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We introduce a novel deep learning framework based on Long Short-Term Memory (LSTM) networks to predict galactic cosmic-ray spectra on a one-day-ahead basis by leveraging historical solar activity data, overcoming limitations inherent in traditional transport models. By flexibly incorporating multiple solar parameters such as the heliospheric magnetic field, solar wind speed, and sunspot numbers, our model achieves accurate short-term and long-term predictions of cosmic-ray flux. The addition of historical cosmic-ray flux data significantly enhances prediction accuracy, allowing the model to capture complex dependencies between past and future flux variations. Additionally, the model reliably predicts full cosmic-ray spectra for different particle species, enhancing its utility for comprehensive space weather forecasting. Our approach offers a scalable, data-driven alternative to traditional physics-based methods, ensuring robust daily and long-term forecasts. This work opens avenues for advanced models that can integrate broader observational data, with significant implications for space weather monitoring and mission planning., Comment: 8 pages, 7 figures, 1 table

We extract the leading Fock-state light front wave functions (LF-LFWFs) of heavy flavor-asymmetric pseudoscalar mesons $D$, $B$ and $B_c$ from their Bethe-Salpeter wave functions based on Dyson-Schwinger equations approach, and study their leading twist parton distribution amplitudes, generalized parton distribution functions and transverse momentum dependent parton distributions. The spatial distributions of the quark and antiquark on the transverse plane are given, along with their charge and energy distributions on the light front. We find that in the considered mesons, the heavier quarks carry most longitudinal momentum fraction and yield narrow $x$-distributions, while the lighter quarks play an active role in shaping the transverse distributions within both spatial and momentum space, exhibiting a duality embodying characteristics from both light mesons and heavy quarkonium., Comment: 10 pages,9 figures

Jets are suppressed and modified in heavy ion collisions, which serve as powerful probes to the properties of the quark-gluon plasma (QGP). Attributed to the abundant information carried by the jet constituents and reconstructed substructures, plenty of interesting applications of machine learning techniques have been made on a jet-by-jet basis to study the jet quenching phenomena. Here we review recent proceedings on this topic including the tasks of reconstructing jet momentum in heavy ion collisions, classifying quenched jets and unquenched jets, identifying jet energy loss, locating the jet creation points as well as distinguishing between quark- and gluon-initiated jets in the QGP. Such jet-by-jet analyses will allow us to have a better handle on the jet reconstruction and selections to investigate the effects of jet modifications and push forward the long-standing goal of jet tomographic probes of the QGP., Comment: 11 pages, 11th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2023)

With deep learning techniques, the degree of modification of energetic jets that traversed hot QCD medium can be identified on a jet-by-jet basis. Due to the strong correlations between the degree of jet modification and its traversed length in the medium, we demonstrate the power of our novel method to locate the creation point of a dijet pair in the nuclear overlap region. In particular, jet properties, such as jet width and orientation can serve as additional handles to locate the creation points to a higher level of precision, which constitutes a significant development towards the long-standing goal of using jets as tomographic probes of the quark-gluon plasma., Comment: 7 pages, 3 figures. Contribution to the proceedings of EPS-HEP 2021, European Physical Society conference on High Energy Physics, 26-30 July 2021

Deep learning techniques have shown the capability to identify the degree of energy loss of high-energy jets traversing hot QCD medium on a jet-by-jet basis. The average amount of quenching of quark and gluon jets in hot QCD medium actually have different characteristics, such as their dependence on the in-medium traversed length and the early-developed jet substructures in the evolution. These observations motivate us to consider these two types of jets separately and classify them from jet images with deep learning techniques. We find that the classification performance gradually decreases with increasing degree of jet modification. In addition, we discuss the predictive power of different jet observables, such as the jet shape, jet fragmentation function, jet substructures as well as their combinations, in order to address the interpretability of the classification task., Comment: 5 pages, 4 figures, 1 table, 22nd Particles and Nuclei International Conference (PANIC 2021)

Deep learning techniques have the power to identify the degree of modification of high energy jets traversing deconfined QCD matter on a jet-by-jet basis. Such knowledge allows us to study jets based on their initial, rather than final energy. We show how this new technique provides unique access to the genuine configuration profile of jets over the transverse plane of the nuclear collision, both with respect to their production point and their orientation. Effectively removing the selection biases induced by final-state interactions, one can in this way analyse the potential azimuthal anisotropies of jet production associated to initial-state effects. Additionally, we demonstrate the capability of our new method to locate with precision the production point of a dijet pair in the nuclear overlap region, in what constitutes an important step forward towards the long term quest of using jets as tomographic probes of the quark-gluon plasma., Comment: 9 pages, 7 figures. Updated version for the publication in Phys. Rev. Lett

Jet interactions in a hot QCD medium created in heavy-ion collisions are conventionally assessed by measuring the modification of the distributions of jet observables with respect to the proton-proton baseline. However, the steeply falling production spectrum introduces a strong bias toward small energy losses that obfuscates a direct interpretation of the impact of medium effects in the measured jet ensemble. Modern machine learning techniques offer the potential to tackle this issue on a jet-by-jet basis. In this paper, we employ a convolutional neural network (CNN) to diagnose such modifications from jet images where the training and validation is performed using the hybrid strong/weak coupling model. By analyzing measured jets in heavy-ion collisions, we extract the original jet transverse momentum, i.e., the transverse momentum of an identical jet that did not pass through a medium, in terms of an energy loss ratio. Despite many sources of fluctuations, we achieve good performance and put emphasis on the interpretability of our results. We observe that the angular distribution of soft particles in the jet cone and their relative contribution to the total jet energy contain significant discriminating power, which can be exploited to tailor observables that provide a good estimate of the energy loss ratio. With a well-predicted energy loss ratio, we study a set of jet observables to estimate their sensitivity to bias effects and reveal their medium modifications when compared to a more equivalent jet population, i.e., a set of jets with similar initial energy. Finally, we also show the potential of deep learning techniques in the analysis of the geometrical aspects of jet quenching such as the in-medium traversed length or the position of the hard scattering in the transverse plane, opening up new possibilities for tomographic studies., Comment: 35 pages + appendices, 32 figures. Updated version for the publication in JHEP

In this proceedings, we review our recent work on the heavy quark radiative energy loss in nuclei due to multiple parton scattering within the recently improved high-twist approach, where gauge invariance can be ensured by a delicate setup of the initial partons' transverse momenta. Our new result is consistent with the previous calculations of light quark energy loss in the massless limit and heavy quark energy loss in the soft gluon radiation limit, respectively. We show numerically the correction to the heavy quark energy loss as compared with previous result and with soft gluon radiation approximation. The necessity to go beyond soft gluon radiation limit is demonstrated for a global description of light and heavy flavor data in heavy-ion collisions., Comment: 6 pages, 4 figures, 10th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2020)

In this proceeding, we review our recent work using deep convolutional neural network (CNN) to identify the nature of the QCD transition in a hybrid modeling of heavy-ion collisions. Within this hybrid model, a viscous hydrodynamic model is coupled with a hadronic cascade "after-burner". As a binary classification setup, we employ two different types of equations of state (EoS) of the hot medium in the hydrodynamic evolution. The resulting final-state pion spectra in the transverse momentum and azimuthal angle plane are fed to the neural network as the input data in order to distinguish different EoS. To probe the effects of the fluctuations in the event-by-event spectra, we explore different scenarios for the input data and make a comparison in a systematic way. We observe a clear hierarchy in the predictive power when the network is fed with the event-by-event, cascade-coarse-grained and event-fine-averaged spectra. The carefully-trained neural network can extract high-level features from pion spectra to identify the nature of the QCD transition in a realistic simulation scenario., Comment: 4 pages, 4 figures, Quark Matter 2019, will be published in Nucl. Phys. A

Using deep convolutional neural network (CNN), the nature of the QCD transition can be identified from the final-state pion spectra from hybrid model simulations of heavy-ion collisions that combines a viscous hydrodynamic model with a hadronic cascade "after-burner". Two different types of equations of state (EoS) of the medium are used in the hydrodynamic evolution. The resulting spectra in transverse momentum and azimuthal angle are used as the input data to train the neural network to distinguish different EoS. Different scenarios for the input data are studied and compared in a systematic way. A clear hierarchy is observed in the prediction accuracy when using the event-by-event, cascade-coarse-grained and event-fine-averaged spectra as input for the network, which are about 80%, 90% and 99%, respectively. A comparison with the prediction performance by deep neural network (DNN) with only the normalized pion transverse momentum spectra is also made. High-level features of pion spectra captured by a carefully-trained neural network were found to be able to distinguish the nature of the QCD transition even in a simulation scenario which is close to the experiments., Comment: 16 pages, 21 figures. Updated version for the publication in Eur. Phys. J. C

We revisit the calculation of multiple parton scattering of a heavy quark in nuclei within the framework of recently improved high-twist factorization formalism, in which gauge invariance is ensured by a delicate setup of the initial partons' transverse momenta. We derive a new result for medium modified heavy quark fragmentation functions in deeply inelastic scattering. It is consistent with the previous calculation of light quark energy loss in the massless limit, but leads to a new correction term in the heavy quark case, which vanishes in the soft gluon radiation limit. We show numerically the significance of the new correction term in the calculation of heavy quark energy loss as compared to previous studies and with soft gluon radiation approximation., Comment: 12 pages, 4 figures. Updated version for upcoming publication in Phys. Rev. D

In this paper, we aim to study the complete self-energy in the fermion propagator within two-flavor NJL model in the case of finite temperature, chemical potential and external magnetic field. Through Fierz transformation we prove that the self-energy is not simply proportional to dynamical mass in the presence of chemical potential, moreover, it contains four kinds of condensates after introducing external magnetic field. We find out the appropriate and complete form of self-energy and establish new gap equations. We take two of the four condensates (scalar and pseudovector condensates) to make an approximation and simplify the gap equations. The numerical results show that not only the dynamical mass get quantitative modification, but also the properties of Nambu phase and Wigner phase are significantly different with classic results. Instead of classic Wigner phase with zero dynamic mass in the massless NJL model, we propose a new phase - quasi-Wigner phase in this article, it has small but nonzero dynamic mass, with increasing chemical potential, eventually Nambu phase will turn into quasi-Wigner phase with first-order phase transition, therefore the chiral symmetry can never be fully restored but be partially restored. Furthermore, we prove that pseudovector condensate in self-energy can generate energy splitting in dispersion relation, it will cause minor differences of particle numbers with the split energy levels., Comment: arXiv admin note: text overlap with arXiv:1601.06637

Depending on deformed canonical anti-commutation relations, massless neutrino oscillation based on Lorentz invariance violation in non-commutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anti-commutation relations should satisfy the condition of new Moyal product and new non standard commutation relations. Furthermore, comparing the Lorentz Invariant Violation parameters $\mathit{A}$ in the previous studies with new Moyal product and new non standard commutation relations, we find that the orders of magnitude of non-commutative parameters (Lorentz invariant Violation parameters $\mathit{A}$) is not self-consistent. This inconsistency means that the previous studies of Lorentz invariance violation in non-commutative field theory may not naturally explain massless neutrino oscillation. In other words, it should be impossible to explain neutrino oscillation by Lorentz invariance violation in non-commutative field theory. This conclusion is supported by the latest atmospheric neutrinos experimental results from the Super-Kamiokande Collaboration, which show that no evidence of Lorentz invariance violation on atmospheric neutrinos was observed.

Within the Dyson-Schwinger equations (DSEs) framework, a gluon propagator model incorporating quark's feedback through operator product expansion (OPE) is introduced to investigate the QCD phase diagram in the temperature--chemical-potential ($T-\mu$) plane. Partial restoration of chiral symmetry at zero temperature and finite temperature are both studied, suggesting a first order phase transition point on the $\mu$ axis and a critical end point at $(T_E,\mu_E)/T_c = (0.85,1.11)$, where $T_c$ is the pseudo-critical temperature. In addition, we find the pseudo-critical line can be well parameterized with the curvature parameter $\kappa$ and a consistent decrease in $\kappa$ with more of gluon propagator distributed to quark's feedback., Comment: 9 pages, 8 figures

The author has consulted with us to withdraw this version from arXiv, and we both reach a consensus agreement. So we would like withdraw this paper from arXiv. For the detail of this paper and following update, one can refer to arXiv:1802.09942, which is uploaded by the author himself., Comment: The first author of this paper has uploaded another version of this paper with his own account, which conflicts with this version [arXiv:1802.09942]

We investigate the dynamical chiral symmetry breaking and its restoration at finite density and temperature within the two-flavor Nambu-Jona-Lasinio model, and mainly focus on the critical behaviors near the critical end point (CEP) and tricritical point (TCP) of quantum chromodynamics. The multi-solution region of the Nambu and Wigner ones is determined in the phase diagram for the massive and massless current quark, respectively. We use the various susceptibilities to locate the CEP/TCP and then extract the critical exponents near them. Our calculations reveal that the various susceptibilities share the same critical behaviors for the physical current quark mass, while they show different features in the chiral limit.

In the mean field approximation of (2+1)-flavor Nambu--Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included., Comment: 13 pages, 6 figures

In this paper, chiral symmetry breaking and its restoration are investigated in the mean field approximation of Nambu--Jona-Lasinio model. A first-order phase transition exists at low temperature, but is smeared out at high temperature. We discuss the rationality of using susceptibilities as the criteria to determine the crossover region as well as the critical point. Based on our results, it is found that to define a critical band instead of an exclusive line in this region might be a more suitable choice.