Precise prediction of the decay rate for $η_b\to γγ$ from lattice QCD
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| Format: | Preprint |
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2024
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| _version_ | 1866908720265428992 |
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| author | Colquhoun, Brian Davies, Christine T. H. Lepage, G. Peter |
| author_facet | Colquhoun, Brian Davies, Christine T. H. Lepage, G. Peter |
| contents | We calculate the decay rate for $η_b \to γγ$ in lattice QCD for the first time, providing a precise prediction for the Belle II experiment. Our calculation includes $u$, $d$, $s$ and $c$ quarks in the sea, using gluon field configurations generated by the MILC collaboration, at three values of the lattice spacing from $0.06\;\mathrm{fm}$ to $0.03\;\mathrm{fm}$. All quarks are treated in the Highly Improved Staggered Quark formalism, which enables us to reach the $b$ quark mass for our valence quarks on these fine lattices. We calculate quark-line connected correlation functions only. By working at additional heavy quark masses between those of $c$ and $b$ we map out the behaviour of the ratio $f_{η_h}/(M_{η_h}^2F_{η_h}(0,0))$, where $f$ is the decay constant, $M$, the mass and $F(0,0)$, the form factor for decay to two on-shell photons for the pseudoscalar heavyonium meson, $η_h$. This ratio takes the approximate value 0.5 in leading-order non-relativistic QCD (NRQCD) but we are able to give a much more accurate analysis than this. Focussing on the $b$ quark mass, we find a ratio of $0.467(11)$, giving $Γ(η_b \to γγ) = 0.559(32)_{\text{fit}}(1)_{\text{syst}} \: \mathrm{keV}$. Combined with a value for the branching fraction from NRQCD, our result can be used to determine the total width of the $η_b$ with a $6\%$ uncertainty. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_24041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Precise prediction of the decay rate for $η_b\to γγ$ from lattice QCD Colquhoun, Brian Davies, Christine T. H. Lepage, G. Peter High Energy Physics - Lattice High Energy Physics - Phenomenology We calculate the decay rate for $η_b \to γγ$ in lattice QCD for the first time, providing a precise prediction for the Belle II experiment. Our calculation includes $u$, $d$, $s$ and $c$ quarks in the sea, using gluon field configurations generated by the MILC collaboration, at three values of the lattice spacing from $0.06\;\mathrm{fm}$ to $0.03\;\mathrm{fm}$. All quarks are treated in the Highly Improved Staggered Quark formalism, which enables us to reach the $b$ quark mass for our valence quarks on these fine lattices. We calculate quark-line connected correlation functions only. By working at additional heavy quark masses between those of $c$ and $b$ we map out the behaviour of the ratio $f_{η_h}/(M_{η_h}^2F_{η_h}(0,0))$, where $f$ is the decay constant, $M$, the mass and $F(0,0)$, the form factor for decay to two on-shell photons for the pseudoscalar heavyonium meson, $η_h$. This ratio takes the approximate value 0.5 in leading-order non-relativistic QCD (NRQCD) but we are able to give a much more accurate analysis than this. Focussing on the $b$ quark mass, we find a ratio of $0.467(11)$, giving $Γ(η_b \to γγ) = 0.559(32)_{\text{fit}}(1)_{\text{syst}} \: \mathrm{keV}$. Combined with a value for the branching fraction from NRQCD, our result can be used to determine the total width of the $η_b$ with a $6\%$ uncertainty. |
| title | Precise prediction of the decay rate for $η_b\to γγ$ from lattice QCD |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.24041 |