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

## Abstract

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.

- Authors:

- Publication Date:

- Research Org.:
- North Carolina State Univ., Raleigh, NC (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1413559

- Alternate Identifier(s):
- OSTI ID: 1499277

- Grant/Contract Number:
- FG02-03ER41260

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 777 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Alvarenga Nogueira, J. H., Ji, Chueng-Ryong, Ydrefors, E., and Frederico, T. Color-suppression of non-planar diagrams in bosonic bound states. Netherlands: N. p., 2018.
Web. https://doi.org/10.1016/j.physletb.2017.12.032.
```

```
Alvarenga Nogueira, J. H., Ji, Chueng-Ryong, Ydrefors, E., & Frederico, T. Color-suppression of non-planar diagrams in bosonic bound states. Netherlands. https://doi.org/10.1016/j.physletb.2017.12.032
```

```
Alvarenga Nogueira, J. H., Ji, Chueng-Ryong, Ydrefors, E., and Frederico, T. Thu .
"Color-suppression of non-planar diagrams in bosonic bound states". Netherlands. https://doi.org/10.1016/j.physletb.2017.12.032.
```

```
@article{osti_1413559,
```

title = {Color-suppression of non-planar diagrams in bosonic bound states},

author = {Alvarenga Nogueira, J. H. and Ji, Chueng-Ryong and Ydrefors, E. and Frederico, T.},

abstractNote = {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.},

doi = {10.1016/j.physletb.2017.12.032},

journal = {Physics Letters B},

number = C,

volume = 777,

place = {Netherlands},

year = {2018},

month = {2}

}

https://doi.org/10.1016/j.physletb.2017.12.032

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

Works referencing / citing this record:

##
Relativistic Studies of Few-Body Systems Using the Bethe–Salpeter Approach

journal, June 2018

- Nogueira, J. H. Alvarenga; Ydrefors, E.; Frederico, T.
- Few-Body Systems, Vol. 59, Issue 5

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*