Accidental Composite Dark Matter

Scalar gauge dynamics and Dark Matter

“…As anticipated above, this symmetry is nothing but charge conjugation C for the U(N/2) subgroup of Sp(N): since U(N/2) = SO(N) ∩ Sp(N), the U(N/2) sub-algebra is given by the anti-symmetric generators, i.e. the first set in (5) and the second set in (6); the imaginary (real) 3 This crucially depends on the overall sign of the transformation of S chosen in (3). Notice that, as a consequence, one has ŜIJ ≡ (Sγ N ) IJ → −(−1) I+J ŜIJ .…”

“…At first sight, an apparently related result is the Fröhlich-Morchio-Strocchi (FMS) theorem [10]. Seeking a manifestly gauge covariant description of the Higgs phase, FMS prove that for each state in the Higgs phase there is a corresponding operator in the unbroken theory covariant under G. 5 In some theories the corresponding operators are invariant singlets, pointing to a relation between the confined and Higgs phases. But in general, the corresponding operators are only covariant: their existence does not imply a duality between the Higgs and confined phases.…”

“…If one w vanishes and N is odd, the corresponding SU(2) extends to SU (3). If two w vanish, their SU(2) 2 extends to SU(4) for N even (to SU (5) for N is odd). If two w are equal their SU(2) 2 extends to Sp(4).…”

“…For N = 4 and N = 6 there is only one quartic in view of Tr(S 4 ) = Tr(S 2 ) 2 /4. For N = 4 the cubic vanishes because the anti-symmetric of Sp(4) is the fundamental of SO (5). Again, cubics are allowed for fields that satisfy a trace-less condition.…”

“…The possibility that DM is a composite state made of elementary fermions in QCD-like theories was explored in[5,6]. As elementary scalars interact with the Higgs through a scalar quartic, while elementary fermions can have Yukawa couplings, the phenomenology is different.…”