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Sinya Aoki

Publications and source records attributed to Sinya Aoki.

At least 37 records · Page 2Linked to original sources
arXiv2023

Study on Lambda(1405) in the flavor SU(3) limit in the HAL QCD method

We study interactions between the S-wave octet pseudo-scalar (PS) meson and octet baryon in the flavor SU(3) limit using the HAL QCD method at the PS meson mass $m_M\approx 670~\textrm{MeV}$. We focus on the singlet and two octet channels, where the poles corresponding to $Λ(1405)$ have been predicted in the chiral unitary model. For calculations with $Λ$-baryon source operators with zero momentum, we employ the conventional stochastic calculation combined with the covariant-approximation averaging to calculate the all-to-all propagators. Due to a zero of the R-correlator (a kind of wave function), the leading order (LO) potential obtained by the single channel analysis has a singular point in all channels, which makes it difficult to obtain reliable binding energies. To overcome this problem, we take a linear combination of two octet R-correlators with a relative weight such that it does not cross zero, as two octet channels are suggested to couple to the same low-energy states with different weights. The potential calculated from such the linear combination shows strong attraction without singularities, though its shape depends on the relative weight. Our estimation for the binding energy in the octet channel is $E^{8_{s(a)}}_{\textrm{bind}}=163(7)(^{+16} _{-64})~\textrm{MeV}$, which is consistent with 156(8) MeV estimated from the two-point correlation function within errors.

hep-lat↗
arXiv2023

Doubly Charmed Tetraquark $T^+_{cc}$ from Lattice QCD near Physical Point

The doubly charmed tetraquark $T^+_{cc}$ recently discovered by the LHCb Collaboration is studied on the basis of $(2+1)$-flavor lattice QCD simulations of the $D^*D$ system with nearly physical pion mass $m_π=146$ MeV. The interaction of $D^*D$ in the isoscalar and $S$-wave channel, derived from the hadronic spacetime correlation by the HAL QCD method, is attractive for all distances and leads to a near-threshold virtual state with a pole position $E_\text{pole}=-59\left(^{+53}_{-99}\right)\left(^{+2}_{-67}\right)$ keV and a large scattering length $1/a_0=0.05(5)\left(^{+2}_{-2}\right)~\text{fm}^{-1}$. The virtual state is shown to evolve into a loosely bound state as $m_π$ decreases to its physical value by using a potential modified to $m_π=135$ MeV based on the pion-exchange interaction. Such a potential is found to give a semiquantitative description of the LHCb data on the $D^0D^0π^+$ mass spectrum. Future study is necessary to perform physical-point simulations with the isospin-breaking and open three-body-channel effects taken into account.

hep-lat↗
arXiv2023

Bulk modified gravity from a thermal CFT by the conformal flow

We construct a bulk spacetime from a boundary CFT, $O(N)$ free scalar model, at finite temperature using a smearing technique, called a conformal flow. The bulk metric is constructed as an information metric associated with the boundary thermal state. Near the boundary (UV region), an asymptotically AdS spacetime is obtained with a leading order perturbation of scalar mode. Based on the falloff behavior of the perturbations and the $O(N)$ symmetry in the CFT, we argue that the corresponding bulk theory is a modified gravity with scalar mode such as $f(R)$ gravity rather than Einstein's general relativity coupled minimally to matter fields. Moving to Einstein frame, we show that the metric is asymptotically the same as the AdS black brane solution. On the other hand, deep in the bulk (IR region), the spacetime turns out to be conformally equivalent to the near horizon limit of AdS extremal black brane, though it is no longer a solution of $f(R)$ gravity, and hence more general classes of modified gravity need to be considered.

hep-th↗
arXiv2023

Energies and a gravitational charge for massive particles in general relativity

In this paper, we investigate relations or differences among various conserved quantities which involve the matter Energy Momentum Tensor (EMT) in general relativity. These charges include the energy with Einstein's pseudo EMT, the generalized Komar integral, or the ADM energy, all of which can be derived from Noether's second theorem, as well as an extra conserved charge recently proposed in general relativity. For detailed analyses, we apply definitions of these charges to a system of free massive particles. We employ the post-Newtonian (PN) expansion to make physical interpretations. We find that the generalized Komar integral is not conserved at the first non-trivial order in the PN expansion due to non-zero contributions at spatial boundaries, while the energy with Einstein's pseudo EMT at this order agrees with a total energy of massive particles with gravitational interactions through the Newtonian potential, and thus is conserved. In addition, this total energy is shown to be identical to the ADM energy not only at this order but also all orders in the PN expansion. We next calculate an extra conserved charge for the system of massive particles, at all orders in the PN expansion, which turns out to be a total number of particles. We call it a gravitational charge, since it is clearly different from the total energy. We finally discuss an implication from a fact that there exist two conserved quantities, energy and gravitational charge, in general relativity.

gr-qc↗
arXiv2023

Lattice study on a tetra-quark state $T_{bb}$ in the HAL QCD method

We study a doubly-bottomed tetra-quark state $(bb\bar{u}\bar{d})$ with quantum number $I(J^P)=0(1^+)$, denoted by $T_{bb}$, in lattice QCD with the Non-Relativistic QCD (NRQCD) quark action for $b$ quarks. Employing $(2+1)$-flavor gauge configurations at $a \approx 0.09$ {fm} on $32^3\times 64$ lattices, we have extracted the coupled channel potential between $\bar{B}\bar{B}^*$ and $\bar{B}^* \bar{B}^*$ in the HAL QCD method, which predicts an existence of a bound $T_{bb}$ below the $\bar{B}\bar{B}^*$ threshold. By extrapolating results at $m_π\approx 410,\, 570,\, 700$ {MeV} to the physical pion mass $m_π\approx140$ {MeV}, we obtain a biding energy with its statistical error as $E_{\rm binding}^{\rm (single)} = 155(17)$ MeV and $E_{\rm binding}^{\rm (coupled)} = 83(10)$ MeV, where ``coupled" means that effects due to virtual $\bar{B}^* \bar{B}^*$ states are included through the coupled channel potential, while only a potential for a single $\bar{B}\bar{B}^*$ channel is used in the analysis for ``single". A comparison shows that the effect from virtual $\bar{B}^* \bar{B}^*$ states is quite sizable to the binding energy of $T_{bb}$. We estimate systematic errors to be $\pm 20$ MeV at most, which are mainly caused by the NRQCD approximation for $b$ quarks.

hep-lat↗
arXiv2023

Entropy and its conservation in expanding Universe

We investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding Universe. We show that the conserved charge in the inflation era becomes the Bekenstein-Hawking entropy for de Sitter space, and it becomes the matter entropy and the radiation entropy in the matter and radiation dominated eras, respectively, while the charge itself is always conserved. These properties are qualitatively confirmed by a numerical analysis of a model with a scalar field and radiations. Results in this paper provide more evidences on the interpretation that the conserved charge in general relativity corresponds to entropy.

hep-th↗
arXiv2023

Colliding gravitational waves and singularities

We have investigated a model of colliding plain gravitational waves, proposed by Szekeres, whose structure of singularities is determined. We have evaluated a total energy of matter as a volume integral of the energy momentum tensor (EMT), whose contributions arise only at these singularities. The total matter energy is conserved before a collision of two plane gravitational waves but decreases during the collision and becomes zero at the end of the collision. We thus interpret that this model of colliding plane gravitational waves is a spacetime describing a pair annihilation of plan gravitational waves. We have also calculated a matter conserved charge proposed by the present author and his collaborators. The matter charge is indeed conserved but is zero due to a cancellation between two plain gravitational waves. This seems natural since nothing remains after a pair annihilation, and give a hint on a physical interpretation of the conserved charge, which we call the gravitational charge. By modifying the space time for the pair annihilation, we newly construct two types of a scattering plane gravitational wave and a pair creation of plane gravitational waves, and combining all, a Minkowski vacuum bottle, a Minkowski spacetime surrounded by two moving plane gravitational waves.

gr-qc↗
arXiv2023

Lattice QCD studies on decuplet baryons as meson-baryon bound states in the HAL QCD method

We study decuplet baryons from meson-baryon interactions in lattice QCD, in particular, $Δ$ and $Ω$ baryons from P-wave $I=3/2$ $Nπ$ and $I=0$ $Ξ\bar{K}$ interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at $m_π \approx 410~\textrm{MeV}$ and $m_{K} \approx 635~\textrm{MeV}$, where $Δ$ as well as $Ω$ baryons are stable. We use the conventional stochastic estimate of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that the $Ξ\bar K$ system has a weaker attraction than the $Nπ$ system while the binding energy from the threshold is larger for $Ω$ than $Δ$. This suggests that an inequality $m_{N}+m_π-m_Δ<m_Ξ+m_{\bar K}-m_Ω$ comes mainly from a smaller spatial size of a $Ξ\bar K$ bound state due to a larger reduced mass, rather than its interaction. Root-mean-square distances of bound states in both systems are small, indicating that $Δ$ and $Ω$ are tightly bound states and thus can be regarded qualitatively as composite states of 3 quarks. Results of binding energies agree with those obtained from temporal 2-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances.

hep-lat↗
arXiv2023

Thermodynamics with Möbius domain wall fermions near physical point II

We report on our finite temperature 2+1 flavor lattice QCD simulation to study the thermodynamic properties of QCD near the (pseudo) critical point employing $N_T=12$ and $16$. The simulation points are chosen along the lines of constant physics. The quark mass for Möbius domain-wall fermion are tuned by taking into account the residual mass either by fine-tuning the input quark masses or by post-process using reweighting. In this talk, we focus on simulation details and present some preliminary results.

hep-lat↗
arXiv2023

Special flow equation and GKP-Witten relation

We develop a framework for the reconstruction of the bulk theory dual to conformal field theory (CFT) without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation to O$(N)$ vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP-Witten relation concurrently emerge in this framework.

hep-th↗
arXiv2023

Extension of the HKLL bulk reconstruction for small $Δ$

We re-analyse the bulk reconstruction for a scalar field in Lorentzian AdS spacetime, both for the case of even and odd dimensions, for an extended range of conformal dimensions where the original HKLL reconstruction has to be modified. We also discuss the use of space-like Green's functions in the bulk reconstruction. We demonstrate that in the extended range also the singular part of the Green's function, omitted in the original papers, has be included. The results are particularly simple and physically interesting for integer conformal dimensions below the range considered in the original HKLL papers.

hep-th↗
arXiv2023

Interaction potentials for two-particle states with non-zero total momenta in lattice QCD

In this study, we extend the HAL QCD method to a case where a total momentum of a two-particle system is non-zero and apply it to the $I=2$ S-wave $ππ$ scattering in order to confirm its validity. We derive a fundamental relation of an energy-independent non-local potential defined in the center of mass frame with NBS wave functions in a laboratory frame. Based on the relation, we propose the time-dependent method to extract potentials, often used in practice for the HALQCD method in the center of mass frame. For numerical simulations in the $I=2$ $ππ$ system, we employ (2+1)-flavor gauge configurations on a $32^3 \times 64$ lattice at the lattice spacing $a \approx 0.0907$ fm and $m_π \approx 700$ MeV. Both effective leading order (LO) potentials and corresponding phase shifts obtained in laboratory frames agree with those obtained in the center-of-mass frame by the conventional HAL QCD method within somewhat larger statistical errors. In addition, we observe a consistency in scattering phase shifts between ours and results by the finite-volume method as well. The HAL QCD method with non-zero total momenta, established in this study, brings more flexibility to the HAL QCD method, which enables us to handle systems having the same quantum numbers with a vacuum or to access energy regions prohibited in the center of mass frame.

hep-lat↗
arXiv2023

Noether's 1st theorem with local symmetries

Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved currents. In this paper, we propose a general method to derive a matter conserved current associated with a special global symmetry in the presence of local symmetries. While currents derived from local symmetries of a matter sector with a covariant background gauge field are not conserved in general, we show that the current associated with a special type of a global symmetry, called a hidden matter symmetry, is on-shell conserved. We apply this derivation to a $U(1)$ gauge theory, general relativity and a non-abelian gauge theory. In general relativity, the associated conserved charge agrees with the one recently proposed from a different point of view.

hep-th↗
arXiv2022

Lattice study on a tetraquark state $T_{bb}$ in the HAL QCD method

We investigate a doubly-bottomed tetraquark state $T_{bb}$ $(bb \bar{u}\bar{d})$ with quantum number $I(J^P)=0(1^+)$ in $(2+1)$-flavor lattice QCD. Using the Non-Relativistic QCD (NRQCD) quark action for $b$ quarks, we have extracted the coupled channel potential between $\bar{B}\bar{B}^*$ and $\bar{B}^* \bar{B}^*$ in the HAL QCD method at $a \approx 0.09$ {fm} on $32^3\times 64$ lattices. The potential predicts an existence of a bound $T_{bb}$ below the $\bar{B}\bar{B}^*$ threshold. At the physical pion mass $m_π\approx140$ {MeV} extrapolated from $m_π\approx 410,\, 570,\, 700$ {MeV}, a binding energy with its statistical error is given by $E_{\rm binding}^{\rm (coupled)} = 83(10)$ MeV from a coupled channel analysis where effects due to virtual $\bar{B}^* \bar{B}^*$ states are included through the coupled channel potential, while we obtain $E_{\rm binding}^{\rm (single)} = 155(17)$ MeV only from a potential for a single $\bar{B}\bar{B}^*$ channel. This difference indicates that the effect from virtual $\bar{B}^* \bar{B}^*$ states is sizable to the binding energy of $T_{bb}$. Adding $\pm 20$ MeV as empirical systematic error caused by the NRQCD approximation for $b$ quarks, our estimate of the $T_{bb}$ binding energy becomes $83(10)(20)$ MeV.

hep-lat↗
arXiv2022

Do we know how to define energy in general relativity?

This essay is dedicated to Prof. K.K. Phua on the occasion of his 80th birthday. While the contents of this essay are based on our recent papers$^{1,2}$ published in the International Journal of Modern Physics A, I have added many personal opinions, so that I am solely responsible for all statements in this essay. 1. S. Aoki, T. Onogi and S. Yokoyama, Int. J. Mod. Phys. A36 (2021) no.10, 2150098. 2. S. Aoki, T. Onogi and S. Yokoyama, Int. J. Mod. Phys. A36 (2021) no.29, 2150201.

gr-qc↗
arXiv2022

Optimized Two-Baryon Operators in Lattice QCD

A set of optimized interpolating operators which are dominantly coupled to each eigenstate of two baryons on the lattice is constructed by the HAL QCD method. To test its validity, we consider heavy dibaryons $Ω_{3Q}Ω_{3Q}$ ($Q=s,c$) calculated by (2+1)-flavor lattice QCD simulations with nearly physical pion mass. The optimized two-baryon operators are shown to provide effective energies of the ground and excited states separately stable as a function of the Euclidean time. Also they agree to the eigenenergies in a finite lattice box obtained from the leading-order HAL QCD potential $V({\boldsymbol{r}})$ within statistical errors. The overlapping factors between the optimized sink operators and the state created by the wall-type source operator indicate that $V( \boldsymbol{r})$ can be reliably extracted, no matter whether the spacetime correlation of two baryons is dominated by the ground state or the excited state. It is suggested that the optimized set of operators is useful for variational studies of hadron-hadron interactions.

hep-lat↗
arXiv2022

Axial U(1) symmetry at high temperatures in $N_f=2+1$ lattice QCD with chiral fermions

We study the $U(1)_A$ anomaly in the high-temperature phase of $N_f=2+1$ lattice QCD with chiral fermions. Gauge ensembles are generated with Möbius domain-wall (MDW) fermions, and in the measurements the determinant is reweighted to that of overlap fermions. We report the results for the overlap Dirac spectrum, $U(1)_A$ susceptibility, and topological susceptibility at $T=204$ and $175$ MeV.

hep-lat↗