Non-Perturbative Collider Phenomenology of Stealth Dark Matter Ethan - - PowerPoint PPT Presentation

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Non-Perturbative Collider Phenomenology of Stealth Dark Matter Ethan - - PowerPoint PPT Presentation

Sep 11, 2023 167 likes •413 views

Non-Perturbative Collider Phenomenology of Stealth Dark Matter Ethan T. Neil (CU Boulder/RIKEN BNL) for the LSD Collaboration USQCD All Hands Meeting May 1, 2015 L attice S trong D ynamics Collaboration Xiao-Yong Jin Joe Kiskis James Osborn

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SLIDE 1

Non-Perturbative Collider Phenomenology of Stealth Dark Matter

Ethan T. Neil (CU Boulder/RIKEN BNL) for the LSD Collaboration USQCD All Hands Meeting May 1, 2015
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SLIDE 2

Lattice Strong Dynamics Collaboration

Xiao-Yong Jin James Osborn Rich Brower Michael Cheng Claudio Rebbi Evan Weinberg Ethan Neil Meifeng Lin Evan Berkowitz Enrico Rinaldi Chris Schroeder Pavlos Vranas Joe Kiskis Tom Appelquist George Fleming Mike Buchoff 2 Ethan Neil Sergey Syritsyn David Schaich Graham Kribs Oliver Witzel
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SLIDE 3

Strongly-coupled composite dark matter

  • Our focus: composite DM as a strongly-bound state of some
more fundamental objects (think of the neutron)
  • Non-Abelian SU(ND) gauge sector, with some fermions in the
fundamental rep. Not the only possibility (e.g. “dark atoms”,
  • ther non-Abelian theories) but a well-motivated, somewhat
familiar foundation.
  • Constituents can carry SM charges, and charged excited
states active in early universe. Composite DM relic interacts via SM particles (photon, Higgs) but with form factor suppression!
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SLIDE 4

Symmetries of stealth DM

  • Start with SU(ND) gauge theory and NF Dirac fermions, in the
fundamental rep, and impose some conditions.
  • First requirement: baryons are bosons - even ND. No
magnetic moment. ND≥4 gives automatic DM stability from Planck-scale violations.
  • Second requirement: couplings to electroweak and Higgs -
  • ne EW doublet and one singlet, NF≥3. Ensures meson decay
as well.
  • Third requirement: custodial SU(2) for electroweak precision -
NF=4. As a bonus, charge radius is eliminated —> stealth DM!
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SLIDE 5

Stealth dark matter: model details

  • SU(4) gauge group with
4 Dirac fermions (SU(2)L and SU(2)R doublets)
  • Two sources of mass
allowed: vector-like and Higgs-Yukawa
  • Custodial symmetry is
identified as u <—> d exchange symmetry Field SU(ND) (SU(2)L, Y ) Q F1 = F u 1 F d 1 ! N (2, 0) +1/2 −1/2 ! F2 = F u 2 F d 2 ! N (2, 0) +1/2 −1/2 ! F u 3 N (1, +1/2) +1/2 F d 3 N (1, −1/2) −1/2 F u 4 N (1, +1/2) +1/2 F d 4 N (1, −1/2) −1/2 L M12✏ijF i 1F j 2 M u 34F u 3 F d 4 + M d 34F d 3 F u 4 + h.c., L yu 14✏ijF i 1HjF d 4 + yd 14F1 · H†F u 4 yd 23✏ijF i 2HjF d 3 yu 23F2 · H†F u 3 + h.c. , EW-preserving mass: EW-breaking mass:
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SLIDE 6

Mass eigenstates

  • Two sources of mass, electroweak breaking and preserving.
Ψu 2 Ψd 2 Ψd 1 Ψu 1 M M u,d 2 M u,d 1 Q = 1 2 Q = −1 2 ± p ∆2 + y14y23v2/2 ∆ to be M ⌘ M12 + M34 2 ∆ ⌘
  • M12 M34
2
  • ,
ark fermion mass eigenvalues are y14 = y + ✏y , y23 = y ✏y , |✏y| ⌧ |y| .
  • Assume yv<<M, to avoid vacuum alignment issues w/EWSB. Then
two regimes arise, depending on the origin of the mass splitting: Linear Case: Quadratic Case: yv ⌧ ∆ yv ∆ yΨ = y √ 2 yΨ = y2v 2∆ (linear/quadratic effect observed before, see Hill and Solon 1401.3339)
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SLIDE 7

Stealth dark matter on the lattice

  • The model: SU(4)
gauge theory at moderately heavy fermion mass
  • On the lattice:
plaquette gauge action, Wilson fermions (quenched)
  • Spectrum shown to
the right Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 0.50 0.55 0.60 0.65 0.70 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mPSêmv aM Π V spin-0 spin-1 spin-2 nucleons

Higgs exchange cross

[LSD collab., Phys. Rev. D89 (2014) 094508]
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SLIDE 8

Stealth dark matter: lattice results so far

  • Spectrum and scalar
current calculation: mass generation from Higgs strongly constrained.
  • ×-
×- ×- ×- ×- ×- ×- ()
  • ()
MB(GeV) mB(GeV)
  • EM polarizability: lower
bound on direct detection for theories with charged
  • constituents. Stealth DM
visible below a TeV or so. MPSêMV=0.70 10 50 100 500 1000 1¥10-46 5¥10-46 1¥10-45 5¥10-45 1¥10-44 5¥10-44 1¥10-43 5¥10-43 mBHGeVL DM-nucleon cross section Hcm2L 훼=0.64 훼=0.16 훼=0.04 훼=0.01 LUX cosmic ν LEP
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SLIDE 9
  • DM is far from lightest particle in the new sector! Much harder to
produce directly in colliders, so MET signals are greatly suppressed.
  • On the other hand, presence of the much lighter and charged Π
states gives strong bounds from complementary searches. La . 'Es¥dsFniF .at#tiFiomDm4 ; z 4 . .
  • i¥#±

i÷#i

E ^ lightest baryon " p "

Li

SY composite Comparison between typical SUSY DM and composite DM:
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SLIDE 10

Meson decay

  • Important consequence of electroweak coupling: allow
mesons to decay, especially the charged ones!
  • Mass flip in final state, due to decay of pseudoscalar bound state
(same for QCD pions.) Gives preferred decay to heaviest SM states:

wo:

0¥⇒¥ne¥I

Γ(Π+ ! ff 0) = G2 F 4⇡ f 2 Πm2 fmΠc2 axial 1 m2 f m2 Π ! h0|jµ axial|Π±i = ifΠpµ
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SLIDE 11

Meson production

  • First signature expected:
Drell-Yan photon production of charged Π
  • To calculate rate, pion
form factor needed at threshold: FV(Q2=4mΠ2)
  • Hard to access at this
momentum on lattice. In QCD, “vector meson dominance” does pretty well… 1
  • 500
500 1000
  • (-q
2) 1/2 (MeV) (q 2) 1/2 (MeV) 0.1 1 10 | Fπ| 2 Breit-Wigner IAM with NLO l6 (arXiv:0812.3270) γ Π+ Π− f ¯ f
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SLIDE 12
  • ()
() mρ = 770 MeV mρ = 255 MeV s = 4m2 π How the picture changes for mρ below threshold:
  • Here, “rho” resonance is below 2π threshold - but it’s also much closer to the
  • threshold. Vector-meson dominance should be reliable, but further study is needed
  • The “dark rho” is very narrow, since decay to ππ is closed. Another (TeV-scale)
state to look for in colliders! π-π scattering amplitude with mπ=140 MeV, for QCD (mπ/mρ~0.18) and for a stealth-DM-like theory (mπ/mρ~0.55) (*note: this is not FV(Q2), it’s a Breit- Wigner model of I=1 π-π scattering.)
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SLIDE 13

Our plan

  • Determine “stealth ρ” decay
constant and calculate decay width
  • Measure “stealth π” FV(Q
2) at space-like momenta from three- point function (pion charge radius)
  • Combine with vector-meson
dominance model to predict FV(4mΠ 2) for collider production

¥ a-

ao•€E÷

Ent

. . (arXiv:0812.3270) FV (Q2) = exp hr2 ΠiQ2 6 + Q4 ⇡ Z ∞ 4m2 Π ds 11(s) s2(s Q2 i✏) ! ρ width, mass pion charge radius
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SLIDE 14

Electroweak precision

  • No T parameter by construction (custodial symm), but S
parameter is an important constraint! Two asymptotic forms of S contribution:
  • 1.5
  • 1.0
  • 0.5
0.5 1.0 1.5 S
  • 1.0
  • 0.5
0.5 1.0 T all (90% CL) ΓZ, σhad, Rl, Rq asymmetries MW, ΓW e & ν scattering APV (PDG 2014) Π3Y (q2) = 1 8 y2v2 y2v2 + 2∆2 ΠV V (q2), Π3Y (q2) ⇡ ✏2 yv2 4M2 ΠLR(q2) = M2 M1 M1 ≈ M2
  • Calculation of strong-
coupling part yields direct bounds on Yukawa couplings (important for asymmetric relic density)
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SLIDE 15

Lattice calculation details

  • Form factor: calculate <π(t)Vμ(t’)π(0)> and <π(t)π(0)>.
Construct appropriate ratio to extract vector-current matrix element.
  • Three vector-current insertion locations, four sources per
config —> 12 Wilson propagators; 500 (pure-gauge) configurations.
  • S-parameter: calculate conserved-local correlators
<VC(x)VL(0)> and <AC(x)AL(0)>. Two source positions, Ls=8.
  • By-products of DWF calculation: Fπ, mass renormalization
(mf/MB).
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SLIDE 16

Resource request

  • Three mass points for domain-wall S parameter calculation; we
expect mild mass dependence, based on experience
  • One point at β=11.5, to test discretization effects (spectroscopy
here shows no significant deviations)
  • We are working on a new fully threaded/vectorized code base,
meant to replace QDP/C; Wilson solver in progress. Up to 2x speed-up in calculations expected, but no benchmarks available yet, and we don’t include this factor above β vol κ mPSL mPS/mV Cost (DWF) Cost (Wilson) Total cost 11.028 323 × 64 0.1554 11.1 0.76 0.61 0.46 1.07 0.15625 9.2 0.69 — 0.68 1.58 0.1568 7.7 0.62 1.28 0.97 2.25 0.1572 6.6 0.55 — 1.36 3.16 0.1575 5.9 0.49 2.55 1.93 4.48 11.5 323 × 64 0.1523 6.1 0.69 0.90 0.68 1.58 Total 5.34 6.08 11.42
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SLIDE 17

Backup slides

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SLIDE 18

Stability of composite dark matter candidates

  • Lightest mesons (Π) can be stabilized by flavor
symmetries* or G-parity**, but then one has to argue against the presence of dimension-5 operators like *M. Buckley and EN, arXiv:1209.6054 **Y. Bai and R. Hill, arXiv:1005.0008 1 Λ ¯ ΨΨH†H instability over lifetime of the universe. Π ∼ ¯ ΨΨ B ∼ ΨΨ...Ψ ND constituents
  • Accidental dark baryon number symmetry provides
automatic stability for B on very long timescales (as long as ND > 2!) E.g. for ND=4, decay through dimension-8(!) 1 Λ4 ΨΨΨΨH†H (nice discussion here: arXiv:1503.08749)
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SLIDE 19

Abundance

Symmetric Asymmetric B B∗ Π Π . . . (more Πs) nD ∼ nB ✓ yv mB ◆2 exp  − mB Tsph
  • e.g., through EW sphalerons
IF EW breaking comparable to EW preserving masses, expect roughly mB . mtechni−B ∼ 1 TeV How much less depends on several factors... If 2 -> 2 dominates thermal annihilate rate and saturates unitarity, expect mB ∼ 100 TeV Unfortunately, this is hard calculation to do using lattice... Griest, Kamionkowski; 1990 Chivukula, Farhi, Barr; 1990 (slide from G. Kribs)
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SLIDE 20

Polarizability on the lattice

  • Measure response to applied
background field E (quadratic Stark shift) 0.000 0.005 0.010 0.015 0.020 0.025 0.030 E 0.89 0.90 0.91 0.92 0.93 E0 SU(4) 0.00 0.01 0.02 0.03 0.04 E 0.61 0.62 0.63 0.64 0.65 0.66 0.67 E0 SU(3) 0.05 EB EB E EB,3c = mB + ✓ 2CF µB 2 8m3 B ◆ |E| 2 + O E4 EB,4c = mB + 2CF|E|2 + O E4
  • SU(3) case simulated for
comparison; complicated by magnetic moment μB
  • Comparable results for SU(3)
and SU(4), in units of mB. ND mP S/mV ˜ mB α ˜ CF α2 ˜ C0 F ˜ µB ˜ µ0 B χ2/dof 4 0.77 0.98204(93) 0.1420(56)
  • 0.089(29)
— — 0.7/3 0.70 0.88805(113) 0.1514(106) -0.142(68) — — 4.8/3 3 0.77 0.69812(51) 0.2829(127) -0.177(45) -6.87(26) 714(103) 3.0/7 0.70 0.61904(59) 0.2829(81)
  • 0.165(24) -5.55(18)
396(78) 13.4/7
  • Technique pioneered by
Detmold, Tiburzi, Walker- Loud (arXiv:1001.1131)
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SLIDE 21

Mass scales

Dynamics SU(4)

ΛD

MPl Dark fermions Mf approx CFT Could arise dynamically

Mf ∼ ΛD

(plot from G. Kribs)
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SLIDE 22

Study of systematic effects

Ê Ê Ê Ê Ê Ê 10.5 11.0 11.5 12.0 12.5 0.95 1.00 1.05 1.10 1.15 beta MêMS0 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 20 30 40 50 60 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 Lêa aM 30 35 40 45 50 55 60 .58 .60 .62 .64 .66 .68 0.70 êa aM Finite-volume effects Cutoff effects
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SLIDE 23 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ * * * * * * ú ú ú ú 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.2 0.4 0.6 0.8 1.0 mPSêmv aM ∗ : M(Nc, J) = Ncm0 + J(J + 1) Nc B + O(1/N 2 c ) ⇧ : M(Nc, J) = Ncm(0) + C + J(J + 1) Nc B + O(1/N 2 c ) PS V spin-0 spin-1 spin-2 spin-1/2 spin-3/2
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SLIDE 24

SU(3) polarizability vs. the PDG

  • Our polarizability differs from the PDG convention:
αE = CF /π
  • Have to compare at
very different masses! Expected scaling is
  • π /ρ
  • α
αE ∼ A mπ + B mB ∼ C + Dm2 π
  • Qualitative agreement
with expected trend! (Can’t fit well - mass range too large.) (LSD, this work) (PDG entry for neutron) (Detmold, Tiburzi, and Walker-Loud, PRD81 (054502), 2010)