Parton Transverse Momentum Research Articles

Perturbative QCD effects observed in 490 GeV deep-inelastic muon scattering.

Results on forward charged hadrons in 490 GeV deep-inelastic muon scattering are presented. The transverse momenta, azimuthal asymmetry, and energy flow of events with four or more forward charged hadrons are studied. The range of the invariant hadronic mass squared 300[lt][ital W][sup 2][lt]900 GeV[sup 2]/[ital c][sup 4] extends higher than previous deep-inelastic muon scattering experiments. Data are compared to the predictions of the Lund Monte Carlo model with perturbative QCD simulated by matrix elements, parton showers, and color dipole radiation. All of the QCD-based models are consistent with the data while a model without QCD processes is not. Correlations with the multiplicity-independent event variable [Pi][congruent][summation][vert bar][ital p][sub [ital T]][vert bar] are studied. The relationship between the azimuthal asymmetry and transverse momentum of forward hadrons is also presented. The data are most consistent with intrinsic parton transverse momentum squared [ital k][sub [ital T]][sup 2] of 0.25 GeV[sup 2]/[ital c][sup 2].

Higher twist signal from R = σL/ σT data in deep inelastic electron scattering

Recent precision measurements of the longitudinal virtual photon cross-section are analysed with the theory of power corrections in QCD. The results show clearly a twist-4 quark-gluon contribution corresponding to a parton transverse momentum of a few hundred Mev

Azimuthal energy flow in deep-inelastic neutrino scattering.

The azimuthal dependence of the flow of hadronic energy about the momentum-transfer direction in charged-current deep-inelastic neutrino-nucleon scattering is used to study gluon emission and the transverse momentum of partons confined inside the nucleon. A 7-standard-deviation azimuthal asymmetry is observed indicating an average = 0.303 +- 0.041 GeVc.

The multiplicity dependence of the transverse momentum distribution at SPS collider energy and the multi-string fragmentation model

We modify a previously developed multi-string model for particle production to include the primordial transverse momentum of the partons in the incoming hadrons. Rapidity spectra, correlations and multiplicity distributions are unsensitive to the modification. The average transverse momentum of secondaries is found to increase with multiplicity, as observed at the SPS collider. However, a rather large parton transverse momentum (1.1–1.4 GeV) is required.

Large-p T production of single and double photons in proton-proton and pion-proton collisions

Quantum chromodynamic (QCD) predictions are made for the large transverse momentum production of single and double photons in proton-proton, proton-antiproton, and pion-proton collisions. In π − p collisions at center-of-mass energy W = 27.4 GeV and p T = 4.0 GeV, it is estimated that about 0.3% of the 90° single photon triggers will be balanced on the “away-side” by a single photon with roughly the same transverse momentum. In π +p collisions this fraction drops to about 0.09%. These fractions increase with p T. In addition to the pure QED annihilation term q q →γγ , it is found that the QCD-induced subprocess gg→ γγ provides an important source of double photons. Photon bremsstrahlung contributions are also examined. Experimental study of the systematics of single and double photon production in hadron-hadron collisions will provide information on the size of the strong interaction coupling constant, α s( Q), and on the charges of the quarks. Knowledge of the gluon distributions within hadrons and of the effective transverse momentum of partons in hadrons can also be gained.

Unravelling higher twists

We present a novel method of deriving the first power corrections (1/ Q 2) to the leptoproduction structure functions. The method is based directly on the manipulation of Feynman diagrams. Correspondence with the operator product expansion approach is established. We find that the transverse components of momenta and the gluon field control both the kinematic and dynamical power corrections. The full QCD result is similar in structure to the naïve parton model with intrinsic transverse momentum. We explain how the concept of parton transverse momentum is generalized in the presence of interaction. In the operator language our method defines a new basis in which all but the transverse components of covariant derivatives are eliminated by the equations of motion. We derive constraints on signs of the 1/ Q 2 terms.

Determination of Parton's Transverse Momentum from High PT Dijet Events

Determination of Parton's Transverse Momentum from High PT Dijet Events

Dilepton production from collisions of polarized spin-½ hadrons. II. Parton-model predictions

Parton-model predictions for lepton-pair production from polarized spin-1/2 particles are considered within the context of a formalism explained in a companion paper. The polarization effects in the quantum-chromodynamic 2 {yields} 2 subprocesses which contribute to lepton-pair production are found to be quite simple. Following the work of Ralston and Soper, polarized distribution functions are defined for gluons as well as quarks. Finally, a detailed discussion of polarization and the hard-scattering formalism is presented for the two cases of intrinsic parton transverse momentum allowed or forbidden.

Deep inelastic Compton scattering and large-p T pion photoproduction in QCD hard collision model

Inclusive photon(pion) production at large-pT in γp collisions is studied in the framework of QCD perturbation theory, taking into account the effects due to parton transverse momenta. The contributions from various components of photons are equally important at relatively smallpT (e.g.,pT≲4 Ge V/c at\(\sqrt s = 17GeV\)). At largepT, however, the contributions from the subprocesses with direct photon coupling are most important; quark Compton scattering is the dominant subprocess in inelastic Compton scattering.

A second-order QCD effect: quark-quark bremsstrahlung contribution to transverse momentum of lepton pairs

We consider in QCD the second-order, in gluon-quark coupling constant, contribution of quark-quark scattering (bremsstrahlung) to the transverse momentum distribution of muon pairs produced in proton-proton collisions. In certain kinematical regions accessible to experimental tests, this contribution is quite large in comparison with the first-order calculations. This happens for a specific choice of scale-violating structure functions which fit the deep inelastic data. Thus, the first-order QCD calculation alone is not conclusive in trying to fit the data; one must necessarily check the effect of second-order quark-quark scattering as compared with first-order quark-gluon and the quark-antiquark scattering. This remark also concerns the case where the effect of primordial transverse momentum of partons is included in the first-order diagrams as well as the case where the first order is replaced by a DDT type of formulae. Mass regularization and different prescriptions for the constant term in the q→g+q vertex are considered. Results are presented for energies √ s=6.5, 27, 63, 800 GeV and are compared with experiment. Implications of these results for the detection of W ± mesons via the p T distribution of their decay products μ ± in proton-proton collisions are mentioned.

A measurement of the transverse momenta of partons, and of jet fragmentation as a function of √ s in p-p collisions

A large solid-angle apparatus consisting of a superconducting solenoid magnet, cylindrical drift chambers and two arrays of lead-glass counters was used to examine particles associated with a high transverse momentum trigger in p-p collisions with three √ s values at the CERN ISR. The trigger was given by energy deposition in lead-glass arrays centred at 90°. The trigger transverse momentum range covered was 3 < p T trig < 11 GeV c . Results are given for p out for both individual charged particles, and also for the sum of charged particle momenta in the hemisphere opposite to the trigger. Mean values are then deduced for the parton transverse momentum k T , and for the jet fragmentation momentum j T .

Recombination model for hadron production

We calculate baryon distributions in the fragmentation region ofpp collision using Das and Hwa picture of quark recombination. A new estimation of the sea quark distributions in proton is obtained by fitting the pseudoscalar meson data at fixedP T taking account of parton transverse momenta.

Introducing the dilatational degree of freedom: Special relativity in V6

The assumption of the universal atomic scale is not justified by observations. The latter indicate just the contrary, namely that the scale is a degree of freedom. The author attempts to state a concise general definition of the principle of relativity. The incorporation of the dilatational degree of freedom into the principle of relativity requires that physical events take place in the six-dimensional space V6, the subspace of which is the Minkowski space M4. The norms and angles of 6-vectors in V6 are assumed to be conserved, whilst their projections into M4 are in general not conserved under the transformations of the group ISO(4,2). The speed of light is invariant in V6 but its projection into M4 is invariant only under certain transformations. The theory provides a description of the muon to electron mass ratio. The 'primordial' transverse momentum of partons is proposed to originate from the dilatational momentum.

Evidence that High-pTJet Pairs Give Direct Information on Parton-Parton Scattering

New results for parton transverse momentum obtained from two-jet high-${p}_{T}$ hadron events are presented. These results, and results for quark structure functions in the pion, are compared with results from dimuon production experiments. The results for the two types of experiments are very similar. This indicates that jet pairs give direct information on parton-parton scattering.

Study of parton transverse momentum using jets from hadron interactions

We study the momentum unbalance in two-jet events which we have obtained with a two-arm calorimeter array at Fermilab. Although the unbalance is relatively sharply peaked near zero, the rms unbalance is considerably greater than that due to instrumental effects alone. We interpret the unbalance as being principally due to effects of parton transverse momentum ${K}_{T}$. We give results for the resolution-corrected rms unbalance (approximately equal to ${K}_{T}$) for a range of values of jet ${p}_{T}$. $\mathrm{pp}$ collisions are studied at three $s$ values, and ${\ensuremath{\pi}}^{+}p$ collisions are compared with them at two of these $s$ values. The results are compared with information on ${K}_{T}$ obtained from other experiments, principally experiments on dimuon production. Implications of the similarities and of the differences are discussed.

Energy flow and energy correlations in deep inelastic scattering

We study two examples of infrared-safe quantities in deep inelastic scattering: the flow of energy in a given angular range and the energy-energy angular pattern. We derive expressions for these quantities in perturbative QCD, to order α s, and show explicitly their infrared safety. Our formulas for the angular energy flow and the energy-energy angular pattern depend only on well-defined QCD factors and on the deep inelastic structure functions. To gauge whether or not these perturbative QCD results are applicable to present day data, we estimate in a simple model the effects of hadronization and primordial parton transverse momentum. In general these non-perturbative effects mask the resulting QCD pattern at present energies, but vanish more rapidly at higher energies than the QCD effects. However, we point out two examples where it may be possible to test the perturbative QCD predictions with available data. One of them involves studying the x-dependence of the azimuthal asymmetry of the energy flow. The other involves studying the angular width of the energy-energy correlation function.

On the intrinsic transverse momentum of partons

Using simple assumptions it is shown that the average transverse momentum of partons is determined by their structure functions. The x-dependence obtained this way agrees well with the experimental data. The size is controlled by the invariant mass of the nucleon core and the behaviour of the structure functions near x = 1. We obtain a lower limit for the intrinsic contribution to 〈 k ⊥〉 μμ of ∼ 400 MeV.

A Two-Jet Calorimeter Experiment at Fermilab

A double arm calorimeter and drift chamber system has been used to study high pT jets at Fermilab in 130, 200, and 400 GeV collisions with a hydrogen target. The response of the calorimeter to jets is discussed. Data are presented on the transverse momentum of partons in the pion and proton and on the pion structure function.

How to Include Parton Transverse Momentum in Quantum Chromodynamics

I show that parton transverse-momentum effects can be included in factorized quantum-chromodynamics inclusive cross sections, but that factorization is maintained only if the transverse-momentum variable which is held fixed is independent of the scale of the parton momentum. I also emphasized that other nonperturbative effects can be just as important as the transverse momentum.

The transverse momentum of partons in large pT processes

An approximate method is used to investigate the effects of parton transverse momentum in large p T particle production within the framework of hard scattering models. We derive an approximate expression for the mean bias towards the trigger of each of the two participating partons and find that event one of the partons is biased more than the other, even with a 90° trigger. We treat the transverse momentum of partons and their closely related off-mass-shell behaviour as a perturbation in the equation for the single-particle inclusive cross section, and then expand in a Taylor series. We calculate the first non-zero correction term and find that to this order, the cross section is increased by parton transverse momentum effects by typically a factor of 1.7 for p T = 3 GeV/c with 〈 k T〉 = 500 MeV/c, or 1.25 for p T = 3 GeV/c with 〈 k T〉 = 300 MeV/c, and that the correction decreases rapidly with increasing p T.