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Register a new userThe complete study on polarization of $Upsilon(nS)$ hadroproduction at QCD next-to-leading order
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Applying the nonrelativistic quantum chromodynamics factorization formalism to the $Upsilon(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters $lambda_{theta}$, $lambda_{thetaphi}$, $lambda_{phi}$ for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter $lambda_{theta}$ of $Upsilon$ hadroproduction, our results provide a good description for the measured parameters $lambda_{thetaphi}$ and $lambda_{phi}$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $tilde{lambda}$ is consistent in the two frames. Finally, it is pointed out that there are discrepancies for $tilde{lambda}$ between available experimental data and corresponding theoretical predictions.
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In this paper, we carry out the next-to-leading-order (NLO) studies on $Z to Upsilon(1S)+g+g$ via the color-singlet (CS) $bbar{b}$ state. We find the newly calculated NLO QCD corrections to this process can significantly influence its leading-order (LO) results, and greatly improve the dependence on the renormalization scale. By including the considerable feeddown contributions, the branching ratio $mathcal{B}_{Z to Upsilon(1S)+g+g}$ is predicted to be $(0.56 sim 0.95)times 10^{-6}$, which can reach up to $19% sim 31%$ of the LO predictions given by the CS dominant process $Z to Upsilon(1S)+b+bar{b}$. Moreover, $Z to Upsilon(1S)+g+g$ also seriously affect the CS predictions on the $Upsilon(1S)$ energy distributions, especially when $z$ is relatively small. In summary, for the inclusive $Upsilon(1S)$ productions in $Z$ decay, besides $Z to Upsilon(1S)+b+bar{b}$, the gluon radiation process $Z to Upsilon(1S)+g+g$ can provide indispensable contributions as well.
We compute the imaginary part of the heavy quark contribution to the photon polarization tensor, i.e. the quarkonium spectral function in the vector channel, at next-to-leading order in thermal QCD. Matching our result, which is valid sufficiently far away from the two-quark threshold, with a previously determined resummed expression, which is valid close to the threshold, we obtain a phenomenological estimate for the spectral function valid for all non-zero energies. In particular, the new expression allows to fix the overall normalization of the previous resummed one. Our result may be helpful for lattice reconstructions of the spectral function (near the continuum limit), which necessitate its high energy behaviour as input, and can in principle also be compared with the dilepton production rate measured in heavy ion collision experiments. In an appendix analogous results are given for the scalar channel.
We present a study at next-to-leading-order (NLO) of the process $pp to W^pm Z to ell u_l ell^+ ell^-$, where $ell,ell =e, mu$, at the Large Hadron Collider. We include the full NLO QCD corrections and the NLO electroweak (EW) corrections in the double-pole approximation. We define eight fiducial polarization coefficients directly constructed from the polar-azimuthal angular distribution of the decay leptons. These coefficients depend strongly on the kinematical cuts on the transverse momentum or rapidity of the individual leptons. Similarly, fiducial polarization fractions are also defined and they can be directly related to the fiducial coefficients. We perform a detailed analysis of the NLO QCD+EW fiducial polarization observables including theoretical uncertainties stemming from the scale variation and parton distribution function uncertainties, using the fiducial phase space defined by the ATLAS and CMS experiments. We provide results in the helicity coordinate system and in the Collins-Soper coordinate system, at a center-of-mass energy of 13 TeV. The EW corrections are found to be important in two of the angular coefficients related to the $Z$ boson, irrespective of the kinematical cuts or the coordinate system. Meanwhile, those EW corrections are very small for the $W^pm$ bosons.
We determine an approximate expression for the O(alpha_s^3) contribution chi_2 to the kernel of the BFKL equation, which includes all collinear and anticollinear singular contributions. This is derived using recent results on the relation between the GLAP and BFKL kernels (including running-coupling effects to all orders) and on small-x factorization schemes. We present the result in various schemes, relevant both for applications to the BFKL equation and to small-x evolution of parton distributions.
We compute the hydrodynamic relaxation times $tau_pi$ and $tau_j$ for hot QCD at next-to-leading order in the coupling with kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds which apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.
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