Kinetic energy and speed powers $v^n$ of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons
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2024
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| author | Li, Wei Wang, Tianhong Feng, Tai-Fu Wang, Guo-Li Chang, Chao-Hsi |
| author_facet | Li, Wei Wang, Tianhong Feng, Tai-Fu Wang, Guo-Li Chang, Chao-Hsi |
| contents | Based on the instantaneous Bethe-Salpeter equation method, we calculate the average values $\overline{|\vec{q}|^n}\equiv q^n$ and speed powers $\overline{|\vec{v}|^n} \equiv v^n$ ($n=1,2,3,4$) of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons, where $\vec{q}$ and $\vec{v}$ are the three dimensional momentum and velocity of the heavy quark, respectively. We obtain the kinetic energy $μ^2_{_π}=0.455$ GeV$^2$ for the $B$ meson, which is consistent with the experimental result $0.464\pm 0.076$ GeV$^2$. For the $B_{s}$, $D$ and $D_{s}$ mesons, the $μ^2_{_π}$ are $0.530$ GeV$^2$, $0.317$ GeV$^2$ and $0.369$ GeV$^2$, respectively. And $v^2=0.0185$, $0.0215$, $0.121$, and $0.140$ for $B$, $B_{s}$, $D$, and $D_{s}$. We obtain some relationships, for example, $q^n_{_{0^-}}(mS)\approx q^n_{_{1^-}}(mS)$, $q^n_{_{0^+}}(mP)\approx q^n_{_{1^{+'}}}(mP^{'})> q^n_{_{1^+}}(mP)\approx q^n_{_{2^+}}(mP)$, and $q^n(mS)< q^n(mP)$ ($m=1,2,3$), etc. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kinetic energy and speed powers $v^n$ of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons Li, Wei Wang, Tianhong Feng, Tai-Fu Wang, Guo-Li Chang, Chao-Hsi High Energy Physics - Phenomenology High Energy Physics - Experiment Based on the instantaneous Bethe-Salpeter equation method, we calculate the average values $\overline{|\vec{q}|^n}\equiv q^n$ and speed powers $\overline{|\vec{v}|^n} \equiv v^n$ ($n=1,2,3,4$) of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons, where $\vec{q}$ and $\vec{v}$ are the three dimensional momentum and velocity of the heavy quark, respectively. We obtain the kinetic energy $μ^2_{_π}=0.455$ GeV$^2$ for the $B$ meson, which is consistent with the experimental result $0.464\pm 0.076$ GeV$^2$. For the $B_{s}$, $D$ and $D_{s}$ mesons, the $μ^2_{_π}$ are $0.530$ GeV$^2$, $0.317$ GeV$^2$ and $0.369$ GeV$^2$, respectively. And $v^2=0.0185$, $0.0215$, $0.121$, and $0.140$ for $B$, $B_{s}$, $D$, and $D_{s}$. We obtain some relationships, for example, $q^n_{_{0^-}}(mS)\approx q^n_{_{1^-}}(mS)$, $q^n_{_{0^+}}(mP)\approx q^n_{_{1^{+'}}}(mP^{'})> q^n_{_{1^+}}(mP)\approx q^n_{_{2^+}}(mP)$, and $q^n(mS)< q^n(mP)$ ($m=1,2,3$), etc. |
| title | Kinetic energy and speed powers $v^n$ of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2405.12440 |