Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure
Abstract Amplitudes of the form $$\gamma ^*(q^2)\rightarrow \gamma P_1P_2$$ γ ∗ ( q 2 ) → γ P 1 P 2 appear as sub-processes in the computation of the muon $$g-2$$ g - 2 . We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at $$q^2=m^2_\p...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-021-09772-8 |
| _version_ | 1819006328628051968 |
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| author | B. Moussallam |
| author_facet | B. Moussallam |
| author_sort | B. Moussallam |
| collection | DOAJ |
| description | Abstract Amplitudes of the form $$\gamma ^*(q^2)\rightarrow \gamma P_1P_2$$ γ ∗ ( q 2 ) → γ P 1 P 2 appear as sub-processes in the computation of the muon $$g-2$$ g - 2 . We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at $$q^2=m^2_\phi $$ q 2 = m ϕ 2 . Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low’s soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of $$P_1P_2=\pi \eta $$ P 1 P 2 = π η , we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from $$\gamma \gamma $$ γ γ scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the $$I=1$$ I = 1 scalar form factors and to the $$a_0(980)$$ a 0 ( 980 ) resonance complex pole are presented. |
| first_indexed | 2024-12-21T00:06:56Z |
| format | Article |
| id | doaj.art-c8da666d77b74893aa05a9a5631e4bf9 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-21T00:06:56Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-c8da666d77b74893aa05a9a5631e4bf92022-12-21T19:22:27ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-11-01811112710.1140/epjc/s10052-021-09772-8Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structureB. Moussallam0Laboratoire Irène Joliot-Curie (CNRS/IN2P3, UMR9012), Pôle Théorie, Université Paris-SaclayAbstract Amplitudes of the form $$\gamma ^*(q^2)\rightarrow \gamma P_1P_2$$ γ ∗ ( q 2 ) → γ P 1 P 2 appear as sub-processes in the computation of the muon $$g-2$$ g - 2 . We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at $$q^2=m^2_\phi $$ q 2 = m ϕ 2 . Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low’s soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of $$P_1P_2=\pi \eta $$ P 1 P 2 = π η , we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from $$\gamma \gamma $$ γ γ scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the $$I=1$$ I = 1 scalar form factors and to the $$a_0(980)$$ a 0 ( 980 ) resonance complex pole are presented.https://doi.org/10.1140/epjc/s10052-021-09772-8 |
| spellingShingle | B. Moussallam Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure European Physical Journal C: Particles and Fields |
| title | Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure |
| title_full | Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure |
| title_fullStr | Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure |
| title_full_unstemmed | Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure |
| title_short | Revisiting $$\gamma ^*\rightarrow \gamma \pi ^0\eta $$ γ ∗ → γ π 0 η near the $$\phi (1020)$$ ϕ ( 1020 ) using analyticity and the left-cut structure |
| title_sort | revisiting gamma rightarrow gamma pi 0 eta γ ∗ γ π 0 η near the phi 1020 ϕ 1020 using analyticity and the left cut structure |
| url | https://doi.org/10.1140/epjc/s10052-021-09772-8 |
| work_keys_str_mv | AT bmoussallam revisitinggammarightarrowgammapi0etaggp0ēnearthephi1020ph1020usinganalyticityandtheleftcutstructure |