Structure Function F2 Research Articles

DEEP INELASTIC SCATTERING AT HERA

Results from the H1 and ZEUS experiments at HERA on deep inelastic scattering are reviewed. The data lead to a consistent picture of a steep rise in the F2 structure function and in the gluon density within the proton. Important new information on the partonic structure of diffraction is emerging from H1 and ZEUS. The spacelike region in which the weak and electromagnetic interactions become of equal strength is being explored for the first time. A possible excess of events at high x and Q2 compared to the expectations of the Standard Model has been observed in both experiments.

Measurement of the diffractive structure functionF 2 D(4) at HERA

This paper presents the first analysis of diffractive photon dissociation events in deep inelastic positron-proton scattering at HERA in which the proton in the final state is detected and its momentum measured. The events are selected by requiring a scattered proton in the ZEUS leading proton spectrometer (LPS) with χ L > 0.97, where xL is the fraction of the incoming proton beam momentum carried by the scattered proton. The use of the LPS significantly reduces the contamination from events with diffractive dissociation of the proton into low mass states and allows a direct measurement of t, the square of the four-momentum exchanged at the proton vertex. The dependence of the cross section ont is measured in the interval 0.073 < |t| < 0.4 GeV2 and is found to be described by an exponential shape with the slope parameterb = 7.2 ± 1.1(stat.) +0.7−0.9 (syst.) GeV−2. The diffractive structure function FD (4) is presented as 0.9 a function of χ H ≃ 1 − χ L and β, the momentum fraction of the struck quark with respect to χ H , and averaged over thet interval 0.073 < |t′ < 0.4 GeV2 and the photon virtuality range 5 <Q 2 < 20 GeV2. In the kinematic range 4 × 104 < χ p < 0.03 and 0.015 < β < 0.5, the χ p dependence ofF D(4) is fitted with a form (1/χ p )α , yieldinga − 1.00 ± 0.09 (stat.) +0.11−0.05 (syst.). Upon integration overL, the structure functionF 2 D(3) is determined in a kinematic range extending to higher χ p and lower β compared to our previous analysis; the results are discussed within the framework of Regge theory.

Measurement of the diffractive structure function

This paper presents the first analysis of diffractive photon dissociation events in deep inelastic positron-proton scattering at HERA in which the proton in the final state is detected and its momentum measured. The events are selected by requiring a scattered proton in the ZEUS leading proton spectrometer (LPS) with χ L > 0.97, where xL is the fraction of the incoming proton beam momentum carried by the scattered proton. The use of the LPS significantly reduces the contamination from events with diffractive dissociation of the proton into low mass states and allows a direct measurement of t, the square of the four-momentum exchanged at the proton vertex. The dependence of the cross section ont is measured in the interval 0.073 < |t| < 0.4 GeV2 and is found to be described by an exponential shape with the slope parameterb = 7.2 ± 1.1(stat.) +0.7−0.9 (syst.) GeV−2. The diffractive structure function FD (4) is presented as 0.9 a function of χ H ≃ 1 − χ L and β, the momentum fraction of the struck quark with respect to χ H , and averaged over thet interval 0.073 < |t′ < 0.4 GeV2 and the photon virtuality range 5 <Q 2 < 20 GeV2. In the kinematic range 4 × 104 < χ p < 0.03 and 0.015 < β < 0.5, the χ p dependence ofF D(4) is fitted with a form (1/χ p )α , yieldinga − 1.00 ± 0.09 (stat.) +0.11−0.05 (syst.). Upon integration overL, the structure functionF 2 D(3) is determined in a kinematic range extending to higher χ p and lower β compared to our previous analysis; the results are discussed within the framework of Regge theory.

Measurement of the photon structure function F2 at low x

Abstract Deep inelastic electron-photon scattering is studied using e+e− data collected by the OPAL detector at centre-of-mass energies s =M Z 0 . The photon structure function F2γ(x, Q 2) is explored in a Q 2 range of 1.1 to 6.6 GeV2 at lower x values than ever before. To probe this kinematic region events are selected with a beam electron scattered into one of the OPAL luminosity calorimeters at scattering angles between 27 and 55 mrad. A measurement is presented of the photon structure function F2γ(x, Q 2) at 〈 Q 2〉 = 1.86 GeV2 and 3.76 GeV2 in five logarithmic x bins from 0.0025 to 0.2.

Measurement of the proton structure function F2 and σ at low and very low x at HERA

A small electromagnetic sampling calorimeter, installed in the ZEUS experiment in 1995, significantly enhanced the acceptance for very low x and low Q2 inelastic neutral current scattering, e+p → e+X, at HERA. A measurement of the proton structure function F2 and the total virtual photon-proton (γ∗p) cross-section is presented for 0.11 ≤ Q2 ≤ 0.65 GeV2 and 2 × 10−6 ≤ x ≤ 6 × 10−5, corresponding to a range in the γ∗p c.m. energy of 100 ≤ W ≤ 230 GeV. Comparisons with various models are also presented.

Physical anomalous dimensions at small $x$

I present a theoretical discussion of the uncertainties related to the QCD analysis of the proton structure function F2(x,Q2) at small x. The role played by the ‘unphysical’ gluon density is pointed out. It is shown how the study of more observables can reduce the theoretical uncertainty and, in particular, an alternative method of analysis, based on the introduction of physical anomalous dimensions, is suggested.

Perturbative part of the non-singlet structure function F2 in the large- N F limit

We have calculated MS ¯ Wilson coefficients and anomalous dimensions for the non-singlet part of the structure function F 2 in the large- N F limit. Our result agrees with exact two and three loop calculations and gives the leading N F dependence of the perturbative non-singlet Wilson coefficients to all orders in α s .

A measurement of the proton structure function F2( x, Q2) at low x and low Q2 at HERA

The results of a measurement of the proton structure function F 2( x, Q 2) and the virtual photon-proton cross section are reported for momentum transfers squared Q 2 between 0.35 GeV 2 and 3.5 GeV 2 and for Bjorken- x values down to 6 × 10 −6 using data collected by the HERA experiment H1 in 1995. The data represent an increase in kinematic reach to lower x and Q 2 values of about a factor of 5 compared to previous H1 measurements. Including measurements from fixed target experiments the rise of F 2 with decreasing x is found to be less steep for the lowest Q 2 values measured. Phenomenological models at low Q 2 are compared with the data.

Parton distributions and heavy quark production on nucleon and nuclear targets

Abstract The perturbative QCD evolution equation and the respective parton distributions in a proton are discussed, mainly in small x region. The different possibilities of shadow corrections are considered which allow one to avoid the unitarity violation. The possibility of estimation of the quality of phenomenological sets of the structure functions on the base of perturbative QCD is presented. Two approximate methods to extract the gluon distributions directly from the F2(x, Q2) data are discussed together with the new HERA data. Charm and beauty hadroproduction and photoproduction processes are considered in the framework of perturbative QCD and the results are compared with conventional parton model predictions. The role of infrared region contribution to F2(xQ2) structure function is discussed. The case of nuclear targets is considered also and A-dependences of charmed and beauty hadron production cross sections are calculated accounting for the difference of parton distributions in free and bound n...

The Longitudinal Structure Function FL as a Function of F2 and dF2/dln Q2 at Small x. The Next-to-Leading Analysis

We present a set of formulas to extract the longitudinal deep inelastic structure function FL from the transverse structure function F2 and its derivative dF2/d ln Q2 at small x. Our expressions are valid for any non-negative value of δ, with x-δ the behavior of the parton densities at low x. Using F2 HERA data we obtain FL in the range 10-4≤ x≤10-2 at Q2=20 GeV 2. Some other applications of the formulas are pointed out.

Some new salient features of deep-inelastic scattering at HERA

Recent results on deep-inelastic scattering from the H1 and ZEUS collaborations are presented. These include new measurements based on 1994 data together with preliminary results of 1995 data on the structure function f2, the gluon density in the proton from analysis of scaling violation, the longitudinal structure function FL and the structure function F2cc. New data on inclusive measurements of diffractive deep-inelastic events and extraction of the debatable Pomeron structure function are also presented.

NLO predictions for the growth ofF 2 at smallx and comparison with experimental data

We present parametrizations for the proton structure functionF 2 in the next to leading order in perturbative QCD. We consider that the dominant term toF 2(x, Q 2) should grow asx −ψ s for smallx values, with the exponentλ S being essentially independent ofQ 2. Comparisons with the most recent H1 and ZEUS data confirm the valueλ S ∼0.35 obtained previously from fits to low energy data.

Next-to-next-to-leading order QCD analysis of the CCFR data for xF3 and F2 structure functions of the deep-inelastic neutrino-nucleon scattering

The next-to-next-to-leading order (NNLO) non-singlet QCD analysis of the experimental data of the CCFR collaboration for the xF 3 and F 2 structure functions of the deep-inelastis scattering of neutrinos and antineutrinos on the nucleon by means of the Jacobi polynomial expansion method is made. We demonstrate that the NNLO corrections have the important physical effects. The obtained NNLO results for α s ( M Z ) are: α s ( M Z ) = 0.109±0.003(stat)±0.005(syst)±0.003(theor) (from xF 3 data) and α s ( M Z ) = 0.111±0.002(stat)±0.003(syst)±0.003(theor) (from the combined xF 3 and F 2 data). We also estimate the values of the order O( α s 2)-corrections to the Gottfried sum rule.

On the possibility of measuringF L (x, Q 2) at HERA using radiative events

It is shown that a significant measurement of the longitudinal structure functionF L (x, Q 2) can be performed at HERA, forQ 2=2 GeV2 andQ 2=5 GeV2 and forx around 10−4, using radiative events with hard photon emission collinear to the incident lepton beam, under the present running conditions and with an integrated luminosity of 10 pb−1. The influence of experimental conditions is discussed.

A measurement and QCD analysis of the proton structure function F2 ( x, Q2) at HERA

A new measurement of the proton structure function F2 ( x, Q 2) is reported for momentum transfers squared Q 2 between ].5 GeV 2 and 5000 GeV 2 and for Bjorken x between 3 · 10 −5 and 0.32 using data collected by the HERA experiment H1 in 1994. The data represent an increase in statistics by a factor of ten with respect to the analysis of the 1993 data. Substantial extension of the kinematic range towards low Q 2 and x has been achieved using dedicated data samples and events with initial state photon radiation. The structure function is found to increase significantly with decreasing x, even in the lowest accessible Q 2 region. The data are well described by a Next to Leading Order QCD fit and the gluon density is extracted.

Measurement of the proton structure functionF 2 at lowx and lowQ 2 at HERA

We report on a measurement of the proton structure functionF 2 in the range 3.5×10−5≤x≤4×10−3 and 1.5 GeV2≤Q 2≤15GeV2 at theep collider HERA operating at a centre-of-mass energy of √s=300GeV. The rise ofF 2 with decreasingx observed in the previous HERA measurements persists in this lowerx andQ 2 range. TheQ 2 evolution ofF 2, even at the lowestQ 2 andx measured, is consistent with perturbative QCD.

A measurement of the photon structure functionF 2 γ at an averageQ 2 of 12 GeV2/c 4

The hadronic photon structure functionF 2 γ has been measured in theQ 2 range from 4 to 30 GeV2/c 4 and down tox values of order 0.001, using data taken with the DELPHI detector at LEP between 1991 and 1993. A comparison is made with severalF 2 γ parameterizations with special emphasis on their lowx behaviour. A result on theQ 2 evolution ofF 2 γ is presented.

Measurement of the proton structure functionF 2 from the 1993 HERA data

The ZEUS detector has been used to measure the proton structure functionF2. During 1993 HERA collided 26.7 GeV electrons on 820 GeV protons. The data sample corresponds to an integrated luminosity of 0.54 pb−1, representing a twenty fold increase in statistics compared to that of 1992. Results are presented for 7<Q2<104 GeV2 andx values as low as 3×10−4. The rapid rise inF2 asx decreases observed previously is now studied in greater detail and persists forQ2 values up to 500 GeV2.

Deep inelastic structure functions from HERA

Results on deep inealstic scattering obtained by H1 and ZEUS from the 1993 data taken at HERA are presented. The measurements of the charged current process provide first evidence for the damping of the total neutrino cross section at high energies by the W propagator. A comparison with neutral current scattering shows that at Q2 values above the W mass squared the weak cross section becomes comparable to the electromagnetic one. The structure function F2 of the proton was determined from neutral current scattering data. The results confirm the steep rise of F2 towards small x below 10−2 seen previously by the two experiments albeit with much less statistics. The rise persists from the lowest Q2 values up to 500 GeV2. The F2 data are in accord with logarithmic scaling violations in a new regime of low x and high Q2. An analysis of F2 data by ZEUS in terms of the total virtual photon proton cross section shows σtot(γ*P) to increase with the total γ*p c.m. energy, the increase being compatible with a linear rise. This is in striking contrast with the behaviour of the total cross section for real photons or for pp scattering.

ON THE SINGULAR BEHAVIOR OF STRUCTURE FUNCTIONS AT LOW x

We discuss the phenomenological extraction of the leading j-plane singularity from singlet structure functions Fs estimated at small x. Using a saddle point method we show that [Formula: see text] is a suitable observable for this purpose in the region x≤10−2. As an application, we confront and distinguish in a model-independent way structure function parametrizations coming from two different QCD evolution equations, namely the Lipatov (or BFKL) equation and the Gribov-Lipatov-Altarelli-Parisi (or GLAP) equation. Recent results on the proton structure function F2 at HERA are discussed in this framework.