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Title: Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra

Abstract

QCD is not supersymmetrical in the traditional sense – the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The pion $$q\bar{q}$$ eigenstate has zero mass for mq = 0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key observation is the remarkable dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling, and the mass parameter underlying the Gaussian functional form of the nonperturbativemore » QCD running coupling: αs(Q2) ∝ exp-Q2/4κ2, in agreement with the effective charge determined from measurements of the Bjorken sum rule. The mass scale κ underlying hadron masses can be connected to the parameter Λ$$\overline{MS}$$ in the QCD running coupling by matching its predicted nonperturbative form to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. In conclusion, one also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.« less

Authors:
 [1]
  1. Stanford Univ., Stanford, CA (United States). SLAC National Accelerator Lab
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1443973
Report Number(s):
SLAC-PUB-17201
Journal ID: ISSN 0177-7963; TRN: US1900950
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Few-Body Systems
Additional Journal Information:
Journal Volume: 59; Journal Issue: 5; Conference: NSTAR 2017, The 11th International Workshop on the Physics of Excited Nucleons, Univ. of South Carolina, Columbia, SC (United States), 20-23 Aug 2017; Journal ID: ISSN 0177-7963
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Brodsky, Stanley J. Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra. United States: N. p., 2018. Web. doi:10.1007/s00601-018-1409-4.
Brodsky, Stanley J. Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra. United States. https://doi.org/10.1007/s00601-018-1409-4
Brodsky, Stanley J. 2018. "Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra". United States. https://doi.org/10.1007/s00601-018-1409-4. https://www.osti.gov/servlets/purl/1443973.
@article{osti_1443973,
title = {Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra},
author = {Brodsky, Stanley J.},
abstractNote = {QCD is not supersymmetrical in the traditional sense – the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The pion $q\bar{q}$ eigenstate has zero mass for mq = 0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key observation is the remarkable dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling, and the mass parameter underlying the Gaussian functional form of the nonperturbative QCD running coupling: αs(Q2) ∝ exp-Q2/4κ2, in agreement with the effective charge determined from measurements of the Bjorken sum rule. The mass scale κ underlying hadron masses can be connected to the parameter Λ$\overline{MS}$ in the QCD running coupling by matching its predicted nonperturbative form to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. In conclusion, one also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.},
doi = {10.1007/s00601-018-1409-4},
url = {https://www.osti.gov/biblio/1443973}, journal = {Few-Body Systems},
issn = {0177-7963},
number = 5,
volume = 59,
place = {United States},
year = {Thu May 24 00:00:00 EDT 2018},
month = {Thu May 24 00:00:00 EDT 2018}
}

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Figures / Tables:

Figure 1 Figure 1: Comparison of the $$ρ$$ mesonic and $$Δ$$ baryonic Regge trajectories by Klempt and Metsch [1].

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Works referenced in this record:

Threefold complementary approach to holographic QCD
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Confinement contains condensates
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Commensurate scale relations in quantum chromodynamics
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Supersymmetry across the light and heavy-light hadronic spectrum. II.
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font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1959-01-01">January 1959</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Penrose, R.</span> </li> <li> Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 55, Issue 1</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1017/S0305004100033776" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1017/S0305004100033776<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevD.8.4574" target="_blank" rel="noopener noreferrer" class="name">Quantum Electrodynamics and Renormalization Theory in the Infinite-Momentum Frame<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; 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font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2002-08-01">August 2002</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Srivastava, Prem P.; Brodsky, Stanley J.</span> </li> <li> Physical Review D, Vol. 66, Issue 4</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1103/PhysRevD.66.045019" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevD.66.045019<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/0550-3213(75)90279-5" target="_blank" rel="noopener noreferrer" class="name">All possible generators of supersymmetries of the S-matrix<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; 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M.</span> </li> <li> Progress in Particle and Nuclear Physics, Vol. 85</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/j.ppnp.2015.07.002" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/j.ppnp.2015.07.002<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevC.82.022201" target="_blank" rel="noopener noreferrer" class="name">New perspectives on the quark condensate<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2010-08-01">August 2010</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Brodsky, Stanley J.; Roberts, Craig D.; Shrock, Robert</span> </li> <li> Physical Review C, Vol. 82, Issue 2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1103/PhysRevC.82.022201" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevC.82.022201<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1063/1.3122202" target="_blank" rel="noopener noreferrer" class="name">Dynamic versus Static Structure Functions and Novel Diffractive Effects in QCD<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">conference</span>, <span class="date" data-date="2009-01-01">January 2009</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Brodsky, Stanley J.; Fiore, Roberto; Ivanov, Igor</span> </li> <li> DIFFRACTION 2008: International Workshop on Diffraction in High Energy Physics, AIP Conference Proceedings</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1063/1.3122202" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1063/1.3122202<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/j.nuclphysbps.2014.04.002" target="_blank" rel="noopener noreferrer" class="name">Applications of Basis Light-Front Quantization to QED<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2014-06-01">June 2014</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Vary, James P.; Zhao, Xingbo; Ilderton, Anton</span> </li> <li> Nuclear Physics B - Proceedings Supplements, Vol. 251-252</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/j.nuclphysbps.2014.04.002" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/j.nuclphysbps.2014.04.002<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/JHEP05(2011)041" target="_blank" rel="noopener noreferrer" class="name">Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2011-05-01">May 2011</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Lorcé, C.; Pasquini, B.; Vanderhaeghen, M.</span> </li> <li> Journal of High Energy Physics, Vol. 2011, Issue 5</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/JHEP05(2011)041" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/JHEP05(2011)041<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span><span class="sr-only">Previous</span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span><span class="sr-only">Next</span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All References</a></li> <li class="small" style="margin-left:.75em; 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border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85078" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85078"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 1<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 2)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085078.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 3" data-order="2" data-imgid="1443973-img85082" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085082.png" data-title="Figure 2" data-desc="Comparison of the slopes of the Regge trajectories in angular momentum: $$M$$<sup>2</sup> $$∝$$ $$L$$ and in the radial quantum number $$n$$: $$M$$<sup>2</sup> $$∝$$ $$n$$." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85082" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85082"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 2<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 3)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085082.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 5" data-order="3" data-imgid="1443973-img85089" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085089.png" data-title="Figure 3" data-desc="Comparison of the $$ρ$$/$$ω$$ meson Regge trajectory with the $$J$$ = 3/2 $$Δ$$ baryon trajectory. Superconformal algebra predicts the mass degeneracy of the meson and baryon trajectories if one identifies a meson with internal orbital angular momentum $$L$$<sub>$$M$$</sub> with its superpartner baryon with $$L$$<sub>$$M$$</sub> = $$L$$<sub>$$B$$</sub> + 1. See Refs. [2, 3]." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85089" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85089"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 3<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 5)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085089.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 7" data-order="4" data-imgid="1443973-img85079" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085079.png" data-title="Figure 4" data-desc="The 4-plet representation of mass-degenerate hadronic states predicted by superconformal algebra. Mesons are $$q\bar{q}$$ bound states, baryons are quark plus anti-diquark bound states and tetraquarks are diquark plus antidiquark bound states. The supersymmetric ladder operator $$R^{†}_{λ}$$ connects quarks and anti-diquark clusters of the same color. The baryons have two Fock states with orbital angular momentum $$L$$<sub>$$B$$ </sub>and $$L$$<sub>$$B$$</sub> + 1 with equal weight. The predicted meson baryon and tetraquark masses are identical if one identifies a meson with internal orbital angular momentum $$L$$<sub>$$M$$</sub> with its superpartner baryon or tetraquark with $$L$$<sub>$$B$$</sub> = $$L$$<sub>$$M$$</sub>− 1." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85079" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85079"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 4<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 7)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085079.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 8" data-order="5" data-imgid="1443973-img85085" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085085.png" data-title="Figure 5" data-desc="The eigenstates of superconformal algebra have a 2 x 2 representation of mass degenerate bosons and fermions: a meson with $$L$$<sub>$$M$$ </sub>= $$L$$<sub>$$B$$ </sub>+ 1, a baryon doublet with $$L$$<sub>$$B$$ </sub>, $$L$$<sub>$$B$$ </sub> + 1 components and a tetraquark with $$L$$<sub>$$T$$</sub> = $$L$$<sub>$$B$$ </sub>. The breakdown of LF kinetic, potential, spin, and quark mass contributions to each hadron is also shown. The virial theorem predicts the equality of the LF kinetic and potential contributions." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85085" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85085"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 5<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 8)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085085.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 11" data-order="6" data-imgid="1443973-img85074" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085074.png" data-title="Figure 6" data-desc="The LF Schrödinger equations for baryons and mesons for zero quark mass derived from the Pauli 2 x 2 4-plet matrix representation of superconformal algebra. The $$ψ$$<sup>±</sup> are the baryon quark-diquark LFWFs where the quark spin $$S^{z}_{q}$$ = ± 1/2 is parallel or antiparallel to the baryon spin $$J$$<sup>$$z$$</sup> = ± 1/2. The predicted meson and baryon masses are identical if one identifies a meson with internal orbital angular momentum $$L$$<sub>$$M$$ </sub>with its superpartner baryon with $$L$$<sub>$$B$$</sub> = $$L$$<sub>$$M$$</sub> − 1. See Refs. [2, 3, 4]." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85074" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85074"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 6<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 11)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085074.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 12" data-order="7" data-imgid="1443973-img85087" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085087.png" data-title="Figure 7" data-desc="Classification and quantum numbers of mesons, baryons, and tetraquarks composed of light quarks related by superconformal algebra." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85087" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85087"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 7<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 12)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085087.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 13" data-order="8" data-imgid="1443973-img85084" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085084.png" data-title="Figure 8" data-desc="Comparison of the meson and baryon Regge trajectories for hadrons with a single charm quark. See Refs. [2, 3]." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85084" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85084"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 8<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 13)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085084.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 14" data-order="9" data-imgid="1443973-img85081" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085081.png" data-title="Figure 9" data-desc="The convergence of theoretical methods for generating a model of hadron spectroscopy and dynamics with color confinement and meson-baryon supersymmetric relations. ." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85081" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85081"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 9<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 14)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085081.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 17" data-order="10" data-imgid="1443973-img85086" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085086.png" data-title="Figure 10" data-desc="The meson LFWF connects the intermediate $$q\bar{q}$$ state, which is off of the $$P$$<sup>− </sup>energy shell and thus off-the-invariant mass shell $$\mathcal{M}$$<sup>2</sup> > $$m^{2}_{H}$$T to the physical meson state with $$\mathcal{M}$$<sup>2</sup> = $$m^{2}_{H}$$. The $$q$$ and $$\bar{q}$$ can be regarded as effective dressed fields ." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85086" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85086"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 10<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 17)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085086.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 21" data-order="11" data-imgid="1443973-img85077" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085077.png" data-title="Figure 11" data-desc="The holographic dictionary which maps the fifth dimension variable $$z$$ of the five-dimensional AdS<sub>5</sub> space to the LF radial variable $$ζ$$ where $$ζ$$ <sup>2</sup> = $$b^{2}_{⊥}$$(1−$$x$$). The same physics transformation maps the AdS<sub>5</sub> and (3 + 1) LF expressions for electromagnetic and gravitational form factors to each other. From ref. [33]" data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85077" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85077"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 11<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 21)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085077.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 23" data-order="12" data-imgid="1443973-img85083" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085083.png" data-title="Figure 12" data-desc="Prediction from AdS/QCD and Light-Front Holography for meson LFWFs $$ψ$$<sub>$$M$$</sub>($$x$$, $$\vec{k}$$<sub>⊥</sub>) and the pion distribution amplitude." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85083" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85083"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 12<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 23)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085083.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 24" data-order="13" data-imgid="1443973-img85088" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085088.png" data-title="Figure 13" data-desc="Comparison of the AdS/QCD prediction $$M$$<sup>2</sup>($$n$$, $$L$$, $$S$$) = 4$$κ$$<sup>2</sup>($$n$$ + $$L$$ + $$S$$/2) for the orbital $$L$$ and radial $$n$$ excitations of the meson spectrum with experiment. The pion is predicted to be massless for zero quark mass. The $$u$$, $$d$$, $$s$$ quark masses can be taken into account by perturbing in $$\langle$$ $$m^{2}_{q}$$/x $$\rangle$$. The fitted value of $$κ$$ = 0.59 GeV for pseudoscalar mesons, and $$κ$$ = 0.54 GeV for vector mesons." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85088" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85088"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 13<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 24)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085088.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 25" data-order="14" data-imgid="1443973-img85075" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085075.png" data-title="Figure 14" data-desc="Predictions for baryon elastic and transition spacelike form factors using AdS/QCD and superconformal algebra." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85075" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85075"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 14<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 25)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085075.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 26" data-order="15" data-imgid="1443973-img85076" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085076.png" data-title="Figure 15" data-desc="Predictions for baryon elastic and transition spacelike form factors using AdS/QCD and superconformal algebra. The fit allows for five-quark |$$uudq\bar{q}$$ > Fock state in the proton." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85076" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85076"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 15<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 26)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085076.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 29" data-order="16" data-imgid="1443973-img85080" data-imgsrc="/biblio/1443973/image/001/160/0011607/3/0085080.png" data-title="Figure 16" data-desc="Doubly Virtual Compton scattering on a proton (or nucleus) can be measured for two <em>spacelike</em> photons $$q^{2}_{1}$$, $$q^{2}_{2}$$ < 0 with minimal, tunable, skewness $$ξ$$ using positronium-proton scattering [$$e$$<sup>+</sup>$$e$$<sup>−</sup>]$$p$$ → $$e$$<sup>+</sup>$$e$$<sup>−</sup>$p′$. One can also measure double deep inelastic scattering and elastic positronium-proton scattering. One can also create a beam of “true muonium” atoms [$$μ$$<sup>−</sup>$$μ$$<sup>−</sup>] using Bethe-Heitler pair production just below threshold." data-ostiid="1443973" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1443973-img85080" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1443973-img85080"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Figure 16<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 29)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1443973/image/001/160/0011607/3/t0085080.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span><span class="sr-only">Previous</span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span><span class="sr-only">Next</span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-images" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Images</a></li> <li class="small" style="margin-left:.75em; text-transform:capitalize;"><a href="" class="reference-type-filter tab-nav ga-click-event" data-tab="biblio-images" data-filter="type" data-pattern="figure" data-category="Extracted Images" data-label="biblio: image filter - figure"><span class="fa fa-angle-right"></span> figures<small class="text-muted"> (16)</small></a></li> </ul> <div style="margin-top:2em;"> <form class="pure-form small text-muted image-search"> <label for="image-search-text" class="sr-only">Search</label> <input class="search form-control pure-input-1" id="image-search-text" placeholder="Search" style="margin-bottom:10px;" /> <fieldset> <legend class="sr-only">Sort options</legend> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort ga-click-event" name="images-sort" data-sort="name" style="position:relative;top:2px;" id="image-search-sort-name" data-category="Extracted Images" data-label="biblio: image sort - name"><label for="image-search-sort-name" style="margin-left: .3em;">Sort by figure / table title</label></div> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort ga-click-event" name="images-sort" data-sort="order" style="position:relative;top:2px;" id="image-search-sort-date" data-category="Extracted Images" data-label="biblio: image sort - order"><label for="image-search-sort-date" style="margin-left: .3em;">Sort by page order</label></div> </fieldset> <div class="text-left" style="margin-top:1.5em;margin-left:1em;"> <a href="" class="filter-clear clearfix" title="Clear filter / sort" style="font-weight:normal; float:none;">[ × clear filter / sort ]</a> </div> <button type="submit" style="display:none;" aria-hidden="true" title="Submit"/> </form> </div> <div class="text-muted small" style="margin-top:2em; padding:1em;"> <em>Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.</em> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar records in OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="0" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1490464" itemprop="url">Supersymmetric and Conformal Features of Hadron Physics</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Brodsky, Stanley</span><span class="text-muted pubdata"> - Universe</span> </span></div> <div class="abstract">The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion $$q\overline{q}$$ eigenstate has zero mass<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> for m<sub>q</sub> = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α<sub>s</sub> (Q<sup>2</sup>) ∝ e<sup>-Q<sup>2</sup>/4κ<sup>2</sup></sup>, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS <sub>5</sub> space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.3390/universe4110120" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1490464" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.3390/universe4110120</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1490464" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1490464" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1433298" itemprop="url">Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Brodsky, Stanley</span><span class="text-muted pubdata"> - Advances in High Energy Physics</span> </span></div> <div class="abstract">T<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> he QCD light-front Hamiltonian equation <math><msub> <mrow> <mi> H </mi> </mrow> <mrow> <mi mathvariant="normal"> L </mi> <mi mathvariant="normal"> F </mi> </mrow> </msub> <mfenced> <mrow> <mi mathvariant="normal"> Ψ </mi> </mrow> </mfenced> <mo> = </mo> <msup> <mrow> <mi> M </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> <mfenced> <mrow> <mi mathvariant="normal"> Ψ </mi> </mrow> </mfenced> </math> derived from quantization at fixed LF time <math><mi> τ </mi> <mo> = </mo> <mi> t </mi> <mo>   </mo> <mo>   </mo> <mo> + </mo> <mo>   </mo> <mo>   </mo> <mi> z </mi> <mo> / </mo> <mi> c </mi> </math> provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. he QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential <math><msup> <mrow> <mi> κ </mi> </mrow> <mrow> <mn> 4 </mn> </mrow> </msup> <msup> <mrow> <mi> ζ </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> </math> for mesons, where <math><mrow> <msup> <mrow> <mi> ζ </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> </mrow> </math> is the LF radial variable conjugate to the <math><mi> q </mi> <mover> <mrow> <mi> q </mi> </mrow> <mo> ¯ </mo> </mover> </math> invariant mass squared. he same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and <math><mrow> <msub> <mrow> <mi mathvariant="normal"> A </mi> <mi mathvariant="normal"> d </mi> <mi mathvariant="normal"> S </mi> </mrow> <mrow> <mn> 5 </mn> </mrow> </msub> </mrow> </math> , if one modifies the <math><mrow> <msub> <mrow> <mi mathvariant="normal"> A </mi> <mi mathvariant="normal"> d </mi> <mi mathvariant="normal"> S </mi> </mrow> <mrow> <mn> 5 </mn> </mrow> </msub> </mrow> </math> action by the dilaton <math><msup> <mrow> <mi> e </mi> </mrow> <mrow> <msup> <mrow> <mi> κ </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> <msup> <mrow> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> </mrow> </msup> </math> in the fifth dimension <math><mrow> <mi> z </mi> </mrow> </math> . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. he pion <math><mi> q </mi> <mover> <mrow> <mi> q </mi> </mrow> <mo> ¯ </mo> </mover> </math> eigenstate has zero mass at <math><msub> <mrow> <mi> m </mi> </mrow> <mrow> <mi> q </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> <mo> . </mo> </math> he superconformal relations also can be extended to heavy-light quark mesons and baryons. his approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling <math><msub> <mrow> <mi> α </mi> </mrow> <mrow> <mi> s </mi> </mrow> </msub> <mo> ( </mo> <msup> <mrow> <mi> Q </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> <mo> ) </mo> <mo> ∝ </mo> <msup> <mrow> <mi> e </mi> </mrow> <mrow> <mo> - </mo> <msup> <mrow> <mi> Q </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> <mo> / </mo> <mn> 4 </mn> <msup> <mrow> <mi> κ </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> </mrow> </msup> </math> . he mass scale <math><mrow> <mi> κ </mi> </mrow> </math> underlying hadron masses can be connected to the parameter <math><mrow> <msub> <mrow> <mi mathvariant="normal"> Λ </mi> </mrow> <mrow> <mover> <mrow> <mi mathvariant="normal"> M </mi> <mi mathvariant="normal"> S </mi> </mrow> <mo> ¯ </mo> </mover> </mrow> </msub> </mrow> </math> in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. he result is an effective coupling <math><msub> <mrow> <mi> α </mi> </mrow> <mrow> <mi> s </mi> </mrow> </msub> <mo> ( </mo> <msup> <mrow> <mi> Q </mi> </mrow> <mrow> <mn> 2 </mn> </mrow> </msup> <mo> ) </mo> </math> defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 4<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1155/2018/7236382" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1433298" data-product-type="Journal Article" data-product-subtype="PA" >https://doi.org/10.1155/2018/7236382</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1389548" itemprop="url">New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Brodsky, S.</span><span class="text-muted pubdata"> - Russian Physics Journal</span> </span></div> <div class="abstract">A fundamental problem in hadron physics is to obtain a relativistic color-confining, first approximation to QCD which can predict both hadron spectroscopy and the frame-independent light-front (LF) wavefunctions underlying hadron dynamics. The QCD Lagrangian with zero quark mass has no explicit mass scale; the classical theory is conformally invariant. Thus, a fundamental problem is to understand how the mass gap and ratios of masses – such as mρ/mp – can arise in chiral QCD. De Alfaro, Fubini, and Furlan have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator and rescales the time variable. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ<sup>4</sup>ζ<sup>2</sup> for mesons, where ζ<sup>2</sup> is the LF radial variable conjugate to the $$q\bar{q}$$ invariant mass squared. The same result, including spin terms, is obtained using light-front holography – the duality between light-front dynamics and AdS<sub>5</sub>, the space of isometries of the conformal group if one modifies the action of AdS<sub>5</sub> by the dilaton e<sup>$κ^2$</sup><sup>z$^2$</sup> in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κ underlying confinement and hadron masses can be connected to the parameter Λ<sub>$$\overline{MS}$$</sub> in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α<sub>s</sub>(Q<sup>2</sup>) defined at all momenta. Lastly, the matching of the high and low momentum transfer regimes also determines a scale Q<sub>0</sub> which sets the interface between perturbative and nonperturbative hadron dynamics.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 2<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/s11182-017-1089-4" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1389548" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/s11182-017-1089-4</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1389548" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1389548" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1367846" itemprop="url">Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Brodsky, Stanley</span><span class="text-muted pubdata"> - Few-Body Systems</span> </span></div> <div class="abstract">A remarkable feature of QCD is that the mass scale $$k$$ which controls color confinement and light-quark hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ<sup>4</sup>ζ<sup>2</sup> for mesons, where ζ<sup>2</sup> is the LF radial variable<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> conjugate to the $$q\bar{q}$$ invariant mass. The same result, including spin terms, is obtained using light-front holography$$-$$the duality between the front form and AdS<sub>5</sub>, the space of isometries of the conformal group$$-$$if one modifies the action of AdS<sub>5</sub> by the dilaton e<sup>$κ^2z^2$</sup> in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κκ underlying confinement and hadron masses can be connected to the parameter Λ<sub>$$\overline{MS}$$</sub> in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α<sub>s</sub> (Q<sup>2</sup>) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q<sub>0</sub> which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q<sub>0</sub> to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front-form vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 1<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/s00601-017-1292-4" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1367846" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/s00601-017-1292-4</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1367846" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1367846" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="5" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1434677" itemprop="url">Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra and other Advances in Light-Front QCD</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Brodsky, Stanley</span><span class="text-muted pubdata"> - Few-Body Systems</span> </span></div> <div class="abstract">Here, light-front holography, together with superconformal algebra, have provided new insights into the physics of color confinement and the spectroscopy and dynamics of hadrons. As shown by de Alfaro, Fubini and Furlan, a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the procedure of de Alfaro et al. to the frame-independent light-front Hamiltonian, it leads uniquely to a confining qq¯ potential κ<sup>4</sup>ζ<sup>2</sup>, where ζ<sup>2</sup> is the light-front radial variable related<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> in momentum space to the qq¯ invariant mass. The same result, including spin terms, is obtained using light-front holography—the duality between the front form and AdS<sub>5</sub>, the space of isometries of the conformal group—if one modifies the action of AdS<sub>5</sub> by the dilaton e<sup>κ<sup>2</sup></sup><sup>z<sup>2</sup></sup> in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions lead to a a unified Regge spectroscopy of meson, baryon, and tetraquarks, including supersymmetric relations between their masses and their wavefunctions. One also predicts hadronic light-front wavefunctions and observables such as structure functions, transverse momentum distributions, and the distribution amplitudes. The mass scale κ underlying confinement and hadron masses can be connected to the parameter Λ<sub>MS¯</sub> in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α<sub>s</sub>(Q<sup>2</sup>) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q<sub>0</sub> which sets the interface between perturbative and nonperturbative hadron dynamics. I also discuss a number of applications of light-front phenomenology.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 1<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/s00601-018-1342-6" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1434677" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/s00601-018-1342-6</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1434677" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1434677" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item d-block d-inline-small"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="d-none d-sm-inline" style="color:#737373;">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none mb-1"></li> <li class="pure-menu-item"><a href="https://doe.responsibledisclosure.com/hc/en-us" target="_blank" class="pure-menu-link">Vulnerability Disclosure Program</a></li> <li class="d-block d-lg-none mb-1"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook"></span><span class="sr-only">Facebook</span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter"></span><span class="sr-only">Twitter</span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play"></span><span class="sr-only">YouTube</span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/css/ostigov.fonts.240327.0425.css" rel="stylesheet"> <script src="/js/ostigov.240327.0425.js"></script><noscript></noscript> <script defer src="/js/ostigov.biblio.240327.0425.js"></script><noscript></noscript> <script async type="text/javascript" src="/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- OSTI.GOV v.240327.0425 --> </html>