Charm Structure Function Research Articles

Comparing AdS/CFT dipole model to HERA F2 data

We apply an AdS/CFT-inspired color-dipole model which contains only three free parameters to describe the HERA data for the inclusive structure function F2 at small Bjorken-x and virtuality. We found that the saturation scale in our AdS/CFT-based parameterization varies in the range of 1 ÷ 3 GeV becoming independent of energy/Bjorken-x at very small x. This leads to the prediction of x-independence of the structure functions at very small x. With the fitted parameters in our model, the predictions for F2, longitudinal structure function, charm structure function and total photo-production cross-sections in the kinematic regions of future experiments can be given.

Heavy quark production in deep inelastic electron-nucleus scattering

Heavy quark production has been very well studied over the last years both theoretically and experimentally. Theory has been used to study heavy quark production in $e p$ collisions at HERA, in $pp$ collisions at Tevatron and at RHIC, in $pA$ and $dA$ collisions at RHIC and in $AA$ collisions at CERN-SPS and at RHIC. However, to the best of our knowledge, heavy quark production in $eA$ has received almost no attention. With the possible construction of a high energy electron-ion collider, updated estimates of heavy quark production are needed. We address the subject from the perspective of saturation physics and compute the heavy quark production cross section with the dipole model. We isolate shadowing and non-linear effects, showing their impact on the charm structure function and on the transverse momentum spectrum.

Beauty, charm, and F L at HERA: New data vs. Early predictions

One of the well known effects of the asymptotic freedom is splitting of the leading-$\log$ BFKL pomeron into a series of isolated poles in complex angular momentum plane. Following our earlier works we explore the phenomenological consequences of the emerging BFKL-Regge factorized expansion for the small-$x$ charm ($F_2^c$) and beauty ($F_{2}^{b}$) structure functions of the proton. As we found earlier,the color dipole approach to the BFKL dynamics predicts uniquely decoupling of subleading hard BFKL exchanges from $F_2^c$ at moderately large $Q^{2}$. We predicted precocious BFKL asymptotics of $F_2^c(x,Q^2)$ with intercept of the rightmost BFKL pole $\alpha_{\Pom}(0)-1=\Delta_{\Pom}\approx 0.4$. High-energy open beauty photo- and electro-production probes the vacuum exchange at much smaller distances and detects significant corrections to the BFKL asymptotics coming from the subleading vacuum poles. In view of the accumulation of the experimental data on small-$x$ $F_{2}^{c}$ and $F_{2}^{b}$ we extended our early predictions to the kinematical domain covered by new HERA measurements.Our structure functions obtained in 1999 agree well with the determination of both $F_2^c$ and $F_2^b$ by the H1 published in 2006 but contradict to very recent (2008, preliminary) H1 results on $F_2^b$. We present also comparison of our early predictions for the longitudinal structure function $F_L$ with recent H1 data (2008) taken at very low Bjorken $x$. We comment on the electromagnetic corrections to the Okun-Pomeranchuk theorem.

Measurement of the charm and beauty structure functions using the H1 vertex detector at HERA

Inclusive charm and beauty cross sections are measured in e-p and e+p neutral current collisions at HERA in the kinematic region of photon virtuality 5<Q^2<2000 GeV^2 and Bjorken scaling variable 0.0002<x<0.05. The data were collected with the H1 detector in the years 2006 and 2007 corresponding to an integrated luminosity of 189 pb^-1. The numbers of charm and beauty events are determined using variables reconstructed by the H1 vertex detector including the impact parameter of tracks to the primary vertex and the position of the secondary vertex. The measurements are combined with previous data and compared to QCD predictions.

Structure functions at HERA

HERA provides the key facility for the measurement of proton structure functions. Formalism and methods are outlined for the measurement and interpretation of inclusive structure functions, including the use of polarised e ± beams. The measurement of charm, beauty and photon structure functions is discussed, together with special runs at low proton energy for measurement of the longitudinal structure function. Finally, the functions accessed using polarised beams on polarised targets are indicated.

Measurement of the charm structure function F2,cγ of the photon at LEP

The production of charm quarks is studied in deep-inelastic electron–photon scattering using data recorded by the OPAL detector at LEP at nominal e +e − centre-of-mass energies from 183 to 209 GeV. The charm quarks have been identified by full reconstruction of charged D ★ mesons using their decays into D 0 π with the D 0 observed in two decay modes with charged particle final states, K π and K πππ. The cross-section σ D ★ for production of charged D ★ in the reaction e +e −→e +e −D ★ X is measured in a restricted kinematical region using two bins in Bjorken x, 0.0014< x<0.1 and 0.1< x<0.87. From σ D ★ the charm production cross-section σ( e + e −→ e + e − c c ̄ X) and the charm structure function of the photon F 2,c γ are determined in the region 0.0014< x<0.87 and 5< Q 2<100 GeV 2 . For x>0.1 the perturbative QCD calculation at next-to-leading order agrees perfectly with the measured cross-section. For x<0.1 the measured cross-section is 43.8±14.3±6.3±2.8 pb with a next-to-leading order prediction of 17.0 +2.9 −2.3 pb.

Comprehensive approach to structure functions

We present a model based on a dipole picture with a hard and a soft pomeron in which large dipoles couple to the soft pomeron and small dipoles couple to the hard pomeron. The parameters in the model are fixed by proton-proton scattering and the proton structure function. The model is then applied successfully to the proton charm structure function, the proton longitudinal structure function, J/psi photoproduction, deep virtual Compton scattering, the real photon-proton total cross section, the real photon-photon cross section, and the photon structure function. Differences between our predictions and data on charm production in real photon-photon interactions and the virtual gamma-gamma cross section are discussed.

New data and the hard pomeron

New structure-function data are in excellent agreement with the existence of a hard pomeron, with intercept about 1.4. It gives a very economical description of the data. Having fixed 2 parameters from the data for the real-photon cross section $\sigma^{\gamma p}$, we need just 5 further parameters to fit the data for $F_2(x,Q^2)$ with $x\leq 0.001$. The available data range from $Q^2=0.045$ to 35 GeV$^2$. With guesses consistent with dimensional counting for the $x$ dependences of our three separate terms, the fit extends well to larger $x$ and to $Q^2=5000$ GeV$^2$. With no additional parameters, it gives a good description of data for the charm structure function $F_2^c(x,Q^2)$ from $Q^2=0$ to 130 GeV$^2$. The two pomerons also give a good description of both the $W$ and the $t$ dependence of $\gamma p\to J/\psi p$.

How open charm production and scaling violations probe the rightmost hard BFKL pole exchange

In 1994 Zakharov and the present authors argued that in color dipole (CD) BFKL approach to DIS excitation of open charm at moderately large Q2 is dominated by hard BFKL exchange. In view of the rapid accumulation of the experimental data on small-x charm structure function of the proton F2cc from HERA, we subject the issue of dominance of the rightmost hard BFKL pole exchange to further scrutiny. Based on CD BFKL-Regge factorization we report parameter-free predictions for the charm structure function F2cc and show that the background to the dominant rightmost hard BFKL exchange from subleading hard BFKL and soft-pomeron exchanges is negligible small from real photo-production to DIS at Q2 lsim 50-100 GeV2. The agreement with the experiment is good and lends strong support for the intercept of the rightmost hard BFKL pole DeltaPom=alphaPom-1=0.4 as found in 1994 in the color dipole approach. We comment on the related determination of DeltaPom from the x-dependence of the longitudinal structure function FL(x,Q2) and of the scaling violation dF2/dlog Q2 taken at a suitable value of Q2. \

Charm and beauty production in photon-photon collisions

Inclusive heavy flavour production in γγ collisions has been studied at the LEP collider by ALEPH, L3, and OPAL. Preliminary results on charm and beauty production at ▪ = 189 GeV are presented. Hadronic final states containing charm particles were identified either by detecting electrons or muons from their semi-leptonic decays or by reconstruction of charged D * meson decays. The bb̄ cross section, the charm structure function F 2, c γ and the high energy behaviour of σ(γγ → cc̄) cross section as function of γγ centre-of-mass energy are measured for the first time in two-photon collisions.

Soft gluon resummation for polarized deep-inelastic production of heavy quarks

We present the threshold resummation for the cross section of heavy quark production in polarized deep-inelastic scattering to next-to-leading logarithmic accuracy and in single-particle inclusive kinematics. We expand our resummed result in α s to next-to-leading and next-to-next-to-leading order and study the impact of these higher order corrections on the charm structure function g 1 c in the kinematical range accessible to the HERMES and COMPASS experiments.

Inclusive production of D $^{\ast\pm}$ mesons in photon-photon collisions at $\sqrt{s}_{\rm ee}=183$ and 189 GeV and a first measurement of $F^\gamma _{2,{\rm c}}$

The inclusive production of ${{\rm D}^{\ast\pm}}$ mesons in photon-photon collisions has been measured using the OPAL detector at LEP at $\mboxe^+\mboxe^-$ centre-of-mass energies $\sqrt{s_{\rm ee}}$ of 183 and 189 GeV. The ${{\rm D}^{\ast+}}$ mesons are reconstructed in their decay to ${\rm D}^0\pi^+$ with the ${\rm D}^0$ observed in the two decay modes ${\rm K}^-\pi^+$ and ${\rm K}^-\pi^+\pi^-\pi^+$ . After background subtraction, $100.4\pm12.6 (\rm stat)$ ${\rm D}^{\ast\pm}$ mesons have been selected in events without observed scattered beam electron (“anti-tagged”) and $29.8 \pm 5.9 ({\rm stat}){{\rm D}^{\ast\pm}}$ mesons in events where one beam electron is scattered into the detector (“single-tagged”). Direct and single-resolved events are studied separately. Differential cross-sections ${\rm d}\sigma/{\rm d}p_{\rm T}^{{\rm D}^{\ast}}$ and ${\rm d} \sigma/{\rm d} \vert \eta^{{\rm D^{\ast}}}\vert$ as functions of the ${{\rm D}^{\ast\pm}}$ transverse momentum $p^{\rm D^{\ast}}_{\rm T}$ and pseudorapidity $\eta^{{\rm D}^{\ast}}$ are presented in the kinematic region $2{\rm GeV} < p^{\rm D^{\ast}}_{\rm T} < 12{\rm GeV}$ and $|\eta^{{\rm D}^{\ast}}|< 1.5$ . They are compared to next-to-leading order (NLO) perturbative QCD calculations. The total cross-section for the process $\mboxe^+\mboxe^- \to \mboxe^+\mboxe^- \mbox c\overline{\mbox c}$ where the charm quarks are produced in the collision of two quasi-real photons is measured to be $\sigma({\rm e}^+{\rm e}^- \to{\rm e}^+{\rm e}^-{\rm c}\bar{{\rm c}}) = 963\pm 110 ({\rm stat})\pm 86({\rm sys})\pm 224 ({\rm extrapolation}){\rm pb}$ . A first measurement of the charm structure function $F^\gamma _{2,{\rm c}}$ of the photon is performed in the kinematic range $0.0014 < x < 0.87$ and $5 {\rm GeV}^2 < Q^2 < 100{\rm GeV}^2$ , and the result is compared to a NLO perturbative QCD calculation.

Measurement of the charm structure function of the proton at HERA

D ∗ meson production cross sections have been measured in deep inelastic ep scattering at HERA. Using an integrated luminosity of 37 pb −1, the ZEUS collaboration has used both the 3-prong D ∗+ → (D 0 → K −π +)π + (+ c.c.) and the 5-prong D ∗+ → (D 0 → K −π +π −π +)π + (+ c.c.) decay channels to extract differential D ∗ cross sections and F 2 c c . These cross sections are compared to NLO QCD calculations. The gluon density of the proton has also been determined directly from D ∗ events by H1 and is compared to that obtained from a QCD analysis of F 2.

Charm production at HERA

The ZEUS data on the charm structure function F 2 c at small x fit well to a single power of x, corresponding to the exchange of a hard pomeron that is flavour-blind. When combined with the contribution from the exchange of a soft pomeron, the hard pomeron gives a good description of elastic J/ ψ photoproduction.

Small x: two pomerons!

Regge theory provides a very simple and economical description of data for (i) the proton structure function with x<0.7 and all available Q 2 values, (ii) the charm structure function, and (iii) γ p→J/ψ p . The data are all in agreement with the assumption that there is a second pomeron, with intercept about 1.4 . They suggest also that the contribution from the soft pomeron is higher twist. This means that there is an urgent need to make perturbative evolution compatible with Regge theory at small and not-so-small x, and to reassess the magnitude of higher-twist contributions at quite small x.

High-energy factorization predictions for the charm structure function F2c at HERA

High-energy factorization predictions for F 2 c are derived using BFKL descriptions of the proton structure function F 2 at HERA. The model parameters are fixed by a fit of F 2 at small x. Two different approaches of the non-perturbative proton input are shown to correspond to the factorization at the gluon or quark level, respectively. The predictions for F 2 c are in agreement with the data within the present error bars. However, the photon wave-function formulation (factorization at quark level) predicts significantly higher F 2 c than both gluon factorization and a next-leading order DGLAP model.

Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory

Starting from fixed-order perturbation theory (FOPT) we derive expressions for the heavy-flavour components of the deep-inelastic structure functions FL and F2 in the variable-flavour number scheme (VFNS). These expressions are valid in all orders of perturbation theory. This derivation establishes a relation between the parton densities parametrized at N and N light flavours. The consequences for the existing parametrizations of the parton densities are discussed. Further we show that in charm electroproduction the exact and asymptotic expressions for the heavy-quark coefficient functions yield identical results for F2 when Q^2>20 (GeV/c)^2. We also study the differences between the FOPT and the VFNS descriptions for F2. It turns out that the charm structure function in the VFNS is larger than the one obtained in FOPT over the whole Q^2-range. Furthermore inspection of the perturbation series reveals that the higher order corrections in the VFNS are smaller than those present in FOPT for Q^2>10 (GeV/c)^2. Therefore the VFNS gives a better prediction for the charm structure function at large Q^2-values than FOPT.

A practical procedure for evolving heavy flavour structure functions

The transition from the low $Q^2$ region in deep inelastic scattering where charm production is described by photon-gluon fusion to a region where the charm structure function $F_2^c$ is largely generated by a charm quark density should be a smooth passage. The all orders prescription for matching between the two schemes does not uniquely determine all the relevant coefficient functions (CF's) or guarantee the correct threshold behaviour at fixed order in $\alpha_s$. The constraints of matching not only the value but also the evolution of $F_2^c$ order by order allows all CF's to be determined at any order, each of which reduces to the appropriate massless $\msb$ expression as $Q^2 \to \infty$, and leads to a smooth transition in the threshold region. This procedure gives an excellent description of the $F_2^c$ data for all $Q^2$.

Heavy quark parton distributions: Mass-dependent or mass-independent evolution?

In a consistently formulated PQCD framework incorporating nonzero mass heavy quark partons, there is still the freedom to define parton distributions obeying either mass-independent or mass-dependent evolution equations, contrary to statements made in a recent paper. With properly matched hard cross sections, different choices merely correspond to different factorization schemes; they yield the same physical cross sections. We demonstrate this principle in a concrete order ${\ensuremath{\alpha}}_{s}$ calculation of the Deeply Inelastic Scattering charm structure function. We also examine the proper matching between parton definitions and subtractions in the hard cross section near threshold where the calculation is particularly sensitive to mass effects of the heavy quark. The results obtained from the general-mass formalism are quite stable against different choices of scale and exhibit a smooth transition in the threshold region (using either mass-independent or mass-dependent evolution), in contrast with results of another recently proposed scheme.

Reanalysis of the EMC charm production data with extrinsic and intrinsic charm at NLO

A calculation of the next-to-leading order exclusive extrinsic charm quark differential distributions in deeply inelastic electroproduction has recently been completed. Using these results we compare the NLO extrinsic contributions to the charm structure function F 2( x, Q 2, m 2 c ) with the corresponding NLO intrinsic contributions. The results of this analysis are compared with the EMC DIS charm quark data and evidence for an intrinsic charm component in the proton is found.