Distribution Functions

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P J Mulders - One of the best experts on this subject based on the ideXlab platform.

  • non universality of transverse momentum dependent parton Distribution Functions
    Nuclear Physics, 2008
    Co-Authors: C J Bomhof, P J Mulders
    Abstract:

    Abstract In the field theoretical description of hadronic scattering processes, single transverse-spin asymmetries arise due to gluon initial and final state interactions. These interactions lead to process dependent Wilson lines in the operator definitions of transverse momentum dependent parton Distribution Functions. In particular for hadronhadron scattering processes with hadronic final states this has important ramifications for possible factorization formulas in terms of (non)universal TMD parton Distribution Functions. In this paper we will systematically separate the universality-breaking parts of the TMD parton correlators from the universal T -even and T -odd parts. This might play an important role in future factorization studies for these processes. We also show that such factorization theorems will (amongst others) involve the gluonic pole cross sections, which have previously been shown to describe the hard partonic scattering in weighted spin asymmetries.

  • time reversal odd Distribution Functions in leptoproduction
    Physical Review D, 1998
    Co-Authors: Daniel Boer, P J Mulders
    Abstract:

    We consider the various asymmetries, notably single spin asymmetries, that appear in leptoproduction as a consequence of the presence of time-reversal odd Distribution Functions. This could facilitate experimental searches for time-reversal odd phenomena.

A V Radyushkin - One of the best experts on this subject based on the ideXlab platform.

  • quasi parton Distribution Functions momentum Distributions and pseudo parton Distribution Functions
    Physical Review D, 2017
    Co-Authors: A V Radyushkin
    Abstract:

    We show that quasi-parton Distribution Functions (quasi-PDFs) may be treated as hybrids of PDFs and primordial rest-frame momentum Distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p3≳3  GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs P(x,z32) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time Distributions M(ν,z32), the Functions of the Ioffe time ν=p3z3 and the distance parameter z32 with respect to which it displays perturbative evolution for small z3. In this form, one may divide out the z32 dependence coming from the primordial rest-frame Distribution and from the problematic factor due to lattice renormalization of the gauge link. The ν dependence remains intact and determines the shape of PDFs.

  • quasi parton Distribution Functions momentum Distributions and pseudo parton Distribution Functions
    Physical Review D, 2017
    Co-Authors: A V Radyushkin
    Abstract:

    We show that quasi-parton Distribution Functions (quasi-PDFs) may be treated as hybrids of PDFs and primordial rest-frame momentum Distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large ${p}_{3}\ensuremath{\gtrsim}3\text{ }\text{ }\mathrm{GeV}$ momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs $\mathcal{P}(x,{z}_{3}^{2})$ that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time Distributions $\mathcal{M}(\ensuremath{\nu},{z}_{3}^{2})$, the Functions of the Ioffe time $\ensuremath{\nu}={p}_{3}{z}_{3}$ and the distance parameter ${z}_{3}^{2}$ with respect to which it displays perturbative evolution for small ${z}_{3}$. In this form, one may divide out the ${z}_{3}^{2}$ dependence coming from the primordial rest-frame Distribution and from the problematic factor due to lattice renormalization of the gauge link. The $\ensuremath{\nu}$ dependence remains intact and determines the shape of PDFs.

Hansjoachim Drescher - One of the best experts on this subject based on the ideXlab platform.

  • model dependence of lateral Distribution Functions of high energy cosmic ray air showers
    Astroparticle Physics, 2004
    Co-Authors: Hansjoachim Drescher, Marcus Bleicher, S Soff, H Stocker
    Abstract:

    Abstract The influence of high and low energy hadronic models on lateral Distribution Functions of cosmic ray air showers for Auger energies is explored. A large variety of presently used high and low energy hadron interaction models are analysed and the resulting lateral Distribution Functions are compared. We show that the slope depends on both the high and low energy hadronic model used. The models are confronted with available hadron–nucleus data from accelerator experiments.

  • dominant contributions to lateral Distribution Functions in ultra high energy cosmic ray air showers
    Astroparticle Physics, 2003
    Co-Authors: Hansjoachim Drescher, G Farrar
    Abstract:

    In hadron induced air showers of highest energies (E>1018 eV), the lateral Distribution Functions of electrons and muons are a superposition of many separate electromagnetic sub-showers, initiated by meson decay at different altitudes and energies. The lateral Distribution function is the primary tool for reconstructing the energy of the primary in a UHE cosmic ray shower, so understanding it in detail is a prerequisite for having confidence in the energy determination. We analyze in this paper the dominant contributions to the ground level lateral Distribution Functions, as a function of the altitude and energy at which the sub-showers are initiated. Far from the core, the dominant contribution to the density of electrons comes from sub-showers initiated at low altitudes and low energies (E<100 GeV). The dominant sub-showers are initiated at large radial distance from the core and at a large angle with respect to the main shower axis. This demonstrates the need for careful treatment of low energy hadron physics modeling even for ultrahigh energy primaries.

Christoph Hinz - One of the best experts on this subject based on the ideXlab platform.

  • Using radius frequency Distribution Functions as a metric for quantifying root systems
    Plant and Soil, 2010
    Co-Authors: Craig A. Scanlan, Christoph Hinz
    Abstract:

    Root radius frequency Distributions have been measured to quantify\nthe effect of plant type, environment and methodology on root systems,\nhowever, to date the results of such studies have not been synthesised.\nWe propose that cumulative frequency Distribution Functions can be\nused as a metric to describe root systems because (1) statistical\nproperties of the frequency Distribution can be determined, (2) the\nparameters for these can be used as a means of comparison, and (3)\nthe analytical expressions can be easily incorporated into models\nthat are dependent upon root geometry. We collated a database of\n96 root radii frequency Distributions and botanical and methodology\ntraits for each Distribution. To determine if there was a frequency\nDistribution function that was best suited to root radii measurements\nwe fitted the exponential, Rayleigh, normal, log-normal, logistic\nand Weibull cumulative Distribution Functions to each Distribution\nin our database. We found that the log-normal function provided the\nbest fit to these Distributions and that none of the Distribution\nFunctions was better or worse suited to particular shapes. We derived\nanalytical expressions for root surface and volume and found that\nthey are a valid, and simpler method for incorporating root architectural\ntraits into analytical models. We also found that growth habit and\ngrowth media had a significant effect on mean root radius.

N G Stefanis - One of the best experts on this subject based on the ideXlab platform.

  • renormalization wilson lines and transverse momentum dependent parton Distribution Functions
    Physical Review D, 2008
    Co-Authors: I O Cherednikov, N G Stefanis
    Abstract:

    We perform an analysis of transverse-momentum dependent parton-Distribution Functions, making use of their renormalization properties in terms of their leading-order anomalous dimensions. We show that the appropriate Wilson line in the light cone gauge, associated with such quantities, is a cusped one at light cone infinity. To cancel the ensuing cusp anomalous dimension, we include in the definition of the transverse-momentum dependent parton-Distribution Functions an additional soft counter term (gauge link) along that cusped transverse contour. We demonstrate that this is tantamount to an 'intrinsic (Coulomb) phase', which accumulates the full gauge history of the color-charged particle.