Longitudinal/Goldstone boson equivalence and phenomenology of probing the electroweak symmetry breaking

We formulate the equivalence between the longitudinal weak-boson and the Goldstone boson as a criterion for sensitively probing the electroweak symmetry breaking mechanism and develop a precise power counting rule for chiral Lagrangian formulated electroweak theories. With these we semi-quatitatively analyze the sensitivities to various effective operators related to electrowaeak symmetry breaking via weak-boson scatterings at the CERN Large Hadron Collider (LHC).Comment: 6 pages, LaTex, 1 postscript figure included using psfig.te

Sensitivity of the LHC to Electroweak Symmetry Breaking: Equivalence Theorem as a Criterion

Based upon our recent study on the intrinsic connection between the longitudinal weak-boson scatterings and probing the electroweak symmetry breaking (EWSB) mechanism, we reveal the profound physical content of the Equivalence Theorem (ET) as being able to discriminate physical processes which are sensitive/insensitive to probing the EWSB sector. With this physical content of the ET as a criterion, we analyze the complete set of the bosonic operators in the electroweak chiral Lagrangian and systematically classify the sensitivities to probing all these operators at the CERN LHC via the weak-boson fusion in $W^\pm W^\pm$ channel. This is achieved by developing a precise power counting rule (a generalization from Weinberg's counting method) to {\it separately} count the power dependences on the energy $E$ and all relevant mass scales.Comment: 33 pages, LaTeX, 10 figures and Table-1b are in the separate file figtab.uu. (The only change made from the previous version is to fix the bugs in the uuencoded file.

Spectral and optical properties in the antiphase stripe phase of the cuprate superconductors

We investigate the superconducting order parameter, the spectral and optical properties in a stripe model with spin (charge) domain-derived scattering potential $V_{s}$ ($V_{c}$). We show that the charge domain-derived scattering is less effective than the spin scattering on the suppression of superconductivity. For $V_{s}\gg V_{c}$, the spectral weight concentrates on the ($\pi,0$) antinodal region, and a finite energy peak appears in the optical conductivity with the disappearance of the Drude peak. But for $V_{s}\approx V_{c}$, the spectral weight concentrates on the ($\pi/2,\pi/2$) nodal region, and a residual Drude peak exists in the optical conductivity without the finite energy peak. These results consistently account for the divergent observations in the ARPES and optical conductivity experiments in several high-$T_c$ cuprates, and suggest that the "insulating" and "metallic" properties are intrinsic to the stripe state, depending on the relative strength of the spin and charge domain-derived scattering potentials.Comment: 7 pages, 4 figure

Coexistence of the antiferromagnetic and superconducting order and its effect on spin dynamics in electron-doped high-TcT_{c} cuprates

In the framework of the slave-boson approach to the $t-t'-t''-J$ model, it is found that for electron-doped high-$T_c$ cuprates, the staggered antiferromagnetic (AF) order coexists with superconducting (SC) order in a wide doping level ranged from underdoped to nearly optimal doping at the mean-field level. In the coexisting phase, it is revealed that the spin response is commensurate in a substantial frequency range below a crossover frequency $\omega_{c}$ for all dopings considered, and it switches to the incommensurate structure when the frequency is higher than $\omega_{c}$. This result is in agreement with the experimental measurements. Comparison of the spin response between the coexisting phase and the pure SC phase with a $d_{x^{2}-y^{2}}$-wave pairing plus a higher harmonics term (DP+HH) suggests that the inclusion of the two-band effect is important to consistently account for both the dispersion of the spin response and the non-monotonic gap behavior in the electron-doped cuprates.Comment: 6 pages, 5 figure

Characterization of removable elements with respect to having k disjoint bases in a matroid

AbstractThe well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs with k edge-disjoint spanning trees. Edmonds generalizes this theorem to matroids with k disjoint bases. For any graph G that may not have k-edge-disjoint spanning trees, the problem of determining what edges should be added to G so that the resulting graph has k edge-disjoint spanning trees has been studied by Haas (2002) [11] and Liu et al. (2009) [17], among others. This paper aims to determine, for a matroid M that has k disjoint bases, the set Ek(M) of elements in M such that for any e∈Ek(M), M−e also has k disjoint bases. Using the matroid strength defined by Catlin et al. (1992) [4], we present a characterization of Ek(M) in terms of the strength of M. Consequently, this yields a characterization of edge sets Ek(G) in a graph G with at least k edge-disjoint spanning trees such that ∀e∈Ek(G), G−e also has k edge-disjoint spanning trees. Polynomial algorithms are also discussed for identifying the set Ek(M) in a matroid M, or the edge subset Ek(G) for a connected graph G