scispace - formally typeset
Search or ask a question
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.

Did you find this useful? Give us your feedback

Figures (1)
Citations
More filters
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
More filters
Journal Article•DOI•
Diffractive deep inelastic lepton scattering

[...]

A. Donnachie1, Peter Landshoff2•
University of Manchester1, University of Cambridge2
11 Jun 1987-Physics Letters B
TL;DR: In this paper, the structure function of the pomeron was calculated for deep inelastic lepton scattering events in which the target proton emerges isolated in rapidly and has its momentum changed very little by the scattering.

131 citations

Journal Article•DOI•
Target mass corrections for polarized structure functions and new sum rules

[...]

Johannes Blümlein, Avtandil Tkabladze
26 Jul 1999-Nuclear Physics
TL;DR: In this article, the impact of the target mass corrections on the general relations between the twist-2 and twist-3 parts of the structure functions is studied and three new relations between these parts are derived.

101 citations

Journal Article•DOI•
Short-distance and light-cone expansions for products of currents

[...]

S.A Anikin, O.I Zavialov
01 Nov 1978-Annals of Physics
TL;DR: In this paper, short distance and light-cone expansions for T-ordered products of currents are derived in the framework of the arbitrary order of the perturbation theory, where the light cone expansion is derived from the shortest distance.

95 citations

Journal Article•DOI•
Erratum: Proof of factorization for diffractive hard scattering [Phys. Rev. D 57, 3051 (1998)]

[...]

John Collins
29 Nov 1999-Physical Review D

93 citations

Book•
Renormalized Quantum Field Theory

[...]

O. I. Zavialov
28 Feb 1990
TL;DR: In this article, the authors present an analytical approach to Renormalized Feynman Diagrams, which can be seen as a form of R-Operation with non-zero subtraction points or other subtraction operators.
Abstract: I. Elements of Quantum Field Theory.- 1. Quantum Free Fields.- 1.1. Fock Space.- 1.2. Free Real Scalar Field.- 1.3. Other Free Fields.- 2. The Chronological Products of Local Monomials of the Free Field.- 2.1. Wick Theorem.- 2.2. Wick Theorem for Chronological Products of Free Fields.- 2.3. Regularized T-Products.- 2.4. Ambiguity in the Choice of Chronological Products.- 3. Interacting Fields.- 3.1. Interpolating Heisenberg Field.- 3.2. Connection Between Two Systems of Axioms.- 3.3. T-Exponential, Lagrangian, Renormalization Constants.- 3.4. Green Functions, Functional Integral, Euclidean Quantum Field Theory.- 3.5. Interaction Lagrangians.- II. Parametric Representations for Feynman Diagrams. R-Operation.- 1. Regularized Feynman Diagrams.- 1.1. Intermediate Regularization. Divergency Index.- 1.2. Parametric Representation for Regularized Diagrams.- 1.3. The Proof of Statements (16)-(21).- 1.4. Parametric Representations in Other Dimensions and in Euclidean Theory. Coordinate Representation.- 2. Bogoliubov-Parasiuk R-Operation.- 2.1. Subtraction Operators M and Finite Renormalization Operators P. Definition of R-Operation.- 2.2. The Structure of the R-Operation.- 2.3. R-Operation with Non-Zero Subtraction Points or Other Subtraction Operators.- 3. Parametric Representations for Renormalized Diagrams.- 3.1. Renormalization over Forests.- 3.2. Non-Zero Subtraction Points.- 3.3. Renormalization over Nests.- 3.4. Renormalization by Means of Integral Operators.- III. Bogoliubov-Parasiuk Theorem. Other Renormalization Schemes.- 1. Existence of Renormalized Feynman Amplitudes.- 1.1. Division of the Integration Domain into Sectors. The Equivalence Classes of Nests.- 1.2. The Ultraviolet Convergence of Parametric Integrals.- 1.3. The Limit ? ? 0.- 2. Infrared Divergencies and Renormalization in Massless Theories.- 2.1. Infrared Convergence of Regularized Amplitudes.- 2.2. Illustrations and Heuristic Arguments.- 2.3. Classification of Theories.- 2.4. Ultraviolet Renormalization.- 2.5. More Refined Arguments.- 3. The Proof of Theorems 1 and 2.- 3.1. Preliminaries.- 3.2. Basic Lemma.- 3.3. Theorem 1. The Case of a Diagram without Massive Lines.- 3.4. Theorem 1. The Case of a Diagram with Massive Lines.- 3.5. The Scheme of the Proof for Theorem 2.- 3.6. The Structure of the Forms D, A, Bl, Kij.- 3.7. Transition from the Space S?(R4v \ {q = 0}) to the Space S?(R4v \ E).- 4. Analytic Renormalization and Dimensional Renormalization.- 4.1. Introductory Remarks.- 4.2. The Recipe for Analytic Renormalization.- 4.3. The Equivalence of R-Operation and Analytic Renormalization.- 4.4. Dimensional Renormalization.- 4.5. The Parametric Representation in the Case of Dimensional Renormalization.- 4.6. Equivalence of the Dimensional Renormalization and R-Operation.- 4.7. Modifications. Zero Mass Theories.- 4.8. Examples.- 5. Renormalization 'without Subtraction'. Renormalization 'over Asymptotes'.- 5.1. Intermediate Regularization and the Recipe of Renormalization 'without Subtraction'.- 5.2. The Equivalence of the R-Operation and the Renormalization 'without Subtractions'.- 5.3. Renormalization 'over Asymptotes'.- IV. Composite Fields. Singularities of the Product of Currents at Short Distances and on the Light Cone.- 1. Renormalized Composite Fields.- 1.1. Basic Notions and Notations.- 1.2. The Subtraction Operator M.- 1.3. The Structure of Renormalization.- 1.4. Generalized Action Principle.- 1.5. Zimmermann Identities.- 2. Products of Fields at Short Distances.- 2.1. A Lowest Order Example.- 2.2. Wilson Expansions.- 2.3. A Massless Case.- 2.4. An Important Particular Case.- 3. Products of Currents at Short Distances.- 3.1. Short-Distance Expansions for Products of Currents.- 3.2. The Proof of the Lemma.- 3.3. The Structure of Renormalization with Incomplete Subgraphs. The Short-Distance Expansion in the Weinberg Renormalization Scheme.- 4. Products of Currents near the Light Cone.- 4.1. Lower Order Consideration.- 4.2. Subtraction Operator $$ {\bar m^{\left( {\rm{a}} \right)}} $$. Light-Ray Fields.- 4.3. The Light-Cone Theorem.- 4.4. An Example. General Discussion. A Massless Case.- 5. Equations for Composite Fields.- 5.1. Equations of Motion for the Interpolating Field.- 5.2. Equations for Higher Composite Fields.- 5.3. The Proof of Relations (273) and (276).- 5.4. Renorm-Group Equations and Callan-Symanzik Equations.- 6. Equations for Regularized Green Functions.- 6.1. Relation of Renormalization Constants to Green Functions.- 6.2. Relations of Green Functions to Derivatives of the Renormalization Constants.- V. Renormalization of Yang-Mills Theories.- 1. Classical Theory and Quantization.- 1.1. Classical Yang-Mills Fields.- 1.2. Quantization.- 1.3. Fields of Matter. Abelian Theory.- 2. Gauge Invariance and Invariant Renormalizability.- 2.1. Abelian Theories. Ward Identities.- 2.2. Non-Abelian Yang-Mills Theories. BRST Symmetry. Slavnov Identities.- 2.3. A Linear Condition for the Gauge Invariance of Non-Abelian Yang-Mills Theories.- 2.4. The Structure of Subtractions.- 2.5. Invariant Renormalizability of the Yang-Mills Theory.- 3. Invariant Regularization and invariant Renormalization Schemes.- 3.1. Preliminary Discussion.- 3.2. Scalar Electrodynamics. Recipes for Regularization.- 3.3. Scalar Electrodynamics. Arguments in Favour of the Recipe.- 3.4. Spinor Electrodynamics. Recipes for Regularization.- 3.5. Spinor Electrodynamics. Argumentation.- 3.6. Examples and Remarks.- 3.7. Non-Abelian Yang-Mills Theories.- 3.8. An Example: Gluon Polarization Operator. Arguments.- 4. Anomalies.- 4.1. Is It Always Possible to Retain a Classical Symmetry in a Quantum Field Theory?.- 4.2. Main Statements.- 4.3. Heuristic Check of Ward Identities (Momentum Representation).- 4.4. The Triangle Diagram in the ?-Representation.- 4.5. Ward Identities.- Appendix. On Methods of Studying Deep-Inelastic Scattering.- A.1. Deep-Inelastic Scattering.- A.2. The Traditional Approach to Deep-Inelastic Scattering.- A.3. The Non-Local Light-Cone Expansion as the Basic Tool to Study Deep-Inelastic Scattering.- A Guide to Literature.- References.

92 citations

Related Papers (5)
Scaling violations of diffractive structure functions: operator approach

[...]

27 Sep 2001-Physics Letters B
Johannes Blümlein, Dieter Robaschik
Polarized deep inelastic diffractive ep scattering: Operator approach

[...]

16 Apr 2002-Physical Review D
Johannes Blümlein, Dieter Robaschik
Gluon radiation in diffractive electroproduction

[...]

03 Mar 1997-Nuclear Physics
W. Buchmuller, M.F. McDermott, Arthur Hebecker
Positivity constraints for anomalous dimensions

[...]

22 Oct 1973-Nuclear Physics
Otto Nachtmann, Otto Nachtmann
Target mass corrections for polarized structure functions and new sum rules

[...]

26 Jul 1999-Nuclear Physics
Johannes Blümlein, Avtandil Tkabladze
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.