arXiv subjects

Hao-Jie Jing

Publications and source records attributed to Hao-Jie Jing.

14 recordsLinked to original sources

arXiv2026

Novel method for determining the light quark mass ratio using $η'\toηππ$ decays

We propose a novel approach for extracting symmetry breaking effects from symmetry conserving three-body decays. The method is based on mapping the Dalitz plot to a unit disk, and the difference of the disk distributions of two related decays isolates purely symmetry breaking effects. We demonstrate this method by extracting the fundamental parameter $Q$, an isospin breaking ratio of light quark masses defined as $Q^2\equiv (m_s^2-\hat m^2)/(m_d^2-m_u^2)$ with $\hat m$ the average of up and down quark masses, from the decays $η'\toηπ^+π^-$ and $η'\toηπ^0π^0$. With the Dalitz plot distributions for these two decays reported by BESIII, we illustrate the method and obtain $Q=22.5\pm1.0$, which is consistent with previous determinations and has a comparable uncertainty. With the full BESIII data set, which is eight times larger than the one used here, a more precise determination of $Q$ should become possible. This promising and novel method can be generalized to other three-body decays to extract symmetry breaking effects.

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arXiv2025

Towards the LHCb pentaquark modes in the single-charm sector

The mass spectrum of $Λ_c$ baryon family is investigated within the $DN$-$D^*N$ coupled-channel framework using two phenomenological approaches for the low-energy $D^{(*)} N$ interactions: the heavy quark effective theory and the flavor-symmetry-constrained effective Lagrangian method. It is shown that the LHCb pentaquark states have direct analogs in the $Λ_c$ family. Specifically, $Λ_c(2765)$, $Λ_c(2910)$, and $Λ_c(2940)$ mirror the patterns of $P_{c\bar{c}}(4312)$, $P_{c\bar{c}}(4440)$, and $P_{c\bar{c}}(4457)$, respectively. These mirror pentaquark modes offer valuable insights into the quantum numbers of the two heavy $P_{c\bar{c}}$ states, which remain experimentally undetermined. Further exploration of such correlations among exotic hadronic states across different flavor sectors will be crucial for developing a comprehensive theoretical understanding of the modern hadron spectrum.

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arXiv2025

Discontinuity calculus and applications to two-body coupled-channel scattering

We present a novel method, termed discontinuity calculus, for computing discontinuities of complex functions. This framework enables a systematic investigation of both analytic continuation and the topological structure of Riemann surfaces. We apply this calculus to analyze the analytic continuation of partial-wave amplitudes in two-body coupled-channel scattering problems and discuss their uniformization of the corresponding Riemann surfaces. This methodology offers new perspectives and tools for analyzing coupled-channel scattering problems in quantum scattering theory.

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arXiv2024

Algorithms for partial wave amplitudes under covariant $L$-$S$ scheme

With the continuous accumulation of data from hadron collision experiments, efficient Partial Wave Analysis tools are indispensable for constructing a clear hadron spectrum. Currently, automated computations of scattering amplitudes primarily use the helicity scheme and covariant effective Lagrangian method. The automated calculations under the covariant $L$-$S$ scheme, which is one of the commonly used partial wave analysis schemes, have not been fully realized. In this work, we provide a general algorithm for computing partial wave amplitudes under the covariant $L$-$S$ scheme. This will lay the foundation for automated computation of partial wave amplitudes under the covariant $L$-$S$ scheme.

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arXiv2024

Phase Conventions in Hadron Physics from the Perspective of the Quark Model

Convenient and consistent phase convention is important in the construction of the hadronic Lagrangian. However, the importance of phase convention has been overlooked for a long time and the sources of different conventions are never explicitly addressed. This obscure situation can cause mistakes and misinterpretations in hadron physics. In this paper, we systematically analyze and compare the flavor $SU_3$ phase conventions from the perspective of the quark model. All sources which could lead to different conventions are pointed out and carefully studied. With the tool of the quark model, we also clarify some misconceptions and demonstrate a consistent way to incorporate different conventions.

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arXiv2023

Covariant orbital-spin scheme for any spin based on irreducible tensor

In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its Lorentz covariant form and determined orbital-spin quantum numbers. This paper presents a general form of the covariant orbital-spin coupling scheme based on the irreducible tensor of the homogeneous proper Lorentz group and its little groups. A systematic procedure for constructing partial wave amplitude in a Lorentz covariant way is provided, which can be applied to both massive and massless particles. Specific examples are also included.

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arXiv2023

Spin-orbit amplitudes for decays with arbitrary spin

In this paper, we propose a method to construct the decay amplitudes in the orbital ($L$) and spin ($S$) coupling scheme for particles with arbitrary spins. For the $1\to 2$ decay with only massive particles involved, the angular dependence is completely encoded in the angular momentum part, and the spins of daughter particles are coupled in the rest frame of the mother particle, which contributes only a constant factor. For the sequential decay, the total amplitude is constructed by the two $1\to2$ amplitudes evaluated in the rest frame of their own mother particles, and then they are transformed to the common frame, usually chosen as the laboratory frame, by certain Lorentz transformations. In this way, it is easy to add the amplitudes of possible different decay chains coherently. If massless particles show up in the final states, the polarizations are expressed in helicity basis and the amplitudes are modified correspondingly.

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arXiv2021

Graphic Method for Arbitrary $n$-body Phase Space

In quantum field theory, the phase space integration is an essential part in all theoretical calculations of cross sections and decay widths. It is also needed for computing the imaginary part of a physical amplitude. A key problem is to get the phase space formula expressed in terms of any chosen invariant masses in an $n$-body system. We propose a graphic method to quickly get the phase space formula of any given invariant masses intuitively for an arbitrary $n$-body system in general $D$-dimensional spacetime, with the involved momenta in any reference frame. The method also greatly simplifies the phase space calculation just as what Feynman diagrams do in calculating scattering amplitudes.

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arXiv2020

Possible precise measurements of the $X(3872)$ mass with the $e^+e^-\toπ^0γX(3872)$ and $p\bar p\toγX(3872)$ reactions

It was recently proposed that the $X(3872)$ binding energy, the difference between the $D^0\bar D^{*0}$ threshold and the $X(3872)$ mass, can be precisely determined by measuring the $γX(3872)$ line shape from a short-distance $D^{*0}\bar D^{*0}$ source produced at high-energy experiments. Here, we investigate the feasibility of such a proposal by estimating the cross sections for the $e^+e^-\toπ^0γX(3872)$ and $p\bar p\toγX(3872)$ processes considering the $D^{*0}\bar D^{*0}D^0/\bar D^{*0}D^{*0}\bar D^0$ triangle loops. These loops can produce a triangle singularity slightly above the $D^{*0}\bar D^{*0}$ threshold. It is found that the peak structures originating from the $D^{*0}\bar D^{*0}$ threshold cusp and the triangle singularity are not altered much by the energy dependence introduced by the $e^+e^-\toπ^0D^{*0}\bar D^{*0}$ and $p\bar p\to\bar D^{*0}D^{*0}$ production parts or by considering a finite width for the $X(3872)$. We find that $σ(e^+e^-\toπ^0γX(3872)) \times {\rm Br}(X(3872)\toπ^+π^-J/ψ)$ is $\mathcal{O}(0.1~{\rm fb})$ with the $γX(3872)$ invariant mass integrated from 4.01 to 4.02 GeV and the c.m. energy of the $e^+e^-$ pair fixed at 4.23 GeV. The cross section $σ(p\bar p\toγX(3872))\times {\rm Br}(X(3872)\toπ^+π^-J/ψ)$ is estimated to be of $\mathcal{O}(10~{\rm pb})$. Our results suggest that a precise measurement of the $X(3872)$ binding energy can be done at PANDA.

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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.

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arXiv2019

Triangle singularities in ${J/ψ\rightarrowηπ^0ϕ}$ and ${π^0π^0ϕ}$

The BESIII Collaboration recently reported the observation of the $a_0(980)^0-f_0(980)$ mixing in the isospin breaking decay $J/ψ\to ηπ^0ϕ$. In the Dalitz plot for that decay with the $η$ reconstructed from two photons, there is a band around $1.4$~GeV on the $π^0 ϕ$ distribution. In general, this peak can be due to a resonance or a kinematic effect. In this paper, we study the effects of a set of $K^*K\bar K$ triangle diagrams, and show that due to triangle singularities such diagrams can lead to a peak around 1.4~GeV in the $π^0ϕ$ invariant mass distribution. The Dalitz plot induced by such a mechanism has a feature consistent with the BESIII observation, namely events along the band accumulate at both ends close to the Dalitz plot boundary. The effect of the same mechanism on the $J/ψ\to π^0π^0ϕ$ and $J/ψ\to ηπ^0 K^+K^-$ decays are also investigated. We suggest to take more data for the $J/ψ\to ηπ^0ϕ\to ηπ^0 K^+ K^-$ and check whether the structure around $1.4$~GeV persists for the $K^+K^-$ invariant mass away from the $ϕ$ mass region. This is crucial for understanding whether the band is due to triangle singularities or due to a resonance. Were it the latter, the band should remain while it would not if it is due to the former.

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arXiv2019

Decays of $P_c$ into $J/ψN$ and $η_cN$ with heavy quark spin symmetry

We investigate the consequences of heavy quark spin symmetry (HQSS) on hidden-charm pentaquark $P_c$ states. As has been proposed before, assuming the $P_c(4440)$ and the $P_c(4457)$ as $S$-wave $\bar{D}^*Σ_c$ molecules, seven hadronic molecular states composed of $\bar{D}Σ_c$, $\bar{D}Σ_c^*$, $\bar{D}^*Σ_c$, and $\bar{D}^*Σ_c^*$ can be obtained, with the $\bar{D}Σ_c$ molecule corresponding to the $P_c(4312)$. These seven states can decay into $J/ψN$ and $η_c N$, and we use HQSS to predict ratios of partial widths of the $S$-wave decays. For the decays into $J/ψN$, it is found that among all six $P_c$ molecules with spin $1/2$ or $3/2$, at least four states decay much more easily into the $J/ψN$ than the $P_c(4312)$, and two of them couple dominantly to the $\bar D^*Σ_c^*$. While no significant peak around the $\bar{D}^*Σ_c^*$ threshold is found in the $J/ψp$ distribution, these higher $P_c$ states either are produced with lower rates or some special production mechanism for the observed $P_c$ states might play an important role, such as an intricate interplay between the production of pentaquarks and triangle singularities.

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arXiv2019

Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$

The LHCb Collaboration announced the observation of three narrow structures consistent with hidden-charm pentaquark states. They are candidates of hadronic molecules formed of a pair of a charmed baryon and an anticharmed meson. Among them, the $P_c(4457)$ mass is consistent with earlier predictions of a $Σ_c\bar D^*$ molecule with $I=1/2$. We point out that if such a picture were true, one would have $\mathcal{B}(P_c(4457)\to J/ψΔ^+)/\mathcal{B}(P_c(4457)\to J/ψp)$ at the level ranging from a few percent to about 30%. Such a large isospin breaking decay ratio is two to three orders of magnitude larger than that for normal hadron resonances. It is a unique feature of the $Σ_c\bar D^*$ molecular model, and can be checked by LHCb.

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arXiv2018

Disentangling the role of the $Y(4260)$ in $e^+e^-\to D^\bar{D}^$ and $D_s^\bar{D}_s^$ via line shape studies

Whether the $Y(4260)$ can couple to open charm channels has been a crucial issue for understanding its nature. The available experimental data suggest that the cross section line shapes of exclusive processes in $e^+e^-$ annihilations have nontrivial structures around the mass region of the $Y(4260)$. As part of a series of studies of the $Y(4260)$ as mainly a $\bar{D}D_1(2420)+c.c.$ molecular state, we show that the partial widths of the $Y(4260)$ to the two-body open charm channels of $e^+e^-\to D^*\bar{D}^*$ and $D_s^*\bar{D}_s^*$ are much smaller than that to $\bar{D}D^*π+c.c.$. The line shapes measured by the Belle Collaboration for these two channels can be well described by the vector charmonium states $ψ(4040)$, $ψ(4160)$ and $ψ(4415)$ together with the $Y(4260)$. It turns out that the interference of the $Y(4260)$ with the other charmonia produces a dip around 4.22~GeV in the $e^+e^-\to D^*\bar{D}^*$ cross section line shape. The data also show an evidence for the strong coupling of the $Y(4260)$ to the $D\bar D_1(2420)$, in line with the expectation in the hadronic molecular scenario for the $Y(4260)$.

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