Higher moments of net-proton multiplicity distributions

Higher moments of event-by-event net-proton multiplicity distributions have been applied to search for the QCD critical point. Model results are used to provide a baseline for this search. The measured moment products, ??? ² and S?? of net-proton distributions, which are directly connected to the thermodynamical baryon number susceptibility ratio in Lattice QCD and Hadron Resonance Gas (HRG) model, are compared to the transport and thermal model results. We argue that a non-monotonic dependence of ??? ² and S?? as a function of beam energy can be used to search for the QCD critical point.     

QCD and hybrid NBD on oscillating moments of multiplicity distributions in lepton-and hadron-initiated reactions

QCD predictions for moments of multiplicity distributions are compared with experimental data on e⁺e^? collisions and their two-NBD fits. Moments of the multiplicity distribution in a two-NBD model for 1.8-TeV pp collisions are considered. Three-NBD model predictions and fits for pp at LHC energies are also discussed. Analytic expressions for moments of hybrid NBD are derived and used to get insight into jet parameters and multicomponent structure of the processes. Interpretation of observed correlations is proposed.     

Magnetic moments of negative parity baryons from the effective Hamiltonian approach to QCD

The magnetic moments of the S ₁₁(1535) and S ₁₁(1650) baryons are studied in the framework of the relativistic three-quark Hamiltonian derived in the Field Correlation Method. The baryon magnetic moments are expressed via the average current quark energies which are defined by the fundamental QCD parameters: the string tension σ, the quark masses, and the strong coupling constant α _s . The resulting magnetic moments for the J ^P = 1/2^? nucleons are compared both to model calculations and to those from lattice QCD.     

Resummed multiplicity moments

The multiplicity distribution of hadrons in a jet is reanalysed. The \(\mathcal{O}(1/\sqrt {\ln (W^2 /\Lambda _{QCD}^2 )} )\) correction to the double-log summation is so large that its addition makes the value of the multiplicity moments unphysical at the current energies ofe ⁺ e ^? annihilation. This implies the necessity of systematic resummation of the whole series in powers of \(1/\sqrt {\ln (W^2 /\Lambda _{QCD}^2 )} \) . In this article we perform this resummation. In fact, a formal exact solution of the integral equation, which gives recursion relations among the multiplicity moments, takes the form of a geometric series. The resummation reduces the correction substantially.     

Soft and hard processes in QCD

QCD equations for the generating functions are applied to separate soft and hard jets in e⁺e^? processes of multiparticle production. The dependence of average multiplicities and higher moments of multiplicity distributions of particles created in “newly born” soft subjets on the share of energy devoted to them is calculated in fixed coupling gluodynamics. This dependence is the same as for the total multiplicity up to a constant factor if soft jets are defined as those carrying out a fixed share of initial energy at all energies. The constant factor depends on this share in a nontrivial way. Other definitions are also proposed. The relation between these quantities for soft and hard processes is discussed.     

Hadron multiplicities

We review results on hadron multiplicities in high-energy particle collisions. Both theory and experiment are discussed. The general procedures used to describe particle multiplicity in quantum chromodynamics (QCD) are summarized. The QCD equations for the generating functions of the multiplicity distributions are presented both for fixed and running coupling strengths. The mean multiplicities of gluon and quark jets, their ratio, higher moments, and the slopes of multiplicities as a function of energy scale, are among the main global features of multiplicity for which QCD results exist. Recent data from high energy e⁺e⁻ experiments, including results for separated quark and gluon jets, allow rather direct tests of these results. The theoretical predictions are generally quite successful when confronted with data. Jet and subjet multiplicities are described. Multiplicity in limited regions of phase space is discussed in the context of intermittency and fractality. The problem of singularities in the generating functions is formulated. Some special features of average multiplicities in heavy quark jets are described.     

A comparison of\bar pp annihilations into charged particles,e + e −→hadrons ande + e −→Ψ, Γ→hadrons

A comparison of multiplicity distributions and \(\left\langle {P_T^2 } \right\rangle of \bar pp\) annihilation reactions at two energies ande ⁺ e ^?→hadrons leads to a model for \(\bar pp\) annihilation into gluons. The \(\bar pp\) data are consistent with the QCD predictions for the ratio of the moments of the fragmentation functions given for isolated gluon jets. The energy dependence of the ratio of the moments is also consistent with the predictions.     

Isotope-selective ionization utilizing molecular alignment and non-resonant multiphoton ionization

We demonstrate laser nitrogen isotope separation, which is based on field-free alignment and angular-dependent ionization of ¹⁴N₂ and ¹⁵N₂ isotopologues. A linearly polarized short laser pulse (???~?795?nm, ?????~?60?fs) creates rotational wave packets in the isotopologues, which periodically revive with different revival times as a result of different moments of inertia. Another linearly polarized short laser pulse (???~?795?nm, ?????~?60?fs) ionizes one of the isotopologues selectively as a result of their different angular distributions. In the present experiments, the ion yield ratio R [=I(¹⁵N₂ ⁺)/I(¹⁴N₂ ⁺)] can be changed in the range from 0.85 to 1.22, depending on the time delay between the two laser pulses.     

αS(KT2) versus αS(K2) in QCD jet development: Some quantitative remarks

Properties of QCD jets for two proposed choices of the variable appearing in the QCD running coupling constant, α_S(K²) or α_S(K_T²) with K_T²=z(1?z)K², have been studied in detail by the use of Monte Carlo techniques. Contrary to expectations based on approximate analytic calculations it is found that when substituting K² with K_T² in α_S the growth with energy of the multiplicity of the quanta is not sensibly altered, and it is even slowed down for extreme values of the non-perturbative cutoff, which delimits the minimum virtual mass of the quanta. It appears, therefore, that the analysis of subleading effects may be totally misleading if phase-space constraints are not taken into account exactly, which is possible to do in Monte Carlo calculations.     

Observation of scaling deviations in the energy distribution of secondary hadrons in inelastic neutrino-proton interactions

An analysis is presented of the z distributions of secondary hadrons produced in 5600 charged current events from a BEBC neutrino-hydrogen experiment. Evidence is presented for scaling deviations in the z distributions and a breakdown of factorization in the single particle inclusive cross sections. The results are consistent with the leading order QCD predictions on the q² dependence of nonsinglet moments of quark fragmentation functions, yielding a value of Λ ≈ 0.6 GeV.     

Multiplicity moments in deep inelastic scattering at HERA

Multiplicity moments of charged particles in deep inelastic e⁺p scattering have been measured with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb⁻¹. The moments for Q²>1000 GeV² were studied in the current region of the Breit frame. The evolution of the moments was investigated as a function of restricted regions in polar angle and, for the first time, both in the transverse momentum and in absolute momentum of final-state particles. Analytic perturbative QCD predictions in conjunction with the hypothesis of Local Parton–Hadron Duality (LPHD) reproduce the trends of the moments in polar-angle regions, although some discrepancies are observed. For the moments restricted either in transverse or absolute momentum, the analytic results combined with the LPHD hypothesis show considerable deviations from the measurements. The study indicates a large influence of the hadronisation stage on the multiplicity distributions in the restricted phase-space regions studied here, which is inconsistent with the expectations of the LPHD hypothesis.     

Normalizing the renormalization group analysis of deep inelastic leptoproduction

The nucleon matrix elements of the leading twist non-singlet operators which arise in the standard QCD analysis of leptoproduction are computed in an improved version of the bag model. QCD radiative corrections are used to evolve the bag predictions which are applicable at a low value of Q² to a high Q² regime where they can be compared with moments of non-singlet structure functions. The agreement with data is good and suggests that higher twist effects are not large.     

Second order QCD contributions to thrust and spherocity

In e⁺e^? annihilation there are regions of high spherocity S and low thrust $\text{T(S >}\text{16}\text{3π}{}^2\text{and}\text{T <}\text{2}\text{3}$ in which these distributions are given in QCD perturbation theory by the subprocesses e⁺e^? → qq?GG and e⁺e^? → qq?qq? neglecting only cubic and higher order terms in α_S. We give the corresponding QCD predictions which suggest that the calculable corrections to these variables may be slowly convergent.     

Evolution of the truncated Mellin moments of the parton distributions in QCD analysis

We review evolution equations for the truncated Mellin moments of the parton distributions and some their applications in QCD analysis. The main finding of the presented approach is that the nth truncated moment of the parton distribution obeys also the DGLAP equation but with a rescaled splitting function P′(z) = z ⁿ P(z). This allows one to avoid the problem of dealing with the experimentally unexplored Bjorken-x region. The evolution equations for truncated moments are universal—they are valid in each order of perturbation expansion and can be useful additional tool in analysis of unpolarized as well as polarized nucleon structure functions.     

Charged particle multiplicity distributions for 32 GeV/c K±p and pp interactions and for 50 GeV/c π±p interactions

Topological cross sections are presented for K⁺p, K^?p and $\text{p}\text{p}$ interations at 32 GeV/c and for π⁺p and π^?p interactions at 50 GeV/c observed in the 4.5 m Mirabelle hydrogen bubble chamber at Serpukhov. Parameters characterizing the behaviour of the multiplicity distributions, namely 〈n_c〉, D and f₂ and the normalized moments are given. The dependence of these parameters on the energy and the nature of the beam particle is discussed. The multiplicity distributions obtained cannot be described by a single function in the KNO variables.     

The phenomenology of coloured scalars

We study the phenomenology of light scalar quarks and the properties of a new family of hadrons containing such quarks in the framework of QCD taking into account non-perturbative effects caused by a possible existence of the condensate of the colored scalar fields. We suggest that 1^?? bound state of scalar quark and antiquark may lie in the already accessible region \(20GeV< \sqrt S< 30GeV\) and be observable as resonance in PETRAe ⁺ e ^? collisions.     

Opposite side quantum number correlations ine + e −-annihilation

We claim that double moments of twoparticle distributions are very sensitive quantities for testing the opposite side quantum number correlations ine ⁺ e ^?-annihilation predicted by the quark parton model. In particular it is found that kaon correlations are extremely transparent in these quantities. This feature survives when the QCD predictedQ ²-dependence is taken into account. We also stress the importance of establishing the higher meson resonance content in quark jets in order to make a sensible QCD-analyses of the fragmentation functions.     

Searching for the QCD critical point in AA collisions at CERN SPS

We investigate the transverse momentum correlations of pairs of opposite charged pions near their production threshold. Through intermittency analysis, we search for power-law dependence on observation scale, as dictated by critical QCD. We analyze the data on the most central collisions in four A systems (A = p, C, Si, Pb) at maximum SPS energy. We find a significant effect for the SiSi system approaching in size the critical QCD predictions as measured by the intermittency index ? ₂. Absence of this effect in the (?? ^?, ?? ^?) sector of the SiSi system gives further support that the observed behavior in the isoscalar mode is of critical origin.     

Transverse momentum in Drell-Yan processes

We study the transverse momentum distribution of muon pairs from Drell-Yan processes in QCD. In particular the dependence of 〈k_⊥²〉 on Q² is considered. QCD predicts an approximately linear rise of 〈k_⊥²〉 with S or Q² only at fixed τ = Q²/S. The slope as a function of τ is quantitatively studied for P$\text{P}$ and P-nucleus scattering. The most recent data showing a rather flat 〈k_⊥²〉 in Q² at fixed S are found to be consistent with QCD.     

Angular intermittency in QCD jets

Using two methods, via fluctuations and correlations, an analytical formula is derived for the factorial multiplicity moments in a QCD jet at the Double Leading Logarithm accuracy. The resulting self-similar dependence on the solid-angle cell size is characteristic of an intermittency behaviour in angular variables. The intermittency indices depend on the diffusion angle through the running of α_S. Physical features of jet fluctuations such as collimation at large angles and saturation at small angles are well described in the perturbative framework. A parameter-free prediction of angular intermittency is proposed for Z⁰ decays into hadrons, assuming hadronparton duality.