The $g^6$ pressure of hot Yang-Mills theory: Canonical form of the integrand
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917767168393216 |
|---|---|
| author | Navarrete, Pablo Schröder, York |
| author_facet | Navarrete, Pablo Schröder, York |
| contents | We present major progress towards the determination of the last missing piece for the pressure of a Yang-Mills plasma at high temperatures at order $g^6$ in the strong coupling constant. This order is of key importance due to its role in resolving the long-standing infrared problem of finite-temperature field theory within a dimensionally reduced effective field theory setup. By systematically applying linear transformations of integration variables, or momentum shifts, we resolve equivalences between different representations of Feynman sum-integrals. on the integrand level, transforming those into a canonical form. At the order $g^6$, this results in reducing a sum of O(100000) distinct sum-integrals which are produced from all four-loop vacuum diagrams down to merely 21. Furthermore, we succeed to map 11 of those onto known lower-loop structures. This leaves only 10 genuine 4-loop sum-integrals to be evaluated, thereby bringing the finalization of three decades of theoretical efforts within reach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $g^6$ pressure of hot Yang-Mills theory: Canonical form of the integrand Navarrete, Pablo Schröder, York High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory We present major progress towards the determination of the last missing piece for the pressure of a Yang-Mills plasma at high temperatures at order $g^6$ in the strong coupling constant. This order is of key importance due to its role in resolving the long-standing infrared problem of finite-temperature field theory within a dimensionally reduced effective field theory setup. By systematically applying linear transformations of integration variables, or momentum shifts, we resolve equivalences between different representations of Feynman sum-integrals. on the integrand level, transforming those into a canonical form. At the order $g^6$, this results in reducing a sum of O(100000) distinct sum-integrals which are produced from all four-loop vacuum diagrams down to merely 21. Furthermore, we succeed to map 11 of those onto known lower-loop structures. This leaves only 10 genuine 4-loop sum-integrals to be evaluated, thereby bringing the finalization of three decades of theoretical efforts within reach. |
| title | The $g^6$ pressure of hot Yang-Mills theory: Canonical form of the integrand |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2408.15830 |