arXiv subjects

Jin-Yi Pang

Publications and source records attributed to Jin-Yi Pang.

At least 19 recordsLinked to original sources

arXiv2026

Machine Learning Unveils Finite-volume Energy Shifts in Three-body System

Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size $L$ remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. $κ_3\ggκ_2$ and $κ_3\simκ_2$. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.

hep-lat↗

arXiv2025

Machine Learning Unveils the Power Law of Finite-Volume Energy Shifts

Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations. However, it is a significant challenge for the system with long-range interactions. We employ symbolic regression to regress finite-volume extrapolation formula for both short-range and long-range interactions. The regressed formula still holds the exponential form with a factor $L^n$ in front of it. The power decreases with the decreasing range of the force. When the range of the force becomes sufficiently small, the power converges to $-1$, recovering the short-range formula as expected. Our work represents a significant advancement in leveraging machine learning to probe uncharted territories within particle physics.

hep-ph↗

arXiv2025

Modified Lüscher zeta-function and the modified effective range expansion in the presence of a long-range force

An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in Ref.~\cite{Bubna:2024izx} for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves.

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arXiv2024

$P_c(4457)$ interpreted as a $J^P=1/2^+$ state by $\bar{D}^0Λ^+_c(2595)$-$π^0 P_c(4312)$ interaction

$P_c(4457)$ has been discovered over five years, but the parity of this particle remains undetermined. In this letter we propose a new interpretation for $P_c(4457)$, which is the state generated from the coupled-channel $\bar{D}^0Λ_c^{+}(2595)$ and $π^0 P_c(4312)$ since they can exchange an almost on-shell $Σ_c^+$. In this scenario, the parity of $P_c(4457)$ will be positive, which is different from the candidate of the bound state of $\bar{D}^*Σ_c$. The main decay channel of $P_c(4457)$ in this model is $P_c(4312)π$. We propose three processes $Λ_b^0 \to J/ψK_s p π^-$, $Λ_b^0 \to J/ψK^- p π^0$, and $Λ_b^0 \to J/ψp π^- π^+ K^-$ to verify $P_c(4457)\to P_c(4312)π$.

hep-ph↗

arXiv2024

Lattice spectra of $DDK$ three-body system with Lorentz covariant kinematic

The $DDK$ system has gain increasing attention in recent research due to its potential to contain a three-hadron bound state. This article utilizes an extension of the Non-Relativistic Effective Field Theory (NREFT) and the finite volume particle-dimer framework to derive Lorentz-invariant quantization conditions for the $DDK$ three-body system. Using current model input conditions, the finite volume energy spectrum of the $DDK$ three-body system was calculated. This new calculation incorporates relativistic kinematics, allowing it to be applicable across a broader energy range starting from the threshold. In this work, we present a comprehensive $ O(p^{2}) $ calculation. The spurious pole is effectively subtracted within the framework of relativistic kinematics. The spectra in the moving frame are also obtained. These analyses provide a broader testing ground for future lattice simulations. They are expected to reveal more detailed properties of the $DDK$ system and other three-hadron systems.

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arXiv2024

Lellouch-Lüscher factor for the $K\to 3π$ decays

We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the $K\to 3π$ decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the $K\to 3π$ decays on the lattice.

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arXiv2024

Lüscher equation with long-range forces

We derive the modified Lüscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t-channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided.

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arXiv2024

The spin alignment of rho mesons in a pion gas

We study the spin alignment of neutral rho mesons in a pion gas using spin kinetic or Boltzmann equations. The $ρππ$ coupling is given by the chiral effective theory. The collision terms at the leading and next-to-leading order in spin Boltzmann equations are derived. The evolution of the spin density matrix of the neutral rho meson is simulated with different initial conditions. The numerical results show that the interaction of pions and neutral rho mesons creates very small spin alignment in the central rapidity region if there is no rho meson in the system at the initial time. Such a small spin alignment in the central rapidity region will decay rapidly toward zero in later time. If there are rho mesons with a sizable spin alignment at the initial time the spin alignment will also decrease rapidly. We also considered the effect on $ρ_{00}$ from the elliptic flow of pions in the blast wave model. With vanishing spin alignment at the initial time, the deviation of $ρ_{00}$ from 1/3 is positive but very small.

nucl-th↗

arXiv2023

Three-particle Lellouch-Lüscher formalism in moving frames

A manifestly relativistic-invariant Lellouch-Lüscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in ref.[2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.

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arXiv2023

Three-body coupled channel framework for two-neutron halo nuclei

We study the Borromean nuclei formed by a core nucleus and two neutrons in a nonrelativistic effective field theory formalism considering both neutron-neutron and neutron-core interactions. We provide formulae of the charge and matter radii, and successfully reproduce the universal relation proposed by Hongo and Son based on the approximation of an infinite neutron-neutron scattering length and neglecting the neutron-core scattering. Once the realistic finite neutron-neutron and neutron-core scattering lengths are used, the charge and matter radii are influenced by the neutron-core channel in a growingly relevant manner. We obtain a relation among the binding energy of the three-body Borromean system, the ratio between charge and matter radii, and the ratio between the neutron-neutron and core-neutron scattering lengths. We find that the two-neutron separation energy for $^{22}$C needs to be $\lesssim 2$ keV in order to be consistent with the experimental constraints of the matter radius of $^{22}$C and the $^{20}{\rm C}\,n$ $S$-wave scattering length.

nucl-th↗

arXiv2022

Generalization of Weinberg's Compositeness Relations

We generalize the time-honored Weinberg's compositeness relations by including the range corrections through considering a general form factor. In Weinberg's derivation, he considered the effective range expansion up to $\mathcal{O}(p^2)$ and made two additional approximations: neglecting the non-pole term in the Low equation; approximating the form factor by a constant. We lift the second approximation, and work out an analytic expression for the form factor. For a positive effective range, the form factor is of a single-pole form. An integral representation of the compositeness is obtained and is expected to have a smaller uncertainty than that derived from Weinberg's relations. We also establish an exact relation between the wave function of a bound state and the phase of the scattering amplitude neglecting the non-pole term. The deuteron is analyzed as an example, and the formalism can be applied to other cases where range corrections are important.

hep-ph↗

arXiv2022

Spurious poles in a finite volume

Using effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the inconsistencies in the three-body equations, e.g., to the breakdown of unitarity. We investigate the effect of the spurious poles on the three-body quantization condition in a finite volume and show that it leads to a peculiar dependence of the energy levels on the box size $L$. Furthermore, within a simple model, it is demonstrated that the procedure for the removal of these poles, which was recently proposed in Ref.[1] in the infinite volume, can be adapted to the finite-volume calculations. The structure of the exact energy levels is reproduced with an accuracy that systematically improves order by order in the EFT expansion.

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arXiv2022

Relativistic-invariant formulation of the NREFT three-particle quantization condition

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.

hep-lat↗

arXiv2021

Entanglement Entropy and Quantum Phase Transition in the $O(N)$ $σ$-model

We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the $σ$-model in 3+1 dimensions which is $O(N)$ symmetric as the mass squared parameter $μ^{2}$ is positive, and undergoes spontaneous symmetry breaking while $μ^{2}$ becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point $μ^{2}=0$, and decreases while $μ^{2}$ is tuned away from 0 into either phase.

hep-th↗

arXiv2021

Strong Coupling Expansion of the Entanglement Entropy of Yang-Mills Gauge Theories

We propose a novel prescription for calculating the entanglement entropy of the $SU(N)$ Yang-Mills gauge theories on the lattice under the strong coupling expansion in powers of $β=2N/g^{2}$, where $g$ is the coupling constant. Using the replica method, our Lagrangian formalism maintains gauge invariance on the lattice. At $O(β^{2})$ and $O(β^{3})$, the entanglement entropy is solely contributed by the central plaquettes enclosing the conical singularity of the $n$-sheeted Riemann surface. The area law emerges naturally to the highest order $O(β^{3})$ of our calculation. The leading $O(β)$ term is negative, which could in principle be canceled by taking into account the "cosmological constant" living in interface of the two entangled subregions. This unknown cosmological constant resembles the ambiguity of edge modes in the Hamiltonian formalism. We further speculate this unknown cosmological constant can show up in the entanglement entropy of scalar and spinor field theories as well. Furthermore, it could play the role of a counterterm to absorb the ultraviolet divergence of entanglement entropy and make entanglement entropy a finite physical quantity.

hep-th↗

arXiv2020

$DDK$ system in finite volume

The $DDK$ 3-body system is supposed to be bound due to the strongly attractive interaction between the $D$ meson and the $K$ meson in the isospin zero channel. The minimum quark content of this 3-body bound state is $cc\bar{q}\bar{s}$ with $q=u,d$. It will be an explicitly exotic tetraquark state once discovered. In order to confirm the phenomenological study of the $DDK$ system, we can refer to lattice QCD as a powerful theoretical tool parallel to the experiment measurement. In this paper, a 3-body quantization condition scheme is derived via the non-relativistic effective theory and the particle-dimer picture in finite volume. Lattice spectrum of this 3-body system is calculated within the existing model inputs. The spectrum shows various interesting properties of the $DDK$ system, and it may reveal the nature of the $D^*(2317)$. This predicated spectrum is expected to be tested in future lattice simulations.

hep-lat↗

arXiv2020

Thermal behaviors of light scalar resonances at low temperatures

We study the thermal properties of the lowest multiplet of the QCD light-flavor scalar resonances, including the $f_0(500)/σ$, $K_{0}^{*}(700)/κ$, $f_0(980)$ and $a_0(980)$, in the framework of unitarized $U(3)$ chiral perturbation theory. After the successful fits to the meson-meson scattering inputs, such as the phase shifts and inelasticities, we obtain the unknown parameters and further calculate the resonance poles and their residues at zero temperature. By including the finite-temperature effects in the unitarized meson-meson scattering amplitudes, the thermal behaviors of the scalar resonance poles in the complex energy plane are studied. The masses of $σ$ and $κ$ are found to considerably decrease when increasing the temperatures, while their widths turn out to be still large when the temperatures reach around $200$ MeV. In contrast, both the masses and widths of the $f_0(980)$ and $a_0(980)$ are only slightly changed.

hep-ph↗

arXiv2019

Energy shift of the three-particle system in a finite volume

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order $L^{-6}$. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order $L^{-3}$. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Luescher equation.

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