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Two-Body Hadronic Weak Decays of Bottomed Hadrons
Ying Zhang, Guangzhao He, Quanxing Ye, Da-Cheng Yan, Jun Hua, and Qian Wang
Chin. Phys. Lett.    2024, 41 (2): 021301 .   DOI: 10.1088/0256-307X/41/2/021301
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The structure of light diquarks plays a crucial role in formation of exotic hadrons beyond the conventional quark model, especially with regard to the line shapes of bottomed hadron decays. We study the two-body hadronic weak decays of bottomed baryons and bottomed mesons to probe the light diquark structure and to pin down the quark–quark correlations in the diquark picture. It is found that the light diquark does not favor a compact structure. For instance, the isoscalar diquark $[ud]$ in $\varLambda_{b}^{0}$ can be easily split and rearranged to form $\varSigma_{c}^{(*)}\bar{D}^{(*)}$ via the color-suppressed transition. This provides a hint that the hidden charm pentaquark states produced in $\varLambda^0_b$ decays could be the $\varSigma_{c}^{(*)}\bar{D}^{(*)}$ hadronic molecular candidates. This quantitative study resolves the apparent conflicts between the production mechanism and the molecular nature of these $P_c$ states observed in experiment.
$e^+ e^- \to \varLambda^+_c \bar{\varLambda}^-_c$ Cross Sections and the $\varLambda_c^+$ Electromagnetic Form Factors within the Extended Vector Meson Dominance Model
Cheng Chen, Bing Yan, and Ju-Jun Xie
Chin. Phys. Lett.    2024, 41 (2): 021302 .   DOI: 10.1088/0256-307X/41/2/021302
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Within the extended vector meson dominance model, we investigate the $e^+ e^- \to \varLambda^+_c \bar{\varLambda}^-_c$ reaction and the electromagnetic form factors of the charmed baryon $\varLambda_c^+$. The model parameters are determined by fitting them to the cross sections of the process $e^+e^-\rightarrow \varLambda_c^+ \bar{\varLambda}_c^-$ and the magnetic form factor $|G_{\scriptscriptstyle{\rm M}}|$ of $\varLambda^+_c$. By considering four charmonium-like states, called $\psi(4500)$, $\psi(4660)$, $\psi(4790)$, and $\psi(4900)$, we can well describe the current data on the $e^+ e^- \to \varLambda^+_c \bar{\varLambda}^-_c$ reaction from the reaction threshold up to $4.96$ GeV. In addition to the total cross sections and $|G_{\scriptscriptstyle{\rm M}}|$, the ratio $|G_{\scriptscriptstyle{\rm E}}/G_{\scriptscriptstyle{\rm M}}|$ and the effective form factor $|G_{\mathrm{eff}}|$ for $\varLambda^+_c$ are also calculated, and found that these calculations are consistent with the experimental data. Within the fitted model parameters, we have also estimated the charge radius of the charmed $\varLambda_c^+$ baryon.
Status and Prospects of Exotic Hadrons at Belle II
Sen Jia, Weitao Xiong, and Chengping Shen
Chin. Phys. Lett.    2023, 40 (12): 121301 .   DOI: 10.1088/0256-307X/40/12/121301
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In the past 20 years, many new hadrons that are difficult to explain within the conventional quark model have been discovered in the quarkonium region; these are called exotic hadrons. The Belle II experiment, as the next-generation $B$ factory, provides a good platform for exploring them. The charmonium-like states can be produced at Belle II in several ways, such as $B$ meson decays, initial-state radiation processes, two-photon collisions and double charmonium production. Bottomonium-like states can be produced directly in $e^+e^-$ colliding energies at Belle II with low continuum backgrounds. Belle II plans to perform a high-statistics energy scan from the $B\bar B$ threshold up to the highest possible energy of 11.24 GeV to search for new $Y_b$ states with $J^{\scriptscriptstyle{\rm PC}}$ = $1^{--}$, $X_b$ [the bottom counterpart of $\chi_{c1}(3872)$, also known as $X(3872)$] and partners of $Z_b$ states. We give a mini-review on the status and prospects of exotic hadrons at Belle II.
All-Orders Evolution of Parton Distributions: Principle, Practice, and Predictions
Pei-Lin Yin, Yin-Zhen Xu, Zhu-Fang Cui, Craig D. Roberts, and José Rodríguez-Quintero
Chin. Phys. Lett.    2023, 40 (9): 091201 .   DOI: 10.1088/0256-307X/40/9/091201
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Parton distribution functions (PDFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton PDFs at the hadron scale, delivers predictions for all its PDFs (unpolarized and polarized) at any higher scale. The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge; and, inter alia, enables derivation of a model-independent identity that relates the strength of the proton's gluon helicity PDF, $\Delta G_p^\zeta$, to that of the analogous singlet polarized quark PDF and valence quark momentum fraction. Using available data fits and theory predictions, the identity yields $\Delta G_p(\zeta_{_{\scriptstyle \rm C}}=\sqrt{3}\,{\rm GeV})=1.48(10)$. It furthermore entails that the measurable quark helicity contribution to the proton spin is $\tilde a_{0p}^{\zeta_{_{\scriptstyle \rm C}}}=0.32(3)$, thereby reconciling contemporary experiment and theory.
Empirical Determination of the Pion Mass Distribution
Y.-Z. Xu, K. Raya, Z.-F. Cui, C. D. Roberts, and J. Rodríguez-Quintero
Chin. Phys. Lett.    2023, 40 (4): 041201 .   DOI: 10.1088/0256-307X/40/4/041201
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Existing pion+nucleus Drell-Yan and electron+pion scattering data are used to develop ensembles of model-independent representations of the pion generalized parton distribution (GPD). Therewith, one arrives at a data-driven prediction for the pion mass distribution form factor, $\theta_2^\pi $. Compared with the pion elastic electromagnetic form factor, $\theta_2^\pi$ is harder: the ratio of the radii derived from these two form factors is $r_\pi^{\theta_2}/r_\pi = 0.79(3)$. Our data-driven predictions for the pion GPD, related form factors and distributions should serve as valuable constraints on theories of pion structure.
$Z_{cs}(4000)^+$ and $Z_{cs}(4220)^+$ in a Multiquark Color Flux-Tube Model
Yi-Heng Wang, Jia Wei, Chun-Sheng An, and Cheng-Rong Deng
Chin. Phys. Lett.    2023, 40 (2): 021201 .   DOI: 10.1088/0256-307X/40/2/021201
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We systematically investigate the mass spectrum, spatial configuration and magnetic moment of the ground and p-wave states $[cu][\bar{c}\bar{s}]$ with various color-spin configurations in a multiquark color flux-tube model. Numerical results indicate that the state $Z_{cs}(4000)^+$ can be described as the compact state $[cu][\bar{c}\bar{s}]$ with $1^3\!S_1$. Its main color-spin configuration is $[cu]^{1}_{\boldsymbol{6}_c} [\bar{c}\bar{s}]^{1}_{\bar{\boldsymbol{6}}_c}$ and its magnetic moment is 0.73$\mu_{\scriptscriptstyle{N}}$. The state $Z_{cs}(4220)^+$ can be depicted as the compact state $[cu][\bar{c}\bar{s}]$ with $1^1\!P_1$ (or $1^3\!P_1$). Its main color-spin configuration is $[cu]^{0}_{\bar{\boldsymbol{3}}_c}[\bar{c}\bar{s}]^{0}_{\boldsymbol{3}_c}$ (or $[cu]^{0}_{\bar{\boldsymbol{3}}_c}[\bar{c}\bar{s}]^{1}_{\boldsymbol{3}_c}$) and its magnetic moment is 0.12$\mu_{\scriptscriptstyle{N}}$ (or 0.64$\mu_{\scriptscriptstyle{N}}$). The physical state should be the mixture of these two different color-spin configurations and deserves further investigation. In addition, we also predict the properties of the states $[cu][\bar{c}\bar{s}]$ with other quantum numbers in the model.
Molecular Nature of $X(3872)$ in $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ Decays
Hao-Nan Wang, Li-Sheng Geng, Qian Wang, and Ju-Jun Xie
Chin. Phys. Lett.    2023, 40 (2): 021301 .   DOI: 10.1088/0256-307X/40/2/021301
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We investigate the decays of $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ based on the picture where the $X(3872)$ resonance is strongly coupled to the $D\bar{D}^* + c.c.$ channel. In addition to the decay mechanism where the $X(3872)$ resonance is formed from the $c\bar{c}$ pair hadronization with the short-distance interaction, we have also considered the $D\bar{D}^*$ rescattering diagrams in the long-distance scale, where $D$ and $\bar{D}^*$ are formed from $c$ and $\bar{c}$ separately. Because of the difference of the mass thresholds of charged and neutral $D\bar{D}^*$ channels, and the rather narrow width of the $X(3872)$ resonance, at the $X(3872)$ mass, the loop functions of $D^0\bar{D}^{*0}$ and $D^+\bar{D}^{*-}$ are much different. Taking this difference into account, the ratio of $\mathcal{B}[B^0\to K^0X(3872)]/\mathcal{B}[B^+ \to K^+ X(3872)] \simeq 0.5$ can be naturally obtained. Based on this result, we also evaluate the decay widths of $B_s^0 \to \eta(\eta') X(3872)$. It is expected that future experimental measurements of these decays can be used to elucidate the nature of the $X(3872)$ resonance.
Axion-Photon Conversion of LHAASO Multi-TeV and PeV Photons
Guangshuai Zhang and Bo-Qiang Ma
Chin. Phys. Lett.    2023, 40 (1): 011401 .   DOI: 10.1088/0256-307X/40/1/011401
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The Large High Altitude Air Shower Observatory (LHAASO) has reported the detection of a large number of multi-TeV-scale photon events also including several PeV-scale gamma-ray-photon events with energy as high as 1.4 PeV. The possibility that some of these events may have extragalactic origins is not yet excluded. Here we propose a mechanism for the traveling of very-high-energy and ultra-high-energy photons based upon the axion-photon conversion scenario, which allows extragalactic above-threshold photons to be detected by observers on the Earth. We show that the axion-photon conversation can serve as an alternative mechanism, besides the threshold anomaly due to Lorentz invariance violation, for the very-high-energy features of the newly observed gamma ray burst GRB 221009A.
Approach the Gell-Mann–Okubo Formula with Machine Learning
Zhenyu Zhang, Rui Ma, Jifeng Hu, and Qian Wang
Chin. Phys. Lett.    2022, 39 (11): 111201 .   DOI: 10.1088/0256-307X/39/11/111201
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Machine learning is a novel and powerful technology and has been widely used in various science topics. We demonstrate a machine-learning-based approach built by a set of general metrics and rules inspired by physics. Taking advantages of physical constraints, such as dimension identity, symmetry and generalization, we succeed to approach the Gell-Mann–Okubo formula using a technique of symbolic regression. This approach can effectively find explicit solutions among user-defined observables, and can be extensively applied to studying exotic hadron spectrum.
Induced Fission-Like Process of Hadronic Molecular States
Jun He, Dian-Yong Chen, Zhan-Wei Liu, and Xiang Liu
Chin. Phys. Lett.    2022, 39 (9): 091401 .   DOI: 10.1088/0256-307X/39/9/091401
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We predict a new physical phenomenon, induced fission-like process and chain reaction of hadronic molecular states. As a molecular state, if induced by a $D$ meson, the $X(3872)$ can split into $D\bar{D}$ final state which is forbidden due to the spin-parity conservation. The breeding of the $D$ meson of the reaction, such as $D^0X(3872)\to D^0\bar{D}^0D^0$, makes the chain reaction of $X(3872)$ matter possible. We estimate the cross section of the $D$ meson induced fission-like process of $X(3872)$ into two $D$ mesons. With very small $D^0$ beam momentum of 1 eV, the total cross section reaches an order of 1000 b, and decreases rapidly with the increasing beam momentum. With the transition of $D^*$ meson in molecular states to a $D$ meson, the $X(3872)$ can release large energy, which is acquired by the final mesons. The momentum distributions of the final $D$ mesons are analyzed. In the laboratory frame, the spectator $D$ meson in molecular state concentrates in the low momentum area. The energy from the transition from $D^*$ to $D$ meson is mainly acquired by two scattered $D$ mesons. The results suggest that the $D$ meson environment will lead to the induced fission-like process and chain reaction of the $X(3827)$. Such a phenomenon can be extended to other hadronic molecular states.
Novel and Self-Consistency Analysis of the QCD Running Coupling $\alpha_{\rm s}(Q)$ in Both the Perturbative and Nonperturbative Domains
Qing Yu, Hua Zhou, Xu-Dong Huang, Jian-Ming Shen, and Xing-Gang Wu
Chin. Phys. Lett.    2022, 39 (7): 071201 .   DOI: 10.1088/0256-307X/39/7/071201
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The quantum chromodynamics (QCD) coupling $\alpha_{\rm s}$ is the most important parameter for achieving precise QCD predictions. By using the well measured effective coupling $\alpha^{g_1}_{\rm s}(Q)$ defined from the Bjorken sum rules as a basis, we suggest a novel self-consistency way to fix the $\alpha_{\rm s}$ at all scales: The QCD light-front holographic model is adopted for its infrared behavior, and the fixed-order pQCD prediction under the principle of maximum conformality (PMC) is used for its high-energy behavior. Using the PMC scheme-and-scale independent perturbative series, and by transforming it into the one under the physical V scheme, we observe that a precise $\alpha_{\rm s}$ running behavior in both the perturbative and nonperturbative domains with a smooth transition from small to large scales can be achieved.
QCD Axial Anomaly Enhances the $\eta \eta^\prime$ Decay of the Hybrid Candidate $\eta_1(1855)$
Hua-Xing Chen, Niu Su, and Shi-Lin Zhu
Chin. Phys. Lett.    2022, 39 (5): 051201 .   DOI: 10.1088/0256-307X/39/5/051201
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We study the hybrid mesons with the exotic quantum number $I^{\rm G}J^{\rm PC} = 0^+1^{-+}$ and investigate their decays into the $\eta \eta^\prime$, $a_1(1260) \pi$, $f_1(1285) \eta$, $f_1(1420) \eta$, $K^*(892) \overline{K}$, $K_1(1270) \overline{K}$, and $K_1(1400) \overline{K}$ channels. It is found that the QCD axial anomaly enhances the decay width of the $\eta \eta^\prime$ channel although this mode is strongly suppressed by the small p-wave phase space. Our results support the interpretation of the $\eta_1(1855)$ recently observed by BESIII as the $\bar s s g$ hybrid meson of $I^{\rm G}J^{\rm PC}=0^+1^{-+}$. The QCD axial anomaly ensures the $\eta \eta^\prime$ decay mode to be a characteristic signal of the hybrid nature of the $\eta_1(1855)$.
Valence Quark Ratio in the Proton
Zhu-Fang Cui, Fei Gao, Daniele Binosi, Lei Chang, Craig D. Roberts, and Sebastian M. Schmidt
Chin. Phys. Lett.    2022, 39 (4): 041401 .   DOI: 10.1088/0256-307X/39/4/041401
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Beginning with precise data on the ratio of structure functions in deep inelastic scattering (DIS) from $^3$He and $^3$H, collected on the domain $0.19 \leq x_{\scriptscriptstyle{\rm B}} \leq 0.83$, where $x_{\scriptscriptstyle{\rm B}}$ is the Bjorken scaling variable, we employ a robust method for extrapolating such data to arrive at a model-independent result for the $x_{\scriptscriptstyle{\rm B}}=1$ value of the ratio of neutron and proton structure functions. Combining this with information obtained in analyses of DIS from nuclei, corrected for target-structure dependence, we arrive at a prediction for the proton valence-quark ratio: $\left. d_v/u_v \right|_{x_{\scriptscriptstyle{\rm B}}\to 1} = 0.230 (57)$. Requiring consistency with this result presents a challenge to many descriptions of proton structure.
Chiral Anomaly in Non-Relativistic Systems: Berry Curvature and Chiral Kinetic Theory
Lan-Lan Gao and Xu-Guang Huang
Chin. Phys. Lett.    2022, 39 (2): 021101 .   DOI: 10.1088/0256-307X/39/2/021101
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Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac and Weyl fermions. In most typical cases, the Lorentz covariance is assumed and thus the linear dispersion relations are maintained. However, in realistic materials, such as Dirac and Weyl semimetals, the nonlinear dispersion relations appear naturally. We develop a kinetic framework to study the chiral anomaly for Weyl fermions with nonlinear dispersions using the methods of Wigner function and semi-classical equations of motion. In this framework, the chiral anomaly is sourced by Berry monopoles in momentum space and could be enhanced or suppressed due to the windings around the Berry monopoles. Our results can help understand the chiral anomaly-induced transport phenomena in non-relativistic systems.
Electromagnetic Form Factors of $\varLambda$ Hyperon in the Vector Meson Dominance Model and a Possible Explanation of the Near-Threshold Enhancement of the $e^+e^- \to \varLambda\bar{\varLambda}$ Reaction
Zhong-Yi Li, An-Xin Dai, and Ju-Jun Xie
Chin. Phys. Lett.    2022, 39 (1): 011201 .   DOI: 10.1088/0256-307X/39/1/011201
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The near-threshold $e^+e^- \to \varLambda\bar{\varLambda}$ reaction is studied with the assumption that the production mechanism is due to a near-$\varLambda \bar{\varLambda}$-threshold bound state. The cross section of the $e^+e^- \to \varLambda\bar{\varLambda}$ reaction is parameterized in terms of the electromagnetic form factors of $\varLambda$ hyperon, which are obtained with the vector meson dominance model. It is shown that the contribution to the $e^+e^- \to \varLambda\bar{\varLambda}$ reaction from a new narrow state with quantum numbers $J^{PC}=1^{--}$ is dominant for energies very close to threshold. The mass of this new state is around 2231 MeV, which is very close to the mass threshold of $\varLambda \bar{\varLambda}$, while its width is just a few MeV. This gives a possible solution to the problem that all previous calculations seriously underestimated the near-threshold total cross section of the $e^+e^- \to \varLambda\bar{\varLambda}$ reaction. We also note that the near-threshold enhancement can also be reproduced by including these well established vector resonances $\omega(1420)$, $\omega(1650)$, $\phi(1680)$, or $\phi(2170)$ with a Flatté form for their total decay width, and a strong coupling to the $\varLambda\bar{\varLambda}$ channel.
Pauli Radius of the Proton
Zhu-Fang Cui, Daniele Binosi, Craig D Roberts, and Sebastian M Schmidt
Chin. Phys. Lett.    2021, 38 (12): 121401 .   DOI: 10.1088/0256-307X/38/12/121401
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Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyze proton magnetic form factor data obtained via electron+proton scattering on $Q^2 \in [0.027,0.55]$ GeV$^2$ with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto $Q^2\simeq 0$ for extraction of the form factor slope. In this way, we find $r_{\scriptscriptstyle {\rm M}} = 0.817(27)$ fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, $F_{1,2}(Q^2)$, are not truly independent observables; to wit, the difference $F_1^\prime(0)-F_2^\prime(0)/\kappa_{\rm p} = [1+\kappa_{\rm p}]/[4 m_{\rm p}^2]$, viz., the proton Foldy term.
Unambiguously Resolving the Potential Neutrino Magnetic Moment Signal at Large Liquid Scintillator Detectors
Ziping Ye, Feiyang Zhang, Donglian Xu, and Jianglai Liu
Chin. Phys. Lett.    2021, 38 (11): 111401 .   DOI: 10.1088/0256-307X/38/11/111401
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Non-vanishing electromagnetic properties of neutrinos have been predicted by many theories beyond the Standard Model, and an enhanced neutrino magnetic moment can have profound implications for fundamental physics. The XENON1T experiment recently detected an excess of electron recoil events in the 1–7 keV energy range, which can be compatible with solar neutrino magnetic moment interaction at a most probable value of $\mu_{\nu} = 2.1 \times 10^{-11} \mu_{\scriptscriptstyle {\rm B}}$. However, tritium backgrounds or solar axion interaction in this energy window are equally plausible causes. Upcoming multi-tonne noble liquid detectors will test these scenarios more in depth, but will continue to face similar ambiguity. We report a unique capability of future large liquid scintillator detectors to help resolve the potential neutrino magnetic moment scenario. With $O$(100) kton$\cdot$year exposure of liquid scintillator to solar neutrinos, a sensitivity of $\mu_{\nu} < 10^{-11} \mu_{\scriptscriptstyle {\rm B}}$ can be reached at an energy threshold greater than 40 keV, where no tritium or solar axion events but only neutrino magnetic moment signal is still present.
Prediction of an $\varOmega_{bbb}\varOmega_{bbb}$ Dibaryon in the Extended One-Boson Exchange Model
Ming-Zhu Liu and Li-Sheng Geng
Chin. Phys. Lett.    2021, 38 (10): 101201 .   DOI: 10.1088/0256-307X/38/10/101201
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Since Yukawa proposed that the pion is responsible for mediating the nucleon-nucleon interaction, meson exchanges have been widely used in understanding hadron-hadron interactions. The most studied mesons are the $\sigma$, $\pi$, $\rho$, and $\omega$, while other heavier mesons are often argued to be less relevant because they lead to short range interactions. However, whether the range of interactions is short or long should be judged with respect to the size of the system studied. We propose that one charmonium exchange is responsible for the formation of the $\varOmega_{ccc}\varOmega_{ccc}$ dibaryon, recently predicted by lattice QCD simulations. The same approach can be extended to the strangeness and bottom sectors, leading to the prediction on the existence of $\varOmega\varOmega$ and $\varOmega_{bbb}\varOmega_{bbb}$ dibaryons, while the former is consistent with the existing lattice QCD results, the latter remains to checked. In addition, we show that the Coulomb interaction may break up the $\varOmega_{ccc}\varOmega_{ccc}$ pair but not the $\varOmega_{bbb}\varOmega_{bbb}$ and $\varOmega\varOmega$ dibaryons.
Thermodynamics of the System of Massive Dirac Fermions in a Uniform Magnetic Field
Ren-Hong Fang, Ren-Da Dong, De-Fu Hou, and Bao-Dong Sun
Chin. Phys. Lett.    2021, 38 (9): 091201 .   DOI: 10.1088/0256-307X/38/9/091201
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We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel–Plana formula, these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable $b=2eB/T^{2}$. The zero-field magnetic susceptibility is expanded at zero mass, and the leading order term is logarithmic. We also calculate scalar, vector current, axial vector current and energy-momentum tensor of the system through ensemble average approach. Mass correction to chiral separation effect is discussed. For massless chiral fermions, our results recover the chiral magnetic effect for right- and left-handed fermions, as well as chiral separation effect.
Regarding the Distribution of Glue in the Pion
Lei Chang and Craig D. Roberts
Chin. Phys. Lett.    2021, 38 (8): 081101 .   DOI: 10.1088/0256-307X/38/8/081101
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Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions (DFs) of all partons within the pion and comparing them with those in the proton; and since glue provides binding in quantum chromodynamics, the glue DF could play a special role. Producing reliable predictions for the proton's DFs is difficult because the proton is a three-valence-body bound-state problem. As sketched herein, the situation for the pion, a two-valence-body problem, is much better, with continuum and lattice predictions for the valence-quark and glue DFs in agreement. This beginning of theory alignment is timely because experimental facilities now either in operation or planning promise to realize the longstanding goal of providing pion targets, thereby enabling precision experimental tests of rigorous theory predictions concerning Nature's most fundamental Nambu–Goldstone bosons.
Dynamically Exploring the QCD Matter at Finite Temperatures and Densities: A Short Review
Shanjin Wu, Chun Shen, and Huichao Song
Chin. Phys. Lett.    2021, 38 (8): 081201 .   DOI: 10.1088/0256-307X/38/8/081201
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We provide a concise review on recent theory advancements towards full-fledged (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density. Heavy-ion collisions at different collision energies produce strongly coupled matter and probe the QCD phase transition at the crossover, critical point, and first-order phase transition regions. Dynamical frameworks provide a quantitative tool to extract properties of hot QCD matter and map fireballs to the QCD phase diagram. Outstanding challenges are highlighted when confronting current theoretical frameworks with current and forthcoming experimental measurements from the RHIC beam energy scan programs.
Resolving the Bethe–Salpeter Kernel
Si-Xue Qin and Craig D. Roberts
Chin. Phys. Lett.    2021, 38 (7): 071201 .   DOI: 10.1088/0256-307X/38/7/071201
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A novel method for constructing a kernel for the meson bound-state problem is described. It produces a closed form that is symmetry-consistent (discrete and continuous) with the gap equation defined by any admissible gluon-quark vertex, $\varGamma$. Applicable even when the diagrammatic content of $\varGamma$ is unknown, the scheme can foster new synergies between continuum and lattice approaches to strong interactions. The framework is illustrated by showing that the presence of a dressed-quark anomalous magnetic moment in $\varGamma$, an emergent feature of strong interactions, can remedy many defects of widely used meson bound-state kernels, including the mass splittings between vector and axial-vector mesons and the level ordering of pseudoscalar and vector meson radial excitations.
Production of $P_{cs}(4459)$ from $\varXi_b$ Decay
Qi Wu, Dian-Yong Chen, and Ran Ji
Chin. Phys. Lett.    2021, 38 (7): 071301 .   DOI: 10.1088/0256-307X/38/7/071301
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Inspired by the $P_{cs}(4459)$ reported by the LHCb collaboration recently, we investigate the $P_{cs}(4459)$ production from $\varXi_b$ decay in a molecular scenario using an effective Lagrangian approach. With different $J^P$ assignments to $P_{cs}(4459)$, the magnitude of branching fractions of $\varXi_b \to P_{cs}(4459) K$ is estimated, which is of the order of $10^{-4}$. Together with the decay properties of $P_{cs}(4459)$, the present estimations could be further testified by precise measurements and contribute to a better understanding of the molecular interpretations and the exploration of $J^P$ quantum numbers of $P_{cs}(4459)$.
Finding Short-Range Parity-Time Phase-Transition Points with a Neural Network
Songju Lei, Dong Bai, Zhongzhou Ren, and Mengjiao Lyu
Chin. Phys. Lett.    2021, 38 (5): 051101 .   DOI: 10.1088/0256-307X/38/5/051101
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The non-Hermitian $PT$-symmetric system can live in either unbroken or broken $PT$-symmetric phase. The separation point of the unbroken and broken $PT$-symmetric phases is called the $PT$-phase-transition point. Conventionally, given an arbitrary non-Hermitian $PT$-symmetric Hamiltonian, one has to solve the corresponding Schrödinger equation explicitly in order to determine which phase it is actually in. Here, we propose to use artificial neural network (ANN) to determine the $PT$-phase-transition points for non-Hermitian $PT$-symmetric systems with short-range potentials. The numerical results given by ANN agree well with the literature, which shows the reliability of our new method.
Exploring $J/\psi$ Production Mechanism at the Future Electron-Ion Collider
Jian-Wei Qiu, Xiang-Peng Wang, and Hongxi Xing
Chin. Phys. Lett.    2021, 38 (4): 041201 .   DOI: 10.1088/0256-307X/38/4/041201
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We propose to use transverse momentum $p_{\rm T}$ distribution of $J/\psi$ production at the future Electron Ion Collider (EIC) to explore the production mechanism of heavy quarkonia in high energy collisions. We apply QCD and QED collinear factorization to the production of a $c\bar{c}$ pair at high $p_{\rm T}$, and non-relativistic QCD factorization to the hadronization of the pair to a $J/\psi$. We evaluate $J/\psi$ $p_{\rm T}$-distribution at both leading and next-to-leading order in strong coupling, and show that production rates for various color-spin channels of a $c\bar{c}$ pair in electron-hadron collisions are very different from that in hadron-hadron collisions, which provides a strong discriminative power to determine various transition rates for the pair to become a $J/\psi$. We predict that the $J/\psi$ produced in electron-hadron collisions is likely unpolarized, and the production is an ideal probe for gluon distribution of colliding hadron (or nucleus). We find that the $J/\psi$ production is dominated by the color-octet channel, providing an excellent probe to explore the gluon medium in large nuclei at the EIC.
Impressions of the Continuum Bound State Problem in QCD
Si-Xue Qin and C. D. Roberts
Chin. Phys. Lett.    2020, 37 (12): 121201 .   DOI: 10.1088/0256-307X/37/12/121201
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Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics (QCD). In order to fulfill that promise, phenomenology and theory must reach a new level, limiting and overcoming model-dependence, so that clean lines can be drawn to connect the data with QCD itself. Progress in that direction, made using continuum methods for the hadron bound-state problem, is sketched herein.
A Search for Solar Axions and Anomalous Neutrino Magnetic Moment with the Complete PandaX-II Data
Xiaopeng Zhou, Xinning Zeng, Xuyang Ning, Abdusalam Abdukerim, Wei Chen, Xun Chen, Yunhua Chen, Chen Cheng, Xiangyi Cui, Yingjie Fan, Deqing Fang, Changbo Fu, Mengting Fu, Lisheng Geng, Karl Giboni, Linhui Gu, Xuyuan Guo, Ke Han, Changda He, Di Huang, Yan Huang, Yanlin Huang, Zhou Huang, Xiangdong Ji, Yonglin Ju, Shuaijie Li, Huaxuan Liu, Jianglai Liu, Xiaoying Lu, Wenbo Ma, Yugang Ma, Yajun Mao, Yue Meng, Kaixiang Ni, Jinhua Ning, Xiangxiang Ren, Changsong Shang, Guofang Shen, Lin Si, Andi Tan, Anqing Wang, Hongwei Wang, Meng Wang, Qiuhong Wang, Siguang Wang, Wei Wang, Xiuli Wang, Zhou Wang, Mengmeng Wu, Shiyong Wu, Weihao Wu, Jingkai Xia, Mengjiao Xiao, Pengwei Xie, Binbin Yan, Jijun Yang, Yong Yang, Chunxu Yu, Jumin Yuan, Ying Yuan, Dan Zhang, Tao Zhang, Li Zhao, Qibin Zheng, Jifang Zhou, and Ning Zhou (PandaX-II Collaboration)
Chin. Phys. Lett.    2021, 38 (1): 011301 .   DOI: 10.1088/0256-307X/38/1/011301
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We report a search for new physics signals using the low energy electron recoil events in the complete data set from PandaX-II, in light of the recent event excess reported by XENON1T. The data correspond to a total exposure of 100.7 ton$\cdot$day with liquid xenon. With robust estimates of the dominant background spectra, we perform sensitive searches on solar axions and neutrinos with enhanced magnetic moment. It is found that the axion-electron coupling $g_{\rm Ae} < 4.6\times 10^{-12}$ for an axion mass less than 0.1 keV/$c^2$ and the neutrino magnetic moment $\mu_{\nu} < 4.9\times 10^{-11}\mu_{\rm B}$ at 90% confidence level. The observed excess from XENON1T is within our experimental constraints.
$X_0(2900)$ and $X_1(2900)$: Hadronic Molecules or Compact Tetraquarks
Hua-Xing Chen, Wei Chen, Rui-Rui Dong, and Niu Su
Chin. Phys. Lett.    2020, 37 (10): 101201 .   DOI: 10.1088/0256-307X/37/10/101201
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Very recently the LHCb collaboration reported their observation of the first two fully open-flavor tetraquark states, the $X_0(2900)$ of $J^P = 0^+$ and the $X_1(2900)$ of $J^P = 1^-$. We study their possible interpretations using the method of QCD sum rules, paying special attention to an interesting feature of this experiment that the higher resonance $X_1(2900)$ has a width significantly larger than the lower one $X_0(2900)$. Our results suggest that the $X_0(2900)$ can be interpreted as the s-wave $D^{*-}K^{*+}$ molecule state of $J^P = 0^+$, and the $X_1(2900)$ can be interpreted as the p-wave $\bar c \bar s u d$ compact tetraquark state of $J^P = 1^-$. Mass predictions of their bottom partners are also given.
Anomalous $tq\gamma$ Couplings and Radiative ${\boldsymbol B}$ Meson Decays
Ying Tan  and Chong-Xing Yue
Chin. Phys. Lett.    2020, 37 (10): 101301 .   DOI: 10.1088/0256-307X/37/10/101301
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Motivated by the recent ATLAS results in terms of the branching ratios $ Br(t\rightarrow q\gamma)$, we consider the effects of the anomalous $tq\gamma$ couplings on the radiative $B$ meson decays $\bar{B}\rightarrow X_{D} \gamma$ and $B\rightarrow V\gamma$ with $V$ being light vector mesons $\rho,\omega,\phi$ and $K^{\ast}$. Comparing with the corresponding experimental measured data, we obtain the constraints on anomalous $tq\gamma$ couplings.
$\mathcal{PT}$ Symmetry of a Square-Wave Modulated Two-Level System
Liwei Duan, Yan-Zhi Wang, and Qing-Hu Chen
Chin. Phys. Lett.    2020, 37 (8): 081101 .   DOI: 10.1088/0256-307X/37/8/081101
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We study a non-Hermitian two-level system with square-wave modulated dissipation and coupling. Based on the Floquet theory, we achieve an effective Hamiltonian from which the boundaries of the $\mathcal{PT}$ phase diagram are captured exactly. Two kinds of $\mathcal{PT}$ symmetry broken phases are found, whose effective Hamiltonians differ by a constant $\omega / 2$. For the time-periodic dissipation, a vanishingly small dissipation strength can lead to the $\mathcal{PT}$ symmetry breaking in the $(2k-1)$-photon resonance ($\varDelta = (2k-1) \omega$), with $k=1,2,3\dots$ It is worth noting that such a phenomenon can also happen in $2k$-photon resonance ($\varDelta = 2k \omega$), as long as the dissipation strengths or the driving times are imbalanced, namely $\gamma_0 \ne - \gamma_1$ or $T_0 \ne T_1$. For the time-periodic coupling, the weak dissipation induced $\mathcal{PT}$ symmetry breaking occurs at $\varDelta_{\rm eff}=k\omega$, where $\varDelta_{\rm eff}=(\varDelta_0 T_0 + \varDelta_1 T_1)/T$. In the high frequency limit, the phase boundary is given by a simple relation $\gamma_{\rm eff}=\pm\varDelta_{\rm eff}$.
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