On-shell recursion and holomorphic HQET for heavy quark hadronic resonances
Abstract We develop a new theoretical framework for the treatment of heavy quark (HQ) resonances within heavy quark effective theory (HQET). This framework uses on-shell recursion techniques to express the resonant amplitude as a product of on-shell subamplitudes, which allows one to employ a form-f...
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2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)239 |
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| author | Claudio Andrea Manzari Dean J. Robinson |
| author_facet | Claudio Andrea Manzari Dean J. Robinson |
| author_sort | Claudio Andrea Manzari |
| collection | DOAJ |
| description | Abstract We develop a new theoretical framework for the treatment of heavy quark (HQ) resonances within heavy quark effective theory (HQET). This framework uses on-shell recursion techniques to express the resonant amplitude as a product of on-shell subamplitudes, which allows one to employ a form-factor representation of the hadronic matrix elements and to obtain an HQ expansion, but at the price of introducing complex momenta. We construct a generalized “holomorphic HQET” onto which such complex-momentum matrix elements can be matched, and we show that PT symmetry ensures the Isgur-Wise functions (and the perturbative corrections) become holomorphic functions of the complex recoil parameter with real coefficients. They are thus an analytic continuation of the standard HQET description. This framework admits a HQ hadron (strong decay) width expansion. At second order, we show it is compatible with data for the B 1 2 ∗ $$ {B}_{1(2)}^{\left(\ast \right)} $$ and D 1 2 ∗ $$ {D}_{1(2)}^{\left(\ast \right)} $$ HQ doublets. Taking the B ¯ → D 1 ∗ 1 − → Dπ lν $$ \overline{B}\to \left({D}_1^{\ast}\left({1}^{-}\right)\to D\pi \right) l\nu $$ system as an example, we compute the holomorphic HQET expansion to first order, as well as the complex-momentum on-shell subamplitudes. A toy numerical study of the resulting differential rates demonstrates that this framework generates HQ resonance lineshapes with large tails, resembling those seen in data. |
| format | Article |
| id | doaj-art-2fa9a09cbcac4af89f7286f3e807b268 |
| institution | OA Journals |
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| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-2fa9a09cbcac4af89f7286f3e807b2682025-08-20T02:05:45ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025515110.1007/JHEP05(2025)239On-shell recursion and holomorphic HQET for heavy quark hadronic resonancesClaudio Andrea Manzari0Dean J. Robinson1Ernest Orlando Lawrence Berkeley National Laboratory, University of CaliforniaErnest Orlando Lawrence Berkeley National Laboratory, University of CaliforniaAbstract We develop a new theoretical framework for the treatment of heavy quark (HQ) resonances within heavy quark effective theory (HQET). This framework uses on-shell recursion techniques to express the resonant amplitude as a product of on-shell subamplitudes, which allows one to employ a form-factor representation of the hadronic matrix elements and to obtain an HQ expansion, but at the price of introducing complex momenta. We construct a generalized “holomorphic HQET” onto which such complex-momentum matrix elements can be matched, and we show that PT symmetry ensures the Isgur-Wise functions (and the perturbative corrections) become holomorphic functions of the complex recoil parameter with real coefficients. They are thus an analytic continuation of the standard HQET description. This framework admits a HQ hadron (strong decay) width expansion. At second order, we show it is compatible with data for the B 1 2 ∗ $$ {B}_{1(2)}^{\left(\ast \right)} $$ and D 1 2 ∗ $$ {D}_{1(2)}^{\left(\ast \right)} $$ HQ doublets. Taking the B ¯ → D 1 ∗ 1 − → Dπ lν $$ \overline{B}\to \left({D}_1^{\ast}\left({1}^{-}\right)\to D\pi \right) l\nu $$ system as an example, we compute the holomorphic HQET expansion to first order, as well as the complex-momentum on-shell subamplitudes. A toy numerical study of the resulting differential rates demonstrates that this framework generates HQ resonance lineshapes with large tails, resembling those seen in data.https://doi.org/10.1007/JHEP05(2025)239Effective Field TheoriesBottom QuarksSemi-Leptonic Decays |
| spellingShingle | Claudio Andrea Manzari Dean J. Robinson On-shell recursion and holomorphic HQET for heavy quark hadronic resonances Journal of High Energy Physics Effective Field Theories Bottom Quarks Semi-Leptonic Decays |
| title | On-shell recursion and holomorphic HQET for heavy quark hadronic resonances |
| title_full | On-shell recursion and holomorphic HQET for heavy quark hadronic resonances |
| title_fullStr | On-shell recursion and holomorphic HQET for heavy quark hadronic resonances |
| title_full_unstemmed | On-shell recursion and holomorphic HQET for heavy quark hadronic resonances |
| title_short | On-shell recursion and holomorphic HQET for heavy quark hadronic resonances |
| title_sort | on shell recursion and holomorphic hqet for heavy quark hadronic resonances |
| topic | Effective Field Theories Bottom Quarks Semi-Leptonic Decays |
| url | https://doi.org/10.1007/JHEP05(2025)239 |
| work_keys_str_mv | AT claudioandreamanzari onshellrecursionandholomorphichqetforheavyquarkhadronicresonances AT deanjrobinson onshellrecursionandholomorphichqetforheavyquarkhadronicresonances |