arXiv subjects

Takeru Yokota

Publications and source records attributed to Takeru Yokota.

21 records · Page 2Linked to original sources

arXiv2016

Spectral functions in functional renormalization group approach -- analysis of the collective soft modes at the QCD critical point --

We first review the method to calculate the spectral functions in the functional renormalization group (FRG) approach, which has been recently developed. We also provide the numerical stability conditions given by the present authors for a generic nonlinear evolution equation that are necessary for obtaining the accurate effective potential from the flow equation in the FRG. As an interesting example, we report the recent calculation of the spectral functions of the mesonic and particle-hole excitations using a chiral effective model of Quantum Chromodynamics (QCD); we extract the dispersion relations from them and try to reveal the nature of the soft modes at the QCD critical point (CP) where the phase transition is second order. Our result shows that a clear development and the softening of the phonon mode in the space-like region as the system approaches the CP; furthermore it turns out that the sigma mesonic mode once in the time-like region gets to merge with the phonon mode in the close vicinity of the CP, implying a novel possibility about the nature of the soft mode of the QCD CP.

hep-ph↗

arXiv2016

Novel picture of the soft modes at the QCD critical point based on the FRG method

We investigate the soft mode at the QCD critical point (CP) on the basis of the functional renormalization group. We calculate the spectral functions in the meson channels in the two-flavor quark--meson model. Our result shows that the energy of the peak position of the particle--hole mode in the sigma channel becomes vanishingly small as the system approaches the QCD CP, which is a manifestation of the softening of the phonon mode. We also extract the dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which leads to a finding that the dispersion curve of the sigma-mesonic mode crosses the light-cone into the space-like momentum region, and then eventually merges into the phonon mode as the system approaches further close to the CP. This may suggest that the sigma-mesonic mode forms the soft mode together with the hydrodynamic mode at the CP.

hep-ph↗

arXiv2016

Functional renormalization group analysis of the soft mode at the QCD critical point

We make an intensive investigation of the soft mode at the quantum chromodynamics (QCD) critical point on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral functions $ρ_{σ, π}(ω,\, p)$ in the scalar ($σ$) and pseudoscalar ($π$) channels beyond the random phase approximation in the quark--meson model. At finite baryon chemical potential $μ$ with a finite quark mass, the baryon-number fluctuation is coupled to the scalar channel and the spectral function in the $σ$ channel has a support not only in the time-like ($ω\,>\,p$) but also in the space-like ($ω\,<\, p$) regions, which correspond to the mesonic and the particle--hole phonon excitations, respectively. We find that the energy of the peak position of the latter becomes vanishingly small with the height being enhanced as the system approaches the QCD critical point, which is a manifestation of the fact that the phonon mode is the {\em soft mode} associated with the second-order transition at the QCD critical point, as has been suggested by some authors. Moreover, our extensive calculation of the spectral function in the $(ω, p)$ plane enables us to see that the mesonic and phonon modes have the respective definite dispersion relations $ω_{σ.{\rm ph}}(p)$, and it turns out that $ω_σ(p)$ crosses the light-cone line into the space-like region, and then eventually merges into the phonon mode as the system approaches the critical point more closely. This implies that the sigma-mesonic mode also becomes soft at the critical point. We also provide numerical stability conditions that are necessary for obtaining the accurate effective potential from the flow equation.

hep-ph↗