The light U boson as the mediator of a new force, coupled to a combination of Q, B, L and dark matter

Abstract

A new light gauge boson $U$ may have both vector and axial couplings. In a large class of theories however, the new $U(1)$ current $J_F^{\mu }$ naturally combines with the weak neutral current $J_{Z_{\mathrm{sm}}}^{\mu }$, both parity-violating, into a vectorial current $J_U^{\mu }$, combination of the $B,L$ and electromagnetic currents with a possible dark matter current. $U^{\mu }$ may be expressed equivalently as $\cos \xi C^{\mu }+\sin \xi Z_{\mathrm{sm}}^{\mu }$ ("mixing with the $Z$") or $(1/\cos \chi ){\hat{C}}^{\mu }+\tan \chi A^{\mu }$ ("mixing with the photon"), with $\hat{C}$ coupled to $B,L$ and dark matter. The $U$ boson may be viewed as a generalized dark photon, coupled to SM particles through $Q_U=Q+{\lambda }_{B}B+{\lambda }_i{L}_i$, with strength $g"\cos \xi {\cos }^2\theta =e\tan \chi$. "Kinetic mixing" terms, gauge invariant or not, simply correspond to a description in a non-orthogonal field basis (rather than to a new physical effect), with the dark photon in general also coupled to $B$ and $L$. In a grand-unified theory $Q_U^{\mathrm{gut}}=Q-2(B-L)$ at the GUT scale for SM particles, invariant under the $SU(4)$ electrostrong symmetry group, with a non-vanishing $ϵ=\tan \chi$ already present at the GUT scale, leading to $Q_U\simeq Q-1.64(B-L)$ at low energy. This also applies, for a very light or massless $U$ boson, to a new long-range force, which could show up through apparent violations of the Equivalence Principle.

Comments: 12 pages, 3 figures