The Four Basic Ways of Creating Dark Matter Through a Portal

The Four Basic Ways of Creating Dark Matter Through a Portal DISCRETE 2012: Third Symposium on Prospects in the Physics of Discrete Symmetries December 4th 2012, Lisboa Based on arxiv:1112.0493, with Thomas Hambye and Michel H. G. Tytgat.

Outline 1 Evidence for WIMP miracle or more? 2 3

Outline Evidence for WIMP miracle or more? 1 Evidence for WIMP miracle or more? 2 3

Evidence for WIMP miracle or more? Why Dark Matter(DM)? 1 Galaxy rotation curve.-rotational velocities of stars mismatch calculation of visible matter. 2 Gravitaional lensing.-non-luminous matter needed to explain distorted galaxy light. 3 Cosmic Microwave Background(CMB). -CMB anisotropies show total and baryonic matter densities not same. 4 Bullet cluster and structure formation etc. -gravitational lensing and luminosity measurements lead to discrepancy.

Evidence for WIMP miracle or more? Visible SM matter is not enough for our Universe! The most plausible solution: Neutral, not hot, weakly interactive, non-baryonic, stable particle How to create this new gradient, with the observed relic density?

Outline Evidence for WIMP miracle or more? 1 Evidence for WIMP miracle or more? 2 3

Evidence for WIMP miracle or more? One way: 1 At the very beginnng of the Universe, DM is in thermal equilibrium with SM, 2 With Universe expansion, temperature T fells below m DM, DM DM annihilation dominates over its inverse process, 3 Eventually when DM interacting rate, Γ, becomes less than expansion rate H, annihilation stops and n DM s freezes out: Standard Freeze-out mechanism σv anni ndm Γ H(T ). (1) relic density, Ω DM h 2 0.11, is generated via its thermal annihilation (for symmetric DM candidates):

Evidence for WIMP miracle or more? A more precise solution by sloving its Boltzmann equation: Ω DM h 2 1 σv FO. (2) anni For observed value, freeze-out happens at z = m DM /T 25, requiring σv FO anni pb. Weakly Interacting Massive Particle (WIMP) Miracle σv FO anni O(1)pb seems natural for weak-scale interactions of O(100) GeV particles.

Evidence for WIMP miracle or more? Its Con side: (1) No convincing evidence for WIMP yet despite puzzling signals, (2) Cold DM may suffer from small-scale problems,... Asymmetric DM? Warm DM? Mixed DM? HS DM?... Hidden Sector (HS) More structure hidden in the sector, probably decoupled from visible sector, only interact with SM extremely weakly, e.g. through a portal only, as discussed in many papers. One possibility: a massless portal 2 (SIDM with velocity-dependent σ). Then how it may generate the observed DM density? 2 A massive portal scalar φ is also studied in our paper.

Outline 1 Evidence for WIMP miracle or more? 2 3

Case study: (GKM) DM particle is gauged under new U(1), which mixes with U(1) Y of SM gauge group via ɛ 2 F µν Y F µν. [B.Holdom 1986] We assume fermionic DM, introduce coupling e. After redefining gauge bosons and normalizing kinetic terms L e J µ DM A µ + ɛe J µ DM A µ ɛe tan θ W J µ DM Z µ, (3) where the first term is the hidden sector interaction, and the last two are the portals 3. We are interested in the one with γ. Then define κ e ɛ e, so all new parameters needed in this model are (m DM, α, κ) if assuming initial DM density is negligible. 3 Here we adopt a basis where γ (A ) doesn t couple to SM.

Most important processes for this scenario: SM offshell annihilation and Z-decay(onshell), DM annihilation: (a) σ connect v κ 2 (b) σ HS v α 2 The Boltzmann equation of HS number density: z H dy s dz = σ connect v i (Yeq(T 2 ) Y 2 )+ σ HS v (Yeq(T 2 ) Y 2 ), 4 i The Boltzmann equation of HS energy density is similar. 4 Here s-entropy density, H-Hubble constant, Y n e /s, z = m DM /T, Y eq(t ) = n eq(t )/s(t ) and Y eq(t ) = n eq(t )/s(t ).

Outline 1 Evidence for WIMP miracle or more? 2 3

I. Freeze-in regime, ρ ini 0 [McDonald 2002, Hall etc. 2009] When κα is small, energy only transfers from SM to DM: (1) For offshell channel (pair creation), which stops at T f Max[m e, m DM ] Y σ connectv n 2 eq s 1 H κ2 /T f, (4) (2) For onshell channel (Z-decay) Y nz eqγ Z sh. (5) As observed Y DM = 4.1 10 10 GeV m DM, so when offshell channel dominates and m DM > m e, κ obs constant.

1 10 9 5 10 10 Κ 1 10 10 5 10 11 1 10 11 5 10 12 1 10 12 10 6 10 4 0.01 1 100 10 4 Figure: Freeze-in values of κ to give the observed DM (red line), and the blue line only includes offshell contributions. DM

II. Reannihilation regime, ρ ini 0 increase κ or α, DM + DM 2γ channel opens, then the final DM depends on the balance of SM DM and DM γ : z H s dy dz = σ connectv Y 2 eq(t ) σ HS v Y 2. A stable solution: Quasi Static Equilibrium (QSE) dy dz = 0 Y = Y QSE For pair creation, it gives Y (T ) = σ connectv Y 2 eq (T ) σ HS v. (for decay: [C. Cheung etc. 2010]) σ connectv σ HS v Y eq (T ).

Numerical results as an example: Y 10 4 10 7 10 10 10 13 10 16 Y eq T Y Y crit Y QSE Y eq T' 0.1 1 10 100 For this set of parameters: (a) Connector: 1 begin: SM SM 2DM(e ), 2 it stops gradually after T < m DM. (b) Hidden Sector: 1 thermalized: e + ē γ γ, so Y = Y eq(t ), 2 when T > m DM > T : only e + ē γ γ, so Y = Y QSE (T ), 3 z increases, Y Y QSE (T f ) freezes out at Γ < H. DM

Analytic results Outline After Y Y QSE, the Boltzmann equation simplifies: z dy dz σconnect v σ HS v n eq (T ) 2 (Y Y QSE ) (6) H Freeze-out condition: σ connect v σ HS v n eq (T )/H 1 It freezes-out at z f = m DM /T f 3 20 (DM), compared to standard Freeze-out z f 25 as σ HS v n eq (T )/H 1. The final DM relic abundance depends on z f, which has a different solution decided by Eq.(6), and Y = Y QSE (T f ) = 3.79 z f g eff g s m Pl m DM σ HS v. (7) It fits the number solution well in most of parameter space.

III. & IV. Two freeze-out regimes, ρ ini 0 When κ is larger than certain value 10 6 m DM GeV g eff, hidden sector thermalizes with visible sector, i.e. T = T. standard Freeze-out via σ connect v or σ HS v, which gives the two last regimes: III. Freeze out via connector to SM Larger κ, DM + DM SM + SM IV. Freeze out to hidden photon γ Larger α, DM + DM γ + γ

Full Relic density phase diagram (Mesa) 0 2 18 phase diagram Log 10 YDM mdm 0.1GeV 16 II III Log 10 Α' 4 12 6 8 10 8 I 4 2 IV 10 6 14 12 10 8 6 4 2 0 Log 10 Κ Four regimes are showed and dashed line shows the observed DM relic density.

What if non-zero initial hidden sector? In this case, essentially final DM relics depend on ρ ini + ρ transfer for freeze-in regime, and on both temperature ratio ξ = T /T and annhilation σv for other regimes. If ρ ini donimates analytic solution of relic density w.r.t. ξ: z f = ξ ln[0.038 ξ 5/2 g e σ annih v m Pl m DM c(c + 2)] g eff which gives ξ 1 2 ln{ξ ln[0.038 g e ξ5/2 σ annih v m Pl m DM c(c + 2)]}, g eff Ω DM h 2 = 2 1.07 109 z f GeV 1. (8) (g s / g eff )m Pl σ annih v

Outline 1 Evidence for WIMP miracle or more? 2 3

Dark Matter Direct detection DM + nucleus DM + nucleus: During the collision, nucleus gains recoiling energy(e R ) to get ionized or excited (as one event of E R ). In our model, mediator of the collision is the massless γ/γ.

A light mediator generates a E R -dependent differential cross section, ν 2 dσ de R 1 instead of a const for heavy mediators: ER 2 1) Collision σ is greatly enhanced due to small E R, making this model detectable even for extremely small κ; 10 6 FREEZE-OUT (IIIB /IV) 10 7 FREEZE-OUT (IIIA) 10 8 REANNIHILATION (II) Κ 10 9 Xenon100 10 10 Xenon1T 1yr 10 11 Xenon1T 4yrs FREEZE-IN (I) 10 12 5 10 50 100 500 DM

2) This differential cross section gives different modulation spectrum w.r.t. E R, so distinguishable from normal WIMP; 3) More sensitive to lower E R detectors, like DAMA and CoGent:

Outline 1 Evidence for WIMP miracle or more? 2 3

on this gauge kinetic mixing model: 1. Extra degrees of freedom bounds on γ Cosmological observations put bounds on extra effective d.o.f of the universe, which is related to the expansion rate H: g < 2.5(BBN) g < 1 1.9(CMB) Considering reheating processes in visible sector, T T is allowed. 2.Interaction bound among DM from Galactic dynamics on α From Bullet cluster and structure formation, α < 10 7 ( m DM GeV )3/2, which in turn requires m DM > O(100)GeV except for Freeze-in regime.

3. Possible depletion of DM in galaxy (on κ ) Local magnetic field may prevent charged DM from coming into galaxy. Also DM in galaxy may be expelled by Fermi acceleration in supernovae shock. So dark matter of this kind can exist in solar system only if κ < 10 11 m DM GeV. One possibility to alleviate it: to break U(1) slightly m γ m DM : Then it s not long-distance interaction, so third constraint disappears.

A massive γ also can relieve the constraint on α : 0.1 0.001 Α 10 5 10 7 10 9 0.01 0.1 1 10 100 0 DM Ellipticity upper bounds 5 on α with m γ = 0, 1, 10, 100keV, 1, 10, 100MeV. The red line shows the bound for a massless γ. 5 We didn t consider QM resonances here. And there are also bounds on κ w.r.t. mγ [Redondo etc. 2010].

Higgs Portal Model:the Lagrangian and the phase diagram This model is realized by a mixing term with Higgs doublet, λ m φφ H H, where DM scalar φ is gauged under new U(1). Relic density phase diagrams have the similar mesa-shape to GKM model: 0 2 16 phase diagram Log 10 YDM mdm 1000GeV 14 II III 10 Log 10 Α' 4 6 8 4 8 I IV 10 12 6 12 10 8 6 4 2 0 Log 10 Λ m

Log 10 Α' 18 2 4 12 6 II 8 III 10 16 and Future Prospects Log 10 Κ 1 Four basic ways to generate symmetric DM through a portal. -Four regimes lead to the characteristic shape of "mesa-like". -In most cases, analytic solutions can be obtained. 8 4 IV I 2 6 10 14 12 10 8 6 4 2 0 2 Mixing U(1) U(1) Y model. -Phenomenologically interesting, motivated by GUTs etc. -Detectable even for very small coupling κ and distinguishable from normal WIMP.

Thanks.