The ΔΔ dibaryon resonance <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> with <math><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>,</mo><mi>I</mi><mo>)</mo><mo>=</mo><mo>(</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></math> is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses (<math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><mn>679</mn><mo>,</mo><mn>841</mn></math> and 1018 MeV). By using the HAL QCD method, the central Δ-Δ potential in the <math><mmultiscripts><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>7</mn></mrow></mmultiscripts></math> channel is obtained from the lattice data with the lattice spacing <math><mi>a</mi><mo>≃</mo><mn>0.121</mn></math> fm and the lattice size <math><mi>L</mi><mo>≃</mo><mn>3.87</mn></math> fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> is formed with the binding energy 25-40 MeV below the ΔΔ threshold for the heavy pion masses. The tensor part of the transition potential from ΔΔ to NN is also extracted to investigate the coupling strength between the S-wave ΔΔ system with <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup></math> and the D-wave NN system. Although the transition potential is strong at short distances, the decay width of <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> to NN in the D-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study.

Japan

Shinya Gongyo

Kenji Sasaki

Takaya Miyamoto

Sinya Aoki

Takumi Doi

Tetsuo Hatsuda

Yoichi Ikeda

Takashi Inoue

Noriyoshi Ishii

(2380) dibaryon from lattice QCD

The approximated partial-wave decomposition method for discrete data on a cubic lattice, developed by Misner, is applied to the calculation of <math><mi>S</mi></math>-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>N</mi></math> system calculated in (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD on a <math><mrow><mo>(</mo><mn>32</mn><mi>a</mi><mtext> </mtext><mtext> </mtext><mi>fm</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> lattice with lattice spacing <math><mi>a</mi><mo>≃</mo><mn>0.0907</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and <math><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>700</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We find that by Misner’s method the <math><mi>l</mi><mo>=</mo><mn>0</mn></math> component can be successfully extracted from the NBS wave function projected to the <math><msubsup><mi>A</mi><mn>1</mn><mo>+</mo></msubsup></math> representation of the cubic group, which contains small <math><mi>l</mi><mo>≥</mo><mn>4</mn></math> components. Furthermore, while the higher partial-wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second-order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misner’s method, where the Laplacian can be evaluated analytically for each partial-wave component. Despite the difference in the potentials, the two methods give almost identical results on the central values and magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misner’s method works well in lattice QCD with the HAL QCD method, but also that the contaminations from higher partial waves in the study of <math><mi>S</mi></math>-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial-wave channels in the HAL QCD method with Misner’s decomposition, where the utility of this new technique may become clearer.

Yutaro Akahoshi

Tatsumi Aoyama

Partial wave decomposition on the lattice and its applications to the HAL QCD method

The nucleon(N)-Omega(Ω) system in the S-wave and spin-2 channel (<math><mmultiscripts><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>5</mn></mrow></mmultiscripts></math>) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses (<math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≃</mo><mn>146</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and <math><msub><mrow><mi>m</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>≃</mo><mn>525</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>). The time-dependent HAL QCD method is employed to convert the lattice QCD data of the two-baryon correlation function to the baryon-baryon potential and eventually to the scattering observables. The <math><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>5</mn></mrow></mmultiscripts><mo>)</mo></math> potential, obtained under the assumption that its couplings to the D-wave octet-baryon pairs are small, is found to be attractive in all distances and to produce a quasi-bound state near unitarity: In this channel, the scattering length, the effective range and the binding energy from QCD alone read <math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>5.30</mn><mo>(</mo><mn>0.44</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.01</mn></mrow><mrow><mo>+</mo><mn>0.16</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>fm</mtext></math>, <math><msub><mrow><mi>r</mi></mrow><mrow><mi>eff</mi></mrow></msub><mo>=</mo><mn>1.26</mn><mo>(</mo><mn>0.01</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.01</mn></mrow><mrow><mo>+</mo><mn>0.02</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>fm</mtext></math>, <math><mi>B</mi><mo>=</mo><mn>1.54</mn><mo>(</mo><mn>0.30</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.10</mn></mrow><mrow><mo>+</mo><mn>0.04</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>, respectively. Including the extra Coulomb attraction, the binding energy of <math><mi>p</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mmultiscripts><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>5</mn></mrow></mmultiscripts><mo>)</mo></math> becomes <math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><mn>2.46</mn><mo>(</mo><mn>0.34</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.11</mn></mrow><mrow><mo>+</mo><mn>0.04</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>. Such a spin-2 <math><mi>p</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup></math> state could be searched through two-particle correlations in p-p, p-nucleus and nucleus-nucleus collisions.

Takumi Iritani

Iran

Faisal Etminan

Ω dibaryon from lattice QCD near the physical point

The <math><mrow><mi>Ξ</mi><mi>Ξ</mi></mrow></math> interaction in the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> channel is studied to examine the convergence of the derivative expansion of the nonlocal HAL QCD potential at the next-to-next-to-leading order (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math>). We find that (i) the leading order potential from the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math> analysis provides the scattering phase shifts accurately at low energies, (ii) the full <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math> potential provides only a small correction to the phase shifts even at higher energies below the inelastic threshold, and (iii) the potential determined from the wall quark source at the leading order analysis agrees with the one at the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math> analysis except at short distances, and thus, it gives correct phase shifts at low energies. We also study the possible systematic uncertainties in the HAL QCD potential, such as the inelastic state contaminations and the finite volume artifact for the potential, and we find that they are well under control for this particular system.

Hidekatsu Nemura

Systematics of the HAL QCD potential at low energies in lattice QCD

Abstract We study the asymptotic behaviors of the Nambu–Bethe–Salpeter (NBS) wave functions, which are important for the HAL QCD potential method to extract hadron interactions, in the case that a bound state exists in the system. We consider the complex scalar particles, two of which lead to the formation of a bound state. In the case of the two-body system, we show that the NBS wave functions for the bound state, as well as scattering states in the asymptotic region, behave like the wave functions in quantum mechanics, which carry the information of the binding energy as well as the scattering phase shift. This analysis theoretically establishes under some conditions that the HAL QCD potential can correctly reproduce not only the scattering phase shift but also the binding energy. As an extension of the analysis, we also study the asymptotic behaviors of all possible NBS wave functions in the case of three-body systems, two of which can form a bound states.

Asymptotic behavior of Nambu–Bethe–Salpeter wave functions for scalar systems with a bound state

The <math><mi>Ω</mi><mi>Ω</mi></math> system in the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> channel (the most strange dibaryon) is studied on the basis of the (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD simulations with a large volume <math><mrow><mo>(</mo><mn>8.1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> and nearly physical pion mass <math><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>146</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> at a lattice spacing of <math><mi>a</mi><mo>≃</mo><mn>0.0846</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length <math><msub><mi>a</mi><mn>0</mn></msub><mo>=</mo><mn>4.6</mn><mo>(</mo><mn>6</mn><mo>)</mo><msubsup><mo>(</mo><mrow><mo>−</mo><mn>0.5</mn></mrow><mrow><mo>+</mo><mn>1.2</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, the effective range <math><msub><mi>r</mi><mi>eff</mi></msub><mo>=</mo><mn>1.27</mn><mo>(</mo><mn>3</mn><mo>)</mo><msubsup><mo>(</mo><mrow><mo>−</mo><mn>0.03</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, and the binding energy <math><msub><mi>B</mi><mrow><mi>Ω</mi><mi>Ω</mi></mrow></msub><mo>=</mo><mn>1.6</mn><mo>(</mo><mn>6</mn><mo>)</mo><msubsup><mo>(</mo><mrow><mo>−</mo><mn>0.6</mn></mrow><mrow><mo>+</mo><mn>0.7</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. These results indicate that the <math><mi>Ω</mi><mi>Ω</mi></math> system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions.

Most Strange Dibaryon from Lattice QCD

We study rotating fermionic matter at finite temperature in the framework of the Nambu-Jona-Lasinio model. In order to respect causality the rigidly rotating system must be bound by a cylindrical boundary with appropriate boundary conditions that confine the fermions inside the cylinder. We show the finite geometry with the MIT boundary conditions affects strongly the phase structure of the model leading to three distinct regions characterized by explicitly broken (gapped), partially restored (nearly gapless) and spontaneously broken (gapped) phases at, respectively, small, moderate and large radius of the cylinder. The presence of the boundary leads to specific steplike irregularities of the chiral condensate as functions of coupling constant, temperature and angular frequency. These steplike features have the same nature as the Shubnikov-de Haas oscillations with the crucial difference that they occur in the absence of both external magnetic field and Fermi surface. At finite temperature the rotation leads to restoration of spontaneously broken chiral symmetry while the vacuum at zero temperature is insensitive to rotation (“cold vacuum cannot rotate”). As the temperature increases the critical angular frequency decreases and the transition becomes softer. A phase diagram in angular frequency-temperature plane is presented. We also show that at fixed temperature the fermion matter in the chirally restored (gapless) phase has a higher moment of inertia compared to the one in the chirally broken (gapped) phase.

Russia

France

M. Chernodub

Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics

We study numerically the phase structure and the gluon propagator of the SU(2) gauge-Higgs model in two dimensions. First, we calculate gauge-invariant quantities, in particular the static potential from Wilson Loop, the W propagator, and the plaquette expectation value. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. In the confinement-like region, the static potential rises linearly, with string breaking at large distances, while in the Higgs-like region, it is of Yukawa type, consistent with a Higgs-type mechanism. The correlation length obtained from the W propagator has a finite maximum between these regions. The plaquette expectation value shows a smooth cross-over consistent with the Fradkin-Shenker-Osterwalder-Seiler theorem. From these results, we suggest that there is no phase transition in two dimensions. We also calculate a gauge-dependent order parameter in Landau gauge. Unlike gauge invariant quantities, the gauge non-invariant order parameter has a line of discontinuity separating these two regions. Finally we calculate the gluon propagtor. We infer from its infrared behavior that the gluon propagator would vanish at zero momentum in the infinite-volume limit, consistent with an analytical study.