Quark fragmentation and trigger side momentum distributions in high-p T processes

It has been widely argued that the experimental evidence concerning the momentum accompanying highp T triggers is a grave problem for models which take the trigger hadron to be a quark fragment. It is claimed that the trigger hadron takes much too large a fraction (z _c ) of the jet momentum for the trigger side jet to be a quark. The jet momentum is not directly measured, but deduced from the derivative of the momentum (p _x ) accompanying the trigger with respect to the trigger transverse momentum-p _T ^t . This argument is shown to be unsafe. Using both an approximate analytic approach to illustrate the physics and subsequently a full numerical computation it is proved that the deduction of the fractional momentum accompanying the trigger, 1/z _c ?1, fromdp _x /dp _T ^t is not correct. Further we show that models—specifically that of Feynman and Field—which do take the trigger to be a quark fragment are essentially in agreement with the data on trigger side momentum distributions. A surprising prediction of our analysis is thatp _x should be approximately constant forp _T ^t ≧6GeV/c.     

Inclusive particle spectra in p(π+)n interactions at 195 GeV/c

We present results on single-particle inclusive distributions in p(π⁺)n reactions from a Fermilab experiment using the hybrid 30″ bubble chamber and PWC facility. Distributions in rapidity, y, Feynman x and p²_T for π⁺ and π^? are presented and compared with other experiments. The effects of different targets and projectiles (neutrons, protons and pions) on the distributions are demonstrated and discussed in terms of projectile and target fragmentation. The average transverse momentum 〈P_T〉 is studied as a function of x, y and multiplicity.     

The production of charged particles with high transverse momentum in proton-proton collisions at the CERN ISR

Results are given on the inclusive production of charged pions, kaons and nucleons in high-energy proton-proton collisions in the centre-of-mass rapidity range |y_cm| < 1 and for transverse momenta up to 4.8 GeV/c. The dependence of the composition of produced particles on y_cm, the total energy $\text{s}$, and transverse momentum p_T is discussed.     

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.     

Charge asymmetry at large pT in inelastic pp reactions at 22.4 GeV/c

Charge asymmetry in $\text{p}\text{p}$ reactions at 22.4 GeV/c is investigated as a function of transverse momentum in the c.m. rapidity interval |y¹| < 1. The charge asymmetries in the forward and backward directions are increasing with increasing transverse momentum. The increase seems to be present both in annihilation and non-annihilation processes.     

Structure of final states with a high transverse momentum π0 in proton-proton collisions

We present a study of the final state structure in proton-proton collisions (√s = 53 GeV) where a large transverse momentum π⁰ (p_t > 2 GeV/c) is produced at an angle of 90°. Charged secondaries have been detected and momentum analysed in the split field magnet detector at the CERN Intersecting Storage Rings. The large angular coverage of this detector extends over ±2.5 units of rapidity and ±30° of azimuth with respect to the trigger π⁰, both towards and away from it. In each of these directions, where we observe similar strong correlations, we present charged particle distributions, in rapidity and momentum. In the hemisphere containing the trigger π⁰ we have measured the cross section for inclusive production of large transverse momentum ?^± mesons. In the opposite hemisphere the data exhibit several features predicted by hard scattering quark-parton models: coplanarity and short-range rapidity correlation for the large transverse momentum secondaries as well as a transverse momentum sharing distribution similar to that observed in deep inelastic electro-production and in e⁺e^? collisions.     

Analysis of transverse momentum distributions forpp interactions at 360 GeV/c in the framework of a quark-diquark fragmentation model

Using a quark-diquark fragmentation model, in which either the Field-Feynman or the Lund model is coupled with a quark-diquark distribution function, we study transverse momentum distributions,p _T, for the inclusive reactionspp→hadron +anything at 360 GeV/c. We find that a primordial mean transverse momentum 〈k _T〉?0.4 GeV/c can well reproduce thep _T ² distributions of charged hadrons, π⁰,K _s ⁰ , Λ⁰,K ^* and Σ^* and the Feynmanx?p _T correlations. We confirm that a diquark in a proton plays an important rôle in reproducing thex?p _T correlation of Λ⁰.     

Spin dependence of the inclusive reaction p + p (polarized) → π0 + X at 24 GeV/c for high-pTπ0 produced in the central region

The spin dependence of π⁰ inclusive production by 24 GeV/c protons has been measured using a polarized target for Fhe Feynman x near 0 in the transverse momentum range 1.0 < p_T < 2.5 GeV/c. The results indicate a negative updown asymmetry growing strongly with p_T and greater than 50% in absolute value for p_T greater than 2 GeV/c.     

Exact Results for Conditional Means of a Passive Scalar in Certain Statistically Homogeneous Flows

For a passive scalar T(r, t) randomly advected by a statistically homogeneous flow, the probability density function (pdf) of its fluctuation can in general be expressed in terms of two conditional means: 〈?² T|T〉 and 〈|?T|²|T〉. We find that in some special cases, either one of the two conditional means can be obtained explicitly from the equation of motion. In the cases when there is no external source and that the normalized fluctuation reaches a steady state or when a steady state results from a negative damping, 〈?² T|T〉=?(〈|?T|²〉/〈T ²〉)T. The linearity of the conditional mean in these cases follows directly from the fact that the advection equation of a passive scalar is linear. On the other hand, when the scalar is supported by a homogeneous white-in-time external source, 〈|?T|²|T〉=〈|?T|²〉.     

Event patterns extracted from top quark-related spectra in proton-proton collisions at 8 TeV

We analyze the transverse momentum(p _T)and rapidity(y)spectra of top quark pairs,hadronic top quarks,and top quarks produced in proton-proton(pp)collisions at center-of-mass energys~(1/2)=8 Te V.For p _(T )spectra,we use the superposition of the inverse power-law suggested by the QCD(quantum chromodynamics)calculus and the Erlang distribution resulting from a multisource thermal model.For y spectra,we use the two-component Gaussian function resulting from the revised Landau hydrodynamic model.The modelling results are in agreement with the experimental data measured at the detector level,in the fiducial phase-space,and in the full phase-space by the ATLAS Collaboration at the Large Hadron Collider(LHC).Based on the parameter values extracted from p _(T )and y spectra,the event patterns in three-dimensional velocity(β_x-β_y-β_z),momentum(p_x-p_y-p_z),and rapidity(y_1-y_2-y)spaces are obtained,and the probability distributions of these components are also obtained.     

Energy dependence of transverse momentum invariant distribution of pions and neutral kaons in K−p interactions between 14.3 and 70 GeV/c

The energy dependence of the transverse momentum invariant distribution of pions and neutral kaons is studied in K^?p interactions between 14.3 and 70 GeV/c. The large P_T part of the distributions violates the Feynman scaling and, above P_T ? 1.5 GeV/c, appears to be reasonably described by hard scattering models. The variation of the average transverse momentum is also studied as a function of the c.m. reduced longitudinal momentum, and its behaviour is compared to the data obtained via the hadronic shower produced in lepton-hadron interactions.     

pp interactions at 303 GeVc: Analysis of diffraction excitation in the reaction pp → pX

The properties of the diffractively excited system observed at low missing mass in the inclusive pp → pX reaction at $\text{303}\text{GeV}\text{c}$ are presented. For diffraction excitation with |x| > 0.9, the cross section, σ_D=(5.6±0.8) mb, the mean charged multiplicity depends on the mass of the diffractive system approximately at 〈n_c〉 ≈ 0.6M_x + 2, and the slope of the momentum transfer distribution with |t| < 0.5 GeV² is 7.5±0.8 GeV^?2.     

Quantum number effects in events with a charged particle of large transverse momentum: (I). Leading particles in single and diquark jets

In an experiment performed with the SFM facility at the CERN ISR, we have studied events with a large-p_T particle (π⁺, π^-, K^-, p) produced at polar angle settings of 20° and 45°. The longitudinal momentum distributions of leading fragments in the spectator jet of the same rapidity hemisphere as the trigger are strongly correlated to the nature of the trigger particle involved. These distributions are compared with predictions from dimensional counting rules, if parton scattering via vector gluon exchange is assumed for the large-p_T process. Given slight modifications of the original counting rules, we observe a fair agreement. As to the fastest particle (jet leader) in the “away” jet, its average charge is about $\text{1}\text{3}$ independent of the charge of the trigger; this value is expected for the case of three valence quarks participating in the hard scattering process. From the analysis of the trigger jet we find ?⁰/π⁺ and ?⁰/π^- production ratios near unity at a value of the transverse momentum of about 2 GeV/c.     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

Determining the KS→3π amplitude in pp(OR e+e−)→K0K0

The amplitude ratio 〈3π|T|K_S〉/〈3π|T|K_L〉 can be well determined in e⁺e^? (or low energy $\text{p}\text{p}\text{)→K}{}^{\mathrm{o}}\text{K}{}^{\mathrm{o}}$ from the decay time-distribution when each produced kaon→3π, other unknown parameters of the distribution being obtainable from corresponding observations involving known channels like ππ.     

Transverse momentum of charged hadrons produced in ν and\bar v deuterium charged current interactions

The transverse momentum properties of charged hadrons produced in charged current ν and \(\bar v\) deuterium interactions are studied. The variation of <P _t ² > withW ²,Q ²,x _F andz ² is analyzed. A study of transverse momentum balance shows that soft gluon emission and some quark primordial transverse momentum with <k _t ² >?(0.4 GeV/c)² are needed to balance highp _t particles. Distributions ofp _tin andP _tout in and out of the event plane are presented. A three jet structure is observed for events withW ²>50 (GeV²) and with a highp _t track, which is compatible with models taking into account hard gluon emission.     

Temperature quenching of luminescence for linear and derivative nuclear operators

An earlier study of the thermal quenching of luminescence using the single-configurational-coordinate model is extended from Condon-approximation overlap integrals 〈u_n|v_m〉² to the linear and derivative integrals 〈u_n|z_v|v_m〉² and 〈u_n|?/?z_v|v_m〉². For non-radiative transitions, the thermally weighted nuclear factor in the transition rate is, for the linear and derivative integrals, the corresponding factor for 〈u_n|v_m〉² integrals multiplied by 2E_Xv/?ω_v and $\text{2[E}{}_{\mathrm{Xv}}\text{- E}{}_{\mathrm{p}}{}_{\mathrm{U}}\text{(T)]/}\text{h}\text{?}\text{ω}{}_{\mathrm{v}}$, respectively. E_Xv is the energy of the crossover above the initial- v-parabola minimum, and E_pU(T) is the single activation energy fitted to the nuclear factor's temperature dependence for 〈u_n|v_m〉² integrals. These multiplying factors are exact for equal parabola force constants and good approximations for unequal force constants. These multiplying factors will be difficult to distinguish experimentally. The more important considerations for fitting the model to thermal-quenching data are the parabola placement and the Condon-approximation integrals described previously.     

Photoproduction of K 0 and Λ at HERA and a comparison with deep inelastic scattering

Inclusive K ⁰ and Λ photoproduction has been investigated at HERA with the H1 detector at an average photon-proton center of mass energy of 200 GeV in the transverse momentum range 0.5 < p _t < 5 GeV. The production rates as a function of p _t and center of mass rapidity are compared to those obtained in deep inelastic scattering at 〈Q ²〉 = 23 GeV². A similar comparison is made of the rapidity spectra of charged particles. The rate of strangeness photoproduction is compared with $p\bar p$ measurements. The observations are also compared with next-to-leading order QCD calculations and the predictions of a Monte Carlo model.     

On the anomalous large transverse energy events observed in proton-lead scattering

It has been shown that a study of correlation between the average rapidity, 〈y〉, and transverse energy,E _T , can be used to distinguish between different origins of large transverse energy events observed inp-Pb scattering in the HELIOS experiment. If the largeE _T events are to be attributed to a nuclear dependence of structure functions then the hard scattering picture implies a positive correlation among the above two quantities, contrary to that seen in experiment.