We compare two approaches to evaluate cross sections of heavy-quarkonium production at next-to-leading order in nonrelativistic QCD involving $S$- and $P$-wave Fock states: the customary approach based on phase space slicing and the approach based on dipole subtraction recently elaborated by us. We find reasonable agreement between the numerical results of the two implementations, but the dipole subtraction implementation outperforms the phase space slicing one both with regard to accuracy and speed.
We discuss factorization in heavy quarkonium production in high energy collisions using NRQCD. Infrared divergences at NNLO are not matched by conventional NRQCD matrix elements. However, we show that gauge invariance and factorization require that conventional NRQCD production matrix elements be modified to include Wilson lines or non-abelian gauge links. With this modification NRQCD factorization for heavy quarkonium production is restored at NNLO.
We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-p_T particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the NRQCD formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include nonabelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at NNLO, and verify that they are absorbed into the new, gauge invariant matrix elements.
We study the transition of a heavy quark pair from octet to singlet color configurations at next-to-next-to-leading order (NNLO) in heavy quarkonium production. We show that the infrared singularities in this process are consistent with NRQCD factorization to all orders in the heavy quark relative velocity v. This factorization requires the gauge-completed matrix elements that we introduced previously to prove NNLO factorization to order v ^2.
I discuss NRQCD and, in particular, the NRQCD factorization formalism for quarkonium production and decay. I also summarize the current status of the comparison between the predictions of NRQCD factorization and experimental measurements.
We study the diffractive photo- and leptoproductions of $J / psi$ and $psi $ on the proton, and examine the validity of the small-size color dipole approximation to the production of radially excited heavy quarkonium. The dipole model predicts a small ratio of $psi $ to $J / psi$ photoproduction cross sections, which does not agree with experimental data. We show that this discrepancy originates from a large transverse size of $psi $ which makes the convergence of the transverse size expansion questionable, and the calculation without the dipole approximation turns out to be consistent with the data. Productions of $Upsilon (2S,3S)$ are also discussed, and the dipole approximation is found to be reasonable for the $Upsilon$-family.
Mathias Butenschoen
,Bernd A. Kniehl
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(2020)
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"Dipole Subtraction vs. Phase Space Slicing in NLO NRQCD Heavy-Quarkonium Production Calculations"
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Bernd Kniehl
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