Session KK: Hadron Physics and Lattice QCD

Quark fragmentation functions in NJL - jet model

We report on our studies of quark fragmentation functions in the Nambu-Jona-Lasinio (NJL) - jet model. The results of Monte-Carlo simulations for the fragmentation functions to mesons and nucleons, as well as to pion and kaon pairs (dihadron fragmentation functions) are presented. The important role of intermediate vector meson resonances for those semi-inclusive deep inelastic production processes is emphasized. Our studies are very relevant for the extraction of transverse momentum dependent quark distribution functions from measured scattering cross sections.   

Analysis of meson screening mass at finite temperature and density in the effective model

Meson masses are not only fundamental quantities of hadrons but also a key to know the properties of QCD vacuum and the equation of state. At finite temperature ($T$), we can define two kinds of meson masses, which are so called pole mass ($M_{\rm pole}$) and screening mass ($M_{\rm scr}$). $M_{\rm pole}$ ($M_{\rm scr}$) is defined by the exponential decay of the meson propagator in the temporal (spatial) direction. At finite $T$, in lattice QCD (LQCD) simulation, the calculation of $M_{\rm pole}$ is more difficult than that of $M_{\rm scr}$ because the temporal direction is limited up to $1/T$. Moreover, it is possible to calculate the imaginary chemical potential ($\mu$) dependence of $M_{\rm scr}$ because LQCD simulation is feasible. Therefore, it is important to construct effective model which can describe the $T$ and $\mu$ dependence of $M_{\rm pole}$ and $M_{\rm scr}$ simultaneously. In this study, we calculate $M_{\rm scr}$ at imaginary $\mu$. Then, we discuss how to extrapolate $M_{\rm scr}$ from imaginary to real $\mu$ region. Finally, we predict the $\mu$ dependence of $M_{\rm pole}$ from that of $M_{\rm scr}$.   

Possibility of nuclear deformation by anti-kaon in Thomas-Fermi model

Meson-nucleus systems are valuable objects to obtain meson properties in a nuclear medium. Especially anti-kaonic system is very interesting since it could form a kaonic nuclear state with a large binding energy, which is expected to be large enough to change the nuclear structure. We report the possibility of nuclear deformation by the existence of anti-kaon. The nuclear deformation has been discussed in Refs. [1,2]. In our work, nuclear densities are obtained by the Thomas-Fermi model with anti-kaon, where nuclear and anti-kaon densities are obtained by the minimum energy condition in a self-consistent manner as in the standard Thomas-Fermi calculation. We could also calculate the density of the various meson-nuclear systems systematically for nuclei all over the nuclear chart for various strength of interaction. These results would be a guide to know the essential physics of the each system. For antikaonic nuclei, the depth of the potential is known to be still controversial. Thus, in this talk, we show the calculated results for two types of antikaon-nucleus optical potential with much different strength systematically.\\[4pt] [1] A. Dote et al., PRC70(04)044313, PLB590(04)51\\[0pt] [2] J. Mares, E. Friedman, A. Gal, NPA770(06)84   

Omega-Omega interaction on the Lattice

We report our results of central potential between two Omega baryons from 2+1 flavor full Lattice QCD simulation. In the past studies, there is a possibility that some decouplet baryons have a bound state. However, almost all decuplet baryons are unstable due to decays via the strong interaction. An exception is the Omega decuplte baryon, which is stable against the strong decays, so its interaction is suitable to be investigated. It is, however, still difficult to investigate the Omega-Omega interaction experimentally due to its short-life time via weak decays. Therefore, the lattice QCD study for the Omega-Omega interaction is necessary and important. We present results obtained by the extension of the HAL QCD method to the system of two decuplet baryons. Our numerical results are obtained from 2+1 flavor full QCD gauge configurations at $L \sim 2.9 $fm $m_\pi \sim 701$ MeV and m$_\Omega\sim 1966$ MeV, generated by the PACS-CS Collaboration. We find that the Omega-Omega interaction is strong attractive, but it's not strong enough to make a bound state at out simulation set up.   

Determination of the strength of vector interaction by Lattice QCD

Recently, Lattice QCD (LQCD) has become possible to provide the information of QCD phase diagram not only in the finite temperature(T) region but also in the finite quark chemical potential ($\mu_{q})$ region. For small $\mu _{q}$, say $\mu_{q}$ /T1, we can obtain the reliable physical quantities calculated by LQCD. However, it is still difficult to perform LQCD calculation in the large $\mu_{q}$ region, where physics such as neutron stars exists. On the other hand, the effective models allow us to analyze the large $\mu _{q}$ region. Especially, entanglement Polyakov-loop extended Nambu-Jona-Lasinio (EPNJL) model is useful one. But EPNJL model includes an ambiguity of the strength of vector interaction acting on quarks. This ambiguity should be eliminated by LQCD results. By using LQCD, quark number density is calculated in the $\mu_{q}$ /T1.2 region. Quark number density is sensitive to the strength of vector interaction, so we aim to determine the strength of vector interaction from the quark number density calculated by LQCD. In addition, we investigate whether our results are consistent with the observation of neutron stars with two solar mass.   

Canonical approach to the finite density lattice QCD with winding number expansion (I) Lee-Yang Zeros

In lattice QCD, the sign problem hinders us from calculating the grand partition functions at finite density. Based on this present situation, our collaboration employs the canonical approach to overcome the difficulty of the sign problem: it reconstructs the grand partition functions at any valued of finite chemical potential by the fugacity expansion in terms of the canonical partition functions. We evaluate the fermion determinant through the new hopping parameter expansion which exactly treats the spatial hopping contribution. We construct the grand canonical partition functions with this new method and discuss its validity. Then, we study the Lee-Yang zeros to analyze the phase structure on temperature-chemical potential plane using the complexified fugacity expansion of the grand canonical partition functions.   

The extrapolation of the Quark number density by lattice QCD and effective model from imaginary to real chemical potential

We evaluate quark number densities at imaginary chemical potential by doing lattice QCD calculations on an 8$^2$*16*4 lattice with clover-improved Wilson quarks of two flavors. The quark number densities are extrapolated to the real chemical potential region by assuming some functional forms. The extrapolated quark number densities are consistent with those calculated at real chemical potential directly by using the Taylor expansion method for the reweighting factors. Moreover, in order to analyze the physical properties of the quark number density at the large real chemical potential, we use the simple effective model. Then, we aim to explore the other physical quantities and phenomena such as chiral condensates and chiral phase transition using our simple model at imaginary and/or real chemical potentials.   

Canonical approach to the finite density lattice QCD with winding number expansion (II) hadronic observables

The grand canonical ensemble is a difficult subject to treat in the lattice QCD because of the sign problem. The canonical partition function is related to the grand canonical one through the fugacity expansion. In this talk our collaboration perform the fugacity expansion by a method of the hopping parameter expansion in temporal direction for the lattice QCD: winding number expansion. The canonical partition function is constructed for $N_f=2$ QCD starting from gauge configurations at zero chemical potential and in the imaginary chemical potential region. After derivation of the canonical partition function we study the chemical potential dependences of hadronic observables like chiral condensate, quark number density and chiral susceptibility. We also evaluate the Lee-Yang zeros of the complexified grand partition function and study its volume dependence.   

Analysis of 2 color Lattice QCD results by using effective model

We analyze the results of 2 color Lattice QCD at finite temperature and finite density with effective model. We use Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model as effective model. First, we study the properties at the real and imaginary chemical potential ($\mu)$. Then, we study the phase transition line that depends on $\mu$. Finally, we discuss what is important for our effective model to reproduce the lattice simulation results.   

Nucleon spectral function at finite density from QCD sum rules

The QCD sum rule method is a powerful tool for studying hadron properties directly from QCD. Recently, the Maximum Entropy Method (MEM) has been applied and is successful in the analysis of the rho meson sum rule in vacuum [1]. The advantage of this approach is that the spectral functions can be extracted without assuming a specific form. We have applied this analysis method of QCD sum rules to the spectral function of the nucleon and its negative parity excited states in vacuum and have constructed the parity projected nucleon sum rules including the first order $\alpha_s$ corrections [2]. Both the positive and negative parity spectral function of the nucleon are extracted after the MEM is applied to the sum rule. We find that the difference between the positive and negative parity spectral function is mainly caused by the chiral condensate. Applying this method to the analyses in nuclear matter, the mass modification of both the positive and negative parity states can be examined. By doing this, we investigate the relation between the masses and partial restoration of chiral symmetry breaking. \\[4pt] [1] P. Gubler and M. Oka, Prog. Theor. Phys. 124, 995 (2010).\\[0pt] [2] K. Ohtani, P. Gubler and M. Oka, Phys. Rev. D 87, 034027 (2013).   

Unifying Quantum Physics with Biology

We find that the natural logarithm of the age of the universe in quantum mechanical units is close to 137. Since science is not religion, it is our moral duty to recognize the importance of this finding on the following ground. The experimentally obtained number 137 is a mystical number in science, as if written by the hand of God. It is found in cosmology; unlike other theories, it works in biology too. A formula by Boltzmann also works in both: biology and physics, as if it is in the heart of God. His formula simply leads to finding the logarithm of microstates. One of the two conflicting theories of physics (1) Einstein's theory of General Relativity and (2) Quantum Physics, the first applies only in cosmology, but the second applies in biology too. Since we have to convert the age of the universe, 13 billion years, into 1,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 Planck times to get close to 137, quantum physics clearly shows the characteristics of unifying with biology. The proof of its validity also lies in its ability to extend information system observed in biology.