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Register a new userComprehensive studies of $Upsilon$ inclusive production in $Z$ boson decay
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In this paper, we present a comprehensive study of $Upsilon$ inclusive production in $Z$ boson decay, including the first complete next-to-leading-order calculations of the color-octet (CO) contributions. With the inclusion of the newly-calculated remarkable QCD corrections, the CO processes exhibit crucially phenomenological influence on the existing predictions built on the color-singlet mechanism. We also include the exhaustive evaluations of the feed-down contributions, which remained ignored in the literature, and find them to be considerable. Summing up all the contributions, the $mathcal{B}_{Z to Upsilon(nS)+X}$ still notably undershoot the data released by the L3 Collaboration.
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Inclusive $chi_{cJ}$ $(J=0,1,2)$ production from $Upsilon(1S)$ decay is studied within the framework of nonrelativistic QCD (NRQCD) factorization at leading order in $v_Q^2$, which includes the contributions of $bbar{b}({}^3S_1^{[1]})to cbar{c}(^3P_J^{[1]})+X$ and $bbar{b}({}^3S_1^{[1]})to cbar{c}(^3S_1^{[8]})+X$. For both channels, the short-distance coefficients are calculated through ${cal O}(alpha_s^5)$, which is next-to-leading order for the second one. By fitting to the measured $Upsilon(1S)$ branching fractions to $chi_{c1}$ and $chi_{c2}$, we obtain the color-octet long-distance matrix element (LDME) $langlemathcal{O}^{chi_{c0}}({}^3S_1^{[8]})rangle =(4.04pm0.47_{-0.34}^{+0.67})times10^{-3}$ GeV$^3$, where the first error is experimental and the second one due to the renormalization scale dependence, if we use as input $langlemathcal{O}^{chi_{c0}}({}^3P_0^{[1]})rangle=0.107$ GeV$^5$ as obtained via potential-model analysis. Previous LDME sets, extracted from data of prompt $chi_{cJ}$ hadroproduction, yield theoretical predictions that systematically undershoot or mildly overshoot the experimental values of $mathcal{B}(Upsilonto chi_{cJ}+X)$.
In this paper, we carry out the complete $mathcal O(alphaalpha_s^{2})$-order study on the inclusive productions of $Upsilon(nS)$ and $chi_b(nP)$ ($n=1,2,3$) via the Standard Model Higgs boson decay, within the framework of nonrelativistic QCD. The feeddown effects via the higher excited states are found to be substantial. The color-octet $^3S_1^{[8]}$ state related processes consisting of $H^0 to bbar{b}[^3S_1^{[8]}]+g$ and $H^0 to bbar{b}[^3S_1^{[8]}]+Q+bar{Q}$ ($Q=c,b$) play a vital role in the predictions on the decay widths. Moreover, our newly calculated next-to-leading order QCD corrections to $H^0 to bbar{b}[^3S_1^{[8]}]+g$ can enhance its leading-order result by 3-4 times, subsequently magnifying the total $^3S_1^{[8]}$ contributions by about $40%$. Such a remarkable enhancement will to a large extent influence the phenomenological conclusions. For the color-singlet $^3P_J^{[1]}$ state, in addition to $H^{0} to bbar{b}[^3P_J^{[1]}]+b+bar{b}$, the newly introduced light hadrons associated process, $H^{0} to bbar{b}[^3P_J^{[1]}]+g+g$, can also provide non-negligible contributions, especially for $^3P_2^{[1]}$. Summing up all the contributions, we have $mathcal B_{H^0 to chi_b(nP)+X} sim 10^{-6}-10^{-5}$ and $mathcal B_{H^0 to Upsilon(nS)+X} sim 10^{-5}-10^{-4}$, which meets marginally nowadays LHC experimental data and can help in understanding the heavy quarkonium production mechanism as well as the Yukawa couplings.
We study $J/psi$ and $eta_c$ inclusive production in $Upsilon$ decay within the framework of nonrelativistic-QCD (NRQCD) factorization. In the latter case, for which no experimental data exist so far, we also include the $h_c$ feed-down contribution. We calculate the short distance coefficients completely through $mathcal{O}(alpha_s^5)$. The NRQCD predictions for the branching fraction $mathcal{B}(Upsilonto J/psi+X)$ via direct production, evaluated with different sets of long-distance matrix elements (LDMEs), all agree with the experimental data in a reasonable range of renormalization scale. Using $eta_c$ and $h_c$ LDMEs obtained from $J/psi$ and $chi_c$ ones via heavy-quark spin symmetry, we find that the bulk of $mathcal{B}(Upsilontoeta_c+X)$ via prompt production arises from the $cbar{c}({}^3!S_1^{[8]})$ Fock state. The experimental study of this decay process would, therefore, provide a particularly clean probe of the color octet mechanism of heavy-quarkonium production.
Upsilon (1S) decay to Xi_cc +anything is studied. It is shown that the branching ratio can be as significant as that of Upsilon (1S) decay to J/Psi +anything. The non-relativistic heavy quark effective theory framework is employed for the calculation on the decay width. Measurements on the production of Xi_cc and likely production characteristic of the partonic state with four charm quarks at BELLE2 are suggested.
This article presents results for the last unknown two-loop contributions to the $Z$-boson partial widths and $Z$-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where bosonic refers to diagrams without closed fermion loops. Together with the corresponding results for the $Z$-pole asymmetries $A_l, A_b$, which have been presented earlier, this completes the theoretical description of $Z$-boson precision observables at full two-loop precision within the Standard Model. The calculation has been achieved through a combination of different methods: (a) numerical integration of Mellin-Barnes representations with contour rotations and contour shifts to improve convergence; (b) sector decomposition with numerical integration over Feynman parameters; (c) dispersion relations for sub-loop insertions. Numerical results are presented in the form of simple parameterization formulae for the total width, $Gamma_{rm Z}$, partial decay widths $Gamma_{e,mu},Gamma_{tau},Gamma_{ u},Gamma_{u},Gamma_{c},Gamma_{d,s},Gamma_{b}$, branching ratios $R_l,R_c,R_b$ and the hadronic peak cross-section, $sigma_{rm had}^0$. Theoretical intrinsic uncertainties from missing higher orders are also discussed.
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