The Pion Velocity at Chiral Restoration and the Vector Manifestation

We study the effects of Lorentz non-invariance on the physical pion velocity at the critical temperature $T_c$ in an effective theory of hidden local symmetry (HLS) with the "vector manifestation" fixed point. We match at a "matching scale" $\Lambda_M$ the axial-vector current correlator in the HLS with the one in the operator product expansion for QCD, and present the matching condition to determine the bare pion velocity. We find that the physical pion velocity, which is found to be one at $T=T_c$ when starting from the Lorentz invariant bare HLS, remains close to one with the Lorentz non-invariance, $v_\pi (T_c) = 0.83 - 0.99$. This result is quite similar to the pion velocity in dense matter.Comment: 13 pages, discussions for clarifying the matching procedure are adde

Effective Degrees of Freedom at Chiral Restoration and the Vector Manifestation in HLS theory

The question as to what the relevant effective degrees of freedom at the chiral phase transition are remains largely unanswered and must be addressed in confronting both terrestrial and space laboratory observations purporting to probe matter under extreme conditions. We address this question in terms of the vector susceptibility \chi_V (VSUS in short) and the axial-vector susceptibility \chi_A (ASUS in short) at the temperature-induced chiral transition. We consider two possible, albeit simplified, cases that are contrasting, one that is given by the standard chiral theory where only the pions figure in the vicinity of the transition and the other that is described by hidden local symmetry (HLS) theory with the Harada-Yamawaki vector manifestation (VM) where nearly massless vector mesons also enter. We find that while in the standard chiral theory, the pion velocity v_\pi proportional to the ratio of the space component f_\pi^s of the pion decay constant over the time component f_\pi^t tends to zero near chiral restoration with f_\pi^t\neq 0, in the presence of the vector mesons with vanishing mass, the result is drastically different: HLS with VM {\it predicts} that \chi_V automatically equals \chi_A in consistency with chiral invariance and that v_\pi\sim 1$with$f_\pi^t\approx f_\pi^s\to 0 as T\to T_c. These results are obtained in the leading order in power counting but we expect their qualitative features to remain valid more generally in the chiral limit thanks to the VM point.Comment: 32 pages, 2 figure

Discrimination of Σ\Sigma-nucleus potentials in the angular distribution of elastic scattering of Σ−\Sigma^- hyperons from nuclei

We theoretically investigate the elastic scattering of 50-MeV $\Sigma^-$ hyperons from $^{28}$Si and $^{208}$Pb in order to clarify the radial distribution of $\Sigma$-nucleus (optical) potentials. The angular distributions of differential cross sections are calculated using several potentials that can explain experimental data of the $\Sigma^-$ atomic X-ray and ($\pi^-$, $K^+$) reaction spectra simultaneously. The magnitude and oscillation pattern of the angular distributions are understood by the use of nearside/farside decompositions of their scattering amplitudes. It is shown that the resultant angular distributions can considerably discriminate among the radial distributions of the potentials that have a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption

Entanglement branching operator

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.Comment: 11 pages, 13 figure

Vector Manifestation in Hot and/or Dense Matter

In this talk I summarize main features of the vector manifestation (VM) which was recently proposed as a novel manifestation of the Wigner realization of chiral symmetry in which the symmetry is restored at the critical point by the massless degenerate pion (and its flavor partners) and the rho meson (and its flavor partners) as the chiral partner. I show how the VM is realized in hot and dense QCD using the effective field theory of QCD based on the hidden local symmetry.Comment: Talk given at YITP-RCNP Workshop ``Chiral Restoration in Nuclear Medium'' (October 7-9,2002). 12 pages, PTPTe