Varieties of electrically charged physical states in SU(2)$\times$U(1) lattice gauge Higgs theory

Abstract

We consider a quenched SU(2)$\times$U(1) gauge Higgs theory on the lattice, coupled to a static vector-like fermion which, in this case, is in the same gauge group representation as the Higgs field. Physical (i.e. locally gauge invariant) electrically charged and electrically neutral states of matter particles in the electroweak theory were described decades ago, but those constructions do not exhaust all the possibilities, and new types of electrically charged/neutral states, orthogonal to former constructions, are described here. The difference has to do with how the static source, which by itself does not create a physical state, is dressed by dynamical fields. We find that, unsurprisingly, the neutral static fermion is much lighter than any of the charged fermion states. But a lattice study of the propagation of the charged fermion states indicates the existence of (at least) two particle states with different masses in charged particle spectrum.

Figures (5)

• Figure 1: A plot of the expectation value of the gauge invariant link operator $\langle \phi^\dagger(x) U_\mu(x) \phi(x+\hat{\mu})\rangle$ vs. $\gamma$, at fixed $\beta_1=\beta_2=3, \lambda=0.13$, averaged over the $12^4$ lattice volume. There seems to be a very strong first order transition from the symmetric to the Higgs phase near $\gamma=2.02$.
• Figure 2: Single particle $A\rightarrow A$ time correlators $C_A$, the keys show the $A$ values of data points. (a) Log plot of the time correlator of the neutral type I state. The energy derived is, within errors, equal to half the energy of derived from the corresponding neutral type I particle-antiparticle time correlators shown below. (b) No isolated particle apart from type I neutral can propagate; the time correlator of all others must be zero. This seems to be the case (up to errorbars) in the data shown for charge types I and II, and neutral type II.
• Figure 3: Logarithmic plot of the $AA\rightarrow AA$ time correlator for a static fermion-antifermion pair, for a type I neutral pair, a type 1 charged pair, and two type II charged pairs with pseudomatter $\xi_2$ ($n=2$) and $\xi_{10}$ ($n=10$) respectively. The data was obtained on a $12^3\times 60$ lattice volume, and the static particles are separated by six lattice spacings.
• Figure 4: The two lowest energies of the type II charged pairs, via the generalized eigenvalue method.
• Figure 5: A selection of time correlators for (a) neutral type I (N1) and neutral type II fermion pairs, and (b) charged type I fermions, using pseudovectors $\rho_n(x,V)$ defined in (\ref{['pseudo']}). There is a near perfect overlap between the $n=1$ and $n=2$ data points.