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Journal Article•DOI•

Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scattering

Johannes Blümlein, Bodo Geyer1, Dieter Robaschik2•
Center for Theoretical Studies, University of Miami1, Brandenburg University of Technology2
30 Oct 2006-Nuclear Physics (North-Holland)-Vol. 755, Iss: 1, pp 112-136
TL;DR: In this article, a quantum field theoretic treatment of deep-inelastic diffractive scattering is given, where different diffractive structure functions are expressed through integrals over the relative momentum of non-perturbative t-dependent 2-particle distribution functions.
About: This article is published in Nuclear Physics.The article was published on 2006-10-30 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Momentum transfer & Parton.

Summary (1 min read)

Jump to: [1 Introduction] – [5 Relations between Diffractive Structure Functions] – [5.1 Unpolarized Case] and [6 Conclusions]

1 Introduction

  • This ratio still awaits a rigorous non-perturbative explanation.
  • In section 3 the symmetric part of the Compton amplitude is dealt with, through which the diffractive structure functions for unpolarized nucleons are derived.
  • The polarized structure functions are determined in section 4.
  • In section 5 the authors derive relations between different structure functions and section 6 contains the conclusions.

5 Relations between Diffractive Structure Functions

  • The situation is more involved for the case studied in the present paper, since the structure functions emerge as a ζ−integral of sub-system structure functions, which accounts for the twoparticle nature of the wave-function.
  • Thus the corresponding relations can be established for the un-integrated ζ-dependent functions only.

5.1 Unpolarized Case

  • (5.5) Three of the above distribution functions are independent.
  • As shown in section 3 the respective linear combinations are weighted by different ζ-dependent functions, that in general no relations exist on the level of structure functions.

6 Conclusions

  • The presence of target mass and t-effects enlarges the number of structure functions determining the hadronic tensor.
  • In the unpolarized case four structure functions contribute, which cannot be related to each other directly.
  • In the polarized case the Wandzura-Wilzcek relation remains unbroken and holds even separately for the contributions to the different invariants K a | 5 a=3 .
  • The present formalism can be used in experimental analysis of deep-inelastic diffractive scattering data referring to suitable models for the un-integrated distribution functions depending on ζ, for which rigorous determination using methods of non-perturbative QCD do not yet exits.
  • In this way the structures being derived in the present paper can be tested.

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Citations
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Journal Article•DOI•
Target mass corrections

[...]

I. Schienbein1, Voica Radescu, G P Zeller2, M. Eric Christy3, C. E. Keppel3, C. E. Keppel4, Kevin Scott McFarland5, Wally Melnitchouk4, Fredrick I. Olness1, Mary Hall Reno6, F. M. Steffens7, Ji-Young Yu1 •
Southern Methodist University1, Los Alamos National Laboratory2, Hampton University3, Thomas Jefferson National Accelerator Facility4, University of Rochester5, University of Iowa6, Mackenzie Investments7
01 May 2008-Journal of Physics G
TL;DR: A comprehensive review of these target mass corrections (TMC) to structure functions data, summarizing the relevant formulas for TMCs in electromagnetic and weak processes, is presented in this article.
Abstract: With recent advances in the precision of inclusive lepton–nuclear scattering experiments, it has become apparent that comparable improvements are needed in the accuracy of the theoretical analysis tools. In particular, when extracting parton distribution functions in the large-x region, it is crucial to correct the data for effects associated with the nonzero mass of the target. We present here a comprehensive review of these target mass corrections (TMC) to structure functions data, summarizing the relevant formulas for TMCs in electromagnetic and weak processes. We include a full analysis of both hadronic and partonic masses, and trace how these effects appear in the operator product expansion and the factorized parton model formalism, as well as their limitations when applied to data in the x → 1 limit. We evaluate the numerical effects of TMCs on various structure functions, and compare fits to data with and without these corrections.

70 citations

Journal Article•DOI•
Operator product expansion in QCD in off-forward kinematics: separation of kinematic and dynamical contributions

[...]

Vladimir M. Braun1, Alexander N. Manashov2, Alexander N. Manashov1•
University of Regensburg1, Saint Petersburg State University2
19 Jan 2012-Journal of High Energy Physics
TL;DR: In this article, a general approach to the calculation of target mass and finite t = (p′ − p)2 corrections in hard processes which can be studied in the framework of the operator product expansion and involve momentum transfer from the initial to the final hadron state was developed.
Abstract: We develop a general approach to the calculation of target mass and finite t = (p′ − p)2 corrections in hard processes which can be studied in the framework of the operator product expansion and involve momentum transfer from the initial to the final hadron state. Such corrections, which are usually referred to as kinematic, can be defined as contributions of operators of all twists that can be reduced to total derivatives of the leading twist operators. As the principal result, we provide a set of projection operators that pick up the “kinematic” part of an arbitrary flavor-nonsinglet twist-four operator in QCD. A complete expression is derived for the time-ordered product of two electromagnetic currents that includes all kinematic corrections to twist-four accuracy. The results are immediately applicable to the studies of deeply-virtual Compton scattering, transition γ * → Mγ form factors and related processes. As a byproduct of this study, we find a series of “genuine” twist-four flavor-nonsinglet quark-antiquark-gluon operators which have the same anomalous dimensions as the leading twist quark-antiquark operators.

59 citations

DOI•
3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS

[...]

Alexander Hasselhuhn
13 Jan 2014

21 citations

Cites background from "Target mass and finite momentum tra..."

  • ...This relation also holds for target mass and initial and final state quark mass corrections [144, 298], as well as in case of non-forward [299] and diffractive scattering [300–302]....

    [...]

Journal Article•DOI•
The polarized two-loop massive pure singlet Wilson coefficient for deep-inelastic scattering

[...]

Johannes Blümlein, Clemens G. Raab1, K. Schönwald•
Johannes Kepler University of Linz1
18 Apr 2019-Nuclear Physics
TL;DR: In this paper, the polarized massive two-loop pure singlet Wilson coefficient was calculated analytically in the whole kinematic region and the Wilson coefficient contains Kummer-elliptic integrals.

20 citations

Journal Article•DOI•
Target-mass and finite t corrections to diffractive deep-inelastic scattering

[...]

Johannes Blümlein, Dieter Robaschik1, Bodo Geyer2•
Brandenburg University of Technology1, Leipzig University2
28 Mar 2009-European Physical Journal C
TL;DR: In this paper, the authors considered the off-cone twist-2 light-cone operators to derive the target-mass and finite t corrections to diffractive deep-inelastic scattering and deep-inverse GPD.
Abstract: The quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering given in a previous paper (Blumlein et al. in Nucl. Phys. B 755:112–136, 2006) is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis. We consider the off-cone twist-2 light-cone operators to derive the target-mass and finite t corrections to diffractive deep-inelastic scattering and deep-inelastic scattering. The corrections turn out to be at most proportional to x|t|/Q 2, xM 2/Q 2, x=x BJ or x ℙ, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or meson-exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive GPD or its moments are derived. In the limit t,M 2→0 one obtains the results of (Blumlein and Robaschik in Phys. Lett. B 517:222, 2001) and (Blumlein and Robaschik in Phys. Rev. D 65:096002, 2002).

18 citations

References
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Journal Article•DOI•
Freedom at Moderate Energies: Masses in Color Dynamics

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Howard Georgi1, H. David Politzer1•
Harvard University1
01 Oct 1976-Physical Review D
TL;DR: In this paper, the effects of quark and target masses in lepton-hadron scattering were discussed, assuming a color SU(3) gauge theory of strong interactions, and the best renormalization procedure is to specify all parameters in the Lagrangian (coupling constants and masses) as well as wave function normalizations at Euclidean momenta of scale M.
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19 Dec 1977-Physics Letters B
TL;DR: In this article, an infinite set of approximate sum rules, reducing two kinematically independent structure functions to a single one, are proposed by a combination of general short-distance analysis and arguments about matrix elements.

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University of Manchester1, University of Cambridge2
01 Oct 1984-Nuclear Physics
TL;DR: In this article, high-energy elastic and inelastic scattering at small t are discussed in terms of pomeron and double-pomeron exchange and the similarity between them allows an almost parameter-free description of various elastic process, a and diffraction dissociation, in good agreement with experiment.

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O ( 2 , 1 ) Analysis of Single-Particle Spectra at High Energy

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Alfred H. Mueller1•
Brookhaven National Laboratory1
15 Dec 1970-Physical Review D
TL;DR: In this article, the Pomeranchuk trajectory is shown to be the dominant singularity at high energy, and the existence of pionization and limiting fragmentation is shown in the presence of strong Regge cuts.
Abstract: Processes of the type proton+proton \ensuremath{\rightarrow} pion+anything at high energy are discussed. The differential cross section for such reactions is expressed in terms of a three-particle \ensuremath{\rightarrow} three-particle amplitude. This amplitude is then expanded into $O(2, 1)$ representations. If the Pomeranchuk trajectory is the dominant $O(2, 1)$ singularity at high energy, the existence of pionization and limiting fragmentation is obtained. Furthermore, the pionization products are essentially independent of the target and projectile, while the fragments of the target are independent of the projectile. Modifications in the presence of strong Regge cuts at $J=1$ are discussed.

262 citations

Journal Article•DOI•
Proof of Factorization for Diffractive Hard Scattering

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John Collins1•
Pennsylvania State University1
01 Mar 1998-Physical Review D
TL;DR: In this article, a proof is given that hard-scattering factorization is valid for deep-inelastic processes which are diffractive or have some other condition imposed on the final state in the target fragmentation region.
Abstract: A proof is given that hard-scattering factorization is valid for deep-inelastic processes which are diffractive or which have some other condition imposed on the final state in the target fragmentation region.

255 citations

Related Papers (5)
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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scattering" ?

The different diffractive structure functions are expressed through integrals over the relative momentum of non–perturbative t–dependent 2–particle distribution functions.