Charm Structure Research Articles

CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data

In this paper we confront the color glass condensate and saturation approach of Contreras [Non-linear equation in the re-summed next-to-leading order of perturbative QCD: The leading twist approximation, ] with the experimental combined HERA data and obtain its parameters. The model includes two features that are in accordance with our theoretical knowledge of deep inelastic scattering. These consist of: (i) the use of analytical solution for the nonlinear Balitsky-Kovchegov evolution equation and () the exponential behavior of the saturation momentum on the impact parameter b-dependence, characterized by Qs∝exp(−mb) which reproduces the correct behavior of the scattering amplitude at large b in accord with Froissart theorem. The model results are then compared to data at small-x for the structure function of the proton F2, the longitudinal structure function FL, the charm structure function F2cc¯, the exclusive vector meson (J/ψ,ϕ,ρ) production and deeply virtual Compton scattering. We obtain a good agreement for the processes in a wide kinematic range of Q2 at small-x. Our results provide a strong guide for finding an approach, based on color glass condensate and saturation effective theory for high-energy QCD, to make reliable predictions from first principles and for forthcoming experiments like the Electron Ion Collider and the LHeC. Published by the American Physical Society 2024

A simple model for the charm structure function of nuclei

In this paper, we have investigated the importance of quark charm in nuclear structure functions in the color dipole model at small x. The charm structure function per nucleon F2cA/A for light and heavy nuclei in a wide range of transverse separations r with renormalization and factorization scales is considered. Bounds on the ratio F2cA/AF2A for nuclei are well described with respect to the electron-ion future colliders kinematic range, i.e., EIC and EIcC colliders.

From the line shape of the X(3872) to its structure

From a study of the lineshape of the $X(3872)$, the LHCb collaboration measures a sizeable negative effective range. This cannot be reconciled with a shallow $D\bar{D}^*$ bound state hypothesis. Based on Weinberg's compositeness criterion, together with a theorem by Smorodinsky, it follows that the $X$ has to have a compact hidden charm structure, most likely a tetraquark, interacting with unbound $D\bar{D}^*$ pairs via short-distance color forces. This conclusion is strengthened by the general pattern recently emerging for exotic mesons.

Constraints on gluon distribution functions in the nucleon and nucleus from open charm hadron production at the Electron-Ion Collider

The Electron-Ion Collider (EIC) at Brookhaven National Laboratory will be a precision Quantum Chromodynamics machine that will enable a vast physics program with electron+proton/ion collisions across a broad center-of-mass range. Measurements of hard probes such as heavy flavor in deep inelastic scatterings will be an essential component to the EIC physics program and are one of the detector R\&D driving aspects. In this paper we study the projected statistical precision of open charm hadron production through exclusive hadronic channel reconstruction with a silicon detector concept currently being developed using a PYTHIA-based simulation. We further study the impact of possible intrinsic charm in the proton on projected data, and estimate the constraint on the nuclear gluon parton distribution function (PDF) from the charm structure functions $F_{2}^{c\overline{c}}$ in $e$+Au collisions using a Bayesian PDF re-weighting technique. Our studies show the EIC will be capable delivering an unprecedented measurement of charm hadron production across a broad kinematic region and will provide strong constraints to both intrinsic charm and nuclear gluon PDFs.

Importance of heavy quark longitudinal structure function measurements at future circular collider energies

In this article, we consider the ratio of structure functions for heavy quark pair production at low values of . The importance of this ratio for charm and beauty pair production is examined according to the Hadron Electron Ring Accelerator (HERA) data. The behavior of these ratios is considered due to the hard pomeron behavior of the gluon distribution function. The results are in good agreement with the HERA data. Expanding this data to the range of new energies underscores the importance of these measurements for heavy quarks. The ratio of charm and beauty structure functions at the proposed Large Hadron electron Collider (LHeC) is considered as a function of invariant center-of-mass energy. For top pair production this ratio is extracted with known kinematics of the LHeC and Future Circular Collider electron-hadron (FCC-eh) colliders. Comparison of the results obtained for the ratio of top structure functions in LHeC and FCC-eh are proportional to the specified inelasticity range.

Influence of gluon behavior on heavy-quark pair production

We check the impact of the gluon distribution due to the number of active flavor employed in the calculation of heavy-quark deep-inelastic scattering (DIS) electro-production on the reduced cross-section and structure functions determined in the leading-order (LO) and next-to-leading-order (NLO) quantum chromodynamics (QCD) analysis using the Hadron Electron Ring Accelerator (HERA) combined data. The charm and beauty structure functions are determined and compared with the HERA combined data. The results are in good agreement with respect to the experimental data. We also compare the obtained charm and bottom structure functions with the results from CTEQ6.6 (CTEQ Collaboration (Nadolsky P. M. et al.), Phys. Rev. D, 78 (2008) 013004) and NNPDF3.1 (NNPDF Collaboration (Ball R. D. et al.), Eur. Phys. J. C, 77, (2017) 663) parameterization models. The effect of gluon density on these calculations depends on the number of active flavor at asymptotical values of the momentum transfer Q 2. Also, in the HERA kinematic range, the ratios and are obtained. These results and comparison with the HERA combined data demonstrate that the suggested method can be applied in the analysis of new colliders.

A detailed study of charm content of a proton in the frameworks of the Kimber-Martin-Ryskin and Martin-Ryskin-Watt approaches

The charm structure function, (F2cc‾(x,Q2)), is calculated in the framework of the kt-factorization formalism by using the unintegrated parton distribution functions (UPDF), which are generated through the Kimber et al. (KMR) and Martin et al. (MRW) procedures. The Martin group (MMHT2014) parton distribution functions (PDF) is used as the input PDF for the corresponding UPDF. The resulted F2cc‾(x,Q2) is compared with the predicted data and the calculations given by the ZEUS and H1 collaborations, the parton pQCD theory, i.e. the general-mass variable-flavor-number scheme (GMVFNS), the LO collinear procedure and the saturation model introduced by Golec-Biernat and Wu¨sthoff (GBW), respectively. In general, it is shown that the calculated charm structure functions based on the stated above two UPDF schemes are consistent with the experimental data and other theoretical predictions. Also, a short discussion is presented regarding the KMR and MRWUPDF behaviors.

Parton distribution functions and constraints on the intrinsic charm content of the proton using the Brodsky-Hoyer-Peterson-Saka approach

In this work, a new set of parton distribution functions taking into account the intrinsic charm (IC) contribution is presented. We focus on the impact of the EMC measurements on the large $x$ charm structure function as the strongest evidence for the intrinsic charm when combined with the HERA, SLAC and BCDMS data. The main goal of this paper is the simultaneous determination of the intrinsic charm probability ${P}_{c{\bar c/p}}$ and strong coupling $\alpha_s$. This allows us to study the interaction of these two quantities as well as the influence on the PDFs in the presence of IC contributions. By considering $\alpha_s$ which can be fix or free parameter from our QCD analysis, we find that although there is not a significant change in the extracted central value of PDFs and their uncertainties, the obtained value of ${P}_{c{\bar c/p}}$ change by factor 7.8\%. The extracted value of ${P}_{c{\bar c/p}}$ in the present QCD analysis is consistent with the recent reported upper limit of $1.93\%$, which is obtained for the first time from LHC measurements. We show the intrinsic charm probability is sensitive to the strong coupling constant and also the charm mass. The extracted value of the strong coupling constant $\alpha_s(M_Z^2) = 0.1191 \pm 0.0008$ at NLO is in good agreement with world average value and available theoretical models.

Probing the saturation effects in the inclusives observables at the future ep/eA collider at the LHC

In this paper we investigate the impact of the saturation effects in the inclusive observables that will be measured in the future Large Hadron Electron Collider (LHeC). The reduced total and heavy quark cross sections are estimated considering the more recent phenomenological models for the dipole-proton scattering amplitude, which are based on the Color Glass Condensate formalism and are able to describe the inclusive and exclusive ep HERA data. We compare, for the first time, the predictions of these models with the recent combined H1 and ZEUS data for the charm and bottom production, and present predictions for the reduced cross sections considering the kinematical range that will be probed in ep collisions at the LHeC. Moreover, we estimate the magnitude of the saturation effects for the nuclear, longitudinal and charm structure functions in the case of eA collisions at the LHeC. Our results indicate that the future experimental data will be useful to discriminate between the different models for the nonlinear QCD dynamics.

Bayesian analysis of light-front models and the nucleon’s charmed sigma term

We present the results of a recent analysis to study the nucleon's charm sigma term, $\sigma_{c\overline{c}}$. We construct a minimal model in terms of light-front variables and constrain the range of possibilities using extant knowledge from deeply inelastic scattering (DIS) and Bayesian parameter estimation, ultimately computing $\sigma_{c\overline{c}}$ in an explicitly covariant manner. We find a close correlation between a possible nonperturbative component of the charm structure function, $F^{c\overline{c}}_{2,\, \mathrm{IC}}$, and $\sigma_{c\overline{c}}$. Independent of prescription for the covariant relativistic quark-nucleon vertex, we determine $\sigma_{c\overline{c}}$ under several different scenarios for the magnitude of intrinsic charm (IC) in DIS, namely $\langle x \rangle_{c+\overline{c}} = 0.1\%$, $0.35\%$, and $1\%$, obtaining for these $\sigma_{c\overline{c}} = 4 \pm 4$, $12 \pm 13$, and $32 \pm 34$ MeV, respectively. These results imply the existence of a reciprocity between the IC parton distribution function (PDF) and $\sigma_{c\overline{c}}$ such that new information from either DIS or improved determinations of $\sigma_{c \overline{c}}$ could significantly impact constraints to the charm sector of the proton wave function.

Uncertainty of parton distribution functions due to physical observables in a global analysis

The recent measurement of the differential γ + c-jet cross section, performed at the Tevatron collider in Run II by the D0 collaboration, is studied in a next-to-leading order (NLO) global QCD analysis to assess its impact on the proton parton distribution functions (PDFs). We show that these data lead to a significant change in the gluon and charm quark distributions. We demonstrate also that there is an inconsistency between the new high precision HERA I+II combined data and Tevatron measurement. Moreover, in this study we investigate the impact of older EMC measurements of charm structure function on the PDFs and compare the results with those from the analysis of Tevatron data. We show that both of them have the same impact on the PDFs, and thus can be recognized as the same evidence for the inefficiency of perturbative QCD in dealing with charm production in some kinematic regions.

Next-to-leading order QCD analysis of parton distribution functions with LHC data

We present a next-to-leading order (NLO) QCD fit of parton distribution functions (PDFs) with and without the LHC data. In this analysis, we use the HERA I+II combine inclusive proton DIS cross sections, H1-ZEUS combined charm structure function, SLAC structure function, and EMC charm structure data as a base data, and then we investigate the effect of LHC data on the determination of PDFs. Our analysis and PDFs extraction is performed by xFitter framework.

A determination of the charm content of the proton: The NNPDF Collaboration.

We present an unbiased determination of the charm content of the proton, in which the charm parton distribution function (PDF) is parametrized on the same footing as the light quarks and the gluon in a global PDF analysis. This determination relies on the NLO calculation of deep-inelastic structure functions in the FONLL scheme, generalized to account for massive charm-initiated contributions. When the EMC charm structure function dataset is included, it is well described by the fit, and PDF uncertainties in the fitted charm PDF are significantly reduced. We then find that the fitted charm PDF vanishes within uncertainties at a scale Qsim 1.6 GeV for all xlesssim 0.1, independent of the value of m_c used in the coefficient functions. We also find some evidence that the charm PDF at large xgtrsim 0.1 and low scales does not vanish, but rather has an “intrinsic” component, very weakly scale dependent and almost independent of the value of m_c, carrying less than 1% of the total momentum of the proton. The uncertainties in all other PDFs are only slightly increased by the inclusion of fitted charm, while the dependence of these PDFs on m_c is reduced. The increased stability with respect to m_c persists at high scales and is the main implication of our results for LHC phenomenology. Our results show that if the EMC data are correct, then the usual approach in which charm is perturbatively generated leads to biased results for the charm PDF, though at small x this bias could be reabsorbed if the uncertainty due to the charm mass and missing higher orders were included. We show that LHC data for processes, such as high p_T and large rapidity charm pair production and Z+c production, have the potential to confirm or disprove the implications of the EMC data.

The behavior of the heavy quarks structure functions at small-x

The behavior of the charm and bottom structure functions [Formula: see text], where i = c, and b; k = 2, and L) at small-x is considered with respect to the hard-Pomeron and saturation models. Having checked that this behavior predicate the heavy flavor reduced cross-sections concerning the unshadowed and shadowed corrections. We will show that the effective exponents for the unshadowed and saturation corrections are independent of x and Q2, and also the effective coefficients are dependent to ln Q2 compared to Donnachie–Landshoff (DL) and color dipole models (CDMs).

Parton distributions in the LHC era: MMHT 2014 PDFs.

We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the ‘MSTW2008’ parton sets, but they are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the ‘MSTW2008’ parton sets. In most cases the PDFs, and the predictions, are within one standard deviation of those of MSTW2008. The major changes are the u-d valence quark difference at small x due to an improved parameterisation and, to a lesser extent, the strange quark PDF due to the effect of certain LHC data and a better treatment of the D rightarrow mu branching ratio. We compare our MMHT PDF sets with those of other collaborations; in particular with the NNPDF3.0 sets, which are contemporary with the present analysis.

Geometrical scaling in charm structure function ratios

By using a Laplace-transform technique, we solve the next-to-leading-order master equation for charm production and derive a compact formula for the ratio $R^{c}=\frac{F^{^{c\overline{c}}}_L}{F^{^{c\overline{c}}}_2}$, which is useful for extracting the charm structure function from the reduced charm cross section, in particular, at DESY HERA, at small x. Our results show that this ratio is independent of xat small x. In this method of determining the ratios, we apply geometrical scaling in charm production in deep inelastic scattering (DIS). Our analysis shows that the renormalization scales have a sizable impact on the ratio Rcat high $Q^{2}$. Our results for the ratio of the charm structure functions are in a goodagreement with some phenomenological models.

Impact-parameter dependent color glass condensate dipole model and new combined HERA data

The Impact-Parameter dependent Color Glass Condensate (b-CGC) dipole model is based on the Balitsky-Kovchegov non-linear evolution equation and improves the Iancu-Itakura-Munier dipole model by incorporating the impact-parameter dependence of the saturation scale. Here we confront the model to the recently released high precision combined HERA data and obtain its parameters. The b-CGC results are then compared to data at small-x for the structure function, the longitudinal structure function, the charm structure function, exclusive vector meson (J/\psi, \phi, \rho) production and Deeply Virtual Compton Scattering (DVCS). We also compare our results with the Impact-Parameter dependent Saturation model (IP-Sat). We show that most features of inclusive DIS and exclusive diffractive data, including the Q^2, W, |t| and x dependence are correctly reproduced in both models. Nevertheless, the b-CGC and the IP-Sat models give different predictions beyond the current HERA kinematics, namely for the structure functions at very low x and high virtualities Q^2, and for the exclusive diffractive vector meson and DVCS production at high t. This can be traced back to the different power-law behavior of the saturation scale in x, and to a different impact-parameter b dependence of the saturation scale in these models. Nevertheless, both models give approximately similar saturation scale Q_S<1 GeV for the proton in HERA kinematics, and also both models lead to the same conclusion that the typical impact-parameter probed in the total \gamma^{*}p cross-section is about b\approx 2\div 3 GeV^{-1}. Our results provide a benchmark for further investigation of QCD at small-x in heavy ion collisions at RHIC and the LHC and also at future experiments such as an Electron-Ion Collider and the LHeC.

Longitudinal Structure Function FL from Charm Structure Function F2c

We predict the effect of the charm structure function on the longitudinal structure function at small x. In NLO analysis we find that the hard Pomeron behavior gives a good description of FL and F2c (k = 2, L) at small x values. We conclude that a direct relation between FL ∝ F2c would provide useful information on how to measure longitudinal structure function at high Q2 values. Having checked that this model gives a good description of the data, when compared with other models.

The new [formula omitted] measurement from HERA and the dipole model

From the new measurement of FL at HERA we derive fixed-Q2 averages 〈FL/F2〉. We compare these with bounds which are rigorous in the framework of the standard dipole picture. The bounds are sharpened by including information on the charm structure function F2(c). Within the experimental errors the bounds are respected by the data. But for 3.5 GeV2⩽Q2⩽20 GeV2 the central values of the data are close to and in some cases even above the bounds. Data on FL/F2 significantly exceeding the bounds would rule out the standard dipole picture at these kinematic points. We discuss, furthermore, how data respecting the bounds but coming close to them can give information on questions like colour transparency, saturation and the dependencies of the dipole-proton cross section on the energy and the dipole size.

Analysis of combined HERA data in the impact-parameter dependent saturation model

The Impact-Parameter dependent Saturation Model (IP-Sat) is a simple dipole model that incorporates key features of the physics of gluon saturation and matches smoothly to the perturbative QCD dipole expression at large Q^2 for a given x. It was previously shown that the model gives a good description of HERA data suggesting evidence for gluon saturation effects at small x. The model has also been applied to proton-proton and proton-nucleus collisions and provides the basis for the IP-Glasma model of initial conditions in heavy ion collisions. Here we present a reanalysis of available data in electron-proton collisions at small Bjorken-x, including the recently released combined data from the ZEUS and H1 collaborations. We first confront the model to the high precision combined data for the reduced cross-section and obtain its parameters. With these parameters fixed, we compare model results to data for the structure function F_2, the longitudinal structure function F_L, the charm structure function F_2^{c\bar{c}}, exclusive vector meson (J/\psi, \phi and \rho) production and Deeply Virtual Compton Scattering (DVCS). Excellent agreement is obtained for the processes considered at small x in a wide range of Q^2. Our results strongly hint at universality of the IP-Sat dipole amplitude and the extracted impact-parameter distribution of the proton. They also provide a benchmark for further refinements in studies of QCD saturation at colliders.