Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ −
Abstract We present a strategy for calculating the rare decay of a Σ+(uus) baryon to a proton (uud) and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point correlation functions related to the target process. In parti...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-04-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2023)108 |
| _version_ | 1797769736896905216 |
|---|---|
| author | Felix Erben Vera Gülpers Maxwell T. Hansen Raoul Hodgson Antonin Portelli |
| author_facet | Felix Erben Vera Gülpers Maxwell T. Hansen Raoul Hodgson Antonin Portelli |
| author_sort | Felix Erben |
| collection | DOAJ |
| description | Abstract We present a strategy for calculating the rare decay of a Σ+(uus) baryon to a proton (uud) and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point correlation functions related to the target process. In particular, the four-point function arises from the insertion of incoming and outgoing baryons, together with a weak Hamiltonian mediating the s → d transition and an electromagnetic current creating the outgoing leptons. As is described in previous work in other contexts, this four-point function has a highly non-trivial relation to the physical observable, due to proton and proton-pion intermediate states. These lead to growing Euclidean time dependence and, in the case of the two-particle intermediate states, to power-like volume effects. We discuss how to treat these issues in the context of the Σ+ → pℓ + ℓ − decay and, in particular, detail the relation between the finite-volume estimator and the physical, complex-valued amplitude. In doing so, we also make connections between various approaches already described in the literature. |
| first_indexed | 2024-03-12T21:13:19Z |
| format | Article |
| id | doaj.art-d00d30308c774e5cb353eaefcf87249f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T21:13:19Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d00d30308c774e5cb353eaefcf87249f2023-07-30T11:03:59ZengSpringerOpenJournal of High Energy Physics1029-84792023-04-012023414010.1007/JHEP04(2023)108Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ −Felix Erben0Vera Gülpers1Maxwell T. Hansen2Raoul Hodgson3Antonin Portelli4School of Physics and Astronomy, University of EdinburghSchool of Physics and Astronomy, University of EdinburghSchool of Physics and Astronomy, University of EdinburghSchool of Physics and Astronomy, University of EdinburghSchool of Physics and Astronomy, University of EdinburghAbstract We present a strategy for calculating the rare decay of a Σ+(uus) baryon to a proton (uud) and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point correlation functions related to the target process. In particular, the four-point function arises from the insertion of incoming and outgoing baryons, together with a weak Hamiltonian mediating the s → d transition and an electromagnetic current creating the outgoing leptons. As is described in previous work in other contexts, this four-point function has a highly non-trivial relation to the physical observable, due to proton and proton-pion intermediate states. These lead to growing Euclidean time dependence and, in the case of the two-particle intermediate states, to power-like volume effects. We discuss how to treat these issues in the context of the Σ+ → pℓ + ℓ − decay and, in particular, detail the relation between the finite-volume estimator and the physical, complex-valued amplitude. In doing so, we also make connections between various approaches already described in the literature.https://doi.org/10.1007/JHEP04(2023)108Algorithms and Theoretical DevelopmentsHadronic Matrix Elements and Weak DecaysLattice QCD |
| spellingShingle | Felix Erben Vera Gülpers Maxwell T. Hansen Raoul Hodgson Antonin Portelli Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ − Journal of High Energy Physics Algorithms and Theoretical Developments Hadronic Matrix Elements and Weak Decays Lattice QCD |
| title | Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ − |
| title_full | Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ − |
| title_fullStr | Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ − |
| title_full_unstemmed | Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ − |
| title_short | Prospects for a lattice calculation of the rare decay Σ+ → pℓ + ℓ − |
| title_sort | prospects for a lattice calculation of the rare decay σ pl l |
| topic | Algorithms and Theoretical Developments Hadronic Matrix Elements and Weak Decays Lattice QCD |
| url | https://doi.org/10.1007/JHEP04(2023)108 |
| work_keys_str_mv | AT felixerben prospectsforalatticecalculationoftheraredecayspll AT veragulpers prospectsforalatticecalculationoftheraredecayspll AT maxwellthansen prospectsforalatticecalculationoftheraredecayspll AT raoulhodgson prospectsforalatticecalculationoftheraredecayspll AT antoninportelli prospectsforalatticecalculationoftheraredecayspll |