Color-suppression of non-planar diagrams in bosonic bound states

Alvarenga Nogueira, J. H.; Ji, Chueng-Ryong; Ydrefors, E.; Frederico, T.

doi:10.1016/j.physletb.2017.12.032

Title: Color-suppression of non-planar diagrams in bosonic bound states

Journal Article · 15 December 2017 · Physics Letters B

DOI: https://doi.org/10.1016/j.physletb.2017.12.032 · OSTI ID:1413559

^[1]; Ji, Chueng-Ryong ^[2]; Ydrefors, E. ^[3]; Frederico, T. ^[3]

Instituto Tecnológico de Aeronáutica (Brazil); Istituto Nazionale di Astrofisica (INAF), Roma (Italy)
North Carolina State Univ., Raleigh, NC (United States)
Instituto Tecnológico de Aeronáutica (Brazil)

We study the suppression of non-planar diagrams in a scalar QCD model of a meson system in space–time dimensions due to the inclusion of the color degrees of freedom. As a prototype of the color-singlet meson, we consider a flavor-nonsinglet system consisting of a scalar-quark and a scalar-antiquark with equal masses exchanging a scalar-gluon of a different mass, which is investigated within the framework of the homogeneous Bethe–Salpeter equation. The equation is solved by using the Nakanishi representation for the manifestly covariant bound-state amplitude and its light-front projection. The resulting non-singular integral equation is solved numerically. The damping of the impact of the cross-ladder kernel on the binding energies are studied in detail. The color-suppression of the cross-ladder effects on the light-front wave function and the elastic electromagnetic form factor are also discussed. As our results show, the suppression appears significantly large for , which supports the use of rainbow-ladder truncations in practical non-perturbative calculations within QCD.

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Research Organization:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-03ER41260

OSTI ID:: 1413559

Alternate ID(s):: OSTI ID: 1499277

Journal Information:: Physics Letters B, Vol. 777, Issue C; ISSN 0370-2693

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (22)

The self-energy corrections to the light-cone two-body equation in ø3-theories Ji, Chueng-Ryong Physics Letters B, Vol. 322, Issue 4 https://doi.org/10.1016/0370-2693(94)91170-3	journal	February 1994
Light-front dynamic analysis of bound states in a scalar field model Ji, Chueng-Ryong; Tokunaga, Yukihisa Physical Review D, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevD.86.054011	journal	September 2012
Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation Savkli, C.; Gross, F.; Tjon, J. Physics of Atomic Nuclei, Vol. 68, Issue 5 https://doi.org/10.1134/1.1935017	journal	May 2005
Confinement and the analytic structure of the one-body propagator in scalar QED Şavklı, Çetin; Gross, Franz; Tjon, John Physical Review D, Vol. 62, Issue 11 https://doi.org/10.1103/PhysRevD.62.116006	journal	November 2000
The role of interaction vertices in bound state calculations Şavklı, Çetin; Gross, Franz; Tjon, John Physics Letters B, Vol. 531, Issue 1-2 https://doi.org/10.1016/S0370-2693(02)01362-X	journal	April 2002
Nonperturbative Study of Generalized Ladder Graphs in a ϕ 2 χ Theory Nieuwenhuis, Taco; Tjon, J. A. Physical Review Letters, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevLett.77.814	journal	July 1996
A Relativistic Equation for Bound-State Problems Salpeter, E. E.; Bethe, H. A. Physical Review, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRev.84.1232	journal	December 1951
Light-front Bethe-Salpeter equation Sales, J. H. O.; Frederico, T.; Carlson, B. V. Physical Review C, Vol. 61, Issue 4 https://doi.org/10.1103/PhysRevC.61.044003	journal	March 2000
Properties of Bethe-Salpeter Wave Functions Wick, G. C. Physical Review, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRev.96.1124	journal	November 1954
Solving the Bethe-Salpeter equation for scalar theories in Minkowski space Kusaka, Kensuke; Williams, Anthony G. Physical Review D, Vol. 51, Issue 12 https://doi.org/10.1103/PhysRevD.51.7026	journal	June 1995
Partial-Wave Bethe-Salpeter Equation Nakanishi, Noboru Physical Review, Vol. 130, Issue 3 https://doi.org/10.1103/PhysRev.130.1230	journal	May 1963
A General Survey of the Theory of the Bethe-Salpeter Equation Nakanishi, Noboru Progress of Theoretical Physics Supplement, Vol. 43 https://doi.org/10.1143/PTPS.43.1	journal	January 1969
Solving Bethe-Salpeter equation in Minkowski space Karmanov, V. A.; Carbonell, J. The European Physical Journal A, Vol. 27, Issue 1 https://doi.org/10.1140/epja/i2005-10193-0	journal	January 2006
Explicitly covariant light-front dynamics and relativistic few-body systems Carbonell, J.; Desplanques, B.; Karmanov, V. A. Physics Reports, Vol. 300, Issue 5-6 https://doi.org/10.1016/S0370-1573(97)00090-2	journal	July 1998
Cross-ladder effects in Bethe-Salpeter and light-front equations Carbonell, J.; Karmanov, V. A. The European Physical Journal A, Vol. 27, Issue 1 https://doi.org/10.1140/epja/i2005-10194-y	journal	January 2006
Bound state structure and electromagnetic form factor beyond the ladder approximation Gigante, V.; Nogueira, J. H. Alvarenga; Ydrefors, E. Physical Review D, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevD.95.056012	journal	March 2017
A two-dimensional model for mesons 't Hooft, G. Nuclear Physics B, Vol. 75, Issue 3 https://doi.org/10.1016/0550-3213(74)90088-1	journal	June 1974
Light-cone-quantized QCD in 1+1 dimensions Hornbostel, Kent; Brodsky, Stanley J.; Pauli, Hans-Christian Physical Review D, Vol. 41, Issue 12 https://doi.org/10.1103/PhysRevD.41.3814	journal	June 1990
Group theory for Feynman diagrams in non-Abelian gauge theories Cvitanović, Predrag Physical Review D, Vol. 14, Issue 6 https://doi.org/10.1103/PhysRevD.14.1536	journal	September 1976
Quantitative studies of the homogeneous Bethe-Salpeter equation in Minkowski space Frederico, Tobias; Salmè, Giovanni; Viviani, Michele Physical Review D, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevD.89.016010	journal	January 2014
Solving the Bethe-Salpeter equation for two fermions in Minkowski space Carbonell, J.; Karmanov, V. A. The European Physical Journal A, Vol. 46, Issue 3 https://doi.org/10.1140/epja/i2010-11055-4	journal	November 2010
Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space de Paula, W.; Frederico, T.; Salmè, G. Physical Review D, Vol. 94, Issue 7 https://doi.org/10.1103/PhysRevD.94.071901	journal	October 2016

Cited By (1)

Relativistic Studies of Few-Body Systems Using the Bethe–Salpeter Approach Nogueira, J. H. Alvarenga; Ydrefors, E.; Frederico, T. Few-Body Systems, Vol. 59, Issue 5 https://doi.org/10.1007/s00601-018-1418-3	journal	June 2018