The high-intensity heavy-ion accelerator facility (HIAF), currently under construction in Huizhou, Guangdong Province, China, is expected to be completed by 2025. This facility will be capable of delivering proton and heavy-ion beams with energies of up to several GeV, thereby providing a versatile platform for advanced fundamental physics research. Key scientific objectives include exploring physics beyond the standard model through the search for new particles and interactions, testing fundamental symmetries, investigating exotic hadronic states such as dibaryons, pentaquark states, and multi-strange hypernuclei, conducting precise measurements of hadron and hypernucleus properties, and probing the phase boundary and the critical point of nuclear matter. To facilitate these investigations, we propose the construction of a dedicated experimental apparatus at HIAF—the Huizhou Hadron Spectrometer (HHaS). This paper presents the conceptual design of HHaS, which comprises a solenoid magnet, a five-dimensional silicon pixel tracker, a Low-Gain Avalanche Detector (LGAD) for time-of-flight measurements, and a Cherenkov–scintillation dual-readout electromagnetic calorimeter. The design targets an unprecedented event rate of 1–100 MHz, extensive particle acceptance, a track momentum resolution at the 1 ∼ 3 % at 1 GeV, and broad particle-identification capability. Such capabilities position HHaS as a powerful instrument for high-precision experimental studies in particle and nuclear physics. The successful realization of HHaS is expected to strongly promote the development of medium- and high-energy physics research within China.

We study the mass spectra of hidden-charm tetraquark systems with quantum numbers (IG)JP = (1+)1+ (and their I = 1/2 partners) using QCD sum rules. The analysis incorporates the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the operator product expansions, with particular attention to operator mixing effects due to renormalization group evolution. We find that both the parametric dependence and the perturbative convergence are significantly improved for the two mixed operators J_1,5^Mixed and J_2,6^Mixed , compared with those for the unmixed meson-meson or diquark-antidiquark type ones. For the dccu system, the masses of J_1,5^Mixed and J_2,6^Mixed are determined to be 3.89_-0.12^+0.18 GeV and 4.03_-0.07^+0.06 GeV, respectively, closely matching those of Zc(3900) and Zc(4020). Similarly, for the sccu states, the masses of J_1,5^Mixed and J_2,6^Mixed are found to be 4.02_-0.09^+0.17 GeV and 4.21_-0.07^+0.08 GeV, respectively, in close proximity to Zcs(3985)/Zcs(4000) and Zcs(4220), consistent with the expectation that they are the partners of Zc(3900) and Zc(4020). Our results highlight the crucial role of operator mixing, an inevitable effect in a complete NLO calculation, in achieving a robust phenomenological description for the tetraquark system.

We study the mass spectra of hidden-charm tetraquark systems with quantum numbers (I^G)J^P=(1^+)1^+ using QCD sum rules. The analysis incorporates the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the operator product expansions, with particular attention to operator mixing effects due to renormalization group evolution. For the d̅cc̅u system, the masses of two mixed operators, J_1,5^Mixed and J_2,6^Mixed, are determined to be 3.89^+0.18_-0.12 GeV and 4.03^+0.06_-0.07 GeV, respectively, closely matching those of Z_c(3900) and Z_c(4020). Similarly, for the s̅cc̅u states, the masses of J_1,5^Mixed and J_2,6^Mixed are found to be 4.02^+0.17_-0.09 GeV and 4.21^+0.08_-0.07 GeV, respectively, in close proximity to Z_cs(3983)/Z_cs(4000) and Z_cs(4220), consistent with the expectation that they are the partners of Z_c(3900) and Z_c(4020). Our results highlight the crucial role of operator mixing, an inevitable effect in a complete NLO calculation, in achieving a robust phenomenological description for the tetraquark system.

Next-to-leading order QCD corrections to the $\gamma^{*} \longrightarrow Q\bar{Q}-Reggeon$ vertex are calculated, where $Q\bar{Q}$ denotes a heavy quark pair $c\bar c$ or $b\bar b$. The heavy quark mass effects on the photon impact factor are found to be significant, and hence may influence the results of high energy photon-photon scattering and heavy quark pair leptoproduction. In our NLO calculation, similar to the massless case, the ultraviolate(UV) divergences are fully renormalized in the standard procedure, while the infrared (IR) divergences are regulated by the parameter $\epsilon_{IR}$ in dimensional regularization. For the process $\gamma^* + q \to Q\bar{Q} + q$, we calculate all NLO coefficients in terms of $\epsilon_{IR}$, and find they are enhanced due to the heavy quark mass, as compared with the light quark case, and the enhancement factors increase rapidly as the quark mass increases. This might essentially indicate the quark mass effect, in spite of the absence of real corrections that are needed in a complete NLO calculation. Moreover, unlike the $\gamma^{*}$ to massless-quark-Reggeon vertex, the results in the present work may apply to the real photon case.

Next-to-leading order QCD corrections to the $\gamma^{*} \longrightarrow Q\bar{Q}-Reggeon$ vertex are calculated, where $Q\bar{Q}$ denotes a heavy quark pair $c\bar c$ or $b\bar b$. The heavy quark mass effects on the photon impact factor are found to be significant, and hence may influence the results of high energy photon-photon scattering and heavy quark pair leptoproduction. In our NLO calculation, similar to the massless case, the ultraviolate(UV) divergences are fully renormalized in the standard procedure, while the infrared (IR) divergences are regulated by the parameter $\epsilon_{IR}$ in dimensional regularization. For the process $\gamma^* + q \to Q\bar{Q} + q$, we calculate all NLO coefficients in terms of $\epsilon_{IR}$, and find they are enhanced due to the heavy quark mass, as compared with the light quark case, and the enhancement factors increase rapidly as the quark mass increases. This might essentially indicate the quark mass effect, in spite of the absence of real corrections that are needed in a complete NLO calculation. Moreover, unlike the $\gamma^{*}$ to massless-quark-Reggeon vertex, the results in the present work may apply to the real photon case.

A bstract We study the mass spectra of $$ \overline{Q}Q\overline{Q}Q $$ Q ¯ Q Q ¯ Q ( Q = c, b ) systems in QCD sum rules with the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Instead of meson-meson or diquark-antidiquark currents, we use diagonalized currents under operator renormalization. We find that differing from conventional mesons $$ \overline{q}q $$ q ¯ q and baryons qqq , a unique feature of the multiquark systems like $$ \overline{Q}Q\overline{Q}Q $$ Q ¯ Q Q ¯ Q is the operator mixing or color configuration mixing induced by NLO corrections, which is crucial to understand the color structure of the states. Our numerical results show that the NLO corrections are very important for the $$ \overline{Q}Q\overline{Q}Q $$ Q ¯ Q Q ¯ Q system, because they not only give significant contributions but also reduce the scheme and scale dependence and make Borel platform more distinct, especially for the $$ \overline{b}b\overline{b}b $$ b ¯ b b ¯ b in the $$ \overline{\textrm{MS}} $$ MS ¯ scheme. We use currents that have good perturbation convergence in our phenomenological analysis. With the $$ \overline{\textrm{MS}} $$ MS ¯ scheme, we get three J PC = 0 ++ states, with masses $$ {6.35}_{-0.17}^{+0.20} $$ 6.35 − 0.17 + 0.20 GeV, $$ {6.56}_{-0.20}^{+0.18} $$ 6.56 − 0.20 + 0.18 GeV and $$ {6.95}_{-0.35}^{+0.21} $$ 6.95 − 0.35 + 0.21 GeV, respectively. The first two seem to agree with the broad structure around 6 . 2 ~ 6 . 8 GeV measured by the LHCb collaboration in the J/ψJ/ψ spectrum, and the third seems to agree with the narrow resonance X (6900). For the 2 ++ states we find one with mass $$ {7.03}_{-0.26}^{+0.22} $$ 7.03 − 0.26 + 0.22 GeV, which is also close to that of X (6900), and another one around $$ {7.25}_{-0.35}^{+0.21} $$ 7.25 − 0.35 + 0.21 GeV, which has good scale dependence but slightly large scheme dependence.

AbstractThe next-to-leading order (NLO) ($$ \mathcal{O} $$O($$ {\alpha}_s^3 $$αs3)) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in3$$ {P}_J^{\left[1,8\right]} $$PJ18states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and$$ \mathcal{O} $$O($$ {\alpha}_s^2 $$αs2) perturbative NRQCD matrix elements ⟨$$ {\mathcal{O}}^3{P}_J^{\left[1,8\right]} $$O3PJ18(3$$ {S}_1^{\left[8\right]} $$S18)⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

We study the triply heavy baryons Omega(QQQ) (Q = c,b) in the QCD Sum Rules by calculating the next-to-leading order (NLO) contribution in the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the Omega(QQQ). This is because the NLO not only results in a large correction, but also reduces the parameters dependence and makes the Borel platform more distinct, especially for the Omega(QQQ) in the (MS) over bar scheme, where the platform appears only at NLO but not at LO. In particular, due to the inclusion of the NLO contribution, the renormalization schemes ((MS) over bar and On-Shell) dependence and scale dependence are significantly improved. As a result, after including the NLO contribution of the perturbative part in QCD sum rules, the masses are predicted to be 4.53(-0.11)(+0.26) GeV for Omega(ccc) and 14.27(-0.32)(+0.33) GeV for Omega(bbb), where the results are obtained at mu=M-B with errors including that from the variation of the renormalization scale mu in the range (0.8-1.2)M-B. A careful study for the mu dependence in a wider range is further performed, which shows that the LO results are very sensitive to the choice of mu whereas the NLO results are much better. In addition to the mu=M-B result, a quite stable value, (4.75-4.80) GeV, for the Omega(ccc) mass is found in the range of mu=(1.2-2.0)M-B.

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 ∼80%) and protons (with a polarization of ∼70%) with variable center of mass energies from 15 to 20 GeV and the luminosity of (2–3) × 1033 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.

We give a brief comment on the possible tetraquark states cc c̅c̅ observed by the LHCb experiment.

High-order calculation at the semihard scale in high-energy collisions is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize the rapidity divergence in color glass condensate (CGC) factorization, which makes higher-order calculation rigorous and straightforward. By applying this method to the single hadron production in the pA collision, we find the kinematic constraint effect introduced by hand in previous works comes out automatically, but with different values. The difference is crucial for our next-to-leading-order result to have a smaller theoretical uncertainty compared with leading-order result, which makes the high-order calculation in CGC factorization be useful. As a byproduct, the negativity problem found in the literature can also be overcome in our framework by properly choosing the factorization scale.

The widely used nonrelativistic QCD (NRQCD) factorization theory now encounters some notable difficulties in describing quarkonium production. This may be due to the inadequate treatment of soft hadrons emitted in the hadronization process, which causes bad convergence of velocity expansion in NRQCD. In this paper, starting from QCD we propose a rigorously defined factorization approach, soft gluon factorization (SGF), to better deal with the effects of soft hadrons. After a careful velocity expansion, the SGF can be as simple as the NRQCD factorization in phenomenological studies, but has a much better convergence. The SGF may provide a new insight to understand the mechanisms of quarkonium production and decay.

We calculate the NLO corrections for the gluon fragmentation functions to a heavy quarkantiquark pair in S [1] 0 or S [8] 0 state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of z (light-cone momentum fraction carried by the quark-antiquark pair), which can not only give FFs results with very high precision at any value of z, but also provide fully analytical structure at these singularities. We find that the NLO corrections are significant, with K-factors larger than 2 in most regions. The NLO corrections may have important impact on heavy quarkonia (e.g. ηc and J/ψ) production at the LHC.

Hao Han, Yan-Qing Ma, Ce Meng, Hua-Sheng Shao, Yu-Jie Zhang, Kuang-Ta Chao (a) School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China (b) Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA (c) Center for High Energy physics, Peking University, Beijing 100871, China (d) Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education) and School of Physics, Beihang University, Beijing 100191, China (e)Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

We evaluate the production cross sections of X(3872) at the LHC and Tevatron at NLO in alpha(s) in NRQCD by assuming that the short-distance production proceeds dominantly through chi'(c1) component in our chi'(c1) - D-0(D) over bar*(0) mixing model for X(3872). The outcomes of the fits to the CMS p(T) distribution can well account for the recent ATLAS data in a much larger range of transverse momenta (10 GeV < p(T) < 70 GeV) and the CDF total cross section data, and are also consistent with the value of k = Z(c (c) over bar) . Br(X -> J/Psi pi(+)pi(-)) constrained by the B-meson decay data. For LHCb, the predicted X(3872) total cross section is larger than the data by a factor of 2, which is due to the problem of the fixed-order NRQCD calculation that may not be applicable for the region with small p(T) (p(T) similar to 5 GeV) and large forward rapidity (2.5 < y < 4.5). In comparison, the prediction of the molecule production mechanism for X(3872) is inconsistent with both p(T) distributions and total cross sections of CMS and ATLAS, and the total cross section of CDF.

We compute fragmentation corrections to hadroproduction of the quarkonium states $J/\ensuremath{\psi}$, ${\ensuremath{\chi}}_{cJ}$, and $\ensuremath{\psi}(2S)$ at leading power in ${m}_{c}^{2}/{p}_{T}^{2}$, where ${m}_{c}$ is the charm-quark mass and ${p}_{T}$ is the quarkonium transverse momentum. The computation is carried out in the framework of nonrelativistic QCD. We include corrections to the parton-production cross sections through next-to-leading order in the strong coupling ${\ensuremath{\alpha}}_{s}$ and corrections to the fragmentation functions through second order in ${\ensuremath{\alpha}}_{s}$. We also sum leading logarithms of ${p}_{T}^{2}/{m}_{c}^{2}$ to all orders in perturbation theory. We find that, when we combine these leading-power fragmentation corrections with fixed-order calculations through next-to-leading order in ${\ensuremath{\alpha}}_{s}$, we are able to obtain good fits for ${p}_{T}\ensuremath{\ge}10\text{ }\text{ }\mathrm{GeV}$ to hadroproduction cross sections that were measured at the Tevatron and the LHC. Using values for the nonperturbative long-distance matrix elements that we extract from the cross-section fits, we make predictions for the polarizations of the quarkonium states. We obtain good agreement with measurements of the polarizations, with the exception of the CDF Run II measurement of the prompt $J/\ensuremath{\psi}$ polarization, for which the agreement is only fair. In the predictions for the prompt-$J/\ensuremath{\psi}$ cross sections and polarizations, we take into account feeddown from the ${\ensuremath{\chi}}_{cJ}$ and $\ensuremath{\psi}(2S)$ states.

For $J/\psi$ pair production at hadron colliders, we present the full next-to-leading order (NLO) calculations with the color-singlet channel in nonrelativistic QCD. We find that the NLO result can reasonably well describe the LHCb measured cross section, but exhibits very different behaviors from the CMS data in the transverse momentum distribution and mass distribution of $J/\psi$ pair. Moreover, by adding contributions of gluon fragmentation and quark fragmentation, which occur at even higher order in $\alpha_s$, it is still unable to reduce the big differences. In particular, the observed flat distribution in the large invariant mass region is hard to explain. New processes or mechanisms are needed to understand the CMS data for $J/\psi$ pair production.

We compute fragmentation corrections to hadroproduction of the quarkonium states J/psi,chi(cJ), and psi(2S) at leading power in m(c)(2)/p(T)(2), where m(c) is the charm-quark mass and p(T) is the quarkonium transverse momentum. The computation is carried out in the framework of nonrelativistic QCD. We include corrections to the parton-production cross sections through next-to-leading order in the strong coupling alpha(s) and corrections to the fragmentation functions through second order in alpha(s). We also sum leading logarithms of p(T)(2)/m(c)(2) to all orders in perturbation theory. We find that, when we combine these leading-power fragmentation corrections with fixed-order calculations through next-to-leading order in alpha(s), we are able to obtain good fits for p(T) >= 10 GeV to hadroproduction cross sections that were measured at the Tevatron and the LHC. Using values for the nonperturbative long-distance matrix elements that we extract from the cross-section fits, we make predictions for the polarizations of the quarkonium states. We obtain good agreement with measurements of the polarizations, with the exception of the CDF Run II measurement of the prompt J/psi polarization, for which the agreement is only fair. In the predictions for the prompt-J/psi cross sections and polarizations, we take into account feeddown from the chi(cJ) and psi(2S) states.

Upsilon(nS) and chi(b)(nP) (n = 1, 2, 3) production at the LHC is studied at next-to-leading order in alpha(s) in nonrelativistic QCD. Feeddown contributions from higher chi(b) and Upsilon states are all considered for lower Upsilon cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the Upsilon(nS) polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the Upsilon(3S) polarization puzzle can be understood by a large feeddown contribution from chi(b)(3P) states. Our results may provide a good description for both cross sections and polarizations of prompt Upsilon(nS) and chi(b)(n(P)) production at the LHC.

We compute fragmentation corrections to hadroproduction of the quarkonium states $J/psi$, $chi_{cJ}$, and $psi(2S)$ at leading power in $m_c/p_T$, where $m_c$ is the charm-quark mass and $p_T$ is the quarkonium transverse momentum. The computation is carried out in the framework of nonrelativistic QCD. We include corrections to the parton-production cross sections through next-to-leading order in the strong coupling $alpha_s$ and corrections to the fragmentation functions through second order in $alpha_s$. We also sum leading logarithms of $p_T^2/m_c^2$ to all orders in perturbation theory. We find that, when we combined these leading-power fragmentation corrections with fixed-order calculations through next-to-leading order in $alpha_s$, we are able to obtain good fits for $p_Tgeq 10$ GeV to hadroproduction cross sections that were measured at the Tevatron and the LHC. Using values for the nonperturbative long-distance matrix elements that we extract from the cross-section fits, we make predictions for the polarizations of the quarkonium states. We obtain good agreement with measurements of the polarizations, with the exception of the CDF Run II measurement of the prompt $J/psi$ polarization, for which the agreement is only fair. In the predictions for the prompt-$J/psi$ cross sections and polarizations, we take into account feeddown from the $chi_{cJ}$ and $psi(2S)$ states.