On the Q2 dependence of parton fragmentation functions

The Q² dependences of parton fragmentation functions are calculated using lowest-order quantum chromodynamics (QCD). The resulting scaling deviations have a simple intuitive form when a suitable valence-sea decomposition is employed for the quark fragmentation functions.     

QCD predictions for the distribution functions of the photon using Altarelli-Parisi type equations

In a leading approximation, the distribution functions of the photon are investigated using Altarelli-Parisi type equations including point-like and hadron-like components. Using a new method to make a Mellin transformation, the full inhomogeneous equation is solved numerically. The point-like and hadron-like parts of photon distribution function are discussed separately. The point-like part has a form $\text{?(x, t)}\text{In}\text{Q}{}^2$, where t = In Q². Analytic expressions for the photon distribution functions near x = 1 and x = 0 are also given. These results are compared with others which have been given using other methods.     

The Q2 evolution of flavour singlet wave functions in QCD

We calculate the Q² evolution of the quark-antiquark and gluon-gluon components of helicity-zero, flavour and colour singlet wave functions by summing diagrams to all orders in axial gauge QCD perturbation theory in the leading logarithm approximation. We find that Gegenbauer moments of these components have exactly the same scale-breaking behaviour as moments of singlet quark and gluon distribution functions in leptoproduction. The resulting singlet wave function is used to calculate the amplitudes for quark-antiquark and gluon-gluon jet production in off-shell photon-photon collisions.     

The Q2 dependence of the flavour singlet pseudoscalar meson wave function in QCD

We calculate the Q² dependence of the flavour singlet pseudoscalar meson wave function in QCD by summing up the leading large logarithms with the aid of the ladder approximation of its Bethe-Salpeter equation. The calculation is performed in an axial gauge. We find that the Q² dependence is diagonalized by expanding the wave function in the space of longitudinal momentum fractions in terms of Gegenbauer polynomials. The anomalous dimensions agree with those of one of the two operators to be considered for polarized deep inelastic lepton-hadron scattering in addition to the operators already contributing to the spin-averaged case.     

How can we properly define the Q2 dependent parton distribution function in QCD?

We discuss how we can properly define the Q² dependent parton distribution functions in quantum chromodynamics within the framework of the operator product expansion and renormalization group techniques. It is proposed that the moments of the parton distribution functions at Q² should be defined as the hadronic expectation values of the twist-2 operators renormalized at Q². The integro-differential equations for the parton densities obtained by Altarelli and Parisi are reproduced in the leading logarithmic approximation. An application of our present formalism will be given in the case of a longitudinal structure function.     

Δ++π−-electroproduction near threshold and the Q2 dependence of the contact interaction

The Q² dependence of σ (γvp→π^?Δ⁺⁺) was measured. Close to threshold σ (γvp→π^?Δ⁺⁺) is roughly proportional to 1/(m²_? + Q²)². The data are consistent with dominance of the contact term and imply that the contact term has the Q² dependence of the ? propagator.     

On the QCD perturbative predictions for the signal ofW± production in hadronic collisions

Evidence for the intermediate bosons in high energy pp and p?p collisions as signal in the cross section of large p_T charged lepton pp, $\text{p}\text{p}\text{→}\text{W}{}^{\mathrm{\pm }}\text{+}\text{X}$, W^±→?^±ν_? is considered for CM energy range $\text{s}\text{=100?800}\text{GeV}$. Besides the usual Drell-Yan term which gives a very sharp peak in the lepton p_T distribution, the first order QCD contribution is included thus producing the intermediate boson with transverse momentum and smearing the lepton distribution. Scaling violation of the structure functions is incorporated and compared with the case when it is absent.     

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 $$←pha_s(M_Z)=0.116pm 0.003 (stat.)pm 03009 (syst.).$$     

Effective Lagrangian and equations for valence quark and gluon Green's functions

Starting from the QCD Lagrangian and separating background and valence degrees of freedom, one arrives at the effective Lagrangian for valence quarks and gluons. Each term in the Lagrangian contains a product of valence quark and gluon operators acting at the end of the fundamental or adjoint string, made of the background field. A simple procedure is described how to obtain from the Lagrangian self-coupled equations for quark and gluon Green's function.     

Non-perturbative results for the ω2x2 + λx4 oscillator

For the ω²x² + λx⁴, λ >0, oscillator we prove the existence of a basic set of solutions, the set consisting of a dominant and a subdominant solution. This result does not seem to be obtainable by means of some recently developed perturbation methods.     

Next-to-leading-order QCD corrections to gluon fragmentation into 1S0((1,8)) quarkonia

Within the NRQCD factorization framework,we compute the next-to-leading-order QCD corrections to the gluon fragmentation into the ¹S₀⁽(1,8)) Fock components of a quarkonium,at the lowest order in velocity expansion.We follow the operator definition of the fragmentation function advanced by Collins and Soper.The key technique underpinning our calculation is the sector decomposition method widely used in the area of multi-loop computation.It is found that the NLO Q...     

Measurement of the quark and gluon fragmentation functions in Z^0 hadronic decays

The transverse, longitudinal and asymmetric components of the fragmentation function are measured from the inclusive charged particles produced in collisions at LEP. As in deep inelastic scattering, these data are important for tests of QCD. The transverse and longitudinal components of the total hadronic cross section are evaluated from the measured fragmentation functions. They are found to be and respectively. The strong coupling constant is calculated from in next-to-leading order of perturbative QCD, giving Including non-perturbative power corrections leads to The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity, The fragmentation functions and multiplicities in and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated. Received: 12 September 1997 / Published online: 19 October 1998     

Electroproduction of ϱ0 mesons at 0.3 < Q2 < 1.5 GeV2 and 1.7 < W < 2.8 GeV

Production and decay characteristics of electroproduced rho mesons were studied in the final state epπ⁺π^?.     

Electroproduction of single charged pions from deuterons at Q2 ∼0.5 (GeV/c)2

The ratio of π^? to π⁺ electroproduction cross sections from deuterons has been measured in the resonance region at an average four-momentum transfer squared of 0.5 (GeV/c)². Results are presented over a wide range of pion production angles and comparisons are made with theoretical predictions based on SU(6)_w symmetry and the Melosh transformation.     

Rotational analyses of the A1Π-X1Σ+ and the a3Π-X1Σ+ systems of AlBr

The absorption spectrum of the A¹Π-X¹Σ⁺ system and the emission spectrum of the a³Π-X¹Σ⁺ system of AlBr have been examined at higher resolution than previously used. The present study has produced a significantly improved set of molecular constants for these excited states of AlBr. All data have been fitted in a self-consistent manner for an optimum set of constants. The broadening of features in the A-X system has been attributed to type c⁺ predissociation in the A¹Π state. Also, a comparison is made between the emission and absorption spectra of the A-X system.     

Photoluminescence of the A2Π-X2Σ+ system of the yttrium oxide molecule

A cw dye laser, tunable in the region 570–620 nm, has been used to excite photoluminescence in the A²Π-X²Σ⁺ system of the YO molecule. Two methods have been used to obtain spectra. They are (i) photoluminescence and (ii) spectrally selective excitation spectroscopy. The latter maintains the simplicity of photoluminescence, but has higher resolution. The spectra obtained at medium resolution (～0.05 nm) have been surveyed and the identification of transitions has been outlined. A method was devised in which known lower state constants were used in calculating approximate upper state constants whenever the laser simultaneously excited coincident rotational transitions in the same band. From these calculations, an approximate value of α′_e was calculated which was found to be close to, but slightly larger than values previously computed from the Pekeris formula. Many examples of collisional transfer were observed. In particular, maximum transfer from ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ to ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was always observed to involve an increase of one unit in the vibrational quantum number. No transfer was observed between opposite parity components of Λ doublets, in spite of their closeness in energy, indicating that the symmetry of the electronic eigenfunctions was unaffected by collisions. Reanalysis of previous high resolution data has shown that, when the contribution of Λ-doubling parameters to the separation of the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ states is taken into account, the value of the spin-orbit coupling constant, A, changes significantly. It was also found necessary to include the constant, A_D, to account for the effect of centrifugal distortion on the spin-orbit interaction.