Hadronic Initial States Research Articles

The 3D Entangled Structure of the Proton: Transverse Degrees of Freedom in QCD, Momenta, Spins and More

Light-front quantized quark and gluon states (partons) play a dominant role in high energy scattering processes. Initial state hadrons are mixed ensembles of partons, while produced pure partonic states appear as mixed ensembles of hadrons. The transition from collinear hard physics to the 3D structure including partonic transverse momenta is related to confinement which links color and spatial degrees of freedom. We outline ideas on emergent symmetries in the Standard Model and their connection to the 3D structure of hadrons. Wilson loops, including those with light-like Wilson lines such as used in the studies of transverse momentum dependent distribution functions may play a crucial role here, establishing a direct link between transverse spatial degrees of freedom and gluonic degrees of freedom.

ManeParse : A Mathematica reader for Parton Distribution Functions

Parton Distribution Functions (PDFs) are essential non-perturbative inputs for calculation of any observable with hadronic initial states. These PDFs are released by individual groups as discrete grids as a function of the Bjorken-x and energy scale Q. The LHAPDF project maintains a repository of PDFs from various groups in a new standardized LHAPDF6 format, additionally older formats such as the CTEQ PDS grid format are still in use. ManeParse is a package that provides access to PDFs within Mathematica to facilitate calculation and plotting. The program is self-contained so there are no external links to any FORTRAN, C or C++ programs. The package includes the option to use the built-in Mathematica interpolation or a custom cubic Lagrange interpolation routine which allows for flexibility in the extrapolation (particularly at small x-values). ManeParse is fast enough to enable simple calculations (involving even one or two integrations) in the Mathematica framework. Program summaryProgram Title:ManeParseProgram Files doi:http://dx.doi.org/10.17632/knbsccggg4.1Licensing provisions: MITProgramming language:MathematicaNature of problem: PDFs are currently read and interpolated via a FORTRAN or C++ interface. No method exist to read the LHAPDF6 or CTEQ PDFs directly in Mathematica.Solution method: A Mathematica package reads in LHAPDF6 and CTEQ PDF files. The PDFs are parsed into a three-dimensional array in Bjorken-x, scattering energy Q, and parton flavor, and are stored in memory. Provided functions give access to the PDF, the PDF uncertainty, the PDF correlations, and the parton–parton Luminosities. The LHAPDF6 info files are converted from YAML format into Mathematica rules.

Study of the hadronisation process from single hadron and hadron-pair production in SIDIS at COMPASS

Hadron production in hard scattering reactions is described by the hadronization mechanism which combines quarks into final-state hadrons. Within the theoretical framework of leading-twist collinear QCD, the cross section for hadron production in semi-inclusive deep-inelastic scattering can be factorized into a hard scattering cross section describing the hard interaction at the quark level calculable in perturbative QED, and non-perturbative universal functions: parton distribution functions which reflect the quark structure of initial-state hadrons and collinear fragmentation functions which encode details on the hadronization process. In the last decades, a major effort has been achieved on theoretical and experimental levels and allowed to constraint, with very high precision, parton distribution functions except strange quark distribution, which still carries large uncertainties. Fragmentation functions, however, remain at a very preliminary stage of study with a growing interest in a more accurate and precise knowledge. Nowadays, while pion fragmentation functions are known with a limited precision and kaon fragmentation functions are poorly known, the situation for dihadron fragmentation functions turns out to be behind the schedule and no studies or measurements have been yet performed.Measuring both single hadron and hadron pair multiplicities in semi-inclusive deep inelastic scattering at COMPASS represent a fundamental contribution towards a better understanding of the hadronization process and a first measurement for hadron pair multiplicities in SIDIS. These measurements will be presented and discussed.

NLO Corrections in the Initial-state Parton Shower Monte Carlo

The decade-old technique of combining NLO-corrected hard process with LO-level parton shower Monte Carlo is now mature and used in practice of the QCD calculations in the LHC data analysis. The next step, its extension to an NNLO-corrected hard process combined with the NLO-level parton shower Monte Carlo, will require development of the latter component. It does not exist yet in a complete form. In this note we describe recent progress in developing the NLO parton shower for the initial-state hadron beams. The technique of adding NLO corrections in the fully exclusive form (defined in recent years) is now simplified and tested numerically, albeit for a limited set of NLO diagrams in the evolution kernels.

Antenna showers with hadronic initial states

We present an antenna shower formalism including contributions from initial-state partons and corresponding backwards evolution. We give a set of phase-space maps and antenna functions for massless partons which define a complete shower formalism suitable for computing observables with hadronic initial states. We focus on the initial-state components: initial–initial and initial–final antenna configurations. The formalism includes comprehensive possibilities for uncertainty estimates. We report on some preliminary results obtained with an implementation in the Vincia antenna-shower framework.

Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations

Abstract The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required in unintegrated and integrated forms. In view of extending the antenna subtraction method to next-to-next-to-leading order (NNLO) calculations at hadron colliders, we derive the full set of initial-initial double real radiation antenna functions in integrated form.

Fully-unintegrated parton distribution and fragmentation functions at perturbative k⊥

We define and study the properties of generalized beam functions (BFs) and fragmenting jet functions (FJFs), which are fully-unintegrated parton distribution functions (PDFs) and fragmentation functions (FFs) for perturbative k ⊥. We calculate at one loop the coefficients for matching them onto standard PDFs and FFs, correcting previous results for the BFs in the literature. Technical subtleties when measuring transverse momentum in dimensional regularization are clarified, and this enables us to renormalize in momentum space. Generalized BFs describe the distribution in the full four-momentum k μ of a colliding parton taken out of an initial-state hadron, and therefore characterize the collinear initial-state radiation. We illustrate their importance through a factorization theorem for pp → ℓ+ℓ− + 0 jets, where the transverse momentum of the lepton pair is measured. Generalized FJFs are relevant for the analysis of semi-inclusive processes where the full momentum of a hadron, fragmenting from a jet with constrained invariant mass, is measured. Their significance is shown for the example of e + e − → dijet + h, where the perpendicular momentum of the fragmenting hadron with respect to the thrust axis is measured.

Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations

The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required. In view of extending the antenna subtraction method to next-to-next-to-leading order (NNLO) calculations at hadron colliders, we derive the one-loop initial-initial antenna functions in unintegrated and integrated form.

Longitudinal fluctuations in the partonic and hadronic initial state

Collective flow in collisions between lead nuclei at the CERN Large Hadron Collider (LHC) are influenced by random initial state fluctuations, especially for odd harmonics. Here we extend fluctuation studies to longitudinal fluctuations, which may have significant effect on the rapidity distribution of odd harmonics. Furthermore center-of-mass rapidity fluctuations are measurable, but not yet analyzed. Here in the PACIAE parton and hadron molecular dynamics model we make an analysis of initial state fluctuations. As previous analyses have discussed mainly the effects of fluctuations on eccentricity and the elliptic flow we pay particular attention to the fluctuations of the center-of-mass rapidity of the system, which is conservatively estimated in our model as $\ensuremath{\Delta}{y}_{\mathrm{c}.\mathrm{m}.}=0.1$, by neglecting all pre-equilibrium emission effects that increase the ${y}_{\mathrm{c}.\mathrm{m}.}$ fluctuations.

Kaon and Lambda productions in relativistic heavy ion collisions

A microscopic approach has been employed to study the kaon and $\Lambda$ productions in heavy ion collisions. The productions of $K^+$ and $\Lambda$ have been studied within the framework of Boltzmann transport equation for various beam energies. We find a non-monotonic horn like structure for $K^+/\pi^+$ and $\Lambda/\pi$ when plotted against centre of mass energies ($\sqrt s_{\mathrm NN}$) with the assumption of initial partonic phase for $\sqrt s_{\mathrm NN}$ beyond a certain threshold. However, the ratio $K^+/\pi^+$ shows a monotonic nature when a hadronic initial state is considered for all $\sqrt s_{\mathrm NN}$. Experimental values of $K^-/\pi^-$ for different $\sqrt{s_{\mathrm NN}}$ are also reproduced within the ambit of the same formalism.

Gauge links for transverse momentum dependent correlators at tree-level

In this paper we discuss the incorporation of gauge links in hadronic matrix elements that describe the soft hadronic physics in high energy scattering processes. In this description the matrix elements appear in soft correlators and they contain non-local combinations of quark and gluon fields. In our description we go beyond the collinear approach in which case also the dependence on transverse momenta of partons is taken into consideration. The non-locality in the transverse direction leads to a complex gauge link structure for the full process, in which color is entangled, even at tree-level. We show that at tree-level in a 1-parton unintegrated (1PU) situation, in which only the transverse momentum of one of the initial state hadrons is relevant, one can get a factorized expression involving transverse momentum dependent (TMD) distribution functions. We point out problems at the level of two initial state hadrons, even for relatively simple processes such as Drell-Yan scattering.

Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours

The antenna subtraction formalism allows to calculate QCD corrections to jet observables. Within this formalism, the subtraction terms are constructed using antenna functions describing all unresolved radiation between a pair of hard radiatior partons. In this paper, we focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at NNLO. An essential ingredient to these subtraction terms are the four-parton antenna functions with both radiators in the initial state. We outline the construction of the double real subtraction terms, classify all relevant antenna functions and describe their integration over the relevant antenna phase space. For the initial-initial antenna functions with two quark flavours, we derive the phase space master integrals and obtain the integrated antennae.

A search for heavy Kaluza-Klein electroweak gauge bosons at the LHC

The feasibility for the observation of a certain leptonic Kaluza-Klein (KK) hard process in {\em pp} interactions at the LHC is presented. Within the $S^1/Z_2$ TeV$^{-1}$ extra dimensional theoretical framework with the focus on the KK excitations of the Standard Model $\gamma$ and $Z^0$ gauge bosons, the hard-process, $f\bar f \to \sum_n\left(\gamma^*/Z^*\right)_n \to F \bar F$, has been used where $f$ is the initial state parton, $F$ the final state lepton and $\left(\gamma^*/Z^*\right)_{n}$ is the $n^{\rm th}$ KK excitation of the $\gamma/Z^0$ boson. For this study the analytic form for the hard process cross section has been independently calculated by the authors and has been implemented using the {\sc Moses} framework. The Moses framework itself, that has been written by the authors, was used as an external process within the {\sc Pythia} Monte Carlo generator which provides the phase space generation for the final state leptons and partons from the initial state hadrons, and the simulation of initial and final state radiation and hadronization. A brief discussion of the possibility for observing and identifying the unique signature of the KK signal given the current LHC program is also presented.

The “horn” in the kaon-to-pion ratio

A microscopic approach has been employed to study the kaon productions in heavy ion collisions. The momentum integrated Boltzmann equation has been used to study the evolution of strangeness in the system formed in heavy ion collision at relativistic energies. The kaon productions have been calculated for different centre of mass energies ($\sqrt{s_{\mathrm {NN}}}$) ranging from AGS to RHIC. The results have been compared with available experimental data. We obtain a non-monotonic horn like structure for $K^+/\pi^+$ when plotted with $\sqrt{s_{\mathrm {NN}}}$ with the assumption of an initial partonic phase beyond a certain threshold in $\sqrt{s_{NN}}$. However, a monotonic rise of $K^+/\pi^+$ is observed when a hadronic initial state is assumed for all $\sqrt{s_{\mathrm {NN}}}$. Experimental values of $K^-/\pi^-$ are also reproduced within the ambit of the same formalism. Results from scenarios where the strange quarks and hadrons are formed in equilibrium and evolves with and without secondary productions have also been presented.

Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes.

Subtraction with hadronic initial states at NLO: an NNLO-compatible scheme

We present an NNLO-compatible subtraction scheme for computing QCD jet cross sections of hadron-initiated processes at NLO accuracy. The scheme is constructed specifically with those complications in mind, that emerge when extending the subtraction algorithm to next-to-next-to-leading order. It is therefore possible to embed the present scheme in a full NNLO computation without any modifications.

Exploring the partonic structure of hadrons through the Drell–Yan process

The Drell–Yan process is a standard tool for probing the partonic structure of hadrons. Since the process proceeds through a quark–antiquark annihilation, Drell–Yan scattering possesses a unique ability to selectively probe sea distributions. This review examines the application of Drell–Yan scattering to elucidating the flavour asymmetry of the nucleon's sea and nuclear modifications to the sea quark distributions in unpolarized scattering. Polarized beams and targets add an exciting new dimension to Drell–Yan scattering. In particular, the two initial-state hadrons give Drell–Yan sensitivity to chirally odd transversity distributions.

Antenna subtraction with hadronic initial states

The antenna subtraction method for the computation of higher order corrections to jet observables and exclusive cross sections at collider experiments is extended to include hadronic initial states. In addition to the already known antenna subtraction with both radiators in the final state (final-final antennae), we introduce antenna subtractions with one or two radiators in the initial state (initial-final or initial-initial antennae). For those, we derive the phase space factorization and discuss the allowed phase space mappings at NLO and NNLO. We present integrated forms for all antenna functions relevant to NLO calculations, and describe the construction of the full antenna subtraction terms at NLO on two examples. The extension of the formalism to NNLO is outlined.

Fragmentation, nonrelativistic QCD, and NNLO factorization analysis in heavy quarkonium production

We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-p_T particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the NRQCD formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include nonabelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at NNLO, and verify that they are absorbed into the new, gauge invariant matrix elements.

Charm contribution to the proton structure function in deep-inelastic ep scattering at the HERA collider

The structure function F2c is evaluated within the charm-production model based on perturbative QCD. The results are compared with H1 and ZEUS data obtained at the HERA collider. It is shown that, for D*-meson production, the spectator mechanism, which is independent of the flavors of the hadronic-remnant quarks, comes into play for pT>10 GeV and that, in calculating charm production in the kinematical domain studied at the HERA collider, it is not necessary to take into account the evolution of the c-quark distribution in the initial-state hadron.