Minimal Dark Matter in the Local B−LB-L Extension

The minimal gauge group extension to the standard model (SM) by the local $U(1)_{B-L}$ (MBLSM) is well known as the minimal model to understand neutrino mass origins via the seesaw mechanism, following the gauge principle. This "small" symmetry also has deep implication to another big thing, dark matter (DM) stability. We demonstrate it in the framework of minimal dark matter (MDM), which aims at addressing two basic questions on DM, stability and the nature of interactions. However, stability and perturbativity may only allow the fermionic quintuplet. The situation is very different in the MBLSM, which leaves the subgroup of $U(1)_{B-L}$, the matter parity $(-1)^{3(B-L)}$, unbroken; it is able to stabilize all of the weakly-interacting {MDM candidates } after assigning a proper $U(1)_{B-L}$ charge. For the candidates with nonzero hypercharge, the phenomenological challenge comes from realizing the inelastic DM scenario thus evading the very strict DM direct detention bounds. We present two approaches that can slightly split the CP-even and -odd parts of the neutral components: 1) using the dimension 5 operators, which works for the $U(1)_{B-L}$ spontaneously breaking at very high scale; 2) mixing with {other fields} having zero hypercharge, which instead works for a low $U(1)_{B-L}$ breaking scale.Comment: 13 pages without figure

Quark-gluon correlation functions relevant to single transverse spin asymmetries

We investigate the relative size of various twist-3 quark-gluon correlation functions relevant to single transverse spin asymmetries (SSAs) in a quark-diquark model of the nucleon. We calculate the quark-gluon correlation function $T_{q,F}(x, x)$ that is responsible for the gluonic pole contribution to the SSAs, as well as $T_{q,F}(0, x)$ and $T_{\Delta{q}, F}(0, x)$ responsible for the fermionic pole contributions. We find in both cases of a scalar diquark and an axial-vector diquark that at the first nontrivial order only the \tq(x, x) is finite while all other quark-gluon correlation functions vanish. Using the same model, we evaluate quark Sivers function and discuss its relation to the \tq(x, x). We also discuss the implication of our finding to the phenomenological studies of the SSAs.Comment: 12 pages, 5 figure

SO(5) structure of p-wave superconductivity for spin-dipole interaction model

A closed SO(5) algebraic structure in the the mean-field form of the Hamiltonian the pure p-wave superconductivity is found that can help to diagonalized by making use of the Bogoliubov rotation instead of the Balian-Werthamer approach. we point out that the eigenstate is nothing but SO(5)-coherent state with fermionic realization. By applying the approach to the Hamiltonian with dipole interaction of Leggett the consistency between the diagonalization and gap equation is proved through the double-time Green function. The relationship between the s-wave and p-wave superconductivities turns out to be recognized through Yangian algebra, a new type of infinite-dimensional algebra.Comment: 7 pages, no figures. Accepted Journal of Physcis A: Mathematical and Genera