Bilocal Field Theory for Composite Scalar Bosons
We give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu–Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, <inl...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-02-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/26/2/146 |
| _version_ | 1797298263895834624 |
|---|---|
| author | Christopher T. Hill |
| author_facet | Christopher T. Hill |
| author_sort | Christopher T. Hill |
| collection | DOAJ |
| description | We give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu–Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>(</mo><mover accent="true"><mi>r</mi><mo stretchy="false">→</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>, in the center-of-mass frame that satisfies a Schrödinger–Klein–Gordon equation with eigenvalues <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>m</mi><mn>2</mn></msup></semantics></math></inline-formula>. We analyze the “coloron” model (single perturbative massive gluon exchange) which yields a UV completion of the NJL model. This has a BCS-like enhancement of its interaction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><msub><mi>N</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> the number of colors, and is <i>classically critical</i> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>g</mi><mrow><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi></mrow></msub></semantics></math></inline-formula> remarkably close to the NJL quantum critical coupling. Negative eigenvalues for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>m</mi><mn>2</mn></msup></semantics></math></inline-formula> lead to spontaneous symmetry breaking, and the Yukawa coupling of the bound state to constituent fermions is emergent. |
| first_indexed | 2024-03-07T22:33:25Z |
| format | Article |
| id | doaj.art-32b2840b959d4ad09770c5a9ef051a81 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-07T22:33:25Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-32b2840b959d4ad09770c5a9ef051a812024-02-23T15:15:43ZengMDPI AGEntropy1099-43002024-02-0126214610.3390/e26020146Bilocal Field Theory for Composite Scalar BosonsChristopher T. Hill0Particle Theory Department, Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USAWe give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu–Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>(</mo><mover accent="true"><mi>r</mi><mo stretchy="false">→</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>, in the center-of-mass frame that satisfies a Schrödinger–Klein–Gordon equation with eigenvalues <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>m</mi><mn>2</mn></msup></semantics></math></inline-formula>. We analyze the “coloron” model (single perturbative massive gluon exchange) which yields a UV completion of the NJL model. This has a BCS-like enhancement of its interaction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><msub><mi>N</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> the number of colors, and is <i>classically critical</i> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>g</mi><mrow><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi></mrow></msub></semantics></math></inline-formula> remarkably close to the NJL quantum critical coupling. Negative eigenvalues for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>m</mi><mn>2</mn></msup></semantics></math></inline-formula> lead to spontaneous symmetry breaking, and the Yukawa coupling of the bound state to constituent fermions is emergent.https://www.mdpi.com/1099-4300/26/2/146bound statescompositenesscoloron |
| spellingShingle | Christopher T. Hill Bilocal Field Theory for Composite Scalar Bosons Entropy bound states compositeness coloron |
| title | Bilocal Field Theory for Composite Scalar Bosons |
| title_full | Bilocal Field Theory for Composite Scalar Bosons |
| title_fullStr | Bilocal Field Theory for Composite Scalar Bosons |
| title_full_unstemmed | Bilocal Field Theory for Composite Scalar Bosons |
| title_short | Bilocal Field Theory for Composite Scalar Bosons |
| title_sort | bilocal field theory for composite scalar bosons |
| topic | bound states compositeness coloron |
| url | https://www.mdpi.com/1099-4300/26/2/146 |
| work_keys_str_mv | AT christopherthill bilocalfieldtheoryforcompositescalarbosons |