Hidden Local Symmetry Lagrangian Research Articles

Skyrmions with vector mesons in the hidden local symmetry approach

The roles of light $\rho$ and $\omega$ vector mesons in the Skyrmion are investigated in a chiral Lagrangian derived from the hidden local symmetry (HLS) up to $O(p^4)$ including the homogeneous Wess-Zumino (hWZ) terms. We write a general "master formula" that allows us to determine the parameters of the HLS Lagrangian from a class of holographic QCD models valid at large $N_c$ and $\lambda$ ('t Hooft constant) limit by integrating out the infinite towers of vector and axial-vector mesons other than the lowest $\rho$ and $\omega$ mesons. Within this approach we find that the physical properties of the Skyrmion as the solitonic description of baryons are \textit{independent} of the HLS parameter $a$. Therefore the only parameters of the model are the pion decay constant and the vector meson mass. Once determined in the meson sector, we have a totally parameter-free theory that allows us to study unequivocally the role of light vector mesons in the Skyrmion structure. We find, as suggested by Sutcliffe, that inclusion of the $\rho$ meson reduces the soliton mass, which makes the Skyrmion come closer to the Bogomol'nyi-Prasad-Sommerfield (BPS) soliton, but the role of the $\omega$ meson is found to increase the soliton mass. In a stark contrast, the $\Delta$-$N$ mass difference, which is determined by the moment of inertia in adiabatic collective quantization of the Skyrmion, is increased by the $\rho$ vector meson, while it is reduced by the inclusion of the $\omega$ meson. All these observations show the importance of the $\omega$ meson in the properties of the nucleon and nuclear matter in the Skyrme model.

Resonances Generated by the Vector Meson-Baryon Dynamics

We have recently studied vector meson-octet baryon (VB) interactions with the aim to find dynamical generation of resonances in such systems. For this, we consider the s-, t-, u-channel diagrams along with a contact interaction originating from the hidden local symmetry Lagrangian. We find the contribution from all these sources, except the s-channel, to be important. The amplitudes obtained by solving the coupled channel Bethe–Salpeter equations for the systems with total strangeness zero show generation of one isospin 3/2, spin 1/2 resonance and three isospin 1/2 resonances: two with spin 3/2 and one with spin 1/2. We identify these resonances with Δ (1900) S31, N*(2080) D13, N* (1700) D13, and N*(2090) S11, respectively. Further, we briefly discuss the results of our investigation of the VB systems when coupled to the pseudoscalar meson-baryon (PB) channels. We find that the low-lying resonances couple strongly to the VB channels, a result which can be useful in studying the reactions involving pseudoscalar and vector meson exchanges. In case of the higher mass resonances (in the 1,800–2,200 MeV region), we find that some of the states claimed as dynamically generated states in the VB system can disappear due to their coupling to the PB channels. We also find that new states can appear from PB–VB coupled channel dynamics; for example, we find that a Σ resonance near 1,400 MeV gets developed due to such an effect.

Vector meson-baryon dynamics and generation of resonances

The purpose of this work is to study vector meson-octet baryon interactions with the aim to find dynamical generation of resonances in such systems. For this, we consider $s$-, $t$-, $u$-channel diagrams along with a contact interaction originating from the hidden local symmetry Lagrangian. We find the contribution from all these sources, except the $s$ channel, to be important. The amplitudes obtained by solving coupled channel Bethe-Salpeter equations for systems with total strangeness zero, show the generation of one isospin $3/2$, spin $1/2$ resonance and three isospin $1/2$ resonances: two with spin $3/2$ and one with spin $1/2$. We identify these resonances with $\ensuremath{\Delta}(1900){S}_{31}$, ${N}^{*}(2080){D}_{13}$, ${N}^{*}(1700){D}_{13}$, and ${N}^{*}(2090){S}_{11}$, respectively.

Chiral doubling of heavy-light hadrons and the vector manifestation of hidden local symmetry

Starting with a hidden local symmetry Lagrangian at the vector manifestation (VM) fixed point that incorporates heavy-quark symmetry and matching the bare theory to QCD, we calculate the splitting of chiral doublers of heavy-light mesons proposed by Nowak, Rho and Zahed, and Bardeen and Hill. We show, in the three-flavor chiral limit, that the splitting is directly proportional to the light-quark condensate <\bar{q}q> and comes out to be \sim (1/3) m_N where m_N is the nucleon mass, implying that the splitting vanishes in the chiral limit at the chiral restoration point -- temperature T_c, density n_c or number of flavors N_F^c. The result turns out to be surprisingly simple with the vector (\rho) meson playing the crucial role in quantum corrections, pointing to the relevance of the VM to QCD in the way chiral symmetry is manifested in hadronic matter. We also make predictions on the hadronic decay processes of the excited heavy (charm) -light mesons \tilde{D}.

Vector manifestation and violation of vector dominance in hot matter

We show the details of the calculation of the hadronic thermal corrections to the two-point functions in the effective field theory of QCD for pions and vector mesons based on the hidden local symmetry (HLS) in hot matter using the background field gauge. We study the temperature dependence of the pion velocity in the low-temperature region determined from the hadronic thermal corrections, and show that, due to the presence of the dynamical vector meson, the pion velocity is smaller than the speed of the light already at one-loop level, in contrast to the result obtained in the ordinary chiral perturbation theory including only the pion at one-loop. Including the intrinsic temperature dependences of the parameters of the HLS Lagrangian determined from the underlying QCD through the Wilsonian matching, we show how the vector manifestation (VM), in which the massless vector meson becomes the chiral partner of pion, is realized at the critical temperature. We present a new prediction of the VM on the direct photon– π– π coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion: we find that the VD is largely violated at the critical temperature, which indicates that the assumption of the VD made in several analyses on the dilepton spectra in hot matter may need to be weakened for consistently including the effect of the dropping mass of the vector meson.

The Vector Manifestation and Effective Degrees of Freedom at Chiral Restoration

The role of effective degrees of freedom on the vector and axial-vector susceptibilities and the pion velocity at chiral restoration is analyzed. We consider two possible scenarios, one in which pions are considered to be the only low-lying degrees of freedom -- that we shall refer to as "standard" -- and the other in which pions, vector mesons and constituent quarks (or quasiquarks in short) are the relevant low-lying degrees of freedom -- that we shall refer to as "vector manifestation (VM)." We show at one-loop order in chiral perturbation theory with hidden local symmetry Lagrangian that while in the standard scenario, the pion velocity vanishes at the chiral transition, it instead approaches unity in the VM scenario. If the VM is realized in nature, the chiral phase structure of hadronic matter can be much richer than that in the standard one and the phase transition will be a smooth crossover: Sharp vector and scalar excitations are expected in the vicinity of the critical point. Some indirect indications that lend support to the VM scenario, and in consequence to BR scaling, are discussed.

Vector manifestation in hot matter

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 ρ meson becomes massless degenerate with π as the chiral partner. This is done by including, in addition to the hadronic thermal effects due to the π- and ρ-loops, the intrinsic temperature dependences of the parameters of the HLS Lagrangian through the matching of the HLS with the underlying QCD.

φmeson propagation in a hot hadronic gas

The hidden local symmetry Lagrangian is used to study the interactions of $\ensuremath{\varphi}$ mesons with other pseudoscalar and vector mesons in a hadronic gas at finite temperature. We have found a significantly small $\ensuremath{\varphi}$ mean free path (less than 2.4 fm at $T&gt;170 \mathrm{MeV})$ due to large collision rates with $\ensuremath{\rho}$ mesons, kaons, and predominantly ${K}^{*}$ in spite of their heavy mass. This implies that $\ensuremath{\varphi}$ mesons produced after hadronization in relativistic heavy ion collisions will not leave the hadronic system without scattering. The effect of these interactions on the time evolution of the $\ensuremath{\varphi}$ density in the expanding hadronic fireball is investigated.

Vector manifestation of chiral symmetry.

We propose "vector manifestation" (VM) 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, in sharp contrast to the traditional manifestation á la the linear sigma model where the symmetry is restored by the degenerate pion and the scalar meson. The application to the chiral phase transition of large N(f) QCD is performed using the hidden local symmetry Lagrangian. Combined with the Wilsonian matching proposed recently, VM determines the critical number of massless flavors N(f) approximately equal to 5 without much ambiguity.

Skyrme solitons with vector mesons

We investigate the Skyrme type soliton with vector mesons (ρ, A1 and ω), first in the massive Yang-Mills approach and then using the hidden local symmetry Lagrangian. It is demonstrated that the two schemes give identical results for the soliton properties. A comparison is made with alternative approaches in which the A1 degrees of freedom is eliminated.