Composite Dark Matter Part DM theory Interest Craziness 1 SM !!! ??? 2 SM + heavy Q !! ?? 3 SM + heavy Q + new force ! ? Alessandro Strumia, Pisa U. & INFN & CERN From works with Antipin, deLuca, Mitridate, Redi, Smirnov, Vigiani. KEK-PH2018, 2018.2.14
1) DM within the SM??? Jaffe: the spin 0 iso-singlet di-baryon S = uuddss should have a large binding. Farrar: it could be stable DM if E B > ∼ 2 m s such that M S < 2( M p + M e ).
Thermal abundance Interactions with strange hadrons (e.g. ΛΛ ↔ S X ) keep S in thermal equilibrium until Λ get Boltzmann suppressed at T ∼ M Λ − M p : Ω S ∼ 5Ω b for M S ≈ 1 . 3 GeV: 1.0 X c = 0.88 0.8 S baryon fraction from QCD 0.6 σ = 0.1 GeV - 2 σ = GeV - 2 σ = 10 GeV - 2 0.4 0.2 0.0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Exaplet mass m S in GeV
Nuclear decay If stable, S makes nuclei unstable. Excluded by SuperKamiokande n π 0 τ (O → S X ) > 10 26 − 29 yr Λ ∗ where X = { ππ, π, e, γ } . The decay dominantly proceeds trough double S β production of virtual Λ ∗ . Λ ∗ p Recent fits of nucleon potentials and O wave-function imply a too π + fast decay. Excluded also by balloon direct detection, unless interactions reduce S speed.
2) Colored DM?? Uh? Everybody knows it’s excluded
Theory L = L SM + ¯ Q ( i / D − M Q ) Q . Q is a new colored particle. We assume a Dirac fermion octet with no weak interactions, no asymmetry. (Alternatives: a color triplet, a (3 , 2), a scalar...). Could be a Dirac gluino; could be a fermion of natural KSVZ axion models. Ω Q h 2 ∼ 0 . 1 M Q / 7 TeV before confinement. Later hadrons form: • DM can be the Q -onlyum hadron QQ . It is the ground state: big binding E B ∼ α 2 3 M Q ∼ 200 GeV and small radius a ∼ 1 /α 3 M Q , so small interactions. q ′ have small E B ∼ Λ QCD and large σ ∼ 1 / Λ 2 • Hybrids Q g and/or Q q ¯ QCD . Excluded, unless their relic abundance is small. Hybrids have zero relic abundance, if cosmology has infinite time to thermalise. A hybrid recombines M Pl / Λ QCD ∼ 10 19 times in a Hubble time. Hadronizing with q, g is more likely, n q,g ∼ 10 14 n Q . Result: n hybrid ∼ 10 − 5 n DM .
Cosmological evolution ����������� � �� ��� �� � �� � �� � �� � �� - � �� - � �� - � ������ ���������� � = � / � �� � ���������� ������������ ���������� ���� ��������� Ω � � � �� - �� �� � �� - �� �� - � �� - �� �� - � � = ��� ��� �� - �� �� - � � � σ ��� = � π / Λ ��� �� - �� �� - �� α ��� = � �� - �� �� � �� � �� � �� � �� � �� � � = � / � 1) Usual decoupling at T ∼ M Q / 25, Sommerfeld and bound states included. ∼ Λ QCD because σ bound ∼ 1 /T 2 . 2) Recoupling at T > 3) Hadronization at T ∼ Λ QCD and ‘fall’: half QQ , half Q ¯ Q → gg, q ¯ q . 4) Redecoupling at T ∼ Λ QCD / 40 determines Ω QQ ≈ Ω Q / 2, Ω hybrid ∼ 10 − 5 Ω QQ .
Fall cross section After formation, a QQ can break or fall to an unbreakable (deep enough) level. σ QCD ∼ 1 / Λ 2 QCD ≫ σ pert ∼ α 2 3 /M 2 Q because � � = ��� ��� constituents have large ℓ = M Q vb where b ��� � σ ��� = � π / Λ ��� is the classical impact parameter ���� ����� ������� �� � / ��� � ��� � σ = π / Λ ℓ 2 � � � � � � σ ∼ b 2 ∼ �� . � σ � = / Λ � � � � KM Q � � �� α ��� = �� α ��� = �� QQ becomes unbreakable when it radiates α ��� = ��� � ∆ E > ∼ T before the next collision after � � Λ 2 QCD /T 3 1 T > M π ��� ∆ t ∼ ∼ ���� ���� ��� ��� e M π /T / Λ QCD n π v π σ QCD T < M π ����������� �� ��� The radiated energy is classical for n, ℓ ≫ 1 and minimal for circular orbits: ∆ t = � W Larmor � ≃ 2 α 7 µ 2 3 − ( ℓ/n ) 2 ∆ E × for abelian hydrogen. 3 n 8 2( ℓ/n ) 5 � �� � � �� � circular elliptic enhancement Non perturbative α 3 : could emit 100 g with E ∼ GeV in one shot.
Relic abundances �� � �� - �� � ������������ ٠�� � � �� - � �� - �� ٠� � � �� � �� - � ������ ������� � = � / � �� - �� �� - � ���������� ٠� � ����� ������� � ������������ �� - �� �� - � ٠� � �� - � �� - �� �� - � � � � � � � � � � � � � � � � � � �� - �� �� - � �� - �� � �� - � �� - � �� - �� � �� �� ��� � � � �� �� �� �� ��� � �� ��� � �� ���
Direct detection of DM Interaction QQ /gluon analogous to Rayleigh interaction hydrogen/light: E a 2 . BB � L eff = c E M DM ¯ Polarizability coefficient estimated as c E ∼ 4 πa 3 in terms of the Bohr-like radius a = 2 / (3 α 3 M Q ). Actual computation gives a bit smaller 1 r | B � = (0 . 36 bound + 1 . 17 free ) πa 3 c E = πα 3 � B | � r � H 8 − E 10 so that the spin-independent cross section is below bounds � 6 � � 8 � � � 2 20 TeV 0 . 1 c E σ SI ≈ 2 . 3 10 − 45 cm 2 × . 1 . 5 πa 3 M DM α 3
������ ��������� �������� ��������� �� - �� �� - �� �������� �� �������� �� ������� ����� ����� ��������� �� ������������� ���� - ����������� σ �� �� �� � �� - �� �� - �� σ ��� � ��� �� �� � / � ������� �� ���� ������� �� ���� �� - �� � �� - �� � � � � � � � � �������� σ ��� � ��� �� - �� �� - �� � �� �� ��� � �� �� ��� �� ���� � �� �� ��� �� ���� � �� �� ���
Indirect detection of DM H ) ≫ α 2 /m 2 Analogous to hydrogen: σ ( H ¯ e has atomic size, because enhanced and dominated p ) → ( e ¯ p ) → · · · . by recombination ( ep )+(¯ e ¯ e )+( p ¯ DM annihilation dominated by ( QQ ) + ( ¯ Q ¯ Q ) → ( Q ¯ Q ) + ( Q ¯ Q ) . Classical result: σ ann ∼ πa 2 , enhanced by dipole Sommerfeld. Quantum estimate √ � 2 � � σ ann v rel ∼ πa 2 v rel / 2 = 1 . 5 10 − 24 cm 3 � 2 π 20 TeV 0 . 1 = sec × . � 3 M 2 Q α 3 M DM α 3 E kin /E B
Collider detection of Q QCD pair production, pp → Q ¯ Q , two stable hadron tracks, possibly charged. LHC: M Q > 2 TeV. pp collider at √ s > ∼ 65 TeV needed to discover M Q ∼ 9 . 5 TeV. Low σ at a muon collider.
q ′ Hybrids Q g , Q q ¯ Strongly Interacting Massive Particles with big σ ∼ σ QCD don’t reach under- ground detectors. Excluded by balloons and over-heating if Ω SIMP = Ω DM . Ω SIMP ∼ 10 − 5 Ω DM is allowed SIMP searches in nuclei : best bounds: 3 10 − 14 Oxygen in Earth 10 − 16 N SIMP Enriched C in Earth for M SIMP ∼ 10 TeV < 10 − 12 Iron in Earth N n 4 10 − 14 Meteorites The predicted primordial cosmological average is N SIMP /N n ∼ 5 10 − 9 . Difficult to predict abundance in Earth nuclei. Rough result: Our SIMPs allowed if don’t bind to nuclei, borderline otherwise . q ′ , that thereby decay. Similarly for QQ g , Q qqq . Q g presumably lighter than Q q ¯ Q g is iso-spin singlet: π a cannot mediate long-range nuclear forces. Heavier mesons mediate short-range forces, not computable from 1st principles. If attractive Q g can bind to big nuclei, A ≫ 1. If repulsive Q g remains free. In any case, SIMPs sank in the primordial (fluid) Earth and stars .
Secondary hybrids SIMPs that hit the Earth get captured and thermalise in the upper atmosphere. Accumulated mass = M = ρ SIMP v rel πR 2 E ∆ t ∼ 25 Mton ∼ 10 4 × (fossile energy) . � N SIMP � = M m N ≈ 4 10 − 19 , where are SIMPs now? Average density = N n M Q M Earth Earth • If SIMPs do not bind to nuclei: SIMPs sink with v thermal ≈ 40 m / s, v drift ≈ 0 . 2 km / yr and δh ∼ 25 m. Density in the crust: N SIMP /N n ∼ 10 − 23 . Rutherford back-scattering? • If SIMPs bind to nuclei: BBN could make hybrid He; collisions in the Earth atmosphere could make hybrid N, O, He kept in the crust kept by electromagnetic binding. Meteorites are byproducts of stellar explosions: do not contain primordial SIMPs; accumulate secondary SIMPs only if captured by nuclei � N SIMP = ρ SIMP σ capture � σ capture v rel ∆ t ≈ 7 10 − 15 . � 0 . 01 / Λ 2 N n � meteorite M Q QCD
3) DM composite under a new force
Recommend
More recommend