arXiv subjects
Publications and source records attributed to Masayasu Harada.
The vector manifestation (VM) was proposed as a novel manifestation of chiral symmetry in which the massless vector meson becomes the chiral partner of pion. In this write-up, I briefly summarize the following main ingredients to formulate the VM in hot and/or dense matter: Effective field theory (EFT) based on the hidden local symmetry; Wilsonian matching between the EFT and QCD; Intrinsic thermal and/or dense effects.
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" $Λ_M$ 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, $v_π(T_c) = 0.83 - 0.99$. This result is quite similar to the pion velocity in dense matter.
We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.
We summarize main mechanisms to realize the vector manifestation (VM), in which the massless vector meson becomes the chiral partner of pion, at the critical temperature in hot QCD within the framework of the model based on the hidden local symmetry. Then, we show a recent analysis on the direct photon-pi-pi coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion: The VM predicts that the VD is largely violated at the critical temperature.
We summarize some features of the vector meson dominance model which was recently proposed for studying radiative decays involving the scalar mesons. Using the experimental values of $Γ(a_0 \to γγ)$, $Γ(f_0 \to γγ)$ and $Γ(ϕ\to a_0 γ)$ as inputs, we show that the model predicts a large hierarchy between $Γ(a_0 \to ωγ)$ and $Γ(a_0 \to ργ)$ as well as between $Γ(f_0 \to ωγ)$ and $Γ(f_0 \to ργ)$.
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 χ_V (VSUS in short) and the axial-vector susceptibility χ_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_πproportional to the ratio of the space component f_π^s of the pion decay constant over the time component f_π^t tends to zero near chiral restoration with f_π^t\neq 0, in the presence of the vector mesons with vanishing mass, the result is drastically different: HLS with VM {\it predicts} that χ_V automatically equals χ_A in consistency with chiral invariance and that v_π\sim 1$ with $f_π^t\approx f_π^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.
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 formulated in the effective field theory of QCD based on the hidden local symmetry and realized in the large flavor QCD as well as in hot and/or dense QCD.
We calculate pi+ pi0 mass difference $Δm_π^2 \equiv m_{π^+}^2 -m_{π^0}^2$ in the Hidden Local Symmetry (HLS) model, based on the Wilsonian matching and Wilsonian renormalization-group equations. Even without a1 meson the result agrees well with the experiment in sharp contrast to the conventional approach where the a1 meson plays a crucial role. For large Nf QCD, there arises a large hierarchy between $Δm_π^2$ and the pi decay constant $F_π^2$, $Δm_π^2/F_π^2 \ll 1$, near the critical point where the chiral symmetry gets restored as the vector manifestation and the HLS model becomes a little Higgs model with two sites and two links, with the dynamically generated gauge coupling of the composite rho becoming vanishingly small.
We develop an effective field theory of QCD and QCD-like theories, based on the hidden local symmetry (HLS) model. We formulate the chiral perturbation theory with loops of rho as well as pi and further include quadratic divergences which are crucial to the chiral phase transition. Detailed calculations of the one-loop renormalization-group equation of the parameters of the HLS model are given, with the bare parameters (defined at cutoff Lambda) determined by the matching (``Wilsonian matching'') with the underlying QCD at Lambda through the operator-product expansion of current correlators. The Wilsonian matching predicts low energy phenomenology for the three-flavored QCD in remarkable agreement with the experiments. When the chiral symmetry restoration takes place in the underlying QCD, the HLS model uniquely leads to the Vector Manifestation (VM) as a new pattern of Wigner realization of chiral symmetry, with the rho becoming degenerate with the massless pi as the chiral partner. The VM is in fact realized in the large Nf QCD when Nf to Nf^{crit}-0, with Nf^{crit} = 5 Nc/3 being in rough agreement with the lattice simulation for Nc=3. The VM can be realized also in hot and/or dense QCD.
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.
Based on the hidden local symmetry (HLS) Lagrangian as an effective field theory of QCD, we find that the chiral symmetry restoration for hot QCD can be realized through the Vector Manifestation where the rho meson becomes massless degenerate with pi as the chiral partner. This is done by including, in addition to the hadronic thermal effects due to the pi- and rho-loops, the intrinsic temperature dependences of the parameters of the HLS Lagrangian through the matching of the HLS with the underlying QCD.
We investigate the phase structure of dense QCD using the Schwinger-Dyson equation (SDE) with the improved ladder approximation in the Landau gauge. We use the gluon propagator with the electric mode corrected by Debye screening and the magnetic mode corrected by Landau damping. We solve the coupled SDE for the Majorana masses of the quark and antiquark (separately from the SDE for the Dirac mass) in the low density and intermediate density regions. In the low density region, both the SDEs for the Majorana masses and the Dirac mass have nontrivial solutions that correspond to the color symmetry breaking (CSB) vacuum and the chiral symmetry breaking ($χ$SB) vacuum. Comparing the values of the effective potential in the two vacua, we show that the phase transition from the $χ$SB vacuum to the CSB vacuum is of first order. The resultant value of the critical chemical potential is about 210 MeV, which is smaller than that obtained from the SDE analysis including only the Dirac mass. The momentum dependences of the Majorana masses of the quark and antiquark are shown to be quite different, although the masses are of the same order.
We study a vector dominance model which predicts a fairly large number of currently interesting decay amplitudes of the types S -> γγ, V -> S γand S -> V γ, where S and V denote scalar and vector mesons, in terms of three parameters. As an application, the model makes it easy to study in detail a recent proposal to boost the ratio Gamma(phi -> f_0 gamma) / Gamma(phi -> a_0 gamma) by including the isospin violating a_0 - f_0 mixing. However we find that this effect is actually small in our model.
We describe in-medium properties of hadrons in dense matter near chiral restoration using a Wilsonian matching to QCD of an effective field theory with hidden local symmetry at the chiral cutoff $Λ$. We find that chiral symmetry is restored in vector manifestation à la Harada and Yamawaki at a critical matter density $n_c$. We express the critical density in terms of QCD correlators in dense matter at the matching scale. In a manner completely analogous to what happens at the critical $N_f^c$ and at the critical temperature $T^c$, the vector meson mass is found to vanish (in the chiral limit) at chiral restoration. This result provides a support for Brown-Rho scaling predicted a decade ago.
In this talk I summarize our recent work on the vector dominance in QCD by using the the hidden local symmetry as an effective field theory of QCD.
We reveal the full phase structure of the effective field theory for QCD, based on the hidden local symmetry (HLS) through the one-loop renormalization group equation including quadratic divergences. We then show that vector dominance (VD) is not a sacred discipline of the effective field theory but rather an accidental phenomenon peculiar to three-flavored QCD. In particular, the chiral symmetry restoration in HLS model takes place in a wide phase boundary surface, on which the VD is realized nowhere. This suggests that VD may not be valid for chiral symmetry restoration in hot and/or dense QCD.
In this talk I summarize our recent works on the chiral phase transition in the large flavor QCD studied by the hidden local symmetry (HLS). Bare parameters in the HLS are determined by matching the HLS with the underlying QCD at the matching scale through the Wilsonian matching. This leads to the vector manifestation of the Wigner realization of the chiral symmetry in which the symmetry is restored by the massless degenerate pion (and its flavor partners) and rho meson (and its flavor partners) as the chiral partner.
We propose a novel way of matching effective field theory with the underlying QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive Wilsonian matching conditions between current correlators obtained by the operator product expansion in QCD and those by the hidden local symmetry (HLS) model. This determines without much ambiguity the bare parameters of the HLS at the cutoff scale in terms of the QCD parameters. Physical quantities for the pi and rho system are calculated by the Wilsonian RGE's from the bare parameters in remarkable agreement with the experiment.