Composite Dark Matter

George T. Fleming Yale University E. Rinaldi LLNL

Sakata-Hirata Hall, Nagoya University March 4, 2015

Lattice Strong Dynamics Collaboration Xiao-Yong Jin [LSD collab., Phys. Rev. D88 (2013) 014502] [LSD collab., Phys. Rev. D89 (2014) 094508] + LSD collab., in preparation (x2) Outline

• Motivations for searches of composite dark matter

• Features of strongly-coupled composite dark matter

• Searches for a class of models interesting for phenomenology

• Importance of lattice ﬁeld theory simulations

• Lower bounds on composite dark matter models BSM Is Out There

• Discovery of SM-like Higgs boson doesn’t mean BSM physics is dead:

➡ What is the meaning of the hierarchy problem and naturalness?

➡ What solves the strong CP problem?

➡ What explains the matter-antimatter asymmetry? BSM Is Out There

• Discovery of SM-like Higgs boson doesn’t mean BSM physics is dead:

➡ What is the meaning of the hierarchy problem and naturalness?

➡ What solves the strong CP problem?

➡ What explains the matter-antimatter asymmetry?

➡ What is dark matter? Can it couple to the standard model? Is the mass scale related to the EW Higgs mechanism? Is it self-interacting? The gravity of Dark Matter

?????? New We Are Here Physics!! (QCD, EM, SM, etc.)

How do we know Dark Matter is there? Rotational velocity Curves of Galaxies

Gravitational Lensing

Cosmological Backgrounds The gravity of Dark Matter

?????? New We Are Here Physics!! (QCD, EM, SM, etc.) [Planck and ESA]

How do we know Dark Matter is there? Rotational velocity Curves of Galaxies

Gravitational Lensing

Cosmological Backgrounds The gravity of Dark Matter

?????? New We Are Here Physics!! (QCD, EM, SM, etc.) [Planck and ESA]

How do we know Dark Matter is there? Rotational velocity Curves of Galaxies

Gravitational Lensing Gravitational Interactions Cosmological Backgrounds Problems? Problems?

• Number of observed dwarf galaxies is inconsistent with predictions from dark matter simulations “Missing Satellites” Problems?

• Number of observed dwarf galaxies is inconsistent with predictions from dark matter simulations “Missing Satellites”

• Predicted dwarf galaxies are too dense “Too Big To Fail” Problems?

• Number of observed dwarf galaxies is inconsistent with predictions from dark matter simulations “Missing Satellites”

• Predicted dwarf galaxies are too dense “Too Big To Fail”

• Density proﬁles of dwarf galaxies is more cored than in simulations “Cusp vs. Core” Problems?

• Number of observed dwarf galaxies is inconsistent with predictions from dark matter simulations “Missing Satellites”

• Predicted dwarf galaxies are too dense “Too Big To Fail”

• Density proﬁles of dwarf galaxies is more cored than in simulations “Cusp vs. Core”

ameliorated by Self-Interacting Dark Matter Self-Interacting Dark Matter • In ΛCDM, galactic sub-halos have very dense, cuspy cores.

• Any dwarf galaxies residing in a cuspy sub-halo will be smaller and dimmer than in a sub-halo with more uniform density.

• Larger Milky Way and Andromeda dwarf galaxies are too bright for their expected sub-halos, if those sub-halos are made of non-interacting dark matter (ΛCDM). Self-interacting dark matter (SIDM) will make sub-halo cores less dense, enabling larger dwarf galaxies.

2 1 1 (v )/M 0.5 – 50 cm g ,v 10 – 100 km s rms ⇠ rms ' O. D. Elbert et al., arXiv:1412.1477 [astro-ph.GA] Self-Interacting Dark Matter

Strongly-Coupled Composite Dark Matter

interactions with SM particles that can evade current experimental constraints View from Snowmass (I)

R-parity NMSSM MSSM violating

WIMPless DM Supersymmetry Hidden Sector DM Gravitino DM mSUGRA Self-Interacting DM pMSSM

Q-balls Techni- baryons Dark Photon R-parity Conserving Dirac Asymmetric DM DM

Light Extra Dimensions Dynamical Force Carriers DM

Warm DM Solitonic DM UED DM

Sterile Neutrinos Quark 6d Warped Extra Nuggets Dimensions 5d

RS DM T-odd DM Axion DM ?

Little Higgs QCD Axions

Axion-like Particles T Tait Littlest Higgs

Snowmass 2013: The Cosmic Frontier [arXiv:1401.6085]

Where is composite dark matter? View from Snowmass (I)

R-parity NMSSM MSSM violating

WIMPless DM Supersymmetry Hidden Sector DM Gravitino DM mSUGRA Self-Interacting DM pMSSM

Q-balls Techni- baryons Dark Photon R-parity Conserving Dirac Asymmetric DM DM

Light Extra Dimensions Dynamical Force Carriers DM

Warm DM Solitonic DM UED DM

Sterile Neutrinos Quark 6d Warped Extra Nuggets Dimensions 5d

RS DM T-odd DM Axion DM ?

Little Higgs QCD Axions

Axion-like Particles T Tait Littlest Higgs

Snowmass 2013: The Cosmic Frontier [arXiv:1401.6085]

Where is composite dark matter? View from Snowmass (II)

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

! !42 CRESST !6 10 ZEPLIN-III (2012) 10 SuperCDMS !43 CDMS II Ge (2009) !7 10 EDELWEISS (2011) 10 SNOLAB SuperCDMS Soudan section section N EU TR Xenon100 (2012) !44 IN DarkSide 50 !8 10 O 10 7Be C TT LUX OHE SCA ER cross cross R NT I Neutrinos E 8 N !45 B G PICO250-CF3I !9 10 Neutrinos 10 Xenon1T

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

E WIMP HER WIMP 10 (Red&circle)&SUSY&MSSM& CO 10 RINO &&&&&MSSM:&Pure&Higgsino&& NEUT !49 !13 10 &&&&&MSSM:&A&funnel& Atmospheric and DSNB Neutrinos 10 &&&&&MSSM:&BinoEstop&coannihila7on& !50 &&&&&MSSM:&BinoEsquark&coannihila7on& !14 10 & 10 1 10 100 1000 104 WIMP Mass GeV c2

Snowmass 2013: The Cosmic Frontier [arXiv:1401.6085] ! " # Partial wave unitarity? Where is composite dark matter? View from Snowmass (II)

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

! !42 CRESST !6 10 ZEPLIN-III (2012) 10 SuperCDMS !43 CDMS II Ge (2009) !7 10 EDELWEISS (2011) 10 SNOLAB SuperCDMS Soudan section section N EU TR Xenon100 (2012) !44 IN DarkSide 50 !8 10 O 10 7Be C TT LUX Dark SU(3) Baryon OHE SCA ER cross cross R NT I Neutrinos E 8 N !45 B G PICO250-CF3I !9 10 Neutrinos 10 Xenon1T

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

Snowmass 2013: The Cosmic Frontier [arXiv:1401.6085] ! " # Partial wave unitarity? Where is composite dark matter? Strongly-coupled composite dark matter

• Dark matter is a composite object

• Composite object is electroweak neutral

• Constituents can have electroweak charges

• Dark matter is stable thanks to a global symmetry (like baryon number) Strongly-coupled composite dark matter

• Dark matter is a composite object Akin to a technibaryon

• Composite object is electroweak neutral

• Constituents can have electroweak charges

• Dark matter is stable thanks to a global symmetry (like baryon number) Strongly-coupled composite dark matter

• Dark matter is a composite object Akin to a technibaryon

• Composite object is electroweak neutral Suppressed interactions with SM

• Constituents can have electroweak charges

• Dark matter is stable thanks to a global symmetry (like baryon number) Strongly-coupled composite dark matter

• Dark matter is a composite object Akin to a technibaryon

• Composite object is electroweak neutral Suppressed interactions with SM

• Constituents can have electroweak charges Mechanisms to provide observed relic abundance • Dark matter is stable thanks to a global symmetry (like baryon number) Strongly-coupled composite dark matter

• Dark matter is a composite object Akin to a technibaryon

• Composite object is electroweak neutral Suppressed interactions with SM

• Constituents can have electroweak charges Mechanisms to provide observed relic abundance • Dark matter is stable thanks to a global symmetry (like baryon number) Guaranteed in many models What do we have in mind? • In general we think about a new strongly-coupled gauge sector like QCD with a plethora of composite states in the spectrum

• Dark fermions have dark color and also have electroweak charges

• Depending on the model, dark fermions have electroweak breaking masses (chiral), electroweak preserving masses (vector) or a mixture

• A global symmetry of the theory naturally stabilizes the dark baryonic composite states (e.g. neutron) What do we have in mind? • In general we think about a new strongly-coupled gauge sector like QCD with a plethora of composite states in the spectrum

• Dark fermions have dark color and also have electroweak charges

• Depending on the model, dark fermions have electroweak breaking masses (chiral), electroweak preserving masses (vector) or a mixture

• A global symmetry of the theory naturally stabilizes the dark baryonic composite states (e.g. neutron) we construct a minimal model with these features “How dark is Dark Matter?”

Interactions of neutral object with photons + Higgs

• dimension 4 ➥ Higgs exchange

µ⌫ (¯ )Fµ⌫ • ➥ dimension 5 magnetic dipole ⇤dark

µ⌫ (¯)vµ@⌫ F • dimension 6 ➥ charge radius 2 ⇤dark

µ⌫ (¯)Fµ⌫ F • dimension 7 ➥ polarizability 3 ⇤dark “How dark is Dark Matter?”

Interactions of neutral object with photons + Higgs

• dimension 4 ➥ Higgs exchange

µ⌫ (¯ )Fµ⌫ • ➥ dimension 5 magnetic dipole ⇤dark

µ⌫ (¯)vµ@⌫ F • dimension 6 ➥ charge radius 2 ⇤dark

µ⌫ (¯)Fµ⌫ F • dimension 7 ➥ polarizability 3 ⇤dark “How dark is Dark Matter?”

Interactions of neutral object with photons + Higgs

• dimension 4 ➥ Higgs exchange

µ⌫ (¯ )Fµ⌫ • ➥ dimension 5 magnetic dipole ⇤dark

µ⌫ (¯)vµ@⌫ F • dimension 6 ➥ charge radius 2 ⇤dark

µ⌫ (¯)Fµ⌫ F • dimension 7 ➥ polarizability 3 ⇤dark “How dark is Dark Matter?”

Interactions of neutral object with photons + Higgs

• dimension 4 ➥ Higgs exchange

µ⌫ (¯ )Fµ⌫ • ➥ dimension 5 magnetic dipole ⇤dark

µ⌫ (¯)vµ@⌫ F • dimension 6 ➥ charge radius 2 ⇤dark

µ⌫ (¯)Fµ⌫ F • dimension 7 ➥ polarizability 3 ⇤dark Coupling Dark Baryons to SM

ψ σ (ψψ) (ψψ) F Mag. Moment Charge Radius Polarizability dim. 5 dim. 6 dim. 7

Odd N ✔ ✔ ✔ No Flavor Sym.

Odd N ✔ Flavor Sym

Even N ✔ ✔ No Flavor Sym.

Even N ✔ Flavor Sym. [LSD collab., Phys. Rev. D88 (2013) 014502] MagneticMagnetic moment moment anddominates for MB & 25 GeV —Dashed lines show charge radius r 2 contribution to full rate —Suppressed by 1/M2 relative to magnetic moment contribution charge radius of BDM ⌦ ↵ SU(3) model: DM is neutral baryon with spin 1/2 104 102

100

2 XENON100 results 10 day) • Need non-perturbative · 2 4 only sensitive to r calculation of form-factors 10 6 10 for MB . 0.5 TeV for DM composite object ⌦ ↵ 8 10

Rate, event10 / (kg 10 • Negligible dependence 12 ( . ) 10 Estimate MB . 0 01 TeV on constituent mass and Nf =2 O 14 Nf =6 10 sensitive to polarizability number of ﬂavors XENON100 [1207.5988], 95% CL exclusion 16 10 2 1 0 1 2 10 10 10 10 10 M = MB [TeV] • Magnetic moment dominates for masses  = 0 automatically for SU(N) gauge theories with even N... > 25GeV Composite dark matter on the lattice Theory Seminar, 24 March 2014 13 / 20 [LSD collab., Phys. Rev. D88 (2013) 014502] MagneticMagnetic moment moment anddominates for MB & 25 GeV —Dashed lines show charge radius r 2 contribution to full rate —Suppressed by 1/M2 relative to magnetic moment contribution charge radius of BDM ⌦ ↵ SU(3) model: DM is neutral baryon with spin 1/2 104 102

100

2 XENON100 results 10 day) • Need non-perturbative · 2 4 only sensitive to r calculation of form-factors 10 6 10 for MB . 0.5 TeV for DM composite object ⌦ ↵ 8 10

Rate, event10 / (kg 10 • Negligible dependence 12 ( . ) 10 Estimate MB . 0 01 TeV on constituent mass and Nf =2 O 14 Nf =6 10 sensitive to polarizability number of ﬂavors XENON100 [1207.5988], 95% CL exclusion 16 10 2 1 0 1 2 10 10 10 10 10 M = MB [TeV] • Magnetic moment dominates for masses  = 0 automatically for SU(N) gauge theories with even N... without magnetic > 25GeV moment contribution Composite dark matter on the lattice Theory Seminar, 24 March 2014 13 / 20 [LSD collab., Phys. Rev. D88 (2013) 014502] MagneticMagnetic moment moment anddominates for MB & 25 GeV —Dashed lines show charge radius r 2 contribution to full rate —Suppressed by 1/M2 relative to magnetic moment contribution charge radius of BDM ⌦ ↵ SU(3) model: DM is neutral baryon with spin 1/2 104 102

100

2 XENON100 results 10 day) • Need non-perturbative · 2 4 only sensitive to r calculation of form-factors 10 6 10 for MB . 0.5 TeV for DM composite object ⌦ ↵ 8 10

Rate, event10 / (kg 10 • Negligible dependence 12 ( . ) 10 Estimate MB . 0 01 TeV on constituent mass and Nf =2 O 14 Nf =6 10 sensitive to polarizability number of ﬂavors XENON100 [1207.5988], 95% CL exclusion 16 10 2 1 0 1 2 10 10 10 10 10 M = MB [TeV] • Magnetic moment dominates for masses  = 0 automatically for SU(N) gauge theories with even N... without magnetic > 25GeV moment contribution Excludes dark matter Composite dark matter on the latticemass below 10 TeV! Theory Seminar, 24 March 2014 13 / 20 [LSD collab., in preparation] “Stealth Dark Matter” model

• Let’s focus on a SU(N) dark gauge Field SU(N)D (SU(2)L, Y ) Q will be identiﬁed with U(1)Y , and one U(1) will be iden- u tiﬁed with dark baryon number. The total fermionic con- F1 +1/2 sector with N=4 F1 = N (2, 0) tent of the model is therefore 8 Weyl fermions that pair F d ! 1/2 ! 1 u up to become 4 Dirac fermions in the fundamental or F2 +1/2 F2 = N (2, 0) anti-fundamental representation of SU(N)D with electric • Let dark fermions interact with the F d ! 1/2 ! Q T + Y = 1/2 2 charges of 3,L . We use the notation u ⌘ ± u d u F3 N (1, +1/2) +1/2 where the superscript u and d (as in F , F and later , SM Higgs and obtain current/chiral d u d F d N (1, 1/2) 1/2 , , ) to denote a fermion with electric charge of 3 masses u Q =1/2 and Q = 1/2 respectively. F4 N (1, +1/2) +1/2 d The fermion kinetic terms in the Lagrangian are given F4 N (1, 1/2) 1/2 by • Let’s introduce vector-like masses

µ j† µ j j for dark fermions that do not break TABLE I. Fermion particle content of the composite dark matter = iF †¯ Di,µFi + iF ¯ D F , L i i i,µ i model. All ﬁelds are two-component (Weyl) spinors. SU(2)L i=1,2 i=3,4;j=u,d EW symmetry refers to the standard model electroweak gauge group, and Y is X X (1) the hypercharge. The electric charge Q = T3 + Y for the fermion where the covariant derivatives are components is shown for completeness. D @ igW aa/2 ig Gb tb (2) 1,µ ⌘ µ µ D µ D @ igW aa/2+ig Gb tb⇤ (3) yet have the ability to simulate on the lattice. Naive di- 2,µ ⌘ µ µ D µ j j b b mensional analysis applied to the annihilation rate suggests D3,µ @µ ig0Y Bµ igDG t (4) > ⌘ µ the dark matter mass scale should be 10-100 TeV, but a j j b b D @ ig0Y B + ig G t ⇤ (5) more precise estimate is not possible⇠ at this time. In any 4,µ ⌘ µ µ D µ case, for dark matter with mass below this value, there is with the interactions among the electroweak group and the an underproduction of dark matter through the symmet- u d b new SU(N)D. Here Y =1/2, Y = 1/2 and t ric thermal relic mechanism, and so this does not restrict are the representation matrices for the fundamental N of consideration of dark matter mass scales between the elec- SU(N) . troweak scale up to this thermal abundance bound. D The vector-like mass terms allowed by the gauge sym- metries are

CONSTRUCTING A VIABLE MODEL M ✏ F iF j M u F uF d +M d F dF u +h.c., (6) L 12 ij 1 2 34 3 4 34 3 4 12 [placeholder for a description of how a viable model where ✏12 ✏ud = 1= ✏ and the relative minus with interactions with the Higgs can be constructed while signs between⌘ the mass terms have been chosen for later satisfying the various (gross) experimental constraints] convenience. The mass term M12 explicitly breaks the [SU(2) U(1)]2 global symmetry down to the diagonal ⇥ We consider a new, strongly-coupled SU(N)D gauge SU(2)diag U(1) where the SU(2)diag is identified with ⇥ u,d group with fermionic matter in the vector-like representa- SU(2)L. The mass terms M34 explicitly break the re- tions shown in Table I. maining [SU(2) U(1)]2 down to U(1) U(1) where one ⇥ ⇥ of the U(1)’s is identified with U(1)Y . (In the special case u d This is not the only possible choice for the charges, but when M34 = M34, the global symmetry is accidentally en- the requirement for the presence of Higgs Yukawa cou- hanced to SU(2) U(1), where the global SU(2) acts as a plings, along with extremely strong bounds on the ex- custodial symmetry.)⇥ Thus, after weakly gauging the elec- istence of stable fractionally-charged particles based on troweak symmetry and writing arbitrary vector-like mass searches for rare isotopes [? ], greatly constrains the num- terms, the unbroken flavor symmetry is thus U(1) U(1). ⇥ ber of possible models. Electroweak symmetry breaking mass terms arise from coupling to the Higgs field H that we take to be in the (2, +1/2) representation. They are given by DARK FERMION INTERACTIONS AND MASSES u i j d d u y14✏ijF1H F4 + y14F1 H†F4 u,d L d i j d u · u The fermions Fi transform under a global U(4) y23✏ijF2H F3 y23F2 H†F3 + h.c., (7) U(4) flavor symmetry that is broken to [SU(2) U(1)⇥]4 · by the weak gauging of the electroweak symmetry.⇥ From where again the relative minus signs are chosen for later this large global symmetry, one SU(2) (diagonal) sub- convenience. After electroweak symmetry breaking, H = group will be identified with SU(2) , one U(1) subgroup (0 v/p2)T , with v 246 GeV. Inserting the vev L ' [LSD collab., in preparation] “Stealth Dark Matter” model

µ j† µ j j for dark fermions that do not break TABLE I. Fermion particle content of the composite dark matter = iF †¯ Di,µFi + iF ¯ D F , L i i i,µ i model. All ﬁelds are two-component (Weyl) spinors. SU(2)L i=1,2 i=3,4;j=u,d EW symmetry refers to the standardu modeli j electroweakd d gauge group,u and Y is X X + y14✏ijF1H F4 + y14F1 H†F4 (1) the hypercharge.L The electric charge Q = T ·+ Y for the fermion d i j d u 3 u where the covariant derivatives are components isy shown23✏ijF for2H completeness.F3 y23F2 H†F3 + h.c. · D @ igW aa/2 ig Gb tb (2) 1,µ ⌘ µ µ D µ D @ igW aa/2+ig Gb tb⇤ (3) yet have the ability to simulate on the lattice. Naive di- 2,µ ⌘ µ µ D µ j j b b mensional analysis applied to the annihilation rate suggests D3,µ @µ ig0Y Bµ igDG t (4) > ⌘ µ the dark matter mass scale should be 10-100 TeV, but a j j b b D @ ig0Y B + ig G t ⇤ (5) more precise estimate is not possible⇠ at this time. In any 4,µ ⌘ µ µ D µ case, for dark matter with mass below this value, there is with the interactions among the electroweak group and the an underproduction of dark matter through the symmet- u d b new SU(N)D. Here Y =1/2, Y = 1/2 and t ric thermal relic mechanism, and so this does not restrict are the representation matrices for the fundamental N of consideration of dark matter mass scales between the elec- SU(N) . troweak scale up to this thermal abundance bound. D The vector-like mass terms allowed by the gauge sym- metries are

µ j† µ j j for dark fermions that do not break TABLE I. Fermion particle content of the composite dark matter = iF †¯ Di,µFi + iF ¯ D F , L i i i,µ i model. All ﬁelds are two-component (Weyl) spinors. SU(2)L i=1,2 i=3,4;j=u,d EW symmetry refers to the standardu modeli j electroweakd d gauge group,u and Y is X X + y14✏ijF1H F4 + y14F1 H†F4 (1) the hypercharge.L The electric charge Q = T ·+ Y for the fermion d i j d u 3 u where the covariant derivatives are components isy shown23✏ijF for2H completeness.F3 y23F2 H†F3 + h.c. · D @ igW aa/2 ig Gb tb (2) 1,µ ⌘ µ µ D µ D @ igW aa/2+ig Gb tb⇤ (3) yet have the ability to simulate on the lattice. Naive di- 2,µ ⌘ µ µ D µ i j u u d d d u j j b b M12✏ijF1mensionalF2 M34 analysisF3 F4 applied+ M34 toF3 theF4 annihilation+ h.c. rate suggests D3,µ @µ ig0Y Bµ igDG t (4) L > ⌘ µ the dark matter mass scale should be 10-100 TeV, but a j j b b D @ ig0Y B + ig G t ⇤ (5) more precise estimate is not possible⇠ at this time. In any 4,µ ⌘ µ µ D µ case, for dark matter with mass below this value, there is with the interactions among the electroweak group and the an underproduction of dark matter through the symmet- u d b new SU(N)D. Here Y =1/2, Y = 1/2 and t ric thermal relic mechanism, and so this does not restrict are the representation matrices for the fundamental N of consideration of dark matter mass scales between the elec- SU(N) . troweak scale up to this thermal abundance bound. D The vector-like mass terms allowed by the gauge sym- metries are

• yh Need to non-perturbatively mf (h)=m + evaluate the σ-term of the dark p2 baryon (scalar nuclear form v @ mf (h) yv factor) ↵ = 1 ⌘ m @ h p  f h=v 2m + yv • Effective Higgs coupling non- 5 ¥10-43 MPS MV=0.77 L trivial with mixed chiral and 2 !=0.64

cm -43

H 1 ¥10 vector-like masses 5 ¥10-44 ê !=0.16 section 1 ¥10-44 -45

• Model-dependent answer for the cross 5 ¥10 !=0.04 cross-section in this channels 1 ¥10-45

nucleon -46

- 5 ¥10

• DM !=0.01 A non-negligible vector mass is 1 ¥10-46 needed to evade direct 10 50 100 500 1000 detection bounds mB GeV

H L [LSD collab., Phys. Rev. D89 (2014) 094508] Higgs exchange cross section in Stealth DM

cm -43

H 1 ¥10 vector-like masses 5 ¥10-44 ê !=0.16 section 1 ¥10-44 -45

• Model-dependent answer for the cross 5 ¥10 !=0.04 cross-section in this channels 1 ¥10-45

nucleon -46

- 5 ¥10

• DM !=0.01 A non-negligible vector mass is 1 ¥10-46 needed to evade direct 10 50 100 500 1000 detection bounds mB GeV

LEP bound on charged pseudoscalar mesons H L LHC could be do better here. LUX bound [Phys. Rev. Lett. 112 (2014)] Electromagnetic polarizability

• remove magnetic dipole moment:

p p0 • lightest stable baryon is a boson with S=0 q = k0 k = p p0 ` ` q • remove charge radius:

• 2 ﬂavors with degenerate k k0 masses mu=md k + ` Nucleus Nucleus • polarizability can not be removed = ¯ F µ⌫ F OF CF µ⌫ Electromagnetic polarizability

• remove magnetic dipole moment: p p0

• lightest stable baryon is a boson with S=0 q = k0 k = p p0 • remove charge radius: ` ` q

• 2 ﬂavors with degenerate masses mu=md

k • polarizability cank not be 0 removed k + ` = ¯ F µ⌫ F NucleusOF CF µ⌫Nucleus Electromagnetic polarizability

• remove magnetic dipole moment: p p0

• lightest stable baryon is a boson with S=0 Lattice q = k0 k = p p0 • remove charge radius: ` ` q

• 2 ﬂavors with degenerate masses mu=md

k • polarizability cank not be 0 removed k + ` = ¯ F µ⌫ F NucleusOF CF µ⌫Nucleus Electromagnetic polarizability

• remove magnetic dipole moment: p p0

• lightest stable baryon is a boson with S=0 q = k0 k = p p0 • remove charge radius: ` ` q • 2 ﬂavorsNuclear with degenerate masses mu=md Physics k • polarizability cank not be 0 removed k + ` = ¯ F µ⌫ F NucleusOF CF µ⌫Nucleus Importance of lattice ﬁeld theory techniques

• lattice simulations are naturally suited for models where dark fermion masses are comparable to the conﬁnement scale Importance of lattice ﬁeld theory techniques

• lattice simulations are naturally suited for models where dark fermion masses are comparable to the conﬁnement scale

• controllable systematic errors and room for improvement Importance of lattice ﬁeld theory techniques

• lattice simulations are naturally suited for models where dark fermion masses are comparable to the conﬁnement scale

• controllable systematic errors and room for improvement

• Naive dimensional analysis and EFT approaches can miss important non-perturbative contributions Importance of lattice ﬁeld theory techniques

• lattice simulations are naturally suited for models where dark fermion masses are comparable to the conﬁnement scale

• controllable systematic errors and room for improvement

• Naive dimensional analysis and EFT approaches can miss important non-perturbative contributions

• NDA is not precise enough when confronting experimental results and might not work for certain situations Importance of lattice ﬁeld theory techniques

• lattice simulations are naturally suited for models where dark fermion masses are comparable to the conﬁnement 2 2

scale Uncorrelated Pauli-paired stituentsresult. are uncorrelated, To this end, we the perform polarizabilities lattice are calculations expected for both E E E to bethe comparable. SU(3) and However, SU(4) baryon if alternate polarizabilities flavors tend to quantify to this u u form pairs based on their Pauli statistics, the 4-fermion d effect. • controllable systematic3-color errors and room for improvementbaryon polarizability would be derivative suppressed com- d d Polarizability and Direct Detection – The polarizabil- d pared to the 3-fermion baryon (i.e. two dipoles vs. one ity operator can be written as an effective operator of the dipole and one charge). Thus, the QCD, 3-fermion NDA • u estimateform could be significantly different than the 4-fermion Naive dimensional analysisu u and EFT approachesd can µ⌫ 4-color result. To this end, we do latticeF = C calculationsF †F F ofµ both⌫ , SU(3) (1) miss important non-perturbatived d contributionsu d and SU(4) baryon polarizabilitiesO to quantify this effect in additionwhere to calculating is the scalar the relevant composite cross-section DM field curves. and Fµ⌫ is the ↵33 ↵44 ↵33 ↵44 CF ⇠ CF CF CF standard electromagnetic field strength tensor. This is a ⇠ Polarizability and Direct Detection– The polarizability • NDA is not precise enough when confronting operatortwo-photon can be written vertex, as an so effective that the operator scattering of off the of form nuclei will involve a virtual photon loop.µ⌫ Because this operator is in- experimentalFIG. 1. Fix results notation inand plot frommight to CnotF Visualizations work for of certain F = CF †F Fµ⌫ , (1) simplifiedFIG. 1. Visualizations models comparing of simplified SU(3) and models SU(4) comparing baryon polariz- SU(3) and duced at aO high scale (roughly the dark confinement scale situationsabilities.SU(4) In baryon the case polarizabilities. where charged constituents In the case are where uncorrelated charged con-where⇤D is theM scalar), it compositeis expected dark to generate matter field. other This interactions withinstituents the baryon, are uncorrelated the size of within the polarizabilities the baryon, the are size expected of the to polar-is a two-photonwith⇠ SM particles vertex, so when that the the scattering appropriate off effective of nuclei field the- beizabilities comparable. are For expected the case to in be which comparable. opposite flavorsFor the are case Pauli- in whichwill involveory matching a virtual and photon running loop. down Because to the this nuclear operator scale are pairedopposite (a-la flavorsdipoles), are the Pauli-paired SU(4) baryon (a` la polarizability dipoles), the would SU(4) be baryonis inducedcarried at outa high [22–25]; scale (roughly in fact, the an explicitdark confinement treatment for the suppressedpolarizability compared would to be the suppressed SU(3) polarizability. compared to the SU(3) polar- scale ⇤polarizabilityD M), it operator is expected is to given generate in [26]. other Although interac- the ef- izability. ⇠ tions withfects SM of the particles additional when the induced appropriate operators effective are not field negligible theory matching and running down to the nuclear scale is in general, we find that they are small compared to the un- Nc even. The dominant modes of interaction with the stan- carried out [20–23]; in fact, an explicit treatment for the po- dard model are the polarizability operator, and direct Higgs larizabilitycertainties operator (particularly is given in from [24]. nuclear Although physics) the effects in the lead- Higgs interaction has no adjustable parameters, but rather ing interaction through Eq. 1, and we will therefore omit bosonis completely exchange. determined The latter was by the studied strong in somedynamics detail once in theof these induced operators are not negligible in general, we [19], placing bounds on the allowed dark Higgs couplings. them here. gauge group and matter content are specified. find that they are small compared to the uncertainties (par- In this work we study the polarizability, which unlike the ticularlyFrom from nuclearthe interaction physics) shown in the leading above, interaction the coherent DM- HiggsSU(4) interaction baryons has and no adjustable polarizabilities parameters, – A but full rather construc-throughnucleus Eq. 1, scattering and we will cross therefore section omit (per them nucleon) here. is given by tion of the stealth DM model is given in [20]; here we is completely determined by the strong dynamics once the From the interaction shownµ2 above, the coherent dark gaugebriefly group summarize and matter the content relevant are specified. details. The dark sectormatter-nucleus scattering crossn section (perA 2 nucleon) is 2 CF fF , (2) consistsSU(4) baryons of an unbroken and polarizabilities SU(4) gauge – A theory, full construc- which con-given by ' ⇡A tains baryonic bound states made up of four constituent D E tion of the stealth dark matter model is given in [? ]; here where µn = mn2m/(mn + m), A is the mass number µn A 2 wefermions. briefly summarize The DM thecandidate relevant itself details. is made The dark up of sector two pairs of the target nucleus, andCF f the angular, brackets(2) represent ' ⇡A2 F consistsof fermions of an unbrokenwhich are SU(4) degenerate gauge in theory, mass which and carry con- equal the momentum-averaged form factors for heavy DM can- D E tainsbut baryonic opposite boundelectric states charges made of up1/ of2; four the symmetry constituent prop-where µn = mnm/(mn + m), the angular brackets ± didates in a given experiment [26]. fermions.erties of The this dark candidate matter leave candidate the electromagnetic itself is made up polariz- of representThe the primary momentum-averaged source of systematic form factors uncertainty for heavy in deter- twoability pairs as of the fermions dominant which interaction are degenerate with photons. in mass and dark mattermining candidates the cross in section a given will experiment, be the method used for eval- carry equal but opposite electric charges of 1/2; the sym- Emax A The primary quantity in question is± the strength of the 2 uating the non-perturbative nuclear matrix2 element, fF = metry properties of this candidate leave the electromag- f = µ⌫ dER Acc(ER)g(vmin[ER])f (ER), (3) baryon polarizability in units of the DM (baryon) mass, A F Fµ⌫ A . Due to its long-range nature, this matrix netic polarizability as the dominant interaction with pho- h i Emin from which we can derive an exclusion curve. Previous es- elementh | must| bei determined by a non-perturbative nuclear tons. (E ) timates have led to direct-detection cross sections on the or-Acc structureR is the calculation. acceptance of Various a given attempts experiment to estimate and these The primary48 quantity2 in question is the strength of the g(vmin) is the integrated dark matter velocity distribution der of 10 cm [16], approaching the interaction strength matrix elements have been performed with varying lev- baryon polarizability in units of the dark matter (baryon) as a function of the minimum velocity for a given recoil at which background neutrinos are expected to contami- els of complexity in a perturbative setup [26–28], but this mass, from which we can derive an exclusion curve. energy, ER. Estimatesnate the from DM recoil QCD havesignal. been However, made previously these estimates to be rely Thematrix primary element source has of systematic nontrivial uncertainty excited-state in structuresdeter- that on48 na¨ıve2 dimensional analysis (NDA), which has uncon- 10 cm [15], around the cross-sections when back- mininglikely the cross-section require a fully will non-perturbative be the method used treatment. for eval- This ma- trolled uncertainties. trix element is similar to those needed for double-betaA de- ground neutrinos are expected to contaminate the dark mat- uating the non-perturbative nuclear matrix element fF = µ⌫ ter recoilOne plausible signal. However, reason that these NDA estimates might have give always misleadingA F cayFµ experiments,⌫ A . Due to estimates its long-range for which nature, have this substantial matrix vari- usedresults na¨ıve for dimensional these bosonic analysis baryons (NDA) is depicted with uncontrolled in Fig 1. Fromelementh | ation must [29,| bei 30]. determined Until a by more a non-perturbative accurate extraction nuclear of this ma- errorsa simplified of the interaction model standpoint, strength. This one is one could clear expect area that signifi-structuretrix calculation. element is performed, Various attempts we will to estimate use the these na¨ıve dimen- a latticecantly calculation different behaviors can alleviate. between 3-fermion baryons andmatrixsional elements analysis have arising been performed from non-relativistic with varying loop levels momenta 4-fermionOne plausible baryons reason depending that NDA on might how not the be internal sufficient electricof complexitycounting, in a perturbative set-up [24–26], but this ma- forcharges these bosonic are correlated. baryons In is one depicted limit where in Fig the 1. internal From con-trix element has nontrivial excited state structuresA that re- a simplified model stand-point, one could expect signifi- quire a fully non-perturbativeA treatment2 notM dissimilarF from stituents are uncorrelated, the polarizabilities are expected fF 3Z ↵ , (3) cantlyto be different comparable. behaviors However, between if 3-fermion alternate baryons flavors and tend todouble-beta decay matrix elements,⇠ whichR are not agreed 4-fermionform pairs baryons based depending on their on Pauli how statistics, the internal the electric 4-fermionupon withinwhere aR factor=1 of.2 5A [27,1/3 28].fm, Until as used an accurate in the double extrac- beta de- charges are correlated. In one limit where the internal con- tion of this matrix element is performed, we will use na¨ıve baryon polarizability would be derivative-suppressed com- cay context, Z is the atomic number, ↵ is the fine-structure A pared to the 3-fermion baryon (i.e. two dipoles vs. one constant, and MF is a dimensionless parameter which, dipole and one charge). Thus, the QCD, 3-fermion NDA with the factor of 3 in front, approximately matches on to A estimate could be significantly different than the 4-fermion the results of [26, 27] for heavy nuclei when MF =1. In [Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) 094505 and Phys. Rev. D81 (2010) 054502] [LSD collab., in preparation] Lattice: Polarizability of DM

• Background ﬁeld method: preliminary response of neutral baryon to external electric ﬁeld SU(3) E • Measure the shift of the baryon mass as a function of E 2 1 µ 2 preliminary ESU(3) = M + ( F + 3 ) + h.o. 2 C 4M E ! SU(4) 1 2 ESU(4) = M + ( F ) + h.o. ! 2 C E

• Precise lattice results Nuclear: Polarizability (Rayleigh scattering) • several attempts to estimate this in the past, withM increasingM M level of complexityM M inM a M M M O O O perturbative setup [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] [Weiner & Yavin, Phys. Rev. D86 (2012) 075021] [Frandsen et al., JCAP 1210 (2012) 033] [OvanesyanQ & Vecchi,Q arxiv:1410.0601] • multiple scales are probed by the momentum transfer in the virtualQ photons q g g A loopq q A A

Figure 1. One-loop Feynman graphs showing the contributions to the DM-nucleus cross section • in the casemixing of M . operators Mixing diagram and generating threshold Mcorrections(left), matching contributionµ giving⌫ rise to M q A ¯ F Fµ⌫ A G (middle), andappear matrixO at element leading describing order theand low-energy interferenceO two-photon is scatteringh | of DM on the| i nucleusO (right). Seepossible text for further details. similar structure where•eq isnuclear the electric matrix charge element of the quarkhas non-trivialq and mt <µ

M = M MMG¯ a,µ⌫Ga , (4.3) OG CG µ⌫ where Ga,µ⌫ denotes the ﬁeld strength tensor of QCD. The relevant leading-order (LO) diagram is shown in the middle of Figure 1. The corresponding matching is captured by the simple replacement [30]

m MM¯ tt¯ M (m ) MMG¯ a,µ⌫Ga M (m ) , (4.4) t Ct t ! µ⌫ CG t with M given at next-to-leading order (NLO) by CG ↵ (m ) M (m )= s t 1+ M (m ) , (4.5) CG t 12⇡ t Ct t where t = 11↵s(mt)/(4⇡)[31]. Although t is formally of higher order, we will include such ﬁnite two-loop contributions in our analysis, because they are numerically non-negligible. Notice that once the top quark has been removed, the Wilson coecient M and the corre- Ct sponding logarithm is frozen at the threshold mt in the EFT. After the top quark has been integrated out, we then have to consider the mixing of the set of three operators M , M and M . Like M the operator M mixes into M . O Oq OG O OG Oq The relevant diagram is the QCD counterpart of the one displayed on the left in Figure 1 with the photons replaced by gluons. As shown in Appendix B, the associated corrections are subleading and we will neglect them in what follows. The operator M itself evolves like OG the QCD coupling constant, so that for scales mb <µ

–6– µ⌫ NDA for A ¯ F Fµ⌫ A h | | i

M • itM is Mhard to extract theM momentumM M M M M Odependence of this nuclearO form factor O

• similarities with the double-betaQ Q decay nuclear matrix element could suggest large uncertainties ~ (5)Q q q q g O g A A A • to asses the impact of uncertainties on Figure 1. One-loopthe total Feynman cross graphs section showing we start the contributions from to the DM-nucleus cross section in the case of M . Mixing diagram generating M (left), matching contributionA givingµ⌫ rise to M naive dimensional analysisq fF = A F Fµ⌫ AG (middle), and matrixO element describing the low-energyO two-photon scattering ofh DM| on the nucleus|O i (right). See text• for further details. A we allow a “magnitude” factor M F to A change from 0.3 to 3 A 2 MF fF 3 Z ↵ where eq is the electric charge of the quark q and mt <µ

–6– [LSD collab., in preparation] Stealth DM Polarizability

µ2 n C f A 2 ' ⇡A2 | F F | D ×E- ) ×- (

×- preliminary ×-

×-

- × ×-

() [LSD collab., in preparation] Stealth DM Polarizability

µ2 LUX exclusion n C f A 2 ' ⇡A2 | F F | bound for spin- D ×E- independent cross section ) ×- (

×- preliminary ×-

×-

- × ×-

() [LSD collab., in preparation] Stealth DM Polarizability

µ2 LUX exclusion n C f A 2 ' ⇡A2 | F F | bound for spin- D ×E- independent cross section ) ×- (

×- preliminary ×-

×-

- Coherent neutrino

- × scattering background ×-

() [LSD collab., in preparation] Stealth DM Polarizability

µ2 LUX exclusion n C f A 2 ' ⇡A2 | F F | bound for spin- D ×E- independent cross section ) ×- (

×- preliminary ×-

- × LEPII bound on charged baryons

- Coherent neutrino

- × scattering background ×-

() [LSD collab., in preparation] Stealth DM Polarizability

µ2 LUX exclusion n C f A 2 ' ⇡A2 | F F | bound for spin- D ×E- independent cross section ) ×- (

×- preliminary ×-

- × LEPII bound on charged baryons

- Coherent neutrino

- × scattering background ×-

() lowest allowed direct detection cross-section for composite dark matter theories with EW charged constituents Stealth DM Polarizability

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

! " # Stealth DM Polarizability

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

! " # Stealth DM Polarizability

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

! " # Direct detection signal is below the neutrino coherent scattering background for MB>1TeV Stealth DM Polarizability

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

! " # Direct detection signal is below the neutrino coherent scattering background for MB>1TeV Concluding remarks

• BSM physics has many opportunities for composite particles, e.g. dark matter.

• Dark matter constituents can carry electroweak charges and still the stable composites are currently undetectable. Stealth!

• No new forces required beyond SU(N) conﬁning dark color force.

• Abundance can arise either by symmetric thermal freeze-out or by asymmetric baryogenesis.

• Future experiments could eventually rule out dark baryons with mag moments.

• Composite dark matter around 1 GeV is still a challenge due to LEP bounds.

• We need to work harder to inform the broader DM community about our exciting results! "A new scientiﬁc truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

- Max Planck Backup slides A Composite “Miracle”(I)

• For Mdm ~ 100 GeV and α ~ 0.01 can be a thermal relic, but such WIMPs are being ruled out by XENON100/LUX.

• Current bounds on composite fermion dark matter are Mdm>20 TeV [LSD Collab., Phys. Rev. D 88, 014502 (2013)].

• Analogous to NN̅ annihilation,α ~ 16 which would mean Mdm ~ 320 TeV. Not ruled out but not likely to be observed soon.

• But, by dialing up the quark masses, we can bring down α to make a thermal relic Mdm ~ 20 TeV.

• Challenge: quark mass dependence of NN̅ annihilation, incl. heavy quarks.

• Strongly-interacting DM also helps with “Too Big To Fail” problem. S. Nussinov, Phys. Lett. B165 (1985) 55 S. Barr, R. S. Chivukula, and E. Farhi, Phys. Lett. B241 (1990) 387 D. B. Kaplan, Phys. Rev. Lett. 68 (1992) 741 Asymmetric dark matter S. Nussinov, Phys. Lett. B165 (1985) 55 S. Barr, R. S. Chivukula, and E. Farhi, Phys. Lett. B241 (1990) 387 D. B. Kaplan, Phys. Rev. Lett. 68 (1992) 741 Asymmetric dark matter

• It is an observational fact that the number density for dark matter and baryonic matter are of the same order of magnitude ⌦ 5 ⌦ DM ⇡ B

[Planck and ESA] S. Nussinov, Phys. Lett. B165 (1985) 55 S. Barr, R. S. Chivukula, and E. Farhi, Phys. Lett. B241 (1990) 387 D. B. Kaplan, Phys. Rev. Lett. 68 (1992) 741 Asymmetric dark matter

• It is an observational fact that the number density for dark matter and baryonic matter are of the same order of magnitude ⌦ 5 ⌦ DM ⇡ B • This can be explained in Technicolor theories where dark matter is a baryon of a new strongly-coupled sector which shares an asymmetry with standard baryonic matter [Planck and ESA] n n¯ n n¯ DM DM ⇡ B B S. Nussinov, Phys. Lett. B165 (1985) 55 S. Barr, R. S. Chivukula, and E. Farhi, Phys. Lett. B241 (1990) 387 D. B. Kaplan, Phys. Rev. Lett. 68 (1992) 741 Asymmetric dark matter

nDM n¯DM nB n¯B 2 20 ⇡ [Buckley & Randall, JHEP1109 (2011)]

higher dimensional operators sphaleron processes 15

T = 1000 GeV D X D 10 m /T m TD = 200 GeV

TD = 100 GeV TD = 20 GeV nDM nB MDM 5 MB 5 TD = 10 GeV ⇡ ! ⇡ ? MDM/T MDM MB nB nB e 0 ! ⇡ 0 2 4 6 8 10 ρDM / ρ B

FIG. 1: The ratio of dark matter energy density ⇢DM to baryon energy density ⇢B as a function of dark matter mass mX in units of the temperature at which the B X transfer decouples TD, for labeled values of TD. As light solution (corresponding to mX /TD 0 is not shown. See Section II and Eq. (6) for detailed explanation. The observed ratio of ⇢DM/⇢B is 5.86 [21]. ⇠

These mechanisms have been successfully applied to generate the relevant energy densities in the context of an existing baryon asymmetry being transferred to light dark matter, though mechanisms named darkogenesis [17] and hylogenesis [18] have also been suggested which transfer the asymmetry in the opposite direction. If, on the other hand, dark matter is not relativistic at the temperature TD at which the X-transfer operators decouple, then the number density of dark matter is suppressed. In general, we ﬁnd when the ratio mX /TD is about 10, we get the required density of dark matter compared to baryons in the Universe. This thermal suppression is a generic feature, allowing heavy dark matter in many scenarios of Xogenesis. We also discuss two other reasons that dark matter number density might be suppressed relative to baryon number so that dark matter can naturally be weak scale in mass.. In the ﬁrst, the SU(2)L sphaleron transfer is only active for a bounded temperature range between the masses of two doublets whose net number density would cancel if they were degenerate [22]. In the second, excess X-number is bled o↵ into leptons. That is, even after the baryon asymmetry is established (possibly at the sphaleron temperature where a lepton asymmetry gets transferred into an asymmetry in the baryon sector), X- and lepton-number violating operators are still in thermal equilibrium allowing X number density to be reduced while lepton number density is increased. Both these mechanisms cause the transfer to baryons to not be active for the entire temperature range down to TD when the X-number violating operators decouple. Xogenesis models must also remove the symmetric thermally produced dark matter component, so that the asymmetric component dominates. When the transfer mechanism is due to higher order operators, the operators necessary to transfer the asymmetry may also lead to the annihilation of this component. In other examples, new interactions are assumed, which in some cases also lead to detectable signatures. A new non-abelian W 0 with masses much below mW allows the dark matter to annihilate into dark gauge bosons, but with few – if any – direct detection constraints and probably no visible signatures in the near future. Annihilation via a light Z0 that mixes with the photon allows the chance for direct detection, depending on the size of the mixing parameter. While not strictly necessary, the photon-Z0 mixing is a generic property, and may be accessible in beam experiments [23]. We also note one additional constraint that applies to supersymmetric models in which higher dimension operators link X to L or B via the lepton or baryon superpartners. In these cases, the neutralinos that come from the superpartner decay must also be eliminated via self-annihilation. This generally implies that the neutralino should be primarily wino so that the annihilation cross section is suciently large to make the neutralino component of dark matter a small percentage of the total. A Composite “Miracle”(II)

104 102 100 SU(3) SU(2) U(1) SU(3) day) · 2 10 4 10 Q 1 1 2/3 3 6 10 8 10 Q 1 1 -1/3 3 10 10 Nf =2 12 Rate, event10 / (kg Nf =6 14 10 XENON100 [1207.5988], 95% CL exclusion Q 1 1 0 3 16 10 2 1 0 1 2 10 10 10 10 10 M = MB [TeV]

• [LSD Collab., Phys. Rev. D 88, 014502 (2013)]

• Composite fermion dark matter from new vector-like SU(3) gauge theory with Dirac mass terms. Can be a thermal relic.

• Solid lines: magnetic moment. Dashed lines: charge radius. Stealth Dark Matter (I) • Composite dark matter can be lighter than 20 TeV if the leading low-energy interaction is dim. 7 polarizability.

• Requires even Nc so that baryons are scalars to eliminate magnetic moment interaction.

• Requires a global SU(2) custodial symmetry to eliminate charge radius interaction.

• Minimal coupling to weak SU(2) to enable dark pion decay. Now some coupling to Higgs boson.

• Also need vector-like masses so that dark sector doesn’t impact Higgs vacuum alignment.

• Minimal model: Dark SU(4) color with Nf = 4 Dirac ﬂavors. Stealth Dark Matter (II)

• Stable dark baryon is (ψ1u ψ1u ψ1d ψ1d).

• Splitting between ψ1 and ψ2 Dirac doublets due either to vector mass splitting Δ or Yukawa couplings y.

• Coupling to Higgs can be made as small as needed (not a ﬁne tuning) so that polarizability is dominant DM interaction, yet large enough to ensure no relic density of dark pions.

• Higgs VEV still dominates electroweak vacuum alignment and contributions to S and T parameters are small. SU(4) Polarizability

SuperCDMS Soudan CDMS-lite SuperCDMS Soudan Low Threshold XENON 10 S2 (2013) 10!39 CDMS-II Ge Low Threshold (2011) 10!3 CoGeNT PICO250-C3F8 !40 (2012) !4 10 CDMS Si 10 (2013)

# ! ! 41 5 # 2 10 DAMA SIMPLE (2012) 10

COUPP (2012) pb cm !

!46 DEAP3600 !10 10 DarkSide G2 10 LZ nucleon nucleon

! ! !47 !11 10 (Green&ovals)&Asymmetric&DM&& 10 (Violet&oval)&Magne7c&DM& RING ATTE !48 (Blue&oval)&Extra&dimensions&& NT SC !12

E WIMP 2 HER WIMP 10 (Red&circle)&SUSY&MSSM& CO 10 RINO &&&&&MSSM:&Pure&Higgsino&& NEUT !49 !13 10 &&&&&MSSM:&A&funnel& Atmospheric and DSNB Neutrinos 10 |E| &&&&&MSSM:&BinoEstop&coannihila7on& !50 &&&&&MSSM:&BinoEsquark&coannihila7on& !14 10 & 10 2 1 10 100 1000 104 E ( )=M +2C 2 0 E B F |E| WIMP Mass GeV c µ2 ! " # n A 2 CF f • Coherent DM-nucleus cross section: ' ⇡A F D E A µ⌫ fF = A F Fµ⌫ A • Nuclear matrix element [O(3) uncertainty]: h | | i

• Direct detection signal below neutrino background for MB > 1 TeV. Stealth!