S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
Abstract The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S 2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boun...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2021)125 |
| _version_ | 1818583585771225088 |
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| author | Yifei He Martin Kruczenski |
| author_facet | Yifei He Martin Kruczenski |
| author_sort | Yifei He |
| collection | DOAJ |
| description | Abstract The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S 2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves k ℓ (s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves f ℓ (s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics. |
| first_indexed | 2024-12-16T08:07:37Z |
| format | Article |
| id | doaj.art-36b3c15e637d40e59199f6d9028974e1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T08:07:37Z |
| publishDate | 2021-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-36b3c15e637d40e59199f6d9028974e12022-12-21T22:38:25ZengSpringerOpenJournal of High Energy Physics1029-84792021-08-012021814110.1007/JHEP08(2021)125S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problemYifei He0Martin Kruczenski1Institut Philippe Meyer, École Normale Supérieure, Université PSLDepartment of Physics and Astronomy and Purdue Quantum Science and Engineering Institute (PQSEI), Purdue UniversityAbstract The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S 2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves k ℓ (s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves f ℓ (s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.https://doi.org/10.1007/JHEP08(2021)125Field Theories in Higher DimensionsNonperturbative EffectsScattering Amplitudes |
| spellingShingle | Yifei He Martin Kruczenski S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem Journal of High Energy Physics Field Theories in Higher Dimensions Nonperturbative Effects Scattering Amplitudes |
| title | S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem |
| title_full | S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem |
| title_fullStr | S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem |
| title_full_unstemmed | S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem |
| title_short | S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem |
| title_sort | s matrix bootstrap in 3 1 dimensions regularization and dual convex problem |
| topic | Field Theories in Higher Dimensions Nonperturbative Effects Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP08(2021)125 |
| work_keys_str_mv | AT yifeihe smatrixbootstrapin31dimensionsregularizationanddualconvexproblem AT martinkruczenski smatrixbootstrapin31dimensionsregularizationanddualconvexproblem |