15,525 research outputs found
Low Q^2 Weak Mixing Angle Measurements and Rare Higgs Decays
A weighted average weak mixing angle theta_W derived from relatively low Q^2
experiments is compared with the Standard Model prediction obtained from
precision measurements. The approximate 1.8 sigma discrepancy is fit with an
intermediate mass (~ 10-35 GeV) "dark" Z boson Z_d, corresponding to a U(1)_d
gauge symmetry of hidden dark matter, which couples to our world via kinetic
and Z-Z_d mass mixing. Constraints on such a scenario are obtained from
precision electroweak bounds and searches for the rare Higgs decays H -> Z Z_d
-> 4 charged leptons at the LHC. The sensitivity of future anticipated low Q^2
measurements of sin^2 theta_W(Q^2) to intermediate mass Z_d is also
illustrated. This dark Z scenario can provide interesting concomitant signals
in low energy parity violating measurements and rare Higgs decays at the LHC,
over the next few years.Comment: Version to appear in PR
Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
We study the low energy effective theory for a non-Fermi liquid state in 2+1
dimensions, where a transverse U(1) gauge field is coupled with a patch of
Fermi surface with N flavors of fermion in the large N limit. In the low energy
limit, quantum corrections are classified according to the genus of the 2d
surface on which Feynman diagrams can be drawn without a crossing in a double
line representation, and all planar diagrams are important in the leading
order. The emerging theory has the similar structure to the four dimensional
SU(N) gauge theory in the large N limit. Because of strong quantum fluctuations
caused by the abundant low energy excitations near the Fermi surface, low
energy fermions remain strongly coupled even in the large N limit. As a result,
there are infinitely many quantum corrections that contribute to the leading
frequency dependence of the Green's function of fermion on the Fermi surface.
On the contrary, the boson self energy is not modified beyond the one-loop
level and the theory is stable in the large N limit. The non-perturbative
nature of the theory also shows up in correlation functions of gauge invariant
operators.Comment: 14 pages, 20 figures; v2) Sec. V on correlation function of gauge
invariant operators added; v3) typos corrected, minor changes (to appear in
PRB
Muon Anomaly and Dark Parity Violation
The muon anomalous magnetic moment exhibits a 3.6 \sigma discrepancy between
experiment and theory. One explanation requires the existence of a light vector
boson, Z_d (the dark Z), with mass 10 - 500 MeV that couples weakly to the
electromagnetic current through kinetic mixing. Support for such a solution
also comes from astrophysics conjectures regarding the utility of a U(1)_d
gauge symmetry in the dark matter sector. In that scenario, we show that mass
mixing between the Z_d and ordinary Z boson introduces a new source of "dark"
parity violation which is potentially observable in atomic and polarized
electron scattering experiments. Restrictive bounds on the mixing (m_{Z_d} /
m_Z) \delta are found from existing atomic parity violation results, \delta^2 <
2 x 10^{-5}. Combined with future planned and proposed polarized electron
scattering experiments, a sensitivity of \delta^2 ~ 10^{-6} is expected to be
reached, thereby complementing direct searches for the Z_d boson.Comment: Version to appear in PR
Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
We study the stability of the 2+1 dimensional U(1) spin liquid state against
proliferation of instantons in the presence of spinon Fermi surface. By mapping
the spinon Fermi surface into an infinite set of 1+1 dimensional chiral
fermions, it is argued that an instanton has an infinite scaling dimension for
any nonzero number of spinon flavors. Therefore, the spin liquid phase is
stable against instantons and the non-compact U(1) gauge theory is a good low
energy description.Comment: 14 pages, 7 figures, v3) minor corrections, to appear in PR
Least-squares solutions of multi-valued linear operator equations in Hilbert spaces
AbstractLet M be a linear manifold in H1 ⊕ H2, where H1, and H2 are Hilbert spaces. Two notions of least-squares solutions for the multi-valued linear operator equation (inclusion) y ϵ M(x) are introduced and investigated. The main results include (i) equivalent conditions for least-squares solvability, (ii) properties of a least-squares solution, (iii) characterizations of the set of all least-squares solutions in terms of algebraic operator parts and generalized inverses of linear manifolds, and (iv) best approximation properties of generalized inverses and operator parts of multi-valued linear operators. The principal tools in this investigation are an abstract adjoint theory, orthogonal operator parts, and orthogonal generalized inverses of linear manifolds in Hilbert spaces
Coarsening Dynamics of an Antiferromagnetic XY model on the Kagome Lattice: Breakdown of the Critical Dynamic Scaling
We find a breakdown of the critical dynamic scaling in the coarsening
dynamics of an antiferromagnetic {\em XY} model on the kagome lattice when the
system is quenched from disordered states into the Kosterlitz-Thouless ({\em
KT}) phases at low temperatures. There exist multiple growing length scales:
the length scales of the average separation between fractional vortices are
found to be {\em not} proportional to the length scales of the quasi-ordered
domains. They are instead related through a nontrivial power-law relation. The
length scale of the quasi-ordered domains (as determined from optimal collapse
of the correlation functions for the order parameter )
does not follow a simple power law growth but exhibits an anomalous growth with
time-dependent effective growth exponent. The breakdown of the critical dynamic
scaling is accompanied by unusual relaxation dynamics in the decay of
fractional () vortices, where the decay of the vortex numbers is
characterized by an exponential function of logarithmic powers in time.Comment: 13 pages, 26 figure
- …