Measurements of the absolute branching fractions forD s + → η e + ν e
Abstract: = 0.40 ± 0.14 ± 0.02, where the first uncertainties are statistical and the second ones are systematic. The results are in good agreement with previous measurements within uncertainties; they can be used to determine the η − η ′ mixing angle and improve upon the D + s semileptonic branching ratio precision.
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Cited by 19 publications
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In this paper, we make a detailed discussion on the $$\eta $$ η and $$\eta ^\prime $$ η ′ -meson leading-twist light-cone distribution amplitude $$\phi _{2;\eta ^{(\prime )}}(u,\mu )$$ ϕ 2 ; η ( ′ ) ( u , μ ) by using the QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and the next-to-leading order (NLO) QCD corrections to the perturbative part, its first three moments $$\langle \xi ^n_{2;\eta ^{(\prime )}}\rangle |_{\mu _0} $$ ⟨ ξ 2 ; η ( ′ ) n ⟩ | μ 0 with $$n = (2, 4, 6)$$ n = ( 2 , 4 , 6 ) can be determined, where the initial scale $$\mu _0$$ μ 0 is set as the usual choice of 1 GeV. Numerically, we obtain $$\langle \xi _{2;\eta }^2\rangle |_{\mu _0} =0.231_{-0.013}^{+0.010}$$ ⟨ ξ 2 ; η 2 ⟩ | μ 0 = 0 . 231 - 0.013 + 0.010 , $$\langle \xi _{2;\eta }^4 \rangle |_{\mu _0} =0.109_{ - 0.007}^{ + 0.007}$$ ⟨ ξ 2 ; η 4 ⟩ | μ 0 = 0 . 109 - 0.007 + 0.007 , and $$\langle \xi _{2;\eta }^6 \rangle |_{\mu _0} =0.066_{-0.006}^{+0.006}$$ ⟨ ξ 2 ; η 6 ⟩ | μ 0 = 0 . 066 - 0.006 + 0.006 for $$\eta $$ η -meson, $$\langle \xi _{2;\eta '}^2\rangle |_{\mu _0} =0.211_{-0.017}^{+0.015}$$ ⟨ ξ 2 ; η ′ 2 ⟩ | μ 0 = 0 . 211 - 0.017 + 0.015 , $$\langle \xi _{2;\eta '}^4 \rangle |_{\mu _0} =0.093_{ - 0.009}^{ + 0.009}$$ ⟨ ξ 2 ; η ′ 4 ⟩ | μ 0 = 0 . 093 - 0.009 + 0.009 , and $$\langle \xi _{2;\eta '}^6 \rangle |_{\mu _0} =0.054_{-0.008}^{+0.008}$$ ⟨ ξ 2 ; η ′ 6 ⟩ | μ 0 = 0 . 054 - 0.008 + 0.008 for $$\eta '$$ η ′ -meson. Next, we calculate the $$D_s\rightarrow \eta ^{(\prime )}$$ D s → η ( ′ ) transition form factors (TFFs) $$f^{\eta ^{(\prime )}}_{+}(q^2)$$ f + η ( ′ ) ( q 2 ) within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are $$f^{\eta }_+(0) = 0.476_{-0.036}^{+0.040}$$ f + η ( 0 ) = 0 . 476 - 0.036 + 0.040 and $$f^{\eta '}_+(0) = 0.544_{-0.042}^{+0.046}$$ f + η ′ ( 0 ) = 0 . 544 - 0.042 + 0.046 . After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. $$D_s^+\rightarrow \eta ^{(\prime )}\ell ^+ \nu _\ell $$ D s + → η ( ′ ) ℓ + ν ℓ , i.e. $${{\mathcal {B}}}(D_s^+ \rightarrow \eta ^{(\prime )} e^+\nu _e)=2.346_{-0.331}^{+0.418}(0.792_{-0.118}^{+0.141})\times 10^{-2}$$ B ( D s + → η ( ′ ) e + ν e ) = 2 . 346 - 0.331 + 0.418 ( 0 . 792 - 0.118 + 0.141 ) × 10 - 2 and $${{\mathcal {B}}}(D_s^+ \rightarrow \eta ^{(\prime )} \mu ^+\nu _\mu )=2.320_{-0.327}^{+0.413}(0.773_{-0.115}^{+0.138})\times 10^{-2}$$ B ( D s + → η ( ′ ) μ + ν μ ) = 2 . 320 - 0.327 + 0.413 ( 0 . 773 - 0.115 + 0.138 ) × 10 - 2 for $$\ell = (e, \mu )$$ ℓ = ( e , μ ) channels respectively. And in addition to that, the mixing angle for $$\eta -\eta '$$ η - η ′ with $$\varphi $$ φ and ratio for the different decay channels $${{\mathcal {R}}}_{\eta '/\eta }^\ell $$ R η ′ / η ℓ are given, which show good agreement with the recent BESIII measurements.
In this paper, we make a detailed discussion on the $$\eta $$ η and $$\eta ^\prime $$ η ′ -meson leading-twist light-cone distribution amplitude $$\phi _{2;\eta ^{(\prime )}}(u,\mu )$$ ϕ 2 ; η ( ′ ) ( u , μ ) by using the QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and the next-to-leading order (NLO) QCD corrections to the perturbative part, its first three moments $$\langle \xi ^n_{2;\eta ^{(\prime )}}\rangle |_{\mu _0} $$ ⟨ ξ 2 ; η ( ′ ) n ⟩ | μ 0 with $$n = (2, 4, 6)$$ n = ( 2 , 4 , 6 ) can be determined, where the initial scale $$\mu _0$$ μ 0 is set as the usual choice of 1 GeV. Numerically, we obtain $$\langle \xi _{2;\eta }^2\rangle |_{\mu _0} =0.231_{-0.013}^{+0.010}$$ ⟨ ξ 2 ; η 2 ⟩ | μ 0 = 0 . 231 - 0.013 + 0.010 , $$\langle \xi _{2;\eta }^4 \rangle |_{\mu _0} =0.109_{ - 0.007}^{ + 0.007}$$ ⟨ ξ 2 ; η 4 ⟩ | μ 0 = 0 . 109 - 0.007 + 0.007 , and $$\langle \xi _{2;\eta }^6 \rangle |_{\mu _0} =0.066_{-0.006}^{+0.006}$$ ⟨ ξ 2 ; η 6 ⟩ | μ 0 = 0 . 066 - 0.006 + 0.006 for $$\eta $$ η -meson, $$\langle \xi _{2;\eta '}^2\rangle |_{\mu _0} =0.211_{-0.017}^{+0.015}$$ ⟨ ξ 2 ; η ′ 2 ⟩ | μ 0 = 0 . 211 - 0.017 + 0.015 , $$\langle \xi _{2;\eta '}^4 \rangle |_{\mu _0} =0.093_{ - 0.009}^{ + 0.009}$$ ⟨ ξ 2 ; η ′ 4 ⟩ | μ 0 = 0 . 093 - 0.009 + 0.009 , and $$\langle \xi _{2;\eta '}^6 \rangle |_{\mu _0} =0.054_{-0.008}^{+0.008}$$ ⟨ ξ 2 ; η ′ 6 ⟩ | μ 0 = 0 . 054 - 0.008 + 0.008 for $$\eta '$$ η ′ -meson. Next, we calculate the $$D_s\rightarrow \eta ^{(\prime )}$$ D s → η ( ′ ) transition form factors (TFFs) $$f^{\eta ^{(\prime )}}_{+}(q^2)$$ f + η ( ′ ) ( q 2 ) within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are $$f^{\eta }_+(0) = 0.476_{-0.036}^{+0.040}$$ f + η ( 0 ) = 0 . 476 - 0.036 + 0.040 and $$f^{\eta '}_+(0) = 0.544_{-0.042}^{+0.046}$$ f + η ′ ( 0 ) = 0 . 544 - 0.042 + 0.046 . After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. $$D_s^+\rightarrow \eta ^{(\prime )}\ell ^+ \nu _\ell $$ D s + → η ( ′ ) ℓ + ν ℓ , i.e. $${{\mathcal {B}}}(D_s^+ \rightarrow \eta ^{(\prime )} e^+\nu _e)=2.346_{-0.331}^{+0.418}(0.792_{-0.118}^{+0.141})\times 10^{-2}$$ B ( D s + → η ( ′ ) e + ν e ) = 2 . 346 - 0.331 + 0.418 ( 0 . 792 - 0.118 + 0.141 ) × 10 - 2 and $${{\mathcal {B}}}(D_s^+ \rightarrow \eta ^{(\prime )} \mu ^+\nu _\mu )=2.320_{-0.327}^{+0.413}(0.773_{-0.115}^{+0.138})\times 10^{-2}$$ B ( D s + → η ( ′ ) μ + ν μ ) = 2 . 320 - 0.327 + 0.413 ( 0 . 773 - 0.115 + 0.138 ) × 10 - 2 for $$\ell = (e, \mu )$$ ℓ = ( e , μ ) channels respectively. And in addition to that, the mixing angle for $$\eta -\eta '$$ η - η ′ with $$\varphi $$ φ and ratio for the different decay channels $${{\mathcal {R}}}_{\eta '/\eta }^\ell $$ R η ′ / η ℓ are given, which show good agreement with the recent BESIII measurements.
$η^{(\prime)}$-meson twist-2 distribution amplitude within QCD sum rule approach and its application to the semi-leptonic decay $ D_s^+ \toη^{(\prime)}\ell^+ ν_\ell$
In this paper, we make a detailed discussion on the η-meson leading-twist light-cone distribution amplitude (LCDA) φ 2;η (u, µ) by using the QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and the next-to-leading order (NLO) QCD corrections to the perturbative part, its first three moments ξ n 2;η | µ0 with n = (2, 4, 6) can be determined, where the initial scale µ 0 is set as the usual choice of 1 GeV. Numerically, we obtain ξ 2 2;η | µ0 = 0.204 +0.008 −0.012 , ξ 4 2;η | µ0 = 0.092 +0.006 −0.007 , and ξ 6 2;η | µ0 = 0.054 +0.004 −0.005 . Next, we calculate the D s → η transition form factor (TFF) f + (q 2 ) within the QCD light-cone sum rules approach up to NLO level. Its value at the large recoil region is f + (0) = 0.484 +0.039 −0.036 . After extrapolating the TFF to the allowable physical region, we then obtain the total decay widthes and the branching fractions of the semi-leptonic31.197 +5.456 −4.323 ) × 10 −15 GeV, B(D + s → ηe + ν e ) = 2.389 +0.418 −0.331 for D + s → ηe + ν e channel, and Γ(D + s → ηµ + ν µ ) = (30.849 +5.397 −4.273 ) × 10 −15 GeV, B(D + s → ηµ + ν µ ) = 2.362 +0.413 −0.327 for D + s → ηµ + ν µ channel respectively. Those values show good agreement with the recent BES-III measurements.
Averages of $b$-hadron, $c$-hadron, and $τ$-lepton properties as of 2018
This paper reports world averages of measurements of b-hadron, c-hadron, and τ -lepton properties obtained by the Heavy Flavor Averaging Group using results available through September 2018. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, CP violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements.
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