Explicit estimate of charm rescattering in $B^0 \to K^0 \bar{\ell} \ell$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909633699905536 |
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| author | Isidori, Gino Polonsky, Zachary Tinari, Arianna |
| author_facet | Isidori, Gino Polonsky, Zachary Tinari, Arianna |
| contents | We analyze $B^0 \to K^0 \bar{\ell}\ell$ long-distance contributions induced by the rescattering of a pair of charmed and charmed-strange mesons. We present an explicit estimate of these contributions using an effective description in terms of hadronic degrees of freedom, supplemented by data on the $B^0 \to D^*D_s (D^*_sD)$ transition in order to reproduce the corresponding discontinuity in the $B^0 \to K^0 \bar{\ell}\ell$ amplitude. The $D^* D_s (D^*_s D) K$ vertex is estimated using heavy-hadron chiral perturbation theory, obtaining an accurate description of the whole rescattering process in the low-recoil (or high-$q^2$) limit. We also present an extrapolation to the whole kinematical region introducing hadronic form factors. The explicit estimate of the leading $D^*D_s (D^*_sD)$ intermediate state leads to a long-distance amplitude which does not exceed a few percent relative to the short-distance one. The consequences of this result for the extraction of the short-distance coefficient $C_9$ are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_17551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit estimate of charm rescattering in $B^0 \to K^0 \bar{\ell} \ell$ Isidori, Gino Polonsky, Zachary Tinari, Arianna High Energy Physics - Phenomenology We analyze $B^0 \to K^0 \bar{\ell}\ell$ long-distance contributions induced by the rescattering of a pair of charmed and charmed-strange mesons. We present an explicit estimate of these contributions using an effective description in terms of hadronic degrees of freedom, supplemented by data on the $B^0 \to D^*D_s (D^*_sD)$ transition in order to reproduce the corresponding discontinuity in the $B^0 \to K^0 \bar{\ell}\ell$ amplitude. The $D^* D_s (D^*_s D) K$ vertex is estimated using heavy-hadron chiral perturbation theory, obtaining an accurate description of the whole rescattering process in the low-recoil (or high-$q^2$) limit. We also present an extrapolation to the whole kinematical region introducing hadronic form factors. The explicit estimate of the leading $D^*D_s (D^*_sD)$ intermediate state leads to a long-distance amplitude which does not exceed a few percent relative to the short-distance one. The consequences of this result for the extraction of the short-distance coefficient $C_9$ are discussed. |
| title | Explicit estimate of charm rescattering in $B^0 \to K^0 \bar{\ell} \ell$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2405.17551 |