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Tetsuo Nishikawa

Publications and source records attributed to Tetsuo Nishikawa.

18 recordsLinked to original sources
arXiv2024

QCD sum rules for positive and negative parity heavy baryons at next-to-leading order in $α_s$-expansion

QCD sum rules for positive and negative parity heavy baryons in the heavy quark limit are formulated. We apply the method to $Λ$ and $Σ$ channels. We include the next-to-leading order corrections in $α_s$-expansion to dimension 0 and 3 terms in the operator product expansion. The corrections lead to the considerable reduction of the predicted masses and significantly improves the stability with respect to the Borel parameter, especially for negative parity states. It is also found that in the heavy quark limit chiral odd condensates do not contribute to the negative parity states.

hep-ph↗
arXiv2013

QCD sum rules for quark-gluon three-body components in the B meson

We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters, $λ_E$ and $λ_H$, which correspond to matrix elements representing quark-gluon three-body components in the $B$-meson wavefunction. We derive the sum rules for $λ_{E,H}$ calculating the new higher-order QCD corrections, i.e., the order $α_s$ radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensates, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve the stability of the corresponding Borel sum rules and lead to the reduction of the values of $λ_{E,H}$. We also discuss the renormalization-group improvement for the sum rules and present update on the values of $λ_{E,H}$.

hep-ph↗
arXiv2007

ppK- bound states from Skyrmions

The bound kaon approach to the strangeness in the Skyrme model is applied to investigating the possibility of deeply bound $ppK^-$ states. We describe the $ppK^-$ system as two-Skyrmion around which a kaon field fluctuates. Each Skyrmion is rotated in the space of SU(2) collective coordinate. The rotational motions are quantized to be projected onto the spin-singlet proton-proton state. We derive the equation of motion for the kaon in the background field of two Skyrmions at fixed positions. From the numerical solution of the equation of motion, it is found that the energy of $K^-$ can be considerably small, and that the distribution of $K^-$ shows molecular nature of the $ppK^-$ system. For this deep binding, the Wess-Zumino-Witten term plays an important role. The total energy of the $ppK^-$ system is estimated in the Born-Oppenheimer approximation. The binding energy of the $ppK^-$ state is $B.E.\simeq 126$ MeV. The mean square radius of the $pp$ subsystem is $\sqrt{< r_{pp}^2>}\simeq 1.6$ fm.

hep-ph↗
arXiv2007

Axial Vector Tetraquark with Two s-quarks

Possibility of an axial vector isoscalar tetraquark $ud\bar{s}\bar{s}$ is discussed. If a $f_1$ meson in the mass region $1.4-1.5$ GeV consists of four quarks $ns\bar{n}\bar{s}$, the mass of the isoscalar $ud\bar{s}\bar{s}$($\vartheta^+$-meson) state with $J^P=1^+$ is expected to be lower than that of the $f_1$ meson. Within a flux-tube quark model, a possible resonant state of $ud\bar{s}\bar{s}(J^{P}=1^{+})$ is suggested to appear at $\sim$ 1.4 GeV with the width ${\cal{O}}(20\sim 50)$ MeV. We propose that the $\vartheta^+$-meson is the good candidate for the tetraquark search, which would be observed in the $K^+K^+π^-$ decay channel.

nucl-th↗
arXiv2007

Bound kaon approach for the ppK- system in the Skyrme model

The bound kaon approach to the strangeness in the Skyrme model is applied to exploring the possibility of deeply bound $ppK^-$ states. We derive the equation of motion for the kaon in the background of baryon number two Skyrmion expressed by the product ansatz. Collective coordinate quantization is performed to extract the spin-singlet proton-proton state. The numerical solution of the equation of motion shows that the kaon can acquire large binding energy for reasonable proton-proton relative distances. For this deep binding, the Wess-Zumino-Witten term plays an important role. The kaon tends to be centered between the protons.

hep-ph↗
arXiv2006

Positive and negative-parity flavor-octet baryons in coupled QCD sum rules

We apply the method of the QCD sum rule, in which positive- and negative-parity baryons couple with each other, to the flavor-octet hyperons and investigate the parity splittings. We also reexamine the nucleon in the method, which was studied in our previous paper, by carefully choosing the Borel weight. Both in the nucleon and hyperon channels the obtained sum rules turn out to have a very good Borel stability and also have a Borel window, an energy region in which the OPE converges and the pole contribution dominates over the continuum contribution. The predicted masses of the positive- and negative-parity baryons reproduce the experimental ones fairly well in the $Λ$ and $Σ$ channels, if we assign the $Λ(1670)$ and the $Σ(1620)$ to the parity partners of the $Λ$ and the $Σ$, respectively. This implies that the $Λ(1405)$ is not the party partner of the $Λ$ and may be a flavor-singlet or exotic state. In the $Ξ$ channel, the sum rule predicts the mass of the negative-parity state to be about 1.8 GeV, which leads to two possibilities; one is that the observed state with the closest mass, $Ξ(1690)$, is the parity partner and the other is that the parity partner is not yet found but exists around 1.8 GeV.

hep-ph↗
arXiv2005

Color Ferromagnetic Quark Matter in Neutron Stars

We show that color ferromagnetic phase of quark matter is energetically more favored than color superconducting phases in neutron stars. Namely, increasing baryon density in neutron stars transforms nuclear matter into the quark matter of the color ferromagnetic phase. Further increase of the density makes the quark matter take the color superconducting phases. We find that a critical mass of the neutron star with such an internal structure is about $1.6M_{\odot}$. We stress that analysis of gluon dynamics is crucial for exploring dense quark matter.

hep-ph↗
arXiv2005

Coupled QCD sum rules for positive and negative-parity nucleons

A new approach of the QCD sum rule is proposed in which positive and negative-parity baryons couple with each other. With positive and negative-parity states explicitly taken into account, sum rules are derived by means of the dispersion relation in energy. The method is applied to the nucleon channel and the parity splitting of the nucleon resonance states is studied. It is found that the obtained sum rules have a very good Borel stability. This suggests that the ansatz for the spectral function in the present sum rule approximates the physical spectrum better than the usual lowest pole plus continuum ansatz. The predicted masses of the positive and negative nucleons reproduce the experimental ones fairly well. Especially, the mass difference is extremely close to the experimental value.

hep-ph↗
arXiv2005

Spin-3/2 pentaquark in the QCD sum rule

We study $IJ^P=0{3/2}^\pm$ and $1{3/2}^\pm$ pentaquark states with $S=+1$ in the QCD sum rule approach. The QCD sum rule for positive parity states and that for negative parity are independently derived. The sum rule suggests that there exist the $0{3/2}^-$ and the $1{3/2}^-$ states. These states may be observed as extremely narrow peaks since they can be much below the $S$-wave threshold and since the only allowed decay channels are $NK$ in $D$-wave, whose centrifugal barriers are so large that the widths are strongly suppressed. The $0{3/2}^-$ state may be assigned to the observed $Θ^+(1540)$ and the $1{3/2}^-$ state can be a candidate for $Θ^{++}$.

hep-ph↗
arXiv2004

Theta++ from QCD sum rule

We study the pentaquark $uudd\bar s$ with $J=3/2$ and I=1 ($Θ^{++}$) in the QCD sum rule approach. We derive the QCD sum rules for positive and negative parity states of the pentaquark. The QCD sum rule predicts that there exists $Θ^{++}$ with negative parity and its mass is $1.5\sim1.6$ GeV. The negative parity $Θ^{++}$ can be extremely narrow, since it lies much below the $ΔK$ threshold and the decay into $KN$ state is strongly suppressed due to the $D$-wave centrifugal barrier. Also, the possibility of the existence of the $Θ^{++}$ with positive parity is not excluded. Although it nearly degenerates with the negative parity state, it may be broader than the negative parity state.

hep-ph↗
arXiv2004

Two-pion bound state in sigma channel at finite temperature

We study how we can understand the change of the spectral function and the pole location of the correlation function for sigma at finite temperature, which were previously obtained in the linear sigma model with a resummation technique called optimized perturbation theory. There are two relevant poles in the sigma channel. One pole is the original sigma pole which shows up as a broad peak at zero temperature and becomes lighter as the temperature increases. The behavior is understood from the decreasing of the sigma condensate, which is consistent with the Brown-Rho scaling. The other pole changes from a virtual state to a bound state of pion-pion as the temperature increases which causes the enhancement at the pion-pion threshold. The behavior is understood as the emergence of the pion-pion bound state due to the enhancement of the pion-pion attraction by the induced emission in medium. The latter pole, not the former, eventually degenerates with pion above the critical temperature of the chiral transition. This means that the observable "sigma" changes from the former to the latter pole, which can be interpreted as the level crossing of "sigma" and pion-pion at finite temperature.

hep-ph↗
arXiv2004

Flavour-singlet g_A and the QCD sum rule incorporating instanton effects

We derive a QCD sum rule for the flavour-singlet axial coupling constant $g_A^{(0)}$ from a two point correlation function of flavour-singlet axial vector currents in a one-nucleon state. In evaluating the correlation function by an operator product expansion we take into account the terms up to dimension 6. This correlation function receives an additional two-loop diagram which comes from an (anti-)instanton. If we do not include it, $g_A^{(0)}$ is estimated to be 0.8. However, the additional diagram due to instantons contributes negatively and reduces $g_A^{(0)}$ towards the experimental value.

hep-ph↗
arXiv2004

Two-Hadron-Irreducible QCD Sum Rule for Pentaquark Baryon

We point out that naive pentaquark correlations function include two-hadron-reducible contributions, which are given by convolution of baryon and meson correlation functions and have nothing to do with pentaquark. We show that the two-hadron-reducible contributions are large in the operator product expansion of the correlation functions of three existing works on the pentaquark. Therefore, it is dangerous to draw a conclusion from the sum rules using naive pentaquark correlation functions with naive ansatz for the spectral function under the dispersion integral. Instead, we propose to use the two-hadron-irreducible correlation function, which is obtained by subtracting the two-hadron-reducible contribution from the naive correlation function. Taking one of the works as an example we demonstrate how drastically the results can change if we remove the two-hadron-reducible part from the naive correlation function. We obtain the result opposite to the original work for the parity of the pentaquark.

hep-ph↗
arXiv2004

Quantum Hall States of Gluons in Quark Matter

We have recently shown that dense quark matter possesses a color ferromagnetic phase in which a stable color magnetic field arises spontaneously. This ferromagnetic state has been known to be Savvidy vacuum in the vacuum sector. Although the Savvidy vacuum is unstable, the state is stabilized in the quark matter. The stabilization is achieved by the formation of quantum Hall states of gluons, that is, by the condensation of the gluon's color charges transmitted from the quark matter. The phase is realized between the hadronic phase and the color superconducting phase. After a review of quantum Hall states of electrons in semiconductors, we discuss the properties of quantum Hall states of gluons in quark matter in detail. Especially, we evaluate the energy of the states as a function of the coupling constant. We also analyze solutions of vortex excitations in the states and evaluate their energies. We find that the states become unstable as the gauge coupling constant becomes large, or the chemical potential of the quarks becomes small, as expected. On the other hand, with the increase of the chemical potential, the color superconducting state arises instead of the ferromagnetic state. We also show that the quark matter produced by heavy ion collisions generates observable strong magnetic field $\sim 10^{15}$ Gauss when it enters the ferromagnetic phase.

hep-ph↗
arXiv2003

Effect of pion thermal width on the sigma spectrum

We study the effect of the thermal width of $π$ on the spectral function of $σ$. In order to take into account a finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of the complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without the pion thermal width, the peak is shown to be smeared out. We also search for the poles of the $σ$ propagator and analyze the behavior of the spectral function with these poles.

hep-ph↗
arXiv2003

Effect of pion thermal width on the sigma spectrum

We study the effect of thermal width of $π$ on the spectral function of $σ$ applying a resummation technique called optimized perturbation theory at finite temperature ($T$) to ${\cal O}(4)$ linear sigma model. In order to take into account finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without pion thermal width, the peak is proved to be smeared out. We also search for the poles of the $σ$ propagator and analyze the behavior of the spectral function with these poles.

hep-ph↗
arXiv2003

On the thermal sunset diagram for scalar field theories

We study the so-called `` sunset diagram'', which is one of two-loop self-energy diagrams, for scalar field theories at finite temperature. For this purpose, we first find the complete expression of the bubble diagram, the one-loop subdiagram of the sunset diagram, for arbitrary momentum. We calculate the temperature independent part and dependent part of the sunset diagram separately. For the former, we obtain the discontinuous part first and the finite continuous part next using a twice-subtracted dispersion relation. For the latter, we express it as a one-dimensional integral in terms of the bubble diagram. We also study the structure of the discontinuous part of the sunset diagram. Physical processes, which are responsible for it, are identified. Processes due to the scattering with particles in the heat bath exist only at finite temperature and generate discontinuity for arbitrary momentum, which is a remarkable feature of the two-loop diagrams at finite temperature. As an application of our result, we study the effect of the diagram on the spectral function of the sigma meson at finite temperature in the linear sigma model, which was obtained at one-loop order previously. At high temperature where the decay $σ\toππ$ is forbidden, sigma acquires a finite width of the order of $10 {\rm MeV}$ while within the one-loop calculation its width vanishes. At low temperature, the spectrum does not deviate much from that at one-loop order. Possible consequences with including other two-loop diagrams are discussed.

hep-ph↗