arXiv subjects

Chao-Hsi Chang

Publications and source records attributed to Chao-Hsi Chang.

At least 19 recordsLinked to original sources

arXiv2026

Improved covariant analysis of $B_c^+ \to χ_{c1}(nP)$ decays and implications for the nature of $χ_{c1}(3872)$

We study the weak decays $B_c^+\toχ_{c1}(nP)\ell^+ ν_{\ell}$ and $B_c^+\toχ_{c1}(nP)X$ (n=1,2,3) within the Bethe-Salpeter formalism, treating $χ_{c1}(3872)$ as the conventional $χ_{c1}(2P)$ charmonium. We upgrade the covariant hadronic transition amplitude to consistently evaluate the final-state wave function in its rest frame, enabling a reliable description of large-recoil processes and sizable relativistic corrections pertinent to highly excited charmonium. Our results provide a novel platform to probe the internal structure of $χ_{c1}(3872)$ via $B_c$ decays. While the LHCb search for $B_c^+\toχ_{c1}(3872)π^+$ yielded only an upper limit, we demonstrate that this is primarily due to insufficient luminosity, approximately 20 times the current $B_c$ data sample would be required for a definitive observation. In contrast, we identify the semileptonic mode $B_c^+\toχ_{c1}(3872)μ^+ν_μ$ as a far more promising channel, which could become accessible with merely twice the existing data set. Our predictions offer concrete guidance for upcoming LHCb analyses and complement ongoing efforts to resolve the nature of $χ_{c1}(3872)$.

hep-ph↗

arXiv2025

Meson properties and symmetry emergence based on the deep neural network

As a key property of hadrons, the total width is quite difficult to obtain in theory due to the extreme complexity of the strong and electroweak interactions. In this work, a deep neural network model with the Transformer architecture is built to precisely predict meson widths in the range of $10^{-14} \sim 625$ MeV based on meson quantum numbers and masses. The relative errors of the predictions are $0.12\%, 2.0\%,$ and $0.54\%$ in the training set, the test set, and all the data, respectively. We present the predicted meson width spectra for the currently discovered states and some theoretically predicted ones. The model is also used as a probe to study the quantum numbers and inner structures for some undetermined states including the exotic states. Notably, this data-driven model is investigated to spontaneously exhibit good charge conjugation symmetry and approximate isospin symmetry consistent with physical principles. The results indicate that the deep neural network can serve as an independent complementary research paradigm to describe and explore the hadron structures and the complicated interactions in particle physics alongside the traditional experimental measurements, theoretical calculations, and lattice simulations.

hep-ph↗

arXiv2025

Strong decays of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ within the Bethe-Salpeter framework

By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark states $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ as the isospin-$\frac12$ $[\bar D^*Σ_c]$ molecular states with $J^P$ configuration $(\frac{3}{2})^-$ and $(\frac12)^-$, respectively. We first calculate the one-boson-exchange interaction kernel of $[\bar D^*Σ_c]$ in the isospin-$\frac12$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $\frac12$ baryon with $J^P={\frac12}^-$ and ${\frac32}^-$. The obtained mass results for the $(\frac32)^-$ and $(\frac12)^-$ are $4.442$ and $4.457$ GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels $\bar D^{(*)0}Λ_c^+$, $J/ψ(η_c) p$, and $\bar DΣ_c^{(*)}$ for the two $P_ψ^N$ states. In the favored $\frac32^-$ and $\frac12^-$ configuration, the obtained total widths are $21.8$ MeV and $13.0$ MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest that $\bar D^{0}Λ_c^+$ and $\bar D^{(*)0}Λ_c^+$ are the dominant decay channels to detect $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$, respectively.

hep-ph↗

arXiv2024

Kinetic energy and speed powers $v^n$ of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons

Based on the instantaneous Bethe-Salpeter equation method, we calculate the average values $\overline{|\vec{q}|^n}\equiv q^n$ and speed powers $\overline{|\vec{v}|^n} \equiv v^n$ ($n=1,2,3,4$) of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons, where $\vec{q}$ and $\vec{v}$ are the three dimensional momentum and velocity of the heavy quark, respectively. We obtain the kinetic energy $μ^2_{_π}=0.455$ GeV$^2$ for the $B$ meson, which is consistent with the experimental result $0.464\pm 0.076$ GeV$^2$. For the $B_{s}$, $D$ and $D_{s}$ mesons, the $μ^2_{_π}$ are $0.530$ GeV$^2$, $0.317$ GeV$^2$ and $0.369$ GeV$^2$, respectively. And $v^2=0.0185$, $0.0215$, $0.121$, and $0.140$ for $B$, $B_{s}$, $D$, and $D_{s}$. We obtain some relationships, for example, $q^n_{_{0^-}}(mS)\approx q^n_{_{1^-}}(mS)$, $q^n_{_{0^+}}(mP)\approx q^n_{_{1^{+'}}}(mP^{'})> q^n_{_{1^+}}(mP)\approx q^n_{_{2^+}}(mP)$, and $q^n(mS)< q^n(mP)$ ($m=1,2,3$), etc.

hep-ph↗

arXiv2023

The leptonic di-flavor and di-number violation processes at high energy $μ^\pmμ^\pm $ colliders

The leptonic di-flavor violation (LFV) processes $μ^\pm μ^\pm \rightarrow e^\pm e^\pm $, $μ^\pm μ^\pm \rightarrow τ^\pm τ^\pm $ and the leptonic di-number violation (LNV) processes $μ^\pm μ^\pm \rightarrow W^\pm _iW^\pm _j$ ($i,\;j=1,\;2$) at the same-sign high energy $μ^\pm μ^\pm $ colliders are studied. The new physics (NP) factors that may play roles in these processes are highlighted by cataloging them into three types. Taking into account the experimental constraints, the processes at $μ^\pmμ^\pm$ colliders are computed and the results are presented properly. The results lead to the conclusion that observing the NP factors through the LFV and LNV processes at TeV-energy $μ^\pmμ^\pm$ colliders has significant advantages that cannot be achieved elsewhere. Therefore, in developing the techniques of muon acceleration and collisions, the option of building the same-sign muon high-energy colliders should be considered seriously too.

hep-ph↗

arXiv2023

Strong decays of $P_ψ^N(4312)^+$ to $J/ψ(η_c) p$ and $\bar D^{(*)}Λ_c$ within the Bethe-Salpeter framework

Based on the effective Lagrangian in the heavy quark limit, we calculate the one-boson-exchange interaction kernel of $P_ψ^N(4312)^+$ as the $\bar DΣ_c$ molecular state in isospin-$\frac12$. We present the Bethe-Salpeter equation and wave function for the constituent particles to be a (pseudo)scalar meson and a $\frac12$ baryon. By solving the Bethe-Salpeter equation, we obtain $P_ψ^N(4312)^+$ as the $\bar DΣ_c$ molecular state with $J^P=(\frac{1}{2})^-$. Combining the effective Lagrangian and the obtained BS wave function, the partial decay widths of $P_ψ^N(4312)^+$ to $J/ψp$, $η_c p$, $\bar D^{*0}Λ_c^+$ and $\bar D^0Λ_c^+$ are calculated to be $0.17$, $0.085$, $8.8$, and $0.026$ MeV, respectively, which are roughly consistent with the LHCb experimental measurements and some other theoretical researches. The obtain results indicate the fraction of $\bar D^{*0}Λ_c^+$ channel amounts to $\sim90\%$ of $P_ψ^N(4312)^+$, and is a highly promising channel to be discovered in the near future experiments. Our results favor the interpretation of $P_ψ^N(4312)^+$ as the $\bar DΣ_c$ molecular state with $J^P=(\frac{1}{2})^-$ and isospin $I=\frac12$.

hep-ph↗

arXiv2022

The solution to the `$1/2$ vs $3/2$' puzzle

Using an almost complete relativistic method based on the Bethe-Salpeter equation, we study the mixing angle $θ$, the mass splitting $\bigtriangleup M$, the strong decay widths $Γ(D^{({\prime})}_1)$ and the weak production rates $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ of the $D_1(2420)$ and $D_1^{\prime}(2430)$. We find there is the strong cancellation between the $^1P_1$ and $^3P_1$ partial waves in $D_1^{\prime}(2430)$ with $θ\sim-35.3^{\circ}$, which leads to the `$1/2$ vs $3/2$' puzzle. The puzzle can not be overcome by adding only relativistic corrections since in a large parameter range where $\bigtriangleup M$ is linear varying and not small, the $θ$, $Γ(D^{({\prime})}_1)$ and $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ remain almost unchanged but conflict with data. While in a special range around the mass inverse point where $\bigtriangleup M=0$ and $θ=\pm 90^{\circ}$, they change rapidly but we find the windows where $\bigtriangleup M$, $Γ(D^{({\prime})}_1)$ and $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ are all consistent with data. The small $\bigtriangleup M$ confirmed by experiment, is crucial to solve the `$1/2$ vs $3/2$' puzzle.

hep-ph↗

arXiv2022

Feynman Integrals of Grassmannians

We embed Feynman integrals in the subvarieties of Grassmannians through homogenization of the integrands in projective space, then obtain GKZ-systems satisfied by those scalar integrals. The Feynman integral can be written as linear combinations of the hypergeometric functions of a fundamental solution system in neighborhoods of regular singularities of the GKZ-system, whose linear combination coefficients are determined by the integral on an ordinary point or some regular singularities. Taking some Feynman diagrams as examples, we elucidate in detail how to obtain the fundamental solution systems of Feynman integrals in neighborhoods of regular singularities. Furthermore we also present the parametric representations of Feynman integrals of the 2-loop self-energy diagrams which are convenient to embed in the subvarieties of Grassmannians.

hep-th↗

arXiv2022

Nuclear $0\nu2β$ decays in $B-L$ symmetric SUSY model and in TeV scale left-right symmetric model

In this paper we take B-L supersymmetric standard model (B-LSSM) and TeV scale left-right symmetric model (LRSM) as two representations of the two kinds of new physics models to study the nuclear neutrinoless double beta decays ($0\nu2β$) so as to see the senses onto these two kinds of models when the decays are taken into account additionally. Within the parameter spaces allowed by all the exist experimental data, the decay half-life of the nucleus $^{76}$Ge and $^{136}$Xe, $T^{0ν}_{1/2}$($^{76}$Ge, $^{136}$Xe), is precisely calculated and the results are presented properly. Based on the numerical results, we conclude that the room of LRSM type models for the foreseeable future experimental observations on the decays is greater than that of B-LSSM type models.

hep-ph↗

arXiv2022

Fragmentation functions for gluon into $B_c$ or $B_c^*$ meson

In the paper, we calculate the fragmentation functions for $g \to B_c$ and $g \to B_c^*$. The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{g \to B_c}(z,μ_F)$ and $D_{g \to B_c^*}(z,μ_F)$, which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for $\bar{b}\to B_c(B_c^*)$ and $c\to B_c(B_c^*)$.

hep-ph↗

arXiv2022

The mass spectrum and wave functions of the $B_c$ system

The spectrum and relativistic wave functions of $B_c$ system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each $J^P$ state. Our study shows that there are three categories of $J^P$ states. The first category contains $0^-$ and $0^+$ states, which are ${}^1S_0$ dominant state with a small amount of $P$ wave and ${}^3P_0$ dominant state with a small amount of $S$ wave, respectively. The second category includes the natural parity states, such as $1^-$, $2^+$, $3^-$, etc. Taking the $1^-$ state as an example, we study it in two cases. One is the ${}^3S_1$ dominant state with a small amount of $P$ and $D$ waves, and the other is the ${}^3D_1$ dominant state but contains a large amount of $S$ and $P$ wave components. The third category includes the unnatural parity states, such as $1^+$, $2^-$, $3^+$, etc. For the $1^+$ spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two ${}^1P_1-{}^3P_1$ mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.

hep-ph↗

arXiv2021

Mass spectra, wave functions and mixing effects of the $(bcq)$ baryon

Mass spectra and wave functions of the $J^P=\frac{1}{2}^+$ $(bcq)$ baryons are calculated by the relativistic Bethe-Salpeter equation\,(BSE) with considering the mixing effects between the $1^+$ and $0^+$ $(bc)$-diquarks inside. Based on the diquark picture, the three-body problem of baryons is transformed into two two-body problems. The BSE and wave functions of the $0^+$ diquark are given, and then solved numerically to obtain the effective mass spectra and form factors. Also we present the wave functions at zero point for the $(bc)$-diquark. Considering the obtained diquark form factors, the $(bcq)$ baryons are then described by the BSE as the bound state of a diquark and a light quark, where the interaction kernel includes the inner transitions between the $0^+$ and $1^+$ diquarks. The general wave function of the $\frac{1}{2}^+$ $(bcq)$ baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between $Ξ_{bc}(Ω_{bc})$ and $Ξ_{bc}'(Ω'_{bc})$ in ground states are computed and determined to be small ($\sim \!1\%$). The numerical results indicate that it is a good choice to take $Ξ_{bc}$ and $Ξ'_{bc}$ as the baryon states with the inside $(bc)$-diquarks occupying the definite spin.

hep-ph↗

arXiv2021

Inclusive production of heavy quarkonium $η_Q$ via $Z$ boson decays within the framework of nonrelativistic QCD

In the paper, the inclusive production of heavy quarkonium $η_Q$ ($Q=b$ or $c$) via $Z$ boson decays within the framework of nonrelativistic QCD effective theory are studied. The contributions from the leading color-singlet and color-octet Fock states are considered. Total and differential decay widths for the inclusive decays $Z \to η_Q+X$ are presented. It is found that the decays $Z\to η_Q +X$ are dominated by the $^3S_1^{[8]}$ component, so the decays can be inversely adopted to determine the values of the long-distance matrix elements $\langle {\cal O}^{η_{c}}(^{3}S_{1}^{[8]})\rangle$ and $\langle {\cal O}^{η_{b}}(^{3}S_{1}^{[8]})\rangle$, respectively. Our numerical results show that at an $e^+e^-$ collider running at the $Z$ pole with a high luminosity around $10^{35}{\rm cm}^{-2}{\rm s}^{-1}$ (a super $Z$ factory), there are about $4.5\times 10^7$ $η_c$ meson events and $6.1\times 10^5$ $η_b$ meson events to be produced per operation year, and the inclusive decays may be used for clarifying some problems on the heavy quarkonium $η_Q$ and nonrelativistic QCD.

hep-ph↗

arXiv2021

Mass spectra and wave functions of $T_{QQ\bar Q\bar Q}$ tetraquarks

The compact tetraquark states with fully heavy quark contents $QQ\bar Q\bar Q$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$. Our results show that the three ground states of $cc\bar c\bar c$ locate in the mass range of $6.4\sim6.5$GeV, and the $bb\bar b\bar b$ states in mass range of $19.2\sim19.3$GeV. The obtained relativistic wave functions naturally include the mixing effects from the possible $D$\,(or $G$) partial waves, and then can be further used to do precise calculations of the tetraquark decays. Based on the obtained results, the LHCb's observation $X(6900)$ is less likely to be the ground states of compact $cc\bar c\bar c$ tetraquarks but might be the first or second excited states. In addition, a widely used propagator-like form factor is also investigated and discussed.

hep-ph↗

arXiv2021

Electron-Ion Collider in China

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei. As a future high energy nuclear physics project, an Electron-ion collider in China (EicC) has been proposed. It will be constructed based on an upgraded heavy-ion accelerator, High Intensity heavy-ion Accelerator Facility (HIAF) which is currently under construction, together with a new electron ring. The proposed collider will provide highly polarized electrons (with a polarization of $\sim$80%) and protons (with a polarization of $\sim$70%) with variable center of mass energies from 15 to 20 GeV and the luminosity of (2-3) $\times$ 10$^{33}$ cm$^{-2}$ s$^{-1}$. Polarized deuterons and Helium-3, as well as unpolarized ion beams from Carbon to Uranium, will be also available at the EicC. The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region, including 3D tomography of nucleon; the partonic structure of nuclei and the parton interaction with the nuclear environment; the exotic states, especially those with heavy flavor quark contents. In addition, issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC. In order to achieve the above-mentioned physics goals, a hermetical detector system will be constructed with cutting-edge technologies. This document is the result of collective contributions and valuable inputs from experts across the globe. The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States. The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China.

nucl-ex↗

arXiv2020

The complete study on polarization of $Υ(nS)$ hadroproduction at QCD next-to-leading order

Applying the nonrelativistic quantum chromodynamics factorization formalism to the $Υ(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters $λ_θ$, $λ_{θϕ}$, $λ_ϕ$ for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter $λ_θ$ of $Υ$ hadroproduction, our results provide a good description for the measured parameters $λ_{θϕ}$ and $λ_ϕ$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $\tildeλ$ is consistent in the two frames. Finally, it is pointed out that there are discrepancies for $\tildeλ$ between available experimental data and corresponding theoretical predictions.

hep-ph↗

arXiv2020

Next-to-leading order QCD corrections to the production of $B_c$ and $B_c^*$ through $W^+$-boson decays

In this paper, we calculate the total decay widths for the $W^+$-boson decays, $W^+ \to B_c+b+\bar{s}+X$ and $W^+ \to B^*_c+b+\bar{s}+X$, up to next-to-leading order (NLO) accuracy within the framework of the nonrelativistic QCD theory. Both the fixed-order and the fragmentation approaches are adopted to do the calculation. Differential decay widths $dΓ/dz$ and $dΓ/ds_1$ are also given. We find that the NLO corrections are significant in those two $W^+$ decay channels. Our numerical results show that at the LHC, there are about $7.03\times 10^4$ $B_c$-meson events and $5.10\times 10^4$ $B^*_c$-meson events to be produced via the $W^+$-boson decays per operation year.

hep-ph↗

arXiv2020

GKZ-hypergeometric systems for Feynman integrals

Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Miller's transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, one-loop triangle, two-loop vacuum, and two-loop sunset diagrams, respectively. The codimension of derived GKZ-hypergeometric system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. Taking GKZ-hypergeometric systems of one-loop self energy, massless one-loop triangle, and two-loop vacuum diagrams as examples, we present in detail how to perform triangulation and how to construct canonical series solutions in the corresponding convergent regions. The series solutions constructed for these hypergeometric systems recover the well known results in literature.

hep-th↗