Solving the J/ψ puzzle – NRQCD factorization at next-to-next-to-leading order

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Despite its great corroboration by the recent discovery of the Higgs boson at the CERN Large Hadron Collider (LHC), the Standard Model (SM) of elementary particle physics, which unifies the electromagnetic, weak, and strong forces of nature by a relativistic, renormalizable quantum field theory, is faced by severe challenges in the quantitative description of experimental data. The most striking discrepancies today appear in the production of heavy quarkonia, i.e. heavy quark-antiquark pairs QQ̅ bound by gluons. In fact, the world data of heavy-quarkonium yield and polarization taken in particle collision experiments at high energies, including those at the LHC, elude a coherent interpretation by the best available predictions of quantum chromodynamics (QCD), which governs the strong interactions within the SM. Discrepancies by more than 20 standard deviations are found for the otherwise very familiar J/ψ meson, discovered already in 1974! Such discrepancies between theory and experiment are absolutely unacceptable. We propose to tackle this longstanding fundamental problem by pushing the Bodwin-Braaten-Lepage factorization approach to nonrelativistic QCD (NRQCD), the effective field theory derived from QCD to describe QQ̅ bound-state dynamics, to the next level of precision. This amounts to including quantum and relativistic corrections at the next-to-next-to-leading order, i.e. at relative orders αs2, αsv2, v4 in the strong-coupling constant αs and the velocity v of Q in the QQ̅ rest frame. The quantum corrections involve two-loop Feynman diagrams with two incoming and three outgoing particles, one-loop 2 → 4 diagrams, and tree-level 2 → 5 diagrams. There are at least three different mass scales: two Mandelstam variables s and t, measuring the center-of-mass energy and the scattering angle, respectively, and the mass of Q. The relativistic corrections involve one more mass scale, q2, where q is the momentum of Q. While two-loop calculations are now state of the art in many other areas of particle phenomenology, heavy-quarkonium production is an exception. This is due to the spin and color projections onto the various QQ̅ Fock states, which immensely blow up the analytic expressions. An especially aggravating feature is the appearance of derivatives w.r.t. q via spin projectors with orbital angular momentum L ≥ 1and relativistic corrections. These generate novel classes of infrared singularities unknown outside NRQCD, which require extended patterns of cancellations between virtual and real corrections. The proposed research is likely to solve the J/ψ puzzle because the state-of-the-art predictions are plagued by very sizeable next-to-leading-order corrections seriously impugning their reliability. The envisaged calculations will also probe the underlying factorization hypothesis, universally demarcating the unavoidable non-perturbative phenomena of QCD, in an unexplored region and may necessitate modifications to our understanding of nature.