Distribution Of Hadrons Research Articles

Jet substructure using semi-inclusive jet functions in SCET

We propose a new method to evaluate jet substructure observables in inclusive jet measurements, based upon semi-inclusive jet functions in the framework of Soft Collinear Effective Theory (SCET). As a first example, we consider the jet fragmentation function, where a hadron $h$ is identified inside a fully reconstructed jet. We introduce a new semi-inclusive fragmenting jet function ${\mathcal G}^h_i(z= \omega_J/\omega,z_h=\omega_h/\omega_J,\omega_J, R,\mu)$, which depends on the jet radius $R$ and the large light-cone momenta of the parton `$i$' initiating the jet ($\omega$), the jet ($\omega_J$), and the hadron $h$ ($\omega_h$). The jet fragmentation function can then be expressed as a semi-inclusive observable, in the spirit of actual experimental measurements, rather than as an exclusive one. We demonstrate the consistency of the effective field theory treatment and standard perturbative QCD calculations of this observable at next-to-leading order (NLO). The renormalization group (RG) equation for the semi-inclusive fragmenting jet function ${\mathcal G}_i^h(z,z_h, \omega_J, R,\mu)$ are also derived and shown to follow exactly the usual timelike DGLAP evolution equations for fragmentation functions. The newly obtained RG equations can be used to perform the resummation of single logarithms of the jet radius parameter $R$ up to next-to-leading logarithmic (NLL$_R$) accuracy. In combination with the fixed NLO calculation, we obtain NLO+NLL$_R$ results for the hadron distribution inside the jet. We present numerical results for $pp\to(\mathrm{jet}\,h)X$ in the new framework, and find excellent agreement with existing LHC experimental data.

Fragmentation in the ϕ3 theory and the LPHD hypothesis

We present analytic solution of the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation at leading order (LO) in the [Formula: see text] theory in 6 space-time dimensions. If the [Formula: see text] model was the theory of strong interactions, the obtained solution would describe the distribution of partons in a jet. We point out that the local parton-hadron duality (LPHD) conjecture does not work in this hypothetical situation. That is, treatment of hadronisation of shower partons is essential for the description of hadron distributions in jets stemming from proton-proton (pp) collisions at [Formula: see text] TeV and from electron-positron ([Formula: see text]) annihilations at various collision energies. We use a statistical model for the description of hadronisation.

Hydrodynamic fluctuations and dissipation in an integrated dynamical model

We develop a new integrated dynamical model to investigate the effects of the hydrodynamic fluctuations on observables in high-energy nuclear collisions. We implement hydrodynamic fluctuations in a fully 3-D dynamical model consisting of the hydrodynamic initialization models of the Monte-Carlo Kharzeev-Levin-Nardi model, causal dissipative hydrodynamics and the subsequent hadronic cascades. By analyzing the hadron distributions obtained by massive event-by-event simulations with both of hydrodynamic fluctuations and initial-state fluctuations, we discuss the effects of hydrodynamic fluctuations on the flow harmonics, vn and their fluctuations.

Decomposing energy balance contributions for quenched jets with CMS

Modification of energy balance in dijet events from heavy ion collisions, measured by CMS, was among the first jet quenching observations in the LHC energy domain. Here we further study the spatial extent of medium-induced modifications for such dijets, as well as potential medium response to propagating partons, using two-dimensional angular correlations of charged hadrons measured with respect to jets. New differential measurements of charged particle energy flow about the jet direction as a function of relative azimuth and relative pseudorapidity from 2.76 TeV PbPb collisions are compared with the reference pp data recorded by the CMS at the same energy. Modifications of correlated charged hadron distributions for both the leading and the subleading sides of the dijet are reported, together with comparisons of the long-range asymmetry of the underlying event in PbPb vs pp collisions.

Hadron Wave Functions from Lattice QCD

I give a brief account of the status and perspectives of lattice calculations of the light-front wave functions at small transverse separations, usually referred to as hadron distribution amplitudes (DAs). The existing calculations indicate that the corrections to the asymptotic form of such distributions at large scales are rather small as compared to earlier model estimates. Lattice calculations also suggest an alternating pattern of such corrections for the nucleon resonances with increasing mass. Several recent results are discussed, including precise determination of the second moment of the pion DA, leading-twist DAs of the nucleon and \(N^*(1535)\), and the first calculation of the flavor-symmetry breaking corrections in the DAs of the baryon octet.

Evidence for creation of strong electromagnetic fields in relativistic heavy-ion collisions

It is proposed to identify a strong electric field created during relativistic collisions of asymmetric nuclei via observation of pseudorapidity and transverse momentum distributions of hadrons with the same mass but opposite charges. The detailed calculation results for the directed flow within the Parton-Hadron String Dynamics model are given for Cu-Au interactions at the NICA collision energies of $\sqrt{s_{NN}}=9$ and $5$ GeV. The separation effect is observable at 9 GeV as clearly as at 200 GeV

Spatial distribution function of electrons and thermal neutrons in extensive air showers at sea level

The spatial distributions of electrons and hadrons in extensive air showers, obtained during the PRISMA-32 experiment simulation, are considered. The experiment was simulated for primary protons and iron nuclei using the CORSIKA6.9 and GEANT4.10 software packages. The simulated spatial distribution functions of electrons and neutrons in the extensive air showers (EAS) at the Moscow altitude are compared to the published experimental data of the PRISMA-32 setup.

How many of the scaling trends inppcollisions will be violated atsNN=14 TeV? Predictions from Monte Carlo quark-gluon string model

Multiplicity, rapidity and transverse momentum distributions of hadrons produced both in inelastic and nondiffractive $pp$ collisions at energies from $\sqrt{s} = 200$\,GeV to 14\,TeV are studied within the Monte Carlo quark-gluon string model (QGSM). Good agreement with the available experimental data up to $\sqrt{s} = 13$\,TeV is obtained, and predictions are made for the collisions at top LHC energy $\sqrt{s} = 14$\,TeV. The model indicates that Feynman scaling and extended longitudinal scaling remain valid in the fragmentation regions, whereas strong violation of Feynman scaling is observed at midrapidity. The Koba-Nielsen-Olesen (KNO) scaling in multiplicity distributions is violated at LHC also. The origin of both maintenance and violation of the scaling trends is traced to short range correlations of particles in the strings and interplay between the multistring processes at ultrarelativistic energies.

Jet-track correlations in PbPb and pp collisions at 2.76 TeV

Jet quenching is one of the established signatures of the Quark Gluon Plasma, and this phenomenon has been studied extensively in high energy heavy ion experiments over the last decade. Despite significant progress made in those studies, the specifics of the energy loss mechanisms and the details of jet-medium interactions require further quantitative understanding. Studies of two-dimensional angular correlations of charged hadrons with respect to reconstructed jets make it possible to experimentally assess the energy radiation patterns of an energetic parton traversing the medium as well as its fragmentation function. In these proceedings, we present new differential measurements of charged particle densities and energy flow about the jet direction as a function of relative azimuth and relative pseudorapidity from 2.76 TeV PbPb and pp collisions recorded by the CMS Collaboration. With a sample of back-to-back dijets, previously used to reconstruct the event-wise momentum imbalance (missing pT), we explore modifications to correlated charged hadron distributions for both the leading and the subleading sides of the dijet. With this technique, we can individually assess the contribution of the medium-induced modifications to each side of the dijet and explore the extent of potential medium response to the jet propagation, while also extending these measurements to large angular and radial distances.

Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory

The jet fragmentation function describes the longitudinal momentum distribution of hadrons inside a reconstructed jet. We study the jet fragmentation function in proton-proton collisions in the framework of soft-collinear effective theory (SCET). We find that, up to power corrections, the jet fragmentation function can be expressed as the ratio of the fragmenting jet function and the unmeasured jet function. Using renormalization group techniques, we are able to resum large logarithms of jet radii R in the perturbative expansion of the cross section. We use our theoretical formalism to describe the jet fragmentation functions for light hadron and heavy meson production measured at the Large Hadron Collider (LHC). Our calculations agree very well with the experimental data for the light hadron production. On the other hand, although our calculations for the heavy meson production inside jets are consistent with the PYTHIA simulation, they fail to describe the LHC data. We find that the jet fragmentation function for heavy meson production is very sensitive to the gluon-to-heavy-meson fragmentation function.

Event shape sorting

We propose a novel method for sorting events of multiparticle production according to the azimuthal anisotropy of their momentum distribution. Although the method is quite general, we advocate its use in analysis of ultra-relativistic heavy-ion collisions where large number of hadrons is produced. The advantage of our method is that it can automatically sort out samples of events with histograms that indicate similar distributions of hadrons. It takes into account the whole measured histograms with all orders of anisotropy instead of a specific observable (e.g. $v_2$, $v_3$, $q_2$). It can be used for more exclusive experimental studies of flow anisotropies which are then more easily compared to theoretical calculations. It may also be useful in the construction of mixed-events background for correlation studies as it allows to select events with similar momentum distribution.

Charged hadron distributions in a two component model

Inclusive charged hadron cross sections, dσ/dη, and d2σ/(dηdpT2) are considered within the two component model, which combines the power-like and the exponential terms in pT. The observed dependences of the spectra shape on energy and pseudorapidity qualitatively agree with the proposed model for hadroproduction. A short overview of the results published recently is presented.

Spin-dependent energy distribution of B-hadrons from polarized top decays considering the azimuthal correlation rate

Basically, the energy distribution of bottom-flavored hadrons produced through polarized top quark decays t(↑)→W++b(→Xb), is governed by the unpolarized rate and the polar and the azimuthal correlation functions which are related to the density matrix elements of the decay t(↑)→bW+. Here we present, for the first time, the analytical expressions for the O(αs) radiative corrections to the differential azimuthal decay rates of the partonic process t(↑)→b+W+ in two helicity systems, which are needed to study the azimuthal distribution of the energy spectrum of the hadrons produced in polarized top decays. These spin-momentum correlations between the top quark spin and its decay product momenta will allow the detailed studies of the top decay mechanism. Our predictions of the hadron energy distributions also enable us to deepen our knowledge of the hadronization process and to test the universality and scaling violations of the bottom-flavored meson fragmentation functions.

QCD factorization for quarkonium production in hadron collisions at low transverse momentum

Inclusive production of a quarkonium $\eta_{c,b}$ in hadron collisions at low transverse momentum can be used to extract various Transverse-Momentum-Dependent(TMD) gluon distributions of hadrons, provided the TMD factorization for the process holds. The factorization involving unpolarized TMD gluon distributions of unpolarized hadrons has been examined with on-shell gluons at one-loop level. In this work we study the factorization at one-loop level with diagram approach in the most general case, where all TMD gluon distributions at leading twist are involved. We find that the factorization holds and the perturbative effects are represented by one perturbative coefficient. Since the initial gluons from hadrons are off-shell in general, there exists the so-called super-leading region found recently. We find that the contributions from this region can come from individual diagrams at one-loop level, but they are cancelled in the sum. Our factorized result for the differential cross-section is explicitly gauge-invariant.

Charged particle production in Pb-Pb and p-Pb collisions measured by the ATLAS detector

The ATLAS experiment at the Large Hadron Collider measures charged hadron spectra in Pb+Pb and p+Pb collisions. The results are compared to the pp spectra of charged hadrons at the same centre-of-mass energy. Charged hadron distributions from Pb+Pb are compared to charged particle cross-sections in pp collisions at √s= 2.76 TeV, reference crosssection for p+Pb at √s NN = 5.02 TeV is reconstructed using √s = 2.76 TeV and 7 TeV pp results. These allow for a detailed comparison of the collision systems in a wide transverse momentum and rapidity ranges in different centrality intervals. The nuclear modification factors RAA and RpPb are presented as a function of centrality, pT, η The charged particle RAA is found to vary significantly as a function of transverse momentum, and shows a pronounced minimum at about 7 GeV. Above 60 GeV, RAA is consistent with a flat, centrality-dependent, value within the uncertainties. RpPb results show strong rapidity dependence in the region of so-called Cronin peak at about 2 GeV and above pT of 10 GeV show anomalous enhancement.

Energy dependent growth of nucleon and inclusive charged hadron distributions**Supported by Natural Science Foundation of Hebei Province (A2012210043)

In the Color Glass Condensate formalism, charged hadron pT spectra in p+p and p+Pb collisions are studied by considering an energy-dependent broadening of nucleon density distribution. Then, in the glasma flux tube picture, the n-particle multiplicity distributions at different pseudo-rapidity ranges are investigated. Both the theoretical results show good agreement with the recent experimental data from ALICE and CMS at LHC energies. The predictive results for pT or multiplicity distributions in p+p and p+Pb collisions at the Large Hadron Collider are also given in this paper.

Effects of hadronic rescattering on multistrange hadrons in high-energy nuclear collisions

We study the effects of hadronic rescattering on hadron distributions in high-energy nuclear collisions by using an integrated dynamical approach. This approach is based on a hybrid model combining (3+1)-dimensional ideal hydrodynamics for the quark gluon plasma (QGP), and a transport model for the hadron resonance gas. Since the hadron distributions are the result of the entire expansion history of the system, understanding the QGP properties requires investigating how rescattering during the hadronic stage affects the final distributions of hadrons. We include multistrange hadrons in our study, and quantify the effects of hadronic rescattering on their mean transverse momenta and elliptic flow. We find that multistrange hadrons scatter less during the hadronic stage than nonstrange particles, and thus their distributions reflect the properties of the system in an earlier stage than the distributions of nonstrange particles.

Pseudorapidity distribution of charged hadrons in proton–proton collisions at [formula omitted

The pseudorapidity distribution of charged hadrons in pp collisions at s=13 TeV is measured using a data sample obtained with the CMS detector, operated at zero magnetic field, at the CERN LHC. The yield of primary charged long-lived hadrons produced in inelastic pp collisions is determined in the central region of the CMS pixel detector (|η|<2) using both hit pairs and reconstructed tracks. For central pseudorapidities (|η|<0.5), the charged-hadron multiplicity density is dNch/dη||η|<0.5=5.49±0.01(stat)±0.17(syst), a value obtained by combining the two methods. The result is compared to predictions from Monte Carlo event generators and to similar measurements made at lower collision energies.

Identified charged hadron production in Pb-Pb collisions at $$\sqrt {s_{NN} } = 2.76$$ TeV with the ALICE experiment at the LHC

Quark Gluon Plasma (QGP) is an unavoidable consequence of Quantum Chromodynamics (QCD). High-energy heavy-ion collisions offer the unique possibility to reproduce in the laboratory the conditions expected during the very first stages of the evolution of the Universe. The ALICE (A Large Ion Collider Experiment) experiment at the Large Hadron Collider (LHC) allows the study of the dense nuclear environment created in nucleus-nucleus collisions. Particle Identification (PID) is one of the key features of the ALICE experiment. Identified particle spectra represent a crucial tool to understand the behaviour of the matter created in high-energy heavy-ion collisions. The transverse momentum p T distributions of identified hadrons contain information about the transverse expansion of the system and constrain the freeze-out properties of the system. Hydrodynamic models have proved to be very successful reproducing a large number of features of heavy-ion collisions (e.g., particle p T distributions, radial flow, elliptic flow, Hanbury Brown-Twiss correlations, ...). The measurement of the p T distributions of identified π, K and p in Pb-Pb collisions at $$\sqrt {s_{NN} } = 2.76$$ TeV is presented and discussed in terms of hydrodynamics. The V0 detector allows the selection of events based on the eccentricity of the collision (related with the initial geometry). This makes possible the study of the correlation between the p T distribution of hadrons and elliptic flow on an event-by-event basis. Hadron abundances can be obtained from the principle of maximum entropy using statistical concepts. This allows the extrapolation of the chemical freeze-out parameters from the data. Over the last years it has been proved that the chemical freeze-out temperature T ch is connected with the phase transition temperature T C . The measurements of the freeze-out parameters at the LHC energies are described in detail and the results obtained by various groups at lower energies are extended with the inclusion of the LHC measurement. The LHC measurements cast a new light upon the hydrodynamic and thermal behaviour of the hadron production in heavy-ion collisions. The possible scenarios are described and commented.

Parton-medium cross-section and average QGP viscosity in lead–lead collisions at the LHC

The recent experimental CMS and E-by-E ATLAS data on the elliptic anisotropy of particles in Pb–Pb collisions are used to extract parton medium cross-section and the quark–gluon plasma (QGP) viscosity-to-entropy ratio within the incomplete equilibration medium model. Our method assumes extrapolation of the measured pseudorapidity spectrum of charged particles to low-pT range. Then the rapidity distribution of both charged and neutral hadrons is restored. The extracted value of the parton-medium cross section is found to be It yields for the ratio of shear viscosity to entropy density in QGP phase. The last result is in a good agreement with the estimates obtained by calculations within the viscous hydrodynamics.