Strongly Coupled Dark Matter at the LHC

Strongly Coupled Dark Matter at the LHC Graham Kribs University of Oregon Appelquist et al (LSD Collaboration): 1402.6656; 1503.04203; 1503.04205 GK, Adam Martin, Ethan Neil, Bryan Ostdiek, Tom Tong [in preparation] Lattice for BSM @ BU 21 April 2017

Strongly Coupled Composite Dark Matter Purely from a model perspective 1) Automatic dark matter stability without imposing additional (discrete) symmetries (dark baryon number conservation) 2) Thermalization with Standard Model proceeds through SM mediators (no new mediators required) 3) Direct detection rates elegantly suppressed through higher dimensional operators suppressed by compositeness scale 4) New scales are (technically) natural 5) Abundance can arise from asymmetric or symmetric mechanism (wide range of scales possible*)

Dark Mesons @ LHC A wide class of strongly-coupled theories have interesting meson phenomenology at LHC. Stealthy composite DM theories (all mesons unstable) The main focus of this talk is the meson sector that arises from stealth dark matter theories. The dark matter part will only play a role in choosing fermion representations and motivating the scales relevant to LHC energies. Dark meson DM (some mesons unstable) Bosonic technicolor / induced EWSB Quirky mesons (confining hidden valleys) Vector-like confinement As we ll see, there are continuous connections between stealthy theories and other strongly-coupled models (some that have nothing to do with dark matter). Dictionary dark sector dark fermions dark mesons strongly-coupled SU(Ndark) sector with Nf dark fermions fermions transforming under SU(Ndark) and part of SM low energy description not dark to LHC searches!

Scales in Direct Detection of WIMPs Usual story is that DM has renormalizable interactions with SM mediators, e.g., that are integrated out in the NR effective theory to give, e.g. dimension-6 spin-independent operator But the only scales in town are, MZ 2 1 1 m 2 h

New scale appears in composite DM theories Effective interactions of strongly-coupled dark matter with SM mediators/matter is higher dimensional: 1 ( dark ) n

New scale appears in composite DM theories Effective interactions of strongly-coupled dark matter with SM mediators/matter is higher dimensional: 1 ( dark ) n e.g.: magnetic moment: charge radius: polarizability: µ F µ dark ( )v µ @ F µ ( dark ) 2 ( )F µ F µ ( dark ) 3

fermionic MB MB0 dark baryon e.g.: anomalous magneticµ eutral baryon moment Fµ for magnetic angles) and Nf = 6moment: (blue circles) theories dark versus ss. This quantity shows no systematic separation d six flavor theories. ( )v @ F µ charge radius: µ ( dark )2 eak-neutral dark-matter baryon are presented e that the results are negative (see discussion As in the case of the anomalous moment, our ttle dependence on Nf and little dependence Rate, event / (kg day) 1.2 2 so our result is (0.009... 0.025) fm, substantiallydark less than the observed result. Previous SU(3) composite matter calculations of nucleon structure with Nf = 2 Wil2 Dark matter is a fermionic baryon (dark neutron-like son fermionsstate) [25] yielded similar values hre, neut i = 2 (0.011... 0.023) fm. These results, too, employed relatively heavy underlying quarks. In our case, further studfermionic dark baryon ies with smaller fermion mass can shed light on the range of direct detection allowed values for the mean square charge radius. 1.4 1.6 1.8 2.0 2.2 2 hre,neut i 104 102 100 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 Nf = 2 Nf = 6 XENON100 [1207.5988], 95% CL exclusion 2 10 1 100 101 102 M = MB [TeV] LSD Collaboration; 1301.1693

Stealth Dark Matter SU(N dark ) Dark matter is a scalar baryon of a strongly-coupled with dark fermions transforming under the electroweak group. confining theory Stealth DM Stealth DM e.g.: magnetic moment: charge radius: polarizability: µ F µ dark ( )v µ @ F µ ( dark ) 2 F µ F µ ( dark ) 3 (DM is scalar baryon) (dark custodial SU(2)) (dimension-7 in non-relativistic EFT) This is quite suppressed ( stealthy ) w.r.t. direct detection

Direct Detection Bounds on Stealth Dark Matter Elastic scattering through polarizability nucleon = Z4 A 2 144 4 µ 2 nb (M A F )2 m 6 B R2 [c 2 F ] Depends on (Z,A); does not have A 2 -like (Higgs-like) scaling. For Zenon, we obtain: - ( ) - - - - - - - LEP bound on charged mesons m M B ( ) (GeV) Confluence of collider and direct detection bounds, but for reasons completely different than ordinary (elementary) WIMPs.

LEP Bound (prelude to meson phenomenology) Drell-Yan production of charged pions e e + + d d + can be constrained from, e.g., recasted stau searches: m ± d > 86 GeV that can be translated into a bound on the baryon (DM) mass, for a given m d m d (Roughly m dark baryon & 300 400 GeV for Ndark = 4) Surely LHC can do better in particular by including ρ exchange (to d d as well as SM)

Theories with Dark Mesons Stealthy composite DM theories (all mesons unstable)

Theories with Dark Mesons Stealthy composite DM theories (all mesons unstable) Dark meson DM (some mesons unstable) Quirky mesons (confining hidden valleys) Bosonic technicolor / induced EWSB Vector-like confinement

Model Space References include (not exhaustive!): Bosonic TC / induced EWSB Quirks Vector-like confinement Quirky DM Stealth DM Dark Meson DM Bai-Hill Buckley-Neil SIMP (WZW 3->2) Light/heavy chiral DM

Model Space I 1) Determined by how the dark fermions transform under SM gauge symmetries: SU(2) L U(1) Y U(1) Y only SU(3) c U(1) dark only Bosonic TC / induced EWSB chiral Quirks vector-like vector-like vector-like Vector-like confinement vector-like vector-like Quirky DM chiral Stealth DM vector-like Dark Meson DM Bai-Hill Buckley-Neil vector-like SU(2) only vector-like SIMP (WZW 3->2) Light/heavy chiral DM vector-like chiral

Model Space II 2) Determined by dark fermion masses relative to confinement scale Chiral limit Darkonia m q dark m q dark dark

Model Space II 2) Determined by dark fermion masses relative to confinement scale m q dark dark & EWSB Stealth DM; Bai-Hill & Buckley-Neil DM; Vector-like Confinement; Bosonic TC / induced EWSB

Model Space II 2) Determined by dark fermion masses relative to confinement scale m q dark dark & EWSB Stealth DM; Bai-Hill & Buckley-Neil DM; Vector-like Confinement; Bosonic TC / induced EWSB m q & EWSB dark (Truly) quirky theories; glueball DM

Model Space III: Fermion content Stealth DM Vector-like confinement Bosonic technicolor / (with SU(2) fermion doublets) induced EWSB SU(N dark ) SU(2) L U(1) Y SU(N dark ) SU(2) L U(1) Y SU(N dark ) SU(2) L U(1) Y F 1 N ( 2, 0) F 1 N ( 2, 0) F 1 N ( 2, 0) F 2 F3u F 3d N N ( 2, 0) 1, +1/2 1/2 F 2 N ( 2, 0) F4u F 4d N 1, +1/2 1/2 F4u F 4d N 1, +1/2 1/2 Hybrid Pure vector-like Pure chiral

Stealthy DM versus Other Models 1) Unlike bosonic technicolor / induced EWSB; > condensate hf L F R i 3 dark does not (hugely) break EW symmetry 2) Like bosonic technicolor, there are Higgs interactions with dark fermions yf 1 HF 4d + yf 1 H F 4u + yf 2 HF 3d + yf 2 H F 3u + h.c. that lead to (small) EW breaking contributions to dark fermion masses (and break global symmetries down to ) U(1) dark baryon 3) Unlike bosonic technicolor / induced EWSB & vector-like confinement (and QCD!); (but like some composite Higgs models) Tunable amount of SU(2) L U(1) Y in U(4) V (preserved vector part of global symmetry) SU(2) L U(1) Y in U(4) A (broken axial part of global symmetry)

Dark Fermion Masses in Stealthy Theories F 1 F 2 F3u F 3d F4u F 4d Stealth DM SU(N dark ) N N N N SU(2) L U(1) Y ( 2, 0) ( 2, 0) 1, +1/2 1/2 1, +1/2 1/2 vector-like masses M 12 M 34 Yukawa couplings (chiral masses) y 14 v y 23 v [And u < > d exact custodial SU(2).] Leads to dark fermion mass spectrum: q = ±1/2 q = ±1/2 M 1,2 = M r 2 + y 14y 23 v 2 2 M 12 M 34 2 M M 12 + M 34 2

Dark Mesons Stealthy composite DM theories (all mesons unstable) M 34 dark < M 12 ( yv) dark m q Dark meson DM (some mesons unstable) Quirky mesons (confining hidden valleys) M 12,M 34 yv yv M 12,M 34 Bosonic technicolor / induced EWSB Vector-like confinement

Explore Stealthy Mesons Consider the limit yv M 12,M 34 < dark Light mesons can be represented in non-linear representation = exp a d 0 B @ applei a d ta p d1 0 2 d1 K p d,b 0 2Kd,b f d p 2 + d1 0 d1 p 2K + d,b K p d,a 0 2Kd,a p d2 0 2 d2 p 2K + d,a K 0 d,a p 2 + d2 1 C A K 0 d,b 0 d2 That includes one set of light dark pions, eight dark kaons, another set of heavier dark mesons, and an η (not shown).

Small EW Breaking from Dark Sector The presence of Yukawa couplings induces a mixing v p 2M f d W a µ @ µ a absorbed where y (y 14 + y 23 )/2 (y 14 y 23 )/2 a d which implies a small amount of gets absorbed into the longitudinal component of W: a absorbed yv p 2M 2 +(yv) 2 ( a d1 a d2)+ p 2M p 2M 2 +(yv) 2 Ka d,a K a d,b A rough estimate of the S parameter S 0.03 v/(p 2M) 0.2! 2 N f 4 N dark 4

Dark Pion Decay Like pion decay in QCD where µ ± h0 j µ ±,axial ± i = if p µ ± / V ud y µ µ Lightest dark mesons decay through h0 j µa axial a di = if d p µ ±,t( t),w ± b, t, Z ± d / c axial y, c axial y t, c axial k µ v 0 d / c axial y b, c axial y t, c axial k µ v Where,b( b),h f f d & weak scale c axial = y yv 2 2M p 2 2 + y 2 v 2 b, t, h so dark mesons decay much faster than QCD pions even with c axial 1

0 d decay through anomaly? Unlike QCD, 0 d The decay through the anomaly may or may not occur. The QCD anomaly is proportional to tr[ 3 Q 2 f ] / N c [(2/3) 2 ( 1/3) 2 ] For stealthy dark matter theories, the u -like and d -like fermions have equal and opposite charge tr[ 3 Q 2 f ] / N dark [(1/2) 2 ( 1/2) 2 ] = 0 (While for other theories, an anomaly may be present.) Hence, d 0! is model dependent.

Dark Pion Branching Fractions 0 d ± d 100 100 100 80 80 80 BR% 60 BR% 40 20 60 40 b b c c t + t - t t è Z h BR% 60 40 20 c s t + n t t b W + h 0 100 200 300 400 500 600 700 m P mê P GeV ê GeV 0 100 200 300 400 500 600 700 m P ê GeV FIG. 2: Branching ratios for the neutral (left) and charged (right) dark pions. Completely determined once the pion mass is specified!

Dark ρ s There are also a set of vector resonances a d 0 B @ p 0 d1 2 d1 K d s p 2 + d1 0 d1 p 0 d2 2 d2 K d s p 2 + d2 0 d2 1 C A Meson-meson interactions include g d d d f abc ( a d) µ b dd µ c d g d d d 4 p Ndark As well as kinetic mixing with the EW gauge bosons B B µ F µ d + W W µ F µ 0 d g p Ndark 4 Two types! U(1)-like ( 0 only) SU(2)-like ±,0

Resonance searches for dark ρ s Upon diagonalizing the kinetic terms, leads to ρ interactions with SM fermions gf µ( d ) µ f which leads to new resonances, e.g., q `+ d q ` The going rate for on-resonant ρ production and decay (q q! d! `+` ) m d 1 tot d s ( d! q q) ( d! `+` ) critically depends on the total width tot d

Resonance searches for dark ρ s Two cases: m d m d < 0.5 m d m d > 0.5 The strong 2-body decay The strong 2-body decay d! d d d! d d is open, dominates, and leads to a wide resonance: ( d! d d ) m d = g2 d d d N d 96 0.25 1 1 4m 2 d m 2 d 4m 2 d m 2 d 3/2 3/2 is closed. ρ decay is narrow and decays to SM modes dominate.

Resonance searches for dark ρ s m d m d 100

Dark pion production Production of charged pions proceeds through Drell-Yan q + d q d as well as d exchange q + d ( ± d ) d q d ( 0 d ) p Ndark The couplings are: g g d d d 4 4 p Ndark m d If < 0.5, dark pions produced resonantly, providing a clear target of opportunity! m d

Dark pion production m d m d 100

Signals of dark pion production m d < (m t + m b ) When + q q d + d d One can recast new physics searches involving final state tau s, e.g. EW gauginos @ ATLAS: Suggests charged dark pions less than about 150-180 GeV are ruled out.

Signals of dark pion production When m d & (m W + m h ) q d + d W + h q d h W There are no optimal searches for this type of final state. However, same-sign lepton searches (again, SUSY inspired) have sensitivity:

Constraints on dark pion production Thus far, we have found: Strong constraints on Weak constraints on pp! d! `+` pp! d! d d when m d m d > 0.5

Gaps in Searches? Optimal searches do not exist. In some cases, sensitivity (from other searches) not even clear (use of BDTs, etc). For example, when (m t + m b ) < m d < (m W + m h ) q q d + d d t b b t Smells like charged Higgs pair production, but with a much larger cross section than Drell-Yan. (No searches easily recast yes we thought about t-t-h!)

Conclusions Highly motivated theories beyond the Standard Model involving new strongly-coupled dark sectors are ripe for exploration. These dark sectors can have particles near EWSB scale and are relevant to a a wide class of theories: - dark baryonic dark matter theories (i.e., Stealth Dark Matter) - dark meson dark matter theories (i.e., Buckley-Neil dark SU(2) mesons) models of EWSB (bosonic technicolor / strongly-coupled induced EWSB) - Specifics in this talk were motivated by Stealth Dark Matter. This theory provides an existence proof of the power of compositeness to suppress leading interactions with matter, allowing dark matter to be as light as several hundred GeV. Outstanding opportunities for high(er) luminosity searches at LHC digging into the several hundred GeV region with searches involving electroweak particles that may well yield amazing discoveries!