MeV

MB, Vaidya, V.: 1510.02470

Thermal Higgsinounconstrained by

current/future tests

1 TeV higgsino needs propertreatment of endpoint region

WINO VIABILITY

42

Initial motivation for Wino stressed its simplicity, but perhaps its role in Dark Matter is more involved, including

a non-thermal history, multi-component DM, mixing with other electroweak states

Possibility for the wino to make up some fractionof DM with NFW profile flattened to a

constant core at some radiusImposing a constant density below

a given radius for NFW (core),at what point does wino become viable total DM?

*MB, Rothstein, I., Vaidya, V.: 1412.8698

Inconsistent with Simulation

CAPTURE TO BOUND STATE

43

10-7 10-6 10-5 10-4 0.001 0.010 0.100v

10-20

10-18

10-16

10-14

σv(cm3

s)

Blue: e+e--> Positronium + γYellow: e+e--> γγ (Sommerfeld)Green: e+e--> γγ (No Sommerfeld)

�v|ann. =2⇡2↵3

m2e vrel

For postitroniumCapture ≈ 3x Annihilation

�v|capture =210⇡2

3e�4 ↵3 1

m2e

1

vrel

Sommerfeld Resonancesreveal bound states in spectrum

χ

γ

γ

γ

Bound State

χ

CAPTURE TO BOUND STATE

10 50 100Mχ(TeV)

1.×10-34

1.×10-32

1.×10-30

1.×10-28

1.×10-26

1.×10-24

σv(cm3

s)

Inclusive annihilationP→S captureγ+X annihilationD→P captureS→P capture

What is the fate of a χ0χ0 (wino) Initial state?v = 10-3

1610.07617: Asadi, P., MB, Fitzpatrick P,. Krupczak, E., Slatyer, T.

WW, ZhLeptonsQuarks

spin-triplet 1s bound state

10 20 50 100 200Mχ(TeV)

1018

1019

1020

1021

Γ(1/s)

Capture loses to annihilation, butnew signature (capture photons)

Importance depends on identity of WIMP

WIMPonium decay rates

GOLDILOCKS & THE 3 RESEARCH GROUPS

45

Exclusive2→2 annihilation:

γγ+γZOvanesyan, Slatyer,

and Stewart: 1409.8294;Cohen et al.: 1409.7392

Semi-inclusiveIntegrate out recoil state

with OPE: γ+XMB, I.Z. Rothstein, V. Vaidya: 1409.4415,MB, I.Z. Rothstein, V. Vaidya: 1412.8698

Semi-inclusive with cutoffMB and V. Vaidya: 1510.02470

Endpoint Region Measurement forcesrecoil into jet: γ+X

MB, Cohen, Moult et al.:1712.07656

TRADITIONAL FACTORIZATION

• SCET modes’ lightcone power counting

• Collinear (p+,p-,p⊥)~Q(1,λ2,λ)

• Soft (p+,p-,p⊥)~Q(λ,λ,λ)

• Ultrasoft (p+,p-,p⊥)~Q(λ2,λ2,λ2)

46

hep-ph/0109045: Bauer, Pirjol, & Stewart

ξ→YξPull ultrasoft Wilson lineout of collinear field →

Collinear/Soft Factorization!

COLLINEAR REFACTORIZATION

47

IncreasingVirtuality

H

Jn

Jn

H

Original SCET doesn’t distinguish soft scales: (1-zcoll), mW

Jn: Perform matching@ Mχ√(1-zcut)

Jn→HJn(Mχ√(1-zcut))Jn(mW)

Remaining collinear:(p+,p-,p⊥)~M(1,λ2,λ)

λ = mW/Mχ

WHITHER SOFT DIVERGENCE?

48

S

a0b0ab11

(x) =

⌧0

�����Y

3kn Y

dkn

�†�

⇥M

2

�(1� z

soft

)�M

2

�(1� z

soft

)⇤

⇥��Xs

↵⌦Xs

��⇣Y

3jn Y

djn

⌘ ���� 0��

a0b0�

ab,

! S

a0b0ab11

⇠ �

a0b0�

abh0|hY

ce0

n Y

3e0

n

i†�

⇥M

2

�(1� z

soft

)⇤ ⇥

Y

cen Y

3en

⇤|0i

= �

a0b0�

ab�

⇥(M2

�(1� z

soft

)⇤

⊗ ⊗

n

n

One-loopsoft

anomalous dimension⇒ ???

WA

Y Can’t live in HS, because HS doesn’t know about scale mW

COLLINEAR SOFT MODE

49

Alternate soft scaling:(p+,p-,p⊥)~M(1-zcut)(λ2,1,λ)

λ = mW/Mχ(1-zcut)

Saba0b0

11 =

⌧0|⇣Y 3f 0

n Y dg0

n

⌘†(0)�(M � cMCs)

⇥��XCs

↵⌦XCs

��⇣Y 3fn Y dg

n

⌘(0)|0

E�f

0g0�a

0b0�fg�ab .

Get back pre-refactorized divergence!

RAPIDITY RG

• SCET is a “modal” theory

• We can get divergences when integrals invade other sectors. Soft-collinear overlap requires boost-violating regulator

• Regulating sets up RG for resumming these rapidity logs

50

Aµ

= Ac,n

µ

+Ac,n

µ

+Asoft

µ

+ . . .

Wn =

X

perms

exp

� g

n · P⌫⌘

|n · P |⌘ n ·An

� Above from Chiu et al. 1202.0814: In SCETII, soft andcollinear modes have same virtualityν-running lets us minimize log between

soft & collinear scales