Quark Combination Research Articles

A Comprehensive Overview of Photon-Proton Scattering and QCD Methodology

The AdS/CFT correspondence is used as a helpful reference in the light front hyperbolic geometry technique, which solves this issue by mapping a confining gauge theory parameterized on the light front to a greater anti-de Sitter space. Three different interaction processes exist Direct or angular the target photon quark and the photon pair directly. When a lepton-antilepton pair is produced, only quantum electrodynamics (QED) is used; however, when a quark-antiquark pair is produced, both QED and perturbative quantum chromodynamics (QCD) are used. A deep-inelastic electron-photon scattering experiment was used to study the photon structure function, which describes the photon inherent quark composition: Single resolved: the desired spectroscopy quark combination creates the vector meson, one of the constituents of relationships to the investigating photon. The main focus of the current study was on photon-proton and QCD methodology. The main theoretical conclusion resulting from the work carried out can be used in the development of the conceptual concept of further researchers and this work also will be a guideline for future researchers.

Transverse momentum and multiplicity dependence of varLambda _{c}^{+}/D^{0} ratio in pp collisions at sqrt{s}=13 TeV

We apply an equal-velocity quark combination model to study the varLambda _{c}^{+}/D^{0} ratio in the range p_{T}lesssim 10 GeV/c in pp collisions at sqrt{s}=13 TeV. We decompose the ratio into four parts which are related to quark numbers, light-flavor quark p_{T} spectrum, charm quark p_{T} spectrum, momentum correlation between light and charm quarks, respectively. Their influence on varLambda _{c}^{+}/D^{0} ratio is individually studied. The curvature property of light-flavor quark p_{T} spectrum is the main reason of the non-monotonic p_{T} dependence of varLambda _{c}^{+}/D^{0} ratio exhibited in high multiplicity events. Moreover, the multiplicity dependence of varLambda _{c}^{+}/D^{0} ratio as the function of p_{T} is mainly because of the multiplicity dependence of light-flavor quark p_{T} spectrum. Using the light-flavor quark p_{T} spectrum obtained from experimental data of light-flavor hadrons and charm quark p_{T} spectrum obtained from FONLL and/or PYTHIA calculations, the p_{T} dependence of experimental data of varLambda _{c}^{+}/D^{0} ratio in high multiplicity events and that in low multiplicity events in pp collisions at sqrt{s}=13 TeV are reasonably understood.

Production of Strange and Charm Hadrons in Pb+Pb Collisions at sNN = 5.02 TeV

Using a quark combination model with the equal-velocity combination approximation, we study the production of hadrons with strangeness and charm flavor quantum numbers in Pb+Pb collisions at sNN= 5.02 TeV. We present analytical expressions and numerical results for these hadrons’ transverse momentum spectra and yield ratios. Our numerical results agree well with the experimental data available. The features of strange and charm hadron production in the quark–gluon plasma at the early stage of heavy ion collisions are also discussed.

D ∗ jet fragmentation function paradox and combination mechanism

In the framework of the perturbative Quantum Chromodynamics factorization, the production of a hadron includes contributions from fragmentation as well as combination, with the latter being of higher twist. In particular, the heavy meson production can be via the combination of a heavy quark with a light one, and the cross section can be factorized to be the convolution of the combination matrix element, the light quark distribution function, and the hard partonic sub-cross section of the heavy quark production. The partonic distribution and the combination matrix element are functions of a scaling variable, respectively, which is the momentum fraction of the corresponding quark with respect to the heavy meson. We studied the D *± production in jet via combination in pp collision at the LHC. The total result is comparable with the experimental data. The combination matrix elements can be further studied in various hadron production processes.

Averaged transverse momentum correlations of hadrons in relativistic heavy-ion collisions

We compile experimental data for the averaged transverse momentum ($\left\langle p_{T}\right\rangle $) of proton, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$ and $\phi$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$ 200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV, and find that experimental data of these hadrons exhibit systematic correlations. We apply a quark combination model with equal-velocity combination approximation to derive analytic formulas of hadronic $\left\langle p_{T}\right\rangle $ in the case of exponential form of quark $p_{T}$ spectra at hadronization. We use them to successfully explain the systematic correlations exhibited in $\left\langle p_{T}\right\rangle $ data of $p\Lambda$, $\Lambda\Xi^{-}$, $\Xi^{-}\Omega^{-}$ and $\Xi^{-}\phi$ pairs. We also use them to successfully explain the regularity observed in $\left\langle p_{T}\right\rangle $ of these hadrons as the function of $(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at both RHIC and LHC energies. Our results suggest that the constituent quark degrees of freedom and the equal-velocity combination of these constituent quarks at hadronization play important role in understanding the production of baryons and $\phi$ meson at these RHIC and LHC energies.

Production characteristics of light (anti-)nuclei from (anti-)nucleon coalescence in heavy ion collisions at energies employed at the RHIC beam energy scan

With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be well reproduced. We further study the yields and yield ratios of different light (anti-)nuclei and naturally explain their interesting behaviors as a function of the collision energy. We especially point out that the multi-particle yield ratio $tp/d^2$ should be carefully corrected from hyperon weak decays for protons to probe the production characteristics of light nuclei. All of our results show that the coalescence mechanism for (anti-)nucleons plays a dominant role for the production of light nuclei and antinuclei at the RHIC beam energy scan energies.

Signals of quark combination at hadronization in pp collisions at s=200 GeV

We find signals of quark combination at hadronization from the experimental data of ${p}_{T}$ spectra of hadrons at midrapidity in $pp$ collisions at $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$. The first is the constituent quark number scaling property for ${p}_{T}$ spectra of ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ and $\ensuremath{\phi}$ and that for ${p}_{T}$ spectra of $p$ and ${\ensuremath{\rho}}^{0}$. The second is that ${p}_{T}$ spectra of $\mathrm{\ensuremath{\Lambda}}$, ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$, and ${K}^{*0}$ can be self-consistently described using the spectrum of strange quarks from $\ensuremath{\phi}$ data and that of up/down quarks from $p$ data in the equal-velocity combination mechanism. The third is that experimental data for ${p}_{T}$ spectrum of ${D}^{*+}$ are also well described by the spectrum of up/down quarks from $p$ data and a spectrum of charm quarks which is consistent with theoretical calculations of the fixed-order next-to-leading-logarithmic approach. These results indicate a similarity between hadron production in $pp$ collisions at $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$ and that at LHC energies. We predict ${p}_{T}$ spectra of single-charm hadrons and their spectrum ratios. We suggest systematic measurements in $pp$ collisions at $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$ in the future so as to better understand the property of the small parton system created in $pp$ collisions at different collision energies.

Universality test of short range nucleon-nucleon correlations in nuclei with strange and charmed probes

Understanding the EMC effect and its relation to the short-range nucleon-nucleon correlations (SRC) in nuclei is a major challenge for modern nuclear physics. One of the key aspects of the connection between these phenomena is the universality. The universality states that the SRC is responsible for the EMC effect and that the modification of the partonic structure of the SRC is the same in different nuclei. The flavor dependence of the universality is one of the unanswered questions. The investigations conducted to date have demonstrated the existence and universality of the SRC for light and quarks. Recently, it was suggested that the universality for heavy flavors can be studied through their deep subthreshold production in and eA collisions. In this paper, we discuss an alternative possibility to access the strange and gluon high-X structure of the SRC and to establish universality for heavy flavors using nuclear semi-inclusive deep inelastic scattering (nSIDIS), which probes different quark flavor combinations depending on the final state hadron. The specific reaction can be "tagged" by observation of a strange or charmed particle registered in coincidence with the scattering lepton. The universality of the SRC can be tested in the kinematic region, i.e., , where the contribution to the cross section from SRC becomes dominant. Exploring the strangeness, charmonium, and open charm will shed light on the role of quarks and gluons in nuclei, thereby developing an understanding of how nuclei emerge within QCD.

Production of light-flavor and single-charmed hadrons in pp collisions at TeV in an equal-velocity quark combination model * *Supported by Shandong Province Natural Science Foundation (ZR2019YQ06,ZR2019MA053), and National Natural Science Foundation of China (11975011) and Higher Educational Youth Innovation Science and Technology Program of Shandong Province (2019KJJ010)

We apply an equal-velocity quark combination model to study the production of light-flavor hadrons and single-charmed hadrons at midrapidity in the collisions at TeV. We find that the experimental data for the spectra of and exhibit the quark number scaling property, which clearly indicates the quark combination mechanism at hadronization. Experimental data for the spectra of , , , , , and are systematically described by the model. The non-monotonic dependence of the ratio is naturally explained, and we find that it is closely related to the shape of the logarithm of the strange quark distribution. Using the spectra of light-flavor quarks obtained from light-flavor hadrons and the spectrum of charm quarks, which is consistent with perturbative QCD calculations, the experimental data for differential cross-sections of , , and as functions of are systematically described. We predict the differential cross-sections of and . The ratio in our model is approximately 0.16, and is approximately 0.012, owing to the cascade suppression of strangeness. In addition, the predicted and ratios exhibit the non-monotonic dependence on in the low range.

Strange hadron production in a quark combination model in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

We apply a quark combination model to study yield densities and transverse momentum ($p_{T}$) spectra of strange (anti-)hadrons at mid-rapidity in central Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 19.6, 27, 39 and 200 GeV. We show that experimental data for $p_{T}$ spectra of (anti-)hadrons in these collisions can be systematically described by the equal velocity combination of constituent quarks and antiquarks at hadronization. We obtain $p_{T}$ spectra of quarks and antiquarks at hadronization and study their collision energy dependence. We also reproduce the yield densities of hadrons and anti-hadrons. In particular, we demonstrate that yield ratios of anti-hadrons to hadrons $K^{-}/K^{+}$, $\bar{p}/p$, $\bar{\Lambda}/\Lambda$, $\bar{\Xi}^{+}/\Xi^{-}$ and $\bar{\Omega}^{+}/\Omega^{-}$ simply correlate with each other and their experimental data except $\bar{\Omega}^{+}/\Omega^{-}$ at $\sqrt{s_{NN}}=$ 7.7 GeV are systematically described by the model. These results suggest that the equal velocity combination mechanism for quarks and antiquarks at hadronization plays an important role in Au+Au collisions at low RHIC energies ($\sqrt{s_{NN}}\geq$ 11.5 GeV).

Elliptic flow of hadrons in equal-velocity quark combination mechanism in relativistic heavy-ion collisions

We apply a quark combination model with equal-velocity combination (EVC) approximation to study the elliptic flow (v_{2}) of hadrons in heavy-ion collisions in a wide collision energy range (sqrt{s_{NN}}= 27–5020 GeV). Utilizing the simple relationship between v_{2} of hadrons and those of quarks under EVC, we find that v_{2} of up/down quarks obtained by experimental data of proton is consistent with that obtained by data of varLambda and varXi . v_{2} of strange quarks obtained by data of varOmega is consistent with that obtained by data of varLambda and varXi , and at RHIC energies it is also consistent with that obtained by data of phi . This means that v_{2} of these hadrons have a common quark-level source. Using data of D^0, we obtain v_{2} of charm quarks with p_Tlesssim 6 GeV/c. We find that under EVC charm quark dominates v_{2} of D mesons at low p_{T} but light-flavor quarks significantly contribute to v_{2} of D mesons in the range 3lesssim p_{T}lesssim 8 GeV/c. We predict v_{2} of charmed baryons varLambda _{c}^{+} and varXi _{c}^{0} which show a significant enhancement at intermediate p_{T} due to the double contribution of light-flavor quarks. The properties of the obtained quark v_{2} under EVC are studied and a regularity for v_{2} of quarks as the function of p_{T}/m is found.

Spectrum of fully-heavy tetraquarks from a diquark+antidiquark perspective

Using a relativized diquark model Hamiltonian, we calculate the masses of J^{PC}=0^{++} ground-state tetraquarks in the following systems: b s {bar{b}} {bar{s}}, bb {bar{n}} {bar{n}} (n=u, d), bb {bar{s}} {bar{s}}, cc{bar{c}} {bar{c}}, b b {bar{b}} {bar{b}}, b c{bar{b}} {bar{c}} and b b {bar{c}} {bar{c}}. We also compute extensive spectra for the fully-heavy quark flavour combinations. Finally, as a test of the diquark model approach, we compute the masses of fully-heavy baryons in the diquark model. Our results may be compared soon to the forthcoming experimental data for fully-heavy three-quark systems.

Discoveries of the pentaquark states

Protons and neutrons are not fundamental particles, instead are formed by quarks. Thousands of multi-quark particles were discovered in cosmic rays or particle accelerators. However, within the past decades after the quark model was proposed by Gell-Mann and Zweig, only two categories of strongly interacting particles were known: Baryons (such as protons and neutrons) that are made from three quarks, and mesons that are made from one quark and one antiquark. But what other configurations of quarks and antiquarks can form a particle? This question is theoretically difficult to answer. Yet new particles with different combinations of quarks keep popping up in experiments. In 2015, the best evidence for the existence of an exotic type of particle called as pentaquark, a never-before-seen formation of five quarks, was discovered by physicists working on the Large Hadron Collider beauty (LHCb) experiment at European Organization for Nuclear Research (CERN). The detection of this particle is a major breakthrough in learning more about the nature of the strong forces that bound quarks together. In a sample of about 26000 Λ b 0 → J/ψK − p decays collected by the LHCb detector, a significant enhancement structure was observed in the J/ψp mass distribution. The pentaquark signal populated well separatedly from those contributions of Λ * → K − p on the “Dalitz” plot using the K–p and J/ψp invariant mass-squared as independent variables. The amplitude analysis revealed two pentaquark states were needed to describe dataset. They were formally named as Pc(4450)+ and Pc(4380)+ with statistical significances greater than 9 standard deviations: One has a mass of (4449.8 ±1.7±2.5) MeV and a width of (39 ±5±19) MeV, while the other is wider, with a mass of (4380 ±8±29) MeV and a width of (205 ±18±86) MeV. Both pentaquarks that LHCb physicists observed decaying strongly into a J/ψ particle and a proton, must have a minimal quark content of c c ¯ uud, and thus are charmonium pentaquarks. Recently the analysis has been reoptimized based on the data collected to date. A sample of 2.5×105 Λ b 0 → J/ψK − p decays was selected, nine times more than those used in the previous analysis. A new pentaquark state Pc(4312) was discovered with a mass near 4312 MeV. The Pc(4450) state was found to be the superposition of two nearby states at 4440 and 4457 MeV respectively. In an attempt to interpret the discoveries by the LHCb experiment, the pentaquark was conjectured as a tightly bound system of all five quarks, or a weakly bound “molecular” system of a baryon and a meson. Accurate description of a multi-quark system using the theory of the strong force and quantum chromodynamics (QCD) is an extremely difficult problem. In fact, there are many combinations how five quarks are bound within the pentaquark. The five quarks could be tightly bound within a single structure, for example. Another possibility is that a quark and an antiquark are bound together to form a meson and the remaining three quarks form a baryon. The meson and baryon could then be bound to each other to create a structure resembling a subatomic molecule. Exploring the structure of pentaquarks as one of novel frontiers in high energy physics paves a new era to study the nature of strong interactions, which is an important stepping-stone in our good understanding of the strong force, the least well known of the four forces in nature.

Quark number scaling of pT spectra for Ω and ϕ in relativistic heavy-ion collisions

We show that the experimental data of transverse momentum ($p_{T}$) spectra of $\Omega$ baryon and $\phi$ meson at mid-rapidity in heavy-ion collisions exhibit the constituent quark number scaling in a wide energy range from RHIC to LHC. Such a scaling behavior is a direct consequence of quark combination mechanism via equal velocity combination and provides a very convenient way to extract the $p_{T}$ spectrum of strange quarks at hadronization. We present the results of strange quarks obtained from the available data and study the properties in particular the energy dependence of the averaged transverse momentum $\langle p_{T}\rangle$ and the transverse radial flow velocity $\langle\beta\rangle$ with a hydrodynamics-motivated blast-wave model.

Heavy baryon spectrum on the lattice with NRQCD bottom and HISQ lighter quarks

We determine the mass spectra of heavy baryons containing one or more bottom quarks along with their hyperfine splittings and various mass differences on MILC 2+1 Asqtad lattices at three different lattice spacings. NRQCD action is used for bottom quarks whereas relativistic HISQ action for the lighter up/down, strange and charm quarks. We consider all possible combinations of bottom and lighter quarks to construct the bottom baryon operators for the states $J^P=1/2^+$ and $3/2^+$.

Charmed hadron production via equal-velocity quark combination in ultrarelativistic heavy ion collisions

Recent data on the production of $D$ mesons and $\Lambda_c^+$ baryons in heavy ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider exhibit a number of striking characteristics such as enhanced yield ratios $D_s^+/D^0$, $\Lambda_c^+/D^0$ and their transverse momentum dependences. In this paper, we derive the momentum dependence of open charm mesons and singly charmed baryons produced in ultra-relativistic heavy ion collisions via the equal-velocity quark combination. We present analytic expressions and numerical results of yield ratios and compare them with the experimental data available. We make predictions for other charmed hadrons.

Centrality and transverse momentum dependence of inclusive J/ψ production at midrapidity in Pb–Pb collisions at [formula omitted] TeV

The inclusive J/ψ meson production in Pb–Pb collisions at a center-of-mass energy per nucleon–nucleon collision of sNN=5.02 TeV at midrapidity (|y|<0.9) is reported by the ALICE Collaboration. The measurements are performed in the dielectron decay channel, as a function of event centrality and J/ψ transverse momentum pT, down to pT=0. The J/ψ mean transverse momentum 〈pT〉 and rAA ratio, defined as 〈pT2〉PbPb/〈pT2〉pp, are evaluated. Both observables show a centrality dependence decreasing towards central (head-on) collisions. The J/ψ nuclear modification factor RAA exhibits a strong pT dependence with a large suppression at high pT and an increase to unity for decreasing pT. When integrating over the measured momentum range pT<10GeV/c, the J/ψRAA shows a weak centrality dependence. Each measurement is compared with results at lower center-of-mass energies and with ALICE measurements at forward rapidity, as well as to theory calculations. All reported features of the J/ψ production at low pT are consistent with a dominant contribution to the J/ψ yield originating from charm quark (re)combination.

Statistical method in quark combination model * * Supported by National Natural Science Foundation of China (11535012, 11890713, 11575100), the 973 program (2015CB856902), the Key Research Program of the Chinese Academy of Sciences (XDPB09), and Shandong Province Natural Science Foundation (ZR2019YQ06, ZR2019MA053)

We present a new method for solving the probability distribution for baryons, antibaryons, and mesons at the hadronization of the constituent quark and antiquark system. The hadronization is governed by the quark combination rule in the quark combination model developed by the Shandong Group. We employ the method of the generating function to derive the outcome of the quark combination rule, which is significantly simpler and easier to generalize than the original method. Furthermore, we use the formula of the quark combination rule and its generalization to study the property of the multiplicity distribution of net-protons. Taking a naive case of quark number fluctuations and correlations at hadronization, we calculate ratios of multiplicity cumulants of final-state net-protons and discuss the potential applicability of the quark combination model by studying hadronic multiplicity fluctuations and the underlying phase transition property in relativistic heavy-ion collisions.

Light-Cone Sum Rules for Gravitational Form Factors

We outline the developed approach within the light-cone sum rules at the leading order for calculation of the gravitational form factors related to the nucleon valence quark combinations. The predictions for the gravitational form factor D(t) (D-term contributions) have been presented.

Constituent quark number scaling from strange hadron spectra in pp collisions at TeV * * Supported by National Natural Science Foundation of China (11575100), and by Shandong Province Natural Science Foundation(ZR2019YQ06, ZR2019MA053), and by A Project of Shandong Province Higher Educational Science and Technology Program (J18KA228)

We show that the spectra of and at midrapidity in the inelastic events in collisions at 13 TeV exhibit a constituent quark number scaling property, which is a clear signal of quark combination mechanism at hadronization. We use a quark combination model with equal velocity combination approximation to systematically study the production of identified hadrons in collisions at = 13 TeV. The midrapidity spectra for protons, , , , and in the inelastic events are simultaneously fitted by the model. The multiplicity dependence of the yields of these hadrons are also well understood. The strong dependence of the ratio is well explained by the model, which further suggests that the production of two hadrons with similar masses is determined by their quark content at hadronization. The spectra of strange hadrons at midrapidity in different multiplicity classes in collisions at 13 TeV are predicted for further tests of the model. The midrapidity spectra of soft ( GeV/c) strange quarks and up/down quarks at hadronization in collisions at 13 TeV are extracted.