Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

Kanazawa, Koichi; Pitonyak, Daniel; Koike, Yuji; Metz, Andreas; Schlegel, Marc

doi:10.1103/PhysRevD.93.054024

Title: Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

Abstract

We investigate the behavior under Lorentz transformations of perturbative coefficient functions in a collinear twist-3 formalism relevant for high-energy observables including transverse polarization of hadrons. We argue that those perturbative coefficient functions can, a priori, acquire quite different yet Lorentz-invariant forms in various frames. This somewhat surprising difference can be traced back to a general dependence of the perturbative coefficient functions on light cone vectors which are introduced by the twist-3 factorization formulas and which are frame-dependent. One can remove this spurious frame dependence by invoking so-called Lorentz invariance relations (LIRs) between twist-3 parton correlation functions. Some of those relations for twist-3 distribution functions were discussed in the literature before. In this paper we derive the corresponding LIRs for twist-3 fragmentation functions. We explicitly demonstrate that these LIRs remove the light cone vector dependence by considering transverse spin observables in the single-inclusive production of hadrons in lepton-nucleon collisions, ℓN→hX. Furthermore, with the LIRs in hand, we also show that twist-3 observables in general can be written solely in terms of three-parton correlation functions.

Authors:

Kanazawa, Koichi ^[1]; Pitonyak, Daniel ^[2]; Koike, Yuji ^[3]; Metz, Andreas ^[1]; Schlegel, Marc ^[4]

Temple Univ., Philadelphia, PA (United States)
Brookhaven National Lab. (BNL), Upton, NY (United States)
Niigata Univ., Niigata (Japan)
Univ. of Tubingen, Tubingen (Germany)

Publication Date:: Mon Mar 14 00:00:00 EDT 2016

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1246800

Report Number(s):: BNL-111976-2016-JA
Journal ID: ISSN 2470-0010; PRVDAQ; R&D Project: PO-3

Grant/Contract Number:: SC00112704

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Riken BNL Research Center

Citation Formats


                    Kanazawa, Koichi, Pitonyak, Daniel, Koike, Yuji, Metz, Andreas, and Schlegel, Marc. Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.93.054024.

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                    Kanazawa, Koichi, Pitonyak, Daniel, Koike, Yuji, Metz, Andreas, & Schlegel, Marc. Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables.  United States.  https://doi.org/10.1103/PhysRevD.93.054024

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                    Kanazawa, Koichi, Pitonyak, Daniel, Koike, Yuji, Metz, Andreas, and Schlegel, Marc. Mon .  
"Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables".  United States.  https://doi.org/10.1103/PhysRevD.93.054024.  https://www.osti.gov/servlets/purl/1246800.

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@article{osti_1246800,

  title        = {Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables},

  author       = {Kanazawa, Koichi and Pitonyak, Daniel and Koike, Yuji and Metz, Andreas and Schlegel, Marc},

  abstractNote = {We investigate the behavior under Lorentz transformations of perturbative coefficient functions in a collinear twist-3 formalism relevant for high-energy observables including transverse polarization of hadrons. We argue that those perturbative coefficient functions can, a priori, acquire quite different yet Lorentz-invariant forms in various frames. This somewhat surprising difference can be traced back to a general dependence of the perturbative coefficient functions on light cone vectors which are introduced by the twist-3 factorization formulas and which are frame-dependent. One can remove this spurious frame dependence by invoking so-called Lorentz invariance relations (LIRs) between twist-3 parton correlation functions. Some of those relations for twist-3 distribution functions were discussed in the literature before. In this paper we derive the corresponding LIRs for twist-3 fragmentation functions. We explicitly demonstrate that these LIRs remove the light cone vector dependence by considering transverse spin observables in the single-inclusive production of hadrons in lepton-nucleon collisions, ℓN→hX. Furthermore, with the LIRs in hand, we also show that twist-3 observables in general can be written solely in terms of three-parton correlation functions.},

  doi          = {10.1103/PhysRevD.93.054024},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 93,

  place        = {United States},

  year         = {Mon Mar 14 00:00:00 EDT 2016},

  month        = {Mon Mar 14 00:00:00 EDT 2016}

}

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Title: Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

Abstract

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Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks journal, December 1977

What can break the Wandzura-Wilczek relation? journal, November 2009

Possible Tests of C st and T st Invariances in l ± + N → l ± + Γ and A → B + e + + e − journal, March 1966

Transverse single spin asymmetries in inclusive deep-inelastic scattering journal, December 2006

Transverse target spin asymmetry in inclusive DIS with two-photon exchange journal, January 2008

Partonic description of the transverse target single-spin asymmetry in inclusive deep-inelastic scattering journal, February 2013

Search for a two-photon exchange contribution to inclusive deep-inelastic scattering journal, January 2010

Measurement of the Target-Normal Single-Spin Asymmetry in Deep-Inelastic Scattering from the Reaction He 3 ↑ ( e , e ′ ) X journal, July 2014

Transverse target single-spin asymmetry in inclusive electroproduction of charged pions and kaons journal, January 2014

Single spin asymmetries of inclusive hadrons produced in electron scattering from a transversely polarized 3 He target journal, April 2014

Transverse polarization of Λ hyperons from quasireal photoproduction on nuclei journal, October 2014

Exploring the structure of the proton through polarization observables in l p → jet X journal, August 2011

Left-right spin asymmetry in ℓ N ↑ → h X journal, October 2014

Longitudinal–transverse double-spin asymmetries in single-inclusive leptoproduction of hadrons journal, March 2015

Single-spin asymmetries in the leptoproduction of transversely polarized Λ hyperons journal, May 2015

Single-inclusive production of hadrons and jets in lepton-nucleon scattering at NLO journal, July 2015

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, February 1996

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, January 1997

Asymmetries in polarized hadron production in e+e− annihilation up to order journal, October 1997

Production of dimuons from high-energy polarized proton-proton collisions journal, May 1979

Chiral-odd parton distributions and polarized Drell-Yan process journal, July 1991

Chiral-odd parton distributions and Drell-Yan processes journal, May 1992

Measurement of Asymmetries of Inclusive Pion Production in Proton-Proton Interactions at 6 and 11.8 GeV/ c
journal, April 1976

$Λ^{0}$ Hyperon Polarization in Inclusive Production by 300-GeV Protons on Beryllium
journal, May 1976

Comparison of spin asymmetries and cross sections in π0 production by 200 GeV polarized antiprotons and protons
journal, May 1991

Analyzing power in inclusive π+ and π− production at high xF with a 200 GeV polarized proton beam
journal, August 1991

Large analyzing power in inclusive π± production at high xF with a 22-GeV/c polarized proton beam
journal, July 1999

Measurement of analyzing powers of $π^{+}$ and $π^{-}$ produced on a hydrogen and a carbon target with a $22 - GeV / c$ incident polarized proton beam
journal, May 2002

Cross Sections and Transverse Single-Spin Asymmetries in Forward Neutral-Pion Production from Proton Collisions at $\sqrt{s} = 200 GeV$
journal, April 2004

Forward Neutral-Pion Transverse Single-Spin Asymmetries in $p + p$ Collisions at $\sqrt{s} = 200 GeV$
journal, November 2008

Measurement of Transverse Single-Spin Asymmetries for Midrapidity Production of Neutral Pions and Charged Hadrons in Polarized $p + p$ Collisions at $\sqrt{s} = 200 GeV$
journal, November 2005

Single Spin Asymmetries of Identified Hadrons in Polarized p+p at s = 62.4 and 200 GeV
conference, January 2007

Single-Transverse-Spin Asymmetries of Identified Charged Hadrons in Polarized $p p$ Collisions at $\sqrt{s} = 62.4 GeV$
journal, July 2008

Longitudinal and transverse spin asymmetries for inclusive jet production at mid-rapidity in polarized $p + p$ collisions at $\sqrt{s} = 200 GeV$
journal, August 2012

Transverse single-spin asymmetry and cross section for $π^{0}$ and $η$ mesons at large Feynman $x$ in $p^{↑} + p$ collisions at $\sqrt{s} = 200 GeV$
journal, September 2012

Cross sections and transverse single-spin asymmetries in forward jet production from proton collisions at $\sqrt{s} = 500 GeV$
journal, November 2015

Measurement of transverse-single-spin asymmetries for midrapidity and forward-rapidity production of hadrons in polarized $p + p$ collisions at $\sqrt{s} = 200$ and 62.4 GeV
journal, July 2014

Cross section and transverse single-spin asymmetry of $η$ mesons in $p^{↑} + p$ collisions at $\sqrt{s} = 200 GeV$ at forward rapidity
journal, October 2014

QCD asymmetry and polarized hadron structure function measurement
journal, January 1985

Single transverse spin asymmetries
journal, October 1991

Single transverse spin asymmetries in direct photon production
journal, July 1992

Single transverse-spin asymmetries in hadronic pion production
journal, November 1998

Chiral-odd contribution to single-transverse spin asymmetry in hadronic pion production
journal, April 2000

Estimate of a chiral-odd contribution to single transverse-spin asymmetry in hadronic pion production
journal, September 2000

Single transverse spin asymmetry for large- pion production in semi-inclusive deep inelastic scattering
journal, September 2006

Single transverse-spin asymmetry in high transverse momentum pion production in $p p$ collisions
journal, December 2006

Twist-3 formalism for single transverse spin asymmetry reexamined: Semi-inclusive deep inelastic scattering
journal, February 2007

Master formula for twist-3 soft-gluon-pole mechanism to single transverse-spin asymmetry
journal, March 2007

Erratum to: “Master formula for twist-3 soft-gluon-pole mechanism to single transverse-spin asymmetry” [Phys. Lett. B 646 (2007) 232]
journal, October 2008

Universal structure of twist-3 soft-gluon-pole cross sections for single transverse-spin asymmetry
journal, July 2007

Soft-fermion-pole contribution to single-spin asymmetry for pion production in pp collisions
journal, May 2009

Collins Function and the Single Transverse Spin Asymmetry
journal, July 2009

Twist-three fragmentation function contribution to the single spin asymmetry in pp collisions
journal, August 2010

New analysis of the single transverse-spin asymmetry for hadron production at RHIC
journal, August 2010

A phenomenological study of single transverse-spin asymmetry for inclusive light-hadron productions at RHIC
journal, June 2011

Fragmentation contribution to the transverse single-spin asymmetry in proton–proton collisions
journal, June 2013

Contribution of the twist-3 fragmentation function to the single transverse-spin asymmetry in semi-inclusive deep inelastic scattering
journal, October 2013

Three-gluon contribution to the single spin asymmetry for light hadron production in $p p$ collision
journal, February 2014

Transverse spin asymmetries for W-production in proton–proton collisions
journal, May 2011

Transverse momentum dependent twist-three result for polarized Drell-Yan processes
journal, December 2011

Double spin asymmetry ALT in direct photon production
journal, June 2012

Analysis of the double-spin asymmetry $A_{L T}$ in inelastic nucleon-nucleon collisions
journal, December 2012

Double-spin asymmetry $A_{L T}$ in open charm production
journal, July 2013

Twist-3 fragmentation effects for A LT in light hadron production from proton–proton collisions
journal, January 2016

Contribution of twist-3 multigluon correlation functions to single spin asymmetry in semi-inclusive deep inelastic scattering
journal, September 2010

Master formula for the three-gluon contribution to single spin asymmetry in semi-inclusive deep inelastic scattering
journal, June 2011

Probing the three-gluon correlation functions by the single spin asymmetry in $p^{↑} p \to D X$
journal, July 2011

Three-gluon contribution to the single spin asymmetry in Drell-Yan and direct-photon processes
journal, February 2012

Single-spin production asymmetries from the hard scattering of pointlike constituents
journal, January 1990

Hard-scattering scaling laws for single-spin production asymmetries
journal, January 1991

Observation concerning the process dependence of the Sivers functions
journal, May 2011

Global fitting of single spin asymmetry: An attempt
journal, April 2012

Single-spin asymmetries in inclusive deep inelastic scattering and multiparton correlations in the nucleon
journal, November 2012

Towards an explanation of transverse single-spin asymmetries in proton-proton collisions: The role of fragmentation in collinear factorization
journal, June 2014

Role of Collins effect in the single spin asymmetry $A_{N}$ in $p^{↑} p \to h$ $X$ processes
journal, October 2012

Sivers effect and the single spin asymmetry $A_{N}$ in $p^{↑} p \to h X$ processes
journal, September 2013

Single spin asymmetries in $ℓ p^{↑} \to h X$ processes and transverse momentum dependent factorization
journal, June 2014

Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks
journal, December 1977

What can break the Wandzura-Wilczek relation?
journal, November 2009

Possible Tests of $C_{st}$ and $T_{st}$ Invariances in $l^{\pm} + N \to l^{\pm} + Γ$ and $A \to B + e^{+} + e^{-}$
journal, March 1966

Transverse single spin asymmetries in inclusive deep-inelastic scattering
journal, December 2006

Transverse target spin asymmetry in inclusive DIS with two-photon exchange
journal, January 2008

Partonic description of the transverse target single-spin asymmetry in inclusive deep-inelastic scattering
journal, February 2013

Search for a two-photon exchange contribution to inclusive deep-inelastic scattering
journal, January 2010

Measurement of the Target-Normal Single-Spin Asymmetry in Deep-Inelastic Scattering from the Reaction ${}^{3}{He}^{↑} (e, e^{'}) X$
journal, July 2014

Transverse target single-spin asymmetry in inclusive electroproduction of charged pions and kaons
journal, January 2014

Single spin asymmetries of inclusive hadrons produced in electron scattering from a transversely polarized $^{3}$ He target
journal, April 2014

Transverse polarization of $Λ$ hyperons from quasireal photoproduction on nuclei
journal, October 2014

Exploring the structure of the proton through polarization observables in $l p \to jet$ $X$
journal, August 2011

Left-right spin asymmetry in $ℓ N^{↑} \to h X$
journal, October 2014

Longitudinal–transverse double-spin asymmetries in single-inclusive leptoproduction of hadrons
journal, March 2015

Single-spin asymmetries in the leptoproduction of transversely polarized Λ hyperons
journal, May 2015

Single-inclusive production of hadrons and jets in lepton-nucleon scattering at NLO
journal, July 2015

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, January 1997

Asymmetries in polarized hadron production in e+e− annihilation up to order
journal, October 1997

Production of dimuons from high-energy polarized proton-proton collisions
journal, May 1979

Chiral-odd parton distributions and polarized Drell-Yan process
journal, July 1991

Chiral-odd parton distributions and Drell-Yan processes
journal, May 1992

Measuring the transverse polarization of quarks in the proton
journal, September 1992

Transverse momentum dependent quark distributions and polarized Drell-Yan processes
journal, March 2010

Partonic Pole Matrix Elements for Fragmentation
journal, May 2009