Scaling Laws at Large Transverse Momentum

Brodsky, Stanley J.; Farrar, Glennys R.

doi:10.1103/PhysRevLett.31.1153

Title: Scaling Laws at Large Transverse Momentum

Abstract

The application of simple dimensional counting to bound states of pointlike particles enables us to derive scaling laws for the asymptotic energy dependence of electromagnetic and hadronic scattering at fixed c.m. angle which only depend on the number of constituent fields of the hadrons. Assuming quark constituents, some of the s→∞, fixed-ts predictions are ($$\frac{dσ}{dt}$$)_πp→πp~s^-8, ($$\frac{dσ}{dt}$$)_pp→pp~s^-10, ($$\frac{dσ}{dt}$$)_γp→πp~s^-7, ($$\frac{dσ}{dt}$$)_γp→γp~s^-6, F_π(q²)~(q²)^-1, and F_1p(q²)~(q²)^-2. We show that such scaling laws are characteristic of renormalizable field theories satisfying certain conditions.

Authors:

Brodsky, Stanley J. ^[1]; Farrar, Glennys R. ^[2]

Stanford Univ., CA (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: 1973-10-29

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1442900

Report Number(s):: SLAC-PUB-1290
Journal ID: ISSN 0031-9007; PRLTAO

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 31; Journal Issue: 18; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Brodsky, Stanley J., and Farrar, Glennys R. Scaling Laws at Large Transverse Momentum.  United States: N. p., 1973. 
Web.  doi:10.1103/PhysRevLett.31.1153.

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                    Brodsky, Stanley J., & Farrar, Glennys R. Scaling Laws at Large Transverse Momentum.  United States.  https://doi.org/10.1103/PhysRevLett.31.1153

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                    Brodsky, Stanley J., and Farrar, Glennys R. Mon .  
"Scaling Laws at Large Transverse Momentum".  United States.  https://doi.org/10.1103/PhysRevLett.31.1153.  https://www.osti.gov/servlets/purl/1442900.

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@article{osti_1442900,

  title        = {Scaling Laws at Large Transverse Momentum},

  author       = {Brodsky, Stanley J. and Farrar, Glennys R.},

  abstractNote = {The application of simple dimensional counting to bound states of pointlike particles enables us to derive scaling laws for the asymptotic energy dependence of electromagnetic and hadronic scattering at fixed c.m. angle which only depend on the number of constituent fields of the hadrons. Assuming quark constituents, some of the s→∞, fixed-ts predictions are ($\frac{dσ}{dt}$)πp→πp~s-8, ($\frac{dσ}{dt}$)pp→pp~s-10, ($\frac{dσ}{dt}$)γp→πp~s-7, ($\frac{dσ}{dt}$)γp→γp~s-6, Fπ(q2)~(q2)-1, and F1p(q2)~(q2)-2. We show that such scaling laws are characteristic of renormalizable field theories satisfying certain conditions.},

  doi          = {10.1103/PhysRevLett.31.1153},

  journal      = {Physical Review Letters},

  number       = 18,

  volume       = 31,

  place        = {United States},

  year         = {1973},

  month        = {10}

}

Copy to clipboard

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Figure 1: Typical Born diagrams for large momentum transfer elastic scattering in the quark picture (a) π p → π p (quark scattering), (b) π p → π p (quark interchange), (c) e π → e π ; (d) an irreducible loop diagram, (e) a reducible loop diagram.

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text, January 2008

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Nonperturbative QCD Coupling and its $β$ function from Light-Front Holography
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Brodsky, Stanley J.; de Téramond, Guy F.; Deur, Alexandre
arXiv
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AdS/QCD, Light-Front Holography, and the Nonperturbative Running Coupling
text, January 2010

Brodsky, Stanley J.; de Teramond, Guy F.; Deur, Alexandre
arXiv
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The Meson Production in Proton-Proton Collisions in Next-To-Leading Order and Infrared Renormalons
text, January 2010

Ahmadov, A. I.; Burjaliyev, R. M.
arXiv
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Deep inelastic scattering of baryons in a modified soft wall model
text, January 2011

Braga, Nelson R. F.; Vega, Alfredo
arXiv
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Physics Achievements from the Belle Experiment
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Brodzicka, Jolanta; Browder, Thomas; Chang, Paoti
arXiv
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Measurement of neutral current e+/-p cross sections at high Bjorken x with the ZEUS detector
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Collaboration, Zeus; Abramowicz, H.; Abt, I.
arXiv
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Nucleon structure in a light-front quark model consistent with quark counting rules and data
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Gutsche, Thomas; Lyubovitskij, Valery E.; Schmidt, Ivan
arXiv
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Constituent Counting Rules and Exotic Hadrons
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Lebed, Richard F.
arXiv
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Nonperturbative strange-quark sea from lattice QCD, light-front holography, and meson-baryon fluctuation models
text, January 2018

Sufian, Raza Sabbir; Liu, Tianbo; de Téramond, Guy F.
arXiv
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Initial-state energy loss in cold QCD matter and the Drell-Yan process
text, January 2018

Arleo, François; Naïm, Charles-Joseph; Platchkov, Stephane
arXiv
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Z-scaling at RHIC
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Tokarev, M. V.
arXiv
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Structure Functions of the Nucleon and their Interpretation
text, January 1997

Cooper-Sarkar, A. M.; Devenish, R. C. E.; De Roeck, A.
arXiv
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Complete Angular Distribution Measurements of Two-Body Deuteron Photodisintegration between 0.5 and 3 GeV
text, January 2004

Mirazita, M.; collaboration, The CLAS
arXiv
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Polarization Transfer in Proton Compton Scattering at High Momentum Transfer
text, January 2004

Hamilton, D. J.; Mamyan, V. H.; Collaboration, the Jefferson Lab Hall A.
arXiv
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Selected Topics in High Energy Semi-Exclusive Electro-Nuclear Reactions
text, January 2001

Sargsian, Misak M.
arXiv
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Dilepton Spectra from Decays of Light Unflavored Mesons
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Faessler, Amand; Fuchs, C.; Krivoruchenko, M. I.
arXiv
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https://doi.org/10.1103/PhysRevD.19.1418

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Title: Scaling Laws at Large Transverse Momentum

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Composite Theory of Inclusive Scattering at Large Transverse Momenta journal, November 1972

Scaling, Duality, and the Behavior of Resonances in Inelastic Electron-Proton Scattering journal, October 1970

Scaling Properties and the Bound-State Nature of the Physical Nucleon journal, April 1972

Connection Between Inelastic Proton-Proton Reactions and Deep Inelastic Electron Scattering journal, December 1970

Elastic Electron-Proton Scattering at Large Four-Momentum Transfer journal, July 1973

Phenomenology of Photon Processes, Vector Dominance, and Crucial Tests for Parton Models journal, July 1972

Inclusive Processes at High Transverse Momentum journal, December 1971

Inclusive processes at high transverse momentum journal, December 1972

t/s scaling in strong interactions journal, November 1972

Strong Interactions at Large Transverse Momentum journal, August 1973

A Survey of Polarization Asymmetries Predicted by QCD journal, January 1981

Renormalization of Path Ordered Phase Factors and Related Hadron Operators in Gauge Field Theories journal, January 1986

Asymptotic behavior of the pion form factor in quantum chromodynamics journal, February 1980

Inclusive interactions of high-energy neutrinos and antineutrinos in iron journal, June 1979

Parton densities from deep inelastic scattering to hadronic processes at super collider energies journal, March 1988

Initial-state energy loss in cold QCD matter and the Drell-Yan process journal, January 2019

A model for pion-pion scattering in large-N QCD journal, April 2017

Pseudoscalar pole light-by-light contributions to the muon (g − 2) in resonance chiral theory journal, June 2018

Constituent Counting Rules and Exotic Hadrons journal, July 2018

The status of glueballs journal, February 2013

Deep inelastic scattering and gauge/string duality journal, May 2003

Deep inelastic scattering from gauge string duality in the soft wall model journal, March 2008

Features of ω photoproduction off nucleon target at forward angles: dominance of π exchange with Regge cuts and scaling of differential cross-sections journal, May 2019

Physics achievements from the Belle experiment journal, January 2012

Elastic electron-deuteron scattering at high energy journal, April 1980

Two-body disintegration of the deuteron with 0.8–1.8 GeV photons journal, October 1993

Complete angular distribution measurements of two-body deuteron photodisintegration between 0.5 and 3GeV journal, July 2004

Global analysis of exclusive kaon and pion electroproduction journal, January 2012

Role of diquark correlations and the pion cloud in nucleon elastic form factors journal, October 2014

Form factor ratio from unpolarized elastic electron-proton scattering journal, November 2016

Polarization transfer observables in elastic electron-proton scattering at Q 2 = 2.5 , 5.2, 6.8, and 8.5 GeV 2 journal, November 2017

Hyperon electromagnetic timelike elastic form factors at large q 2 journal, January 2020

Deep inelastic scattering on an extremal Reissner-Nordström-AdS black hole. I. journal, March 2020

Deep inelastic scattering on an extremal Reissner-Nordström-AdS black hole. II. Holographic fermi surface journal, March 2020

Analysis of particle production at large transverse momentum journal, December 1975

Asymptotic form factors of hadrons and nuclei and the continuity of particle and nuclear dynamics journal, December 1976

Measurements of exclusive photoproduction processes at large values of t and u from 4 to 7.5 GeV journal, August 1976

Neutral-pion photoproduction and proton Compton scattering at large angles journal, April 1979

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Large-angle two-photon exclusive channels in quantum chromodynamics journal, October 1981

Measurement of elastic electron-neutron scattering and inelastic electron-deuteron scattering cross sections at high momentum transfer journal, July 1992

Comparison of 20 exclusive reactions at large t journal, January 1994

Measurements of the electric and magnetic form factors of the proton from Q 2 =1.75 to 8.83 (GeV/ c ) 2 journal, November 1994

Z scaling in hadron-hadron collisions at high energies journal, November 1996

QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum journal, February 2005

Nucleon form factors in QCD journal, May 2006

Generalized z -scaling in proton-proton collisions at high energies journal, May 2007

Gravitational form factors of vector mesons in an AdS/QCD model journal, May 2008

Hadron structure in τ → K K π ν τ decays journal, February 2010

Meson dominance of hadron form factors and large- N c phenomenology journal, January 2013

Light-front quark model consistent with Drell-Yan-West duality and quark counting rules journal, March 2014

Measurement of neutral current e ± p cross sections at high Bjorken x with the ZEUS detector journal, April 2014

V V ′ P form factors in resonance chiral theory and the π − η − η ′ light-by-light contribution to the muon g − 2 journal, April 2014

Nucleon structure in a light-front quark model consistent with quark counting rules and data journal, March 2015

Testing the running coupling k T -factorization formula for the inclusive gluon production journal, September 2016

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region journal, January 2017

Hyperon form factors and diquark correlations journal, November 2017

Electromagnetic structure of nucleon and Roper in soft-wall AdS/QCD journal, March 2018

Global analysis of color fluctuation effects in proton– and deuteron–nucleus collisions at RHIC and the LHC journal, October 2018

Nonperturbative strange-quark sea from lattice QCD, light-front holography, and meson-baryon fluctuation models journal, December 2018

Baryons in a soft-wall AdS-Schwarzschild approach at low temperature journal, June 2019

Toward a First-Principles Calculation of Electroweak Box Diagrams journal, May 2019

Complete Measurement of the Λ Electromagnetic Form Factors journal, September 2019

Hadronic Form Factors in Asymptotically Free Field Theories journal, May 1974

Pion and Nucleon Structure Functions near x = 1 journal, November 1975

Comment on Hadronic Production of Psions journal, May 1976

Measurement of the Energy Dependence of Elastic π p and pp Scattering at Large Angles journal, February 1978

Higgs Bosons from Two-Gluon Annihilation in Proton-Proton Collisions journal, March 1978

Pion Form Factor journal, July 1979

Quantum Chromodynamic Predictions for the Deuteron Form Factor journal, July 1983

Comparison of exclusive reactions at large t journal, March 1988

Charged-Hadron Inclusive Cross Sections and Fractions in e + e − Annihilation at s = 29 GeV journal, September 1988

Perturbative QCD signatures of hybrid hadrons in electroproduction at high Q 2 journal, December 1991

Measurements of the electric and magnetic form factors of the proton from Q 2 =1.75 to 8.83 (GeV/ c ) 2 journal, June 1992

Measurements of the Deuteron Elastic Structure Function A ( Q 2 ) for 0.7 ≤ Q 2 ≤ 6.0 ( GeV / c ) 2 at Jefferson Laboratory journal, February 1999

Precise Measurement of the Deuteron Elastic Structure Function A ( Q 2 ) journal, February 1999

Composite Theory of Inclusive Scattering at Large Transverse Momenta
journal, November 1972

Scaling, Duality, and the Behavior of Resonances in Inelastic Electron-Proton Scattering
journal, October 1970

Scaling Properties and the Bound-State Nature of the Physical Nucleon
journal, April 1972

Connection Between Inelastic Proton-Proton Reactions and Deep Inelastic Electron Scattering
journal, December 1970

Elastic Electron-Proton Scattering at Large Four-Momentum Transfer
journal, July 1973

Phenomenology of Photon Processes, Vector Dominance, and Crucial Tests for Parton Models
journal, July 1972

Inclusive Processes at High Transverse Momentum
journal, December 1971

Inclusive processes at high transverse momentum
journal, December 1972

t/s scaling in strong interactions
journal, November 1972

Strong Interactions at Large Transverse Momentum
journal, August 1973

A Survey of Polarization Asymmetries Predicted by QCD
journal, January 1981

Renormalization of Path Ordered Phase Factors and Related Hadron Operators in Gauge Field Theories
journal, January 1986

Asymptotic behavior of the pion form factor in quantum chromodynamics
journal, February 1980

Inclusive interactions of high-energy neutrinos and antineutrinos in iron
journal, June 1979

Parton densities from deep inelastic scattering to hadronic processes at super collider energies
journal, March 1988

Initial-state energy loss in cold QCD matter and the Drell-Yan process
journal, January 2019

A model for pion-pion scattering in large-N QCD
journal, April 2017

Pseudoscalar pole light-by-light contributions to the muon (g − 2) in resonance chiral theory
journal, June 2018

Constituent Counting Rules and Exotic Hadrons
journal, July 2018

The status of glueballs
journal, February 2013

Deep inelastic scattering and gauge/string duality
journal, May 2003

Deep inelastic scattering from gauge string duality in the soft wall model
journal, March 2008

Features of ω photoproduction off nucleon target at forward angles: dominance of π exchange with Regge cuts and scaling of differential cross-sections
journal, May 2019

Physics achievements from the Belle experiment
journal, January 2012

Elastic electron-deuteron scattering at high energy
journal, April 1980

Two-body disintegration of the deuteron with 0.8–1.8 GeV photons
journal, October 1993

Complete angular distribution measurements of two-body deuteron photodisintegration between 0.5 and 3GeV
journal, July 2004

Global analysis of exclusive kaon and pion electroproduction
journal, January 2012

Role of diquark correlations and the pion cloud in nucleon elastic form factors
journal, October 2014

Form factor ratio from unpolarized elastic electron-proton scattering
journal, November 2016

Polarization transfer observables in elastic electron-proton scattering at $Q^{2} = 2.5$ , 5.2, 6.8, and $8.5 {GeV}^{2}$
journal, November 2017

Hyperon electromagnetic timelike elastic form factors at large $q^{2}$
journal, January 2020

Deep inelastic scattering on an extremal Reissner-Nordström-AdS black hole. I.
journal, March 2020

Deep inelastic scattering on an extremal Reissner-Nordström-AdS black hole. II. Holographic fermi surface
journal, March 2020

Analysis of particle production at large transverse momentum
journal, December 1975

Asymptotic form factors of hadrons and nuclei and the continuity of particle and nuclear dynamics
journal, December 1976

Measurements of exclusive photoproduction processes at large values of $t$ and $u$ from 4 to 7.5 GeV
journal, August 1976

Neutral-pion photoproduction and proton Compton scattering at large angles
journal, April 1979

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

Large-angle two-photon exclusive channels in quantum chromodynamics
journal, October 1981

Measurement of elastic electron-neutron scattering and inelastic electron-deuteron scattering cross sections at high momentum transfer
journal, July 1992

Comparison of 20 exclusive reactions at large $t$
journal, January 1994

Measurements of the electric and magnetic form factors of the proton from $Q^{2}$ =1.75 to 8.83 (GeV/ c $)^{2}$
journal, November 1994

$Z$ scaling in hadron-hadron collisions at high energies
journal, November 1996

QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum
journal, February 2005

Nucleon form factors in QCD
journal, May 2006

Generalized $z$ -scaling in proton-proton collisions at high energies
journal, May 2007

Gravitational form factors of vector mesons in an AdS/QCD model
journal, May 2008

Hadron structure in $τ \to K K π ν_{τ}$ decays
journal, February 2010

Meson dominance of hadron form factors and large- $N_{c}$ phenomenology
journal, January 2013

Light-front quark model consistent with Drell-Yan-West duality and quark counting rules
journal, March 2014

Measurement of neutral current $e^{\pm} p$ cross sections at high Bjorken $x$ with the ZEUS detector
journal, April 2014

$V V^{'} P$ form factors in resonance chiral theory and the $π - η - η'$ light-by-light contribution to the muon $g - 2$
journal, April 2014

Nucleon structure in a light-front quark model consistent with quark counting rules and data
journal, March 2015

Testing the running coupling $k_{T}$ -factorization formula for the inclusive gluon production
journal, September 2016

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region
journal, January 2017

Hyperon form factors and diquark correlations
journal, November 2017

Electromagnetic structure of nucleon and Roper in soft-wall AdS/QCD
journal, March 2018

Global analysis of color fluctuation effects in proton– and deuteron–nucleus collisions at RHIC and the LHC
journal, October 2018

Nonperturbative strange-quark sea from lattice QCD, light-front holography, and meson-baryon fluctuation models
journal, December 2018

Baryons in a soft-wall AdS-Schwarzschild approach at low temperature
journal, June 2019

Toward a First-Principles Calculation of Electroweak Box Diagrams
journal, May 2019

Complete Measurement of the $Λ$ Electromagnetic Form Factors
journal, September 2019

Hadronic Form Factors in Asymptotically Free Field Theories
journal, May 1974

Pion and Nucleon Structure Functions near $x = 1$
journal, November 1975

Comment on Hadronic Production of Psions
journal, May 1976

Measurement of the Energy Dependence of Elastic $π p$ and $pp$ Scattering at Large Angles
journal, February 1978

Higgs Bosons from Two-Gluon Annihilation in Proton-Proton Collisions
journal, March 1978

Pion Form Factor
journal, July 1979

Quantum Chromodynamic Predictions for the Deuteron Form Factor
journal, July 1983

Comparison of exclusive reactions at large t
journal, March 1988

Charged-Hadron Inclusive Cross Sections and Fractions in $e^{+} e^{-}$ Annihilation at $\sqrt{s} = 29$ GeV
journal, September 1988

Perturbative QCD signatures of hybrid hadrons in electroproduction at high $Q^{2}$
journal, December 1991

Measurements of the electric and magnetic form factors of the proton from $Q^{2}$ =1.75 to 8.83 (GeV/ c $)^{2}$
journal, June 1992

Measurements of the Deuteron Elastic Structure Function $A (Q^{2})$ for $0.7 \leq Q^{2} \leq 6.0 (GeV / c)^{2}$ at Jefferson Laboratory
journal, February 1999

Precise Measurement of the Deuteron Elastic Structure Function $A (Q^{2})$
journal, February 1999

Polarization Measurements in High-Energy Deuteron Photodisintegration
journal, April 2001

Photoproduction of the $ω$ Meson on the Proton at Large Momentum Transfer
journal, January 2003

Generalized Counting Rule for Hard Exclusive Processes
journal, June 2003

Perturbative QCD Analysis of the Nucleon’s Pauli Form Factor $F_{2} (Q^{2})$
journal, August 2003