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

尽管最近在欧洲核子研究中心(CERN)大型强子对撞机(LHC)上发现了希格斯玻色子，这一发现得到了极大的证实，但基本粒子物理的标准模型(SM)通过相对论、可重整化的量子场理论统一了自然界中的电磁力、弱力和强力，在对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，也就是重夸克-反夸克对QQ̅被胶子束缚。事实上，包括大型强子对撞机在内的高能粒子碰撞实验中获得的重夸克粒子产额和极化的世界数据，无法得到量子色动力学(QCD)的最佳预测的一致解释，QCD支配着SM内部的强烈相互作用。在1974年已经发现的非常熟悉的J/ψ介子的偏差超过了20个标准差！理论和实验之间的这种差异是绝对不能接受的。为了解决这个长期存在的基本问题，我们建议将Bodwin-Braten-Lepage因式分解方法推广到非相对论QCD(NRQCD)，即从QCD派生的描述QQ̅束缚态动力学的有效场论，将其提高到更高的精度水平。这相当于在倒数第二个序次上包含了量子和相对论修正，即在强耦合常数αS中的相对序数αs2、αsv2、v4和在QQ̅静止标架中的q的速度v。量子修正包括具有两个传入粒子和三个传出粒子的双圈费曼图、单圈2→4图和树级2→5图。至少有三种不同的质量标度：两个曼德尔斯塔姆变量S和t，分别测量质心能量和散射角，以及Q的质量。相对论修正涉及另一个质量标度Q2，其中Q是Q的动量。虽然双圈计算现在在粒子现象学的许多其他领域都是最先进的计算，但重夸克产生是一个例外。这是由于自旋和颜色投射到各种QQ̅福克态上，这极大地破坏了解析表达式。一个特别令人恼火的特征是衍生品的出现。Q通过具有轨道角动量的自旋投影仪L≥1和相对论修正。这些产生了在NRQCD之外未知的新类别的红外线奇点，这需要虚拟和真实校正之间的扩展抵消模式。这项拟议的研究可能会解决J/ψ之谜，因为最先进的预测受到非常大的次要顺序修正的困扰，这些修正严重质疑它们的可靠性。设想的计算还将探索潜在的因式分解假设，普遍界定QCD在一个未被探索的地区不可避免的非微扰现象，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.