arXiv subjects

Jia-Jun Wu

Publications and source records attributed to Jia-Jun Wu.

At least 73 records · Page 4Linked to original sources

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

A new look at the $P_{cs}$ states from a molecular perspective

We have a look at the $P_{cs}$ states generated from the interaction of $\bar D^{(*)} Ξ^{(\prime*)}_c$ coupled channels. We consider the blocks of pseudoscalar-baryon $({\frac12}^+, {\frac32}^+)$ and vector-baryon $({\frac12}^+, {\frac32}^+)$, and find $10$ resonant states coupling mostly to $\bar D Ξ_c, \bar D^* Ξ_c,\bar D Ξ'_c, \bar D^* Ξ'_c,\bar D Ξ^*_c$ and $\bar D^* Ξ^*_c$. A novel aspect of the work is the realization that the $\bar D Ξ_c,\bar D_sΛ_c$ or $\bar D^* Ξ_c,\bar D^*_sΛ_c$ channels, with a strong transition potential, collaborate to produce a larger attraction than the corresponding states $\bar D Σ_c,\bar DΛ_c$ or $\bar D^* Σ_c,\bar D^*Λ_c$ appearing in the generation of the strangenessless $P_{c}$ states, since in the latter case the transition potential between those channels is zero. The extra attraction obtained in the $\bar D Ξ_c,\bar D^* Ξ_c$ pairs preclude the association of these channels to the $P_{cs}(4338)$ and $P_{cs}(4459)$ states respectively. Then we find a natural association of the $P_{cs}(4338)$ state coupling mostly to $\bar D^* Ξ_c$ while the $P_{cs}(4459)$ is associated to the state found that couples mostly to $\bar D Ξ'_c$. Four more states appear, like in other molecular pictures, and some of the states are degenerate in spin. Counting different spin states we find $10$ states, which we hope can be observed in the near future.

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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.

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arXiv2022

The investigations of the $P$-wave $B_s$ states combining quark model and lattice QCD in the coupled channel framework

Combining the quark model, the quark-pair-creation mechanism and $B^{(*)}\bar K$ interaction, we have investigated the near-threshold $P$-wave $B_s$ states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the $D_s$ sector by fitting the lattice data. The masses of the bottom-strange partners of the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ are predicted to be $M_{B^{*}_{s0}}=5730.2_{-1.5}^{+2.4}$ MeV and $M_{B^{*}_{s1}}= 5769.6_{-1.6}^{+2.4}$ MeV, respectively, which are well consistent with the lattice QCD simulation. The two $P$-wave $B_s$ states are the mixtures of the bare $\bar b s$ core and $B^{(*)}\bar K$ component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the $0^+$ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the $T$-matrix of the $B\bar K$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation.

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arXiv2022

The reaction $πN \to ωN$ in a dynamical coupled-channel approach

A refined investigation on light flavor meson-baryon scatterings is performed using a dynamical coupled-channel approach, the Jülich-Bonn model, that respects unitartiy and analyticity constraints. The channel space of $πN$, $πΔ$, $σN$, $ρN$, $ηN$, $K Λ$ and $K Σ$ is extended by adding the $ωN$ final state. The spectra of $N^*$ and $Δ$ resonances are extracted in terms of complex poles of the scattering amplitudes, based on the result of a global fit to a worldwide collection of data, in the energy region from the $πN$ threshold to center-of-mass energy $z=2.3$ GeV. A negative value of the $ωN$ elastic spin-averaged scattering length is extracted, questioning the existence of bound states of the $ω$ meson in the nuclear matter.

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arXiv2022

Regularisation in Nonperturbative Extensions of Effective Field Theory

The process of renormalisation in nonperturbative Hamiltonian Effective Field Theory (HEFT) is examined in the $Δ$-resonance scattering channel. As an extension of effective field theory incorporating the Lüscher formalism, HEFT provides a bridge between the infinite-volume scattering data of experiment and the finite-volume spectrum of energy eigenstates in lattice QCD. HEFT also provides phenomenological insight into the basis-state composition of the finite-volume eigenstates via the state eigenvectors. The Hamiltonian matrix is made finite through the introduction of finite-range regularisation. The extent to which the established features of this regularisation scheme survive in HEFT is examined. In a single-channel $πN$ analysis, fits to experimental phase shifts withstand large variations in the regularisation parameter, $Λ$, providing an opportunity to explore the sensitivity of the finite-volume spectrum and state composition on the regulator. While the Lüscher formalism ensures the eigenvalues are insensitive to $Λ$ variation in the single-channel case, the eigenstate composition varies with $Λ$; the admission of short distance interactions diminishes single-particle contributions to the states. In the two-channel $πN$, $πΔ$ analysis, $Λ$ is restricted to a small range by the experimental data. Here the inelasticity is particularly sensitive to variations in $Λ$ and its associated parameter set. This sensitivity is also manifest in the finite-volume spectrum for states near the opening of the $πΔ$ scattering channel. Finally, HEFT has the unique ability to describe the quark-mass dependence of the finite-volume eigenstates. The robust nature of this capability is presented and used to confront current state-of-the-art lattice QCD calculations.

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arXiv2022

Inverse scattering problem with a bare state

In hadron physics, molecular-like multihadron states can interact with compact multiquark states. The latter are modeled as bare states in the Hilbert space of a potential model. In this work, we study several potential models relevant to the bare state, and solve their inverse scattering problems. The first model, called "cc", is a separable potential model. We show that it can approximate (single-channel short-range) $S$-wave near-threshold physics with an error of $\mathcal{O}(β^3/M_V^3)$, where $β$ sets the maximum momentum of the near-threshold region and $M_V$ is the typical scale of the potential. The second model, called "bc", serves as the bare-state-dominance approximation, where interaction between continuum states is ignored. Under this model, even though the bare state is always crucial for a bound state's generation, a shallow bound state naturally tends to have a small bare-state proportion. Therefore, we need other quantities to quantify the importance of the bare state. The last model, called "bcc", is a combination of the first two models. This model not only serves as a correction to the bare-state-dominance approximation, but can also be used to understand the interplay between quark and hadron degrees of freedom. This model naturally leads to the presence of a Castillejo-Dalitz-Dyson (CDD) zero. We consider the energy decomposition of a bound state. The potential ratio of the bare-continuum interaction to the continuum self-interaction is proposed to understand how the bound state is generated. Model independently, an inequality for the potential ratio is derived. Based on the model "bcc", the CDD zero can be used to estimate the potential ratio. Finally, we apply these studies to the deuteron, $ρ$ meson, and $D_{s0}^*(2317)$, and analyze their properties.

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arXiv2022

Research on the Phase space of three- and four-body final states process

The analytical formulae for the phase space factors and the three-momenta of three- and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables. These formulae will help experimental physicist to perform the data analysis. As an example, we show how to use these formulae to distinguish the different mechanisms of $e+p\to e+J/ψ+ p$ process for searching the signals of $P_c$ states at the energy region of Electron-Ion collider at China (EicC).

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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.

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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

Novel coupled channel framework connecting quark model and lattice QCD: an investigation on near-threshold $D_s$ states

A novel framework is proposed to extract near-threshold resonant states from finite-volume energy levels of lattice QCD and is applied to elucidate structures of the positive parity $D_s$. The quark model, the quark-pair-creation mechanism and $D^{(*)}K$ interaction are incorporated into the Hamiltonian effective field theory. The bare $1^+$ $c\bar s$ states are almost purely given by the states with heavy-quark spin bases. The physical $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$ are the mixtures of bare $c\bar s$ core and $D^{(*)}K$ component, while the $D^*_{s1}(2536)$ and $D^*_{s2}(2573)$ are almost dominated by bare $c\bar{s}$. Furthermore, our model reproduces the clear level crossing of the $D^*_{s1}(2536)$ with the scattering state at a finite volume.

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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.

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arXiv2021

Proposal to detect a moving triangle singularity in $ψ(2S) \to π^+ π^- K^+ K^-$ process

In this work, we propose that there exists a moving triangle singularity in the $ψ(2S) \to π^+ π^- K^+ K^-$ process, whose position can vary from 1.158 to 1.181 GeV in the invariant mass spectrum of $K^+K^-$. After a precise analysis on this process, it turns out that after doing some cuts on $m_{π^+π^-}$, experiments do have the opportunity to observe this triangle singularity. In addition, when changing the cuts on $m_{π^+π^-}$, the movement of the predicted triangle singularity can also be observed. Thus, we suggest future experiments, especially Super Tau-Charm Facility (STCF), to do an anlysis on the $ψ(2S) \to π^+ π^- K^+ K^-$ process to verify our prediction.

hep-ph↗

arXiv2021

Towards high partial waves in lattice QCD with a dumbbell-like operator

An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra of the specific irrep. In particular, this new formulation only requires propagators to be computed from two distinct source locations, at fixed spatial separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice volume with $m_π\approx 900$ MeV by isolating various spectra of the $ππ$ system with isospin-2 including a range of total momenta and irreps. By applying the Lüscher formalism, the phase shifts of $S$-, $D$- and $G$-wave $ππ$ scattering with isospin-2 are extracted from the spectra.

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arXiv2021

Detecting the pure triangle sigularity effect through the $ψ(2S) \to p \bar{p} η/ p \bar{p} π^0$ process

In this work, the triangle singularity mechanism is investigated in the $ψ(2S) \to p \bar{p} η/ p \bar{p} π^0$ process. The triangle loop composed by $J/ψ$, $η$ and $p$ has a singularity in the physical kinematic range for the $ψ(2S) \to p \bar{p} η/ p \bar{p} π^0$ process, and it would generate a very narrow peak in the invariant mass spectrum of $pη(π)$ around $1.56387$ GeV, which is far away from both the threshold and relative resonances. In these processes, all the involved vertices are constrained by the experimental data. Thus, we can make a precise model independent prediction here. It turns out that the peak in the $pη$ invariant mass spectrum is visible, while it is very small in the $pπ^0$ invariant mass spectrum. We expect this effect shown in $p \bar{p} η$ final state can be observed by the Beijing Spectrometer (BESIII) and Super Tau-Charm Facility (STCF) in the future.

hep-ph↗

arXiv2021

The effective radius for production of baryon-antibaryon pairs from $ψ$ decays

By using the covariant L-S Scheme for the partial wave analysis, we deduce the ratios between the S-wave and D-wave contributions from the recent data of $ψ(1^-) \to B_8(1/2^+) \bar{B}_8(1/2^-)$ from the BESIII collaboration. For the $J/ψ\to Λ\barΛ$ and $J/ψ(ψ(2S))\to Σ^{+}\barΣ^{-}$, the ratios are fixed and the average angular momenta are computed to estimate the effective radii of these processes. The results show that the effective radii of these decays of $J/ψ(ψ(2S))$ are very small, which are around 0.04 fm. Thus, it is a nice place to search excited baryon resonances with lower spin in the decays of $J/ψ(ψ(2S))$. Furthermore, for the other $ψ(1^-) \to B_8(1/2^+) \bar{B}_8(1/2^-)$ reactions, we propose some methods to get such effective radius.

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arXiv2020

Exploring possible triangle singularities in the $Ξ^-_{b} \to K^- J/ψΛ$ decay

We analyze possible singularities in the $J/ψΛ$ invariant mass distribution of the $Ξ^-_{b}~\to~K^- J/ψΛ$ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with $Ξ^*$-charmonium-$Λ$ intermediate states, the one from the $χ_{c1} Ξ(2120) Λ$ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs $S$- and $P$-waves in $χ_{c1} Λ$ and $J/ψΛ$ systems, respectively, when the quantum numbers of these systems are $1/2^+$ or $3/2^+$. When the quantum numbers of the $Ξ(2120)$ are $J^P=1/2^+$, $1/2^-$ or $3/2^+$, the peak structure should be sharper than the other $J^P$ choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the $Ξ^*$-charmonium-$Λ$ triangle diagram if structures are observed in the $J/ψΛ$ invariant mass spectrum experimentally. In addition, a few triangle diagrams with the $D_{s1}^*(2700)$ as one of the intermediate particles can also produce singularities in the $J/ψΛ$ distribution, but at higher energies above 4.9 GeV.

hep-ph↗

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.

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