RESUMMED PHOTON SPECTRA FOR WIMP ANNIHILATION

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RESUMMED PHOTON SPECTRA FOR WIMP ANNIHILATION Matthew Baumgart (Arizona State University) Multiscale Problems Using Effective Field Theories University of Washington 5/17/2018 MB, I.Z. Rothstein, V.

1 RESUMMED PHOTON SPECTRA FOR WIMP ANNIHILATION Matthew Baumgart (Arizona State University) Multiscale Problems Using Effective Field Theories University of Washington 5/17/2018 MB, I.Z. Rothstein, V. Vaidya: , PRL 114 (2015) ; MB, I.Z. Rothstein, V. Vaidya: , JHEP 1504 (2015) 106; MB and V. Vaidya: , JHEP 1603 (2016) 213; MB, T. Cohen, I. Moult, N. Rodd, T. Slatyer, M. Solon, I, Stewart, V. Vaidya

2 WHY DARK MATTER? Anomalies on 3 different astrophysical scales! Galactic Rotation curves: Stars move faster than expected Colliding Clusters: Gravitational wells nowhere near visible peaks Not modified gravity Vera Rubin Established Rotation Curve anomaly 2

3 DARK MATTER ABUNDANCE Cosmic Microwave Background: Fluctuations measure Dark Matter as 27% of Universe s energy (Planck) 3 Animations from W. Hu

4 IT S IN THERE SOMEWHERE We know some dark particles! Neutrinos! But they aren t dark matter Boson excluded The Great Ruler of Particle Physics Fermion excluded Mass in GeV GeV Compton Wavelength Visible Universe GeV Compton Wavelength to fit in Dwarf Galaxy 100 ev Tremaine-Gunn Bound Stack fermions in galaxy GeV Planck Mass GeV QCD axion Dark Matter GeV Weakly-Interacting Massive Particle (WIMP) Dark Matter (After S. Rajendran) 4

5 WHY WIMPS? Cosmic Expansion Annihilation No Annihilation DM density decreases: Annihilation & expansion χ ψ χ X <σv>annihilation ~ C α 2 /M χ 2 ψ 5

6 WIMP MIRACLE DM h vi 1 T CMB M Planck h vi 1 TeV 2 M TeV 10 p r DM C 0.27 WIMP can be simple addition to known particles & forces. WHY? DM density decreases: Ω: Annihilation & expansion Y: Annihilation 6 See Dimopoulos PLB 246(1990):347-52

7 STARTING SIMPLE W/ WIMPS χ χ X <σv>annihilation ~ C α 2 /M χ 2 ψ ψ Maybe we already know everything here except χ? X: Z-boson, Higgs? ψ: Elementary Fermion, Higgs? α: αweak? 7

8 RELIC DENSITY ΩDM = 0.27 Measured Dark Matter Density Top Down Candidates: Supersymmetric Dark Matter Simple Candidates! Dark Matter Weak Scale: Weak Triplet: Wino Weak Doublet: Higgsino Correct Dark Matter Density fixes M χ : Wino: 3 TeV Higgsino: 1 TeV 8

9 DISCOVERY AT THE LHC? NO Find Winos by their charged partner s disappearing track Mχ > 270 GeV From Cirelli et al GeV, LHC Wino reach Higgsino reach may not improve over LEP: 110 GeV (ATLAS) 9 Han et al.:

10 MINING FOR WINOS? NO χ q M. Goodman & E. Witten: PRD31 (1985) cm 2 Z portal excluded χ Z q Example: Coupling Dark Matter to Nucleons through Z Ruled Out σwino~10-47 cm 2 Wino: Simple Model, but not Simple Calculation From Rick Gaitskell (LUX) talk J. Hisano et al.: R. Hill & M. Solon: Higgsino limits even weaker

ECHO OF THE WIMP MIRACLE χ 0 W + χ 0 γ χ 0 W γ Indirect

HESS/VERITAS can probe χ 0 Dark Matter Masses up to 20 TeV

Schematic of air shower observed by Cherenkov Telescope

11 ECHO OF THE WIMP MIRACLE χ 0 W + χ 0 γ χ 0 W γ Indirect Detection: Photons from Dark Matter Annihilation HESS/VERITAS can probe χ 0 Dark Matter Masses up to 20 TeV γ O(TeV) γ leads to O(10 4 m) light pool on ground Schematic of air shower observed by Cherenkov Telescope (spie.org) Successor CTA will start in 2023, will test up to 100 TeV 11 HESS event

12 WINO SHOT DEAD BY HESS? The Loophole Navarro-Frank-White (cusped) halo profile assumed rhgevl Cusp vs. Core 10 From : Blue line: Wino annihilation rate Blue shade: Exclusion from HESS Yellow shade: All DM is thermal wino Ruled out by 16x? 5 We are here kpc * : Cohen, Lisanti, Pierce, and Slatyer; see also In Wino Veritas, : Fan & Reece 12

13 WHAT COULD SAVE THE WINO? Halo Model Quantum Corrections Flatten distribution in galactic center (core) Claim in literature of 75% reduction from first quantum corrections 0.25x Core needed: 1.5 kpc Core needed: 0.5 kpc Simulations with baryons show cusped profiles down to 1 kpc ( , , ) 13 From Cohen et al O(1-10) Factor at stake, need state of the art calculation to determine

14 3 separate threats to perturbation theory! M χ /mw >> 1 Long range force M χ /mw >> 1 Electroweak shower Log(1-zcut) Phase space restriction Proliferation of scales Effective Field Theory

15 LONG-RANGE FORCES Classical Analogy Sommerfeld Enhancement, generic for WIMP Dark Matter (v~ ) v R Quantum-Mechanically Potential drags wavefunction to peak at origin h vi = (0) 2 Wavefunction at the origin pert. 15 In absence of gravitation, capture radius is geometric, R b v Turning on gravity, cross section grows for r slower projectile: b capture = R b capture 1 v R 1+ 2GM v 2 R

16 SOMMERFELD ENHANCEMENT A n ' W M m W n αwm χ /mw or αw/v>1 Sum to all orders! (0) 2 / min apple W v, W M m W Parametrically enhanced wavefunction Reduce Relativistic WIMP QFT to Quantum Mechanics + Potential [MB, Rothstein, I., Vaidya, V.: ] 16

17 SOMMERFELD RESONANCES rrange ~ 1/mW rbohr ~ 1/αM χ rbohr >> rrange No bound state rrange >> rbohr Bound state forms mw = αwm M χ = 2.4 TeV Transition from short to long-range force leads to resonance 17

18 NR QCD FOR WIMPS Multimodal Effective Field Theory WIMP χ (E,p)~(M χ v 2,M χ v) M χ Heavy Particle Mass Potential A μ V(r) (E,p)~(M χ v 2,M χ v) M χ v Heavy Particle Momentum Ultrasoft S~Exp[i v.aus] (E,p)~(M χ v 2,M χ v 2 ) M χ v 2 Heavy Particle Energy (kinetic & binding) Soft As μ (E,p)~(M χ v,m χ v) Hierarchy of scales for nonrelativistic particles *Classic treatment of NRQCD in Bodwin, Braaten, LePage hep-ph/

19 NR COMPUTATION = ψ( ) n=1 ψ +- ψ n=2 n=3 Zero-energy bound states Peaks Thermal Relic D 0 D 0 3 T v i 2 v +T v i 2 v χ ( ) 0 0 S S E E =4 p 2 M s 00 ; =4M s 0± αwm χ = n 2 mw Wavefunction at the origin 19

20 3 separate threats to perturbation theory! M χ /mw >> 1 Long range force M χ /mw >> 1 Electroweak shower Log(1-zcut) Phase space restriction Proliferation of scales Effective Field Theory

21 HUGE ACCELERATION CLASSICAL RADIATION (Radiation) v = v 0 exp Charged particles in annihilation process radiate (γ, W, Z) from acceleration h i 2 2 log(e high/e low ) log(e high /E collinear ) Perturbative factor picks up kinematic enhancements Sudakov double log Above rate produces classical spectrum, but hard to see in quantum perturbation theory W log(m 2 wino/m 2 W ) Double log 21 Large correction!

22 BLOCH-NORDSIECK THEOREM VIOLATION * Electroweak physics has infrared divergences, even in fully inclusive observables S a0 b 0 ab 12 = CW - A B A D B e + e - e + νe e - 0 Yn 3k Y n dk! a0 b 0 (m 2 X)h0 (x) (M ˆMs ) Y n σe+e- σe+ν, virtual corrections only cancel emission upon color averaging Wilson lines collapse from measurement inclusivity, but identifying photon in final state precludes sum over degenerate states. Y 3g n e3 Y ae v Yv bf Y n 3f 0i Y df n Yv ag Yv bf (0) 0 a 0 b 0, 22 *hep-ph/ : Ciafaloni, Ciafaloni, & Comelli; hep-ph/ : Ciafaloni

23 SOFT/COLLINEAR ENHANCEMENT Soft radiation: Time-scales much longer than annihilation χ χ p a,w p b,γ p c,w Collinear Radiation: Narrow splitting of one particle into 2 p a,w p b,γ χ p c,w χ θ / 1 p 2 A = 1 2E b E c (1 cos ) Keep modes with kinematic enhancement (soft, collinear) SCET for Dark Matter annihilation [MB, Rothstein, I., Vaidya, V.: ] 23 *Originally developed for study of QCD hep-ph/ : Bauer, Fleming, Luke hep-ph/ : Bauer et al.

24 SEMI-INCLUSIVE ANNIHILATION χ 0 χ 0 γ γ χ 0 W + or or? χ 0 W γ HESS/VERITAS observes photons colliding with the atmosphere Therefore, we compute χχ γ+(whatever else) But we have introduced a new scale, M χ (1-zcut)~ Bin size 24 From HESS collaboration at 3 TeV, energy resolution is ~400 GeV mw = 80 GeV E γ (soft W)=M χ -mw/2 E γ (collinear Ws) = M χ -mw 2 /M χ

25 GOLDILOCKS & THE 3 RESEARCH GROUPS Exclusive 2 2 annihilation: γγ+γz Ovanesyan, Slatyer, and Stewart: ; Cohen et al.: Semi-inclusive Integrate out recoil state with OPE: γ+x MB, I.Z. Rothstein, V. Vaidya: , MB, I.Z. Rothstein, V. Vaidya: Semi-inclusive with cutoff MB and V. Vaidya: Endpoint Region Measurement forces recoil into jet: γ+x MB, Cohen, Moult et al.:

26 SCET WITH 2 EXPANSIONS M χ Center of Mass Energy M χ (1-zcut) Measured Jet Mass M χ (1-zcut) Soft radiation scale MW Electroweak scale 26

27 SOFT-COLLINEAR EFFECTIVE THEORY Large scale-hierarchies can arise within one field Lightcone momenta k + = k 0 + k 3 k - = k 0 - k 3 Hard Jet of energy Q p << Q Mjet 2 ~ p Q We can use Renormalization Group to resum kinematic logs ultrasoft Integrate out hard modes, keep those collinear to null directions and soft fields 27

28 TRADITIONAL FACTORIZATION SCET modes lightcone power counting Collinear (p+,p-,p )~Q(1,λ 2,λ) Soft (p+,p-,p )~Q(λ,λ,λ) Ultrasoft (p+,p-,p )~Q(λ 2,λ 2,λ 2 ) ξ Yξ Pull ultrasoft Wilson line out of collinear field Collinear/Soft Factorization! 28 hep-ph/ : Bauer, Pirjol, & Stewart

29 SCET OBSERVABLES J Factorized Hilbert Space: H S Xi = X collinear i X soft i d = H(Q) J(Q, z collinear ) S(z soft ) Squared Wilson coefficient S = h0 (YY) f(z soft ) (YY) 0i J n = h0 B n? f(q, zcollinear ) X n ihx n B n? 0i 29

30 3 separate threats to perturbation theory! M χ /mw >> 1 Long range force M χ /mw >> 1 Electroweak shower Log(1-zcut) Phase space restriction M χ Hard If J(M χ,(1-zcoll),mw) M χ (1-zcut)~M χ (1-zcut)~MW Jet ~ Soft ~ Electroweak

31 COLLINEAR REFACTORIZATION Original SCET doesn t distinguish soft scales: (1-zcoll), mw H H Jn: Perform M χ (1-zcut) Jn HJn(M χ (1-zcut))Jn(mW) J n Increasing Virtuality Remaining collinear: (p+,p-,p )~M(1,λ 2,λ) λ = mw/m χ J n 31

32 SOFT REFACTORIZATION S: Perform M χ (1-zcut) S HS(M χ (1-zcut))S(mW)??? Remaining soft: (p+,p-,p )~M(λ,λ,λ) λ = mw/m χ H J n H Increasing Virtuality BUT what about measurement function? J n (1 z) = 1 4 M 2 m2 X = 1 4 M 2 X i2x s p µ i + (1 z s )+(1 z c )+O( 2 ) X p µ i i2x c 32! 2

33 WHITHER SOFT DIVERGENCE? S a0 b 0 ab 11 (x) = 0 Yn 3k Y n dk X s Xs! S a0 b 0 ab 11 a0 b 0 ab h0 n M 2 (1 z soft ) M 2 (1 ẑ soft ) Yn 3j Y n dj hy ce0 n Y 3e0 n = a0 b 0 ab (M 2 (1 z soft ) W A 0 One-loop soft anomalous dimension a 0 b 0 ab, i M 2 (1 z soft ) Yn ce Y n 3e 0i??? n Y 33 Can t live in HS, because HS doesn t know about scale mw

34 COLLINEAR SOFT MODE Alternate soft scaling: (p+,p-,p )~M(1-zcut)(λ 2,1,λ) λ = mw/m χ (1-zcut) S aba0 b 0 11 = 0 Y 3f 0 n Y dg0 n X Cs XCs (0) (M c MCs ) Y 3f n Y n dg (0) 0E f 0 g 0 a 0 b 0 fg ab. Get back pre-refactorized divergence! 34

35 FULLY FACTORIZED THEORY d dz = H(m,µ) H J n (m, (1 z),µ) H S (m, (1 z),µ) J (m W,µ, ) S(m W,µ, ) C S (m, (1 z),m W,µ, ) J n (m W,µ, ) Collinear soft modes account for radiation along photon direction, but contribute to recoil jet mass 35

36 RAPIDITY RG SCET is a modal theory A µ = A c,n µ + A c, n µ + A soft µ +... 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 W n = X perms apple exp g n P n P n A n 36 Above from Chiu et al : In SCETII, soft and collinear modes have same virtuality ν-running lets us minimize log between soft & collinear scales

37 3 separate threats to perturbation theory! M χ /mw >> 1 Long range force M χ /mw >> 1 Electroweak shower Log(1-zcut) Phase space restriction Proliferation of scales Effective Field Theory

38 RESUMMED PHOTON SPECTRUM + + " 0 d dz = 2 W sin2 W 2M 2 v h e 2C 2 (W ) W 2 (W ) W log 4M 2 (1 z) M 2! C 2 (W ) W log 4M 2 (1 z) M 2 0 apple e! e apple log 2 2M M C 2 (W ) W 2 +3C 2 (W ) W 3 2 C 2(W ) W log 2 M +C 2M (1 z) 2 (W ) W 2 1 z log 2 i ( (F 0 + F 1 ) (1 z) log 2 1 z log M 2 4M 2 (1 z) M 2 4M 2 (1 z) 1 C A + F 0 M! 2M (1 z) 1 # C A ) F 1 + Squared Wilson Coefficient for wino annihilation 38 Linear combination of Sommerfeld factors

39 WINO SPECTRUM & LIMITS Estimate ~30% strengthening of HESS limit from tree + Sommerfeld (Einasto profile) 39

40 A MORE USEFUL LIMIT 5 Estimated Core Size Constraint 4 Line (this ref) endpoint (this ref) Core Size [kpc] (Cutoff NFW) M [TeV] Preliminary indications show thermal relic wino weakened by quantum corrections ~1 kpc core to save wino Core limits: Simulation: <1 kpc [ ] Observation: <2 kpc [ ] 40

41 HIGGSINO RATE AT LL 1 TeV higgsino needs proper treatment of endpoint region Minimally split Higgsino.* Purest viable doublet *Cheung et al: hep-ph: ΔΜ0= 200 kev; ΔΜ+= 350 MeV Thermal Higgsino unconstrained by current/future tests 41 ΔΜ0= 2 GeV; ΔΜ+= 480 MeV MB, Vaidya, V.:

CONCLUSION Despite simple model and straightforward experiment, proper calculation has rich theoretical structure EFT combines NRQCD, SCET-1, SCET-II, and SCET + (collinear-soft mode) Techniques

42 CONCLUSION Despite simple model and straightforward experiment, proper calculation has rich theoretical structure EFT combines NRQCD, SCET-1, SCET-II, and SCET + (collinear-soft mode) Techniques generic for WIMPs coupled to lighter states (other representations of electroweak group, e.g. 5 of 9 TeV IN PROGRESS!) Put in next set of corrections, Log(1-z) and Log(M χ /m W ) IN PROGRESS! Test alternate simple model, Higgs portal that requires electroweak resummation (χ 2 )(h 2 ) IN PROGRESS! Wino is in tension with Milky Way like simulations, new data on the way (VERITAS, HESS, CTA, WFIRST, LSST, GAIA) HESS projected improvement by 5x, pushing core out to 9kpc! Can anyone find the higgsino, the most elusive motivated particle in high energy physics? NEXT UP AFTER CURRENT PAPERS ARE OUT

WINO VIABILITY 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

43 WINO VIABILITY 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 Inconsistent with Simulation Imposing a constant density below a given radius for NFW (core), at what point does wino become viable total DM? Possibility for the wino to make up some fraction of DM with NFW profile flattened to a constant core at some radius 43 *MB, Rothstein, I., Vaidya, V.:

44 CAPTURE TO BOUND STATE Sommerfeld Resonances reveal bound states in spectrum γ σv( cm3 s ) Blue: e + e - -> Positronium + γ Yellow: e + e - -> γγ (Sommerfeld) Green: e + e - -> γγ (No Sommerfeld) χ χ γ Bound State v v capture = e m 2 e 1 v rel v ann. = m 2 e v rel γ 44 For postitronium Capture 3x Annihilation

45 CAPTURE TO BOUND STATE What is the fate of a χ 0 χ 0 (wino) Initial state? σv( cm3 s ) v = 10-3 Γ(1/s) spin-triplet 1s bound state Quarks Leptons WW, Zh WIMPonium decay rates Inclusive annihilation P S capture γ+x annihilation D P capture S P capture M χ (TeV) Capture loses to annihilation, but new signature (capture photons) Importance depends on identity of WIMP M χ (TeV) : Asadi, P., MB, Fitzpatrick P,. Krupczak, E., Slatyer, T.

The Story of Wino Dark matter

The Story of Wino Dark matter Varun Vaidya Dept. of Physics, CMU DIS 2015 Based on the work with M. Baumgart and I. Rothstein, 1409.4415 (PRL) & 1412.8698 (JHEP) Evidence for dark matter Rotation curves