Direct photon production beyond leading order in QCD

The significance of the quark-quark scattering process (quark+quark→quark+quark+photon) for the production of large-q_T real photons is discussed in the framework of perturbative QCD. To extract the finite contribution of this process to the differential cross section dσ/dy d²q_T (hadron 1+hadron 2→photon+anything) we define the gluon distribution and the quark-to-photon fragmentation function beyond the leading approximation. The calculations are performed consistently in the dimensional regularization scheme. Our numerical estimates show the resulting finite qq→qqγ contribution to be a small (order α_s/2π) correction in comparison with the basic QCD subprocesses.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

Direct photon production from pions and protons at 200 GeV/c

Direct photon production has been studied by an experiment performed with the NA3 spectrometer at CERN, using incident negative and positive beams at 200 GeV/c interacting with an isoscalar Carbon target. Two different triggers have been used; one of them requires the photon conversion. The experiment is sensitive to direct photons produced with 3.0≦P _T ≦6 GeV/c and center-of-mass rapidity ?0.4≦y ^*≦1.2. Inclusive cross sections are given for incident π^± and protons, and compared with second order QCD predictions; finally an estimation of the gluon structure function of the nucleon is given.     

Photon structure functions: Are they measurable?

It is shown that 3 of the 8 independent photon structure functions are simply calculable using leading logarithm techniques in QCD. We then discuss which of these are most readily measurable in the processese ⁺e^?→e⁺e^?+X,γp→μ ⁺ μ ^? X andμp→μμ ⁺ μμ ^? X. Detailed predictions are given for the latter processes including the case where beam and target are longitudinally polarised. Given sufficient beam intensities, the contributions from the anomalous (as opposed to vector meson-like) component of the photon structure function would be easily identifiable above the Bethe-Heitler pair production background. However, currently available beam intensities make such measurements impractical at present. We discuss simple algorithms for estimating the polarised and unpolarised quark and gluon distributions inside the proton and the hadronic (?-like) piece of the photon.     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Estimate of the screening corrections to gluon distributions in the smallx region

The screening corrections to gluon distributions in a proton corresponding to the triple gluonic ladder diagram are estimated. They are found to be relatively small: their values does not exceed 10% of the leading order QCD gluon distribution forx?10^?4 andQ ² ?100 GeV².     

Fully quantum treatment of the Landau-Pomeranchik-Migdal effect in QED and QCD

A rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given for the first time. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed in terms of the Green’s function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of an e ⁺ e ^? pair off an atom, while in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a color center.     

Scaling violation in γγ scattering

An unorthodox model is examined which predicts that scaling violations in structure functions are related to properties of the photon vacuum polarization amplitude. The relationship is approximate, but very useful. It reproduces the leading QCD prediction in all cases, and allows, as for instance in γγ scattering, to fill up on what QCD cannot say by itself. There is a simple formula for the total γγ cross-section, valid for all values of the photon mass. Data frome ⁺ e^? annihilation can be fed into it to obtain a fit to the measured photon structure function. The PLUTO data are not all difficult to reproduce.     

Effect of triple gluon coupling in semi-inclusive polarized scattering processes

We show that the gluon helicity inside a proton and a photon can be deduced from a knowledge of a special combination of cross sections of the semi-inclusive processese+p→e+π+π+... ande ⁺+e ^?→e ⁺+e ^?+π+π+... Such a measurement could thus be used to check the QCD prediction that the gluon helicity increases linearly with lnQ ².     

Soft gluon corrections to large-pT direct photon and dilepton production

QCD O(α_s²) corrections to large-p_T real and virtual photon production from scattering in the quark-gluon channel are studied in the soft gluon limit. In this limit we carefully preserve the analytic structure of amplitudes in the small-momenta integration regions. The result is a rather large correction to the Born term which significantly improves the agreement with data on p + p → γ + X. The application of the approach to other processes is discussed and the dominant terms of the O(α_s²) correction to e⁺e^? → three jets are reproduced.     

The QCD compton process up to tevatron energies

We investigate the QCD Compton effect γq→gq by using Monte Carlo, methods to simulate complete three jet events for photon-nucleon interactions. This process provides unique possibilities for jet studies because the incoming photon transfers its entire energy to the final state gluon and quark jets. We present a number of predictions for photons in the range of energies presently available up to Tevatron energies and find that the QCD Compton effect will dominate over vector meson dominance at large gluon transverse momenta.     

Energy dependence of the differences between the quark and gluon jet fragmentation

Three jet events arising from decays of the Z boson, collected by the DELPHI detector, were used to measure differences in quark and gluon fragmentation. Gluon jets were anti-tagged by identifying b quark jets. Unbiased quark jets came from events with two jets plus one photon. Quark and gluon jet properties in different energy ranges were compared for the first time within the same detector. Quark and gluon jets of nearly the same energy in symmetric three jet event topologies were also compared. Using three independent methods, the average value of the ratio of the mean charged multiplicities of gluon and quark jets is $$< r >=1.241 pm 0.015 (stat.)pm 0.025 (syst.).$$ Gluon jets are broader and produce fragments with a softer energy spectrum than quark jets of equivalent energy. The string effect has been observed in fully symmetric three jet events. The measured ratio R_γ of the charged particle flow in the qq? inter-jet region of the qq?g and qq?γ samples agrees with the perturbative QCD expectation. The dependence of the mean charged multiplicity on the hadronic center-of-mass energy was analysed in photon plus n-jet events. The value for α_s(M _Z) determined from these data using a QCD prediction with corrections at leading and next-to-leading order is $$←pha_s(M_Z)=0.116pm 0.003 (stat.)pm 03009 (syst.).$$     

Topology of the Υ-decay

Multihadron events resulting frome ⁺ e ^? annihilation at the Υ-resonance are analysed with respect to lowest order QCD which predicts a dominant Υ decay into three vector gluons. Smearing effects due to the gluon fragmentation are so large, however, that no clear 3-jet structure or flatness is expected in the hadron final state. Instead, Monte Carlo simulations predict event structures with thrust and triplicity distributions distinctly different from those of two quark-jet and of phase space like decay mechanisms. The data are in perfect agreement with the 3-vector gluon decay as predicted by QCD and exclude dominantly phase space like or 2-quark jet decays. Also, the decay into scalar gluons is excluded by the data. An upper limit for the Υ-decay into one photon and two gluons is obtained.     

A nonperturbative variational approach to the vacuum structure in quantum chromodynamics

We study the vacuum structure in QCD in a nonperturbative manner using a variational approach with gluon condensates. We show that in Coulomb gauge as the coupling becomes moderately strong, the perturbative vacuum of QCD becomes unstable leading to gluon condensates and a gauge dependent effective mass for the gluons related to the gauge independent value of 〈vac‖G _μν ^a G ^aμν‖vac〉 of Shifmanet al.     

Factorization scheme and parton distributions in the polarized virtual photon target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case , where is the mass squared of the probe (target) photon, the parton distributions can be predicted completely up to NLO, but they are factorization-scheme dependent. We analyze the parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of the parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-x behaviors of the quark distributions in the virtual photon. The gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of the gluon distribution is found to be factorization-scheme independent up to NLO. Received: 24 January 2001 / Published online: 18 May 2001     

The production of large transverse momentum jets in plarized photon-photon collisions

A comprehensive survey is presented of the polarization structure of the leading order QCD processes for the production of jets at largep _t in photon-photon collisions which are the result of colliding positrons. Results are given for asymmetries. It is shown that by separating events with various jet topologies it is possible to investigate different aspects of polarization and QCD. For instance the four anf three jet process asymmetries are found to be sensitive to the relative magnitudes of the perturbative anf non-perturbative components of the photon structure function. A discussion is given of the usefulness of polarization in separating the two gluon jet subprocess. It is concluded that such experiments could be very useful in understanding QCD and the strong interactions.     

Application of FIRE for the calculation of photon matrix elements

The next-to-next-to-leading order (the order αα _s ²) corrections to the first moment of the polarized virtual photon structure function g ₁ ^γ (x,Q ², P ²) are studied in perturbative QCD for the kinematical region Λ² ≪ P ² ≪ Q ², where −Q ² (−P ²) is the mass square of the probe (target) photon and Λ is the QCD scale parameter. In order to evaluate the two-loop Feynman diagrams for the photon matrix element of the gluon operator, I apply the recently developed algorithm FIRE which reduces a complicated sum of scalar Feynman integrals to a linear combination of a few master integrals. The details of the calculation are presented.     

Correlation with large transverse momentum photons and the gluon structure function

The inclusive two-particle cross section for the production of largep _T photons and opposite side charged hadrons in proton-proton collisions is examined in detail in the framework of QCD. The model, with the parametrization as in our previous work, agrees with the measured single photon spectra. Quantitative predictions are made for two-particle distributions to be measured at the ISR. The contributions due to the photon bremsstrahlung and the effects coming from the intrinsic constituent motion are estimated. It is shown that indeed the direct subprocess gluon+quark→photon+quark gives the dominant contribution in the experimentally relevant region of phase space, and that direct information about the gluon structure function can be obtained from such measurements.     

A test for the gluon selfcoupling in the reactionse + e −→4 jets andZ 0→4 jets

We consider the reactionse ⁺ e ^?→γ^*→4 jets andZ ^o→4 jets with the 4 jets coming in two pairs of essentially back to back jets of high and low energy. We calculate the angular distribution of the low energy jet axis with respect to the high energy jet axis in QCD, in an abelian gluon model “QED” and a phase space model (PS). Using simple helicity arguments we show that our angular distribution is very sensitive to the triple gluon coupling in QCD. This is then confirmed by a complete calculation. Our correlation offers, therefore, a direct test for QCD as a non-abelian gauge theory.     

A Gribov equation for the photon Green’s function

We present a derivation of the Gribov equation for the gluon/photon Green’s function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Trln?D(q), which we interpret as the gauge-boson ‘self-loop’. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, α _S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribov’s light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a ∝ Q ² behavior for space-like Q ²=?q ². This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.