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

尽管欧洲核子研究中心（CERN）大型强子对撞机（LHC）最近发现的希格斯玻色子极大地证实了基本粒子物理学的标准模型（SM），它通过相对论性的、可重整的量子场论统一了自然界的电磁、弱和强作用力，但在实验数据的定量描述方面面临着严峻的挑战。今天最显著的差异出现在重夸克的产生上，即由胶子束缚的重夸克-反夸克对。事实上，在高能粒子碰撞实验中（包括在大型强子对撞机中）获得的重夸克子产率和极化的世界数据，无法通过量子色动力学（QCD）的最佳预测得到一致的解释，量子色动力学（QCD）控制着SM内的强相互作用。对于我们非常熟悉的J/ψ介子，发现了超过20个标准差的差异，它早在1974年就被发现了！理论与实验之间的这种差异是绝对不能接受的。我们建议通过将Bodwin-Braaten-Lepage分解方法推广到非相对论QCD （NRQCD）来解决这个长期存在的基本问题，NRQCD是由QCD衍生而来的描述QQ _束缚态动力学的有效场论，达到下一个精度水平。这相当于包含了次至上阶的量子和相对论性修正，即强耦合常数αs中的相对阶αs2， αsv2， v4和Q的速度v在QQ坐标系中。量子修正包括两个入射粒子和三个出射粒子的双环费曼图、一环2→4图和树级2→5图。至少有三种不同的质量尺度：两个曼德尔施塔姆变量s和t，分别测量质心能量和散射角，以及q的质量。相对论修正涉及到另一个质量尺度，q2，其中q是q的动量。虽然双环计算现在在粒子现象学的许多其他领域都是最先进的，但重夸克子的产生是一个例外。这是由于在各种QQ _ Fock状态上的自旋和彩色投影极大地放大了解析表达式。一个特别令人恼火的特征是通过轨道角动量L≥1和相对论修正的自旋投影仪出现的导数w.r.t.q。这就产生了在NRQCD之外未知的新型红外奇点，这需要在虚和实校正之间扩展消去模式。这项被提议的研究很可能解决J/ψ难题，因为最先进的预测受到相当大的次一级修正的困扰，严重影响了它们的可靠性。设想的计算还将探索潜在的因子分解假设，在未探索的区域普遍划定QCD不可避免的非扰动现象，并可能需要修改我们对自然的理解。

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.