II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
Phys Rev Lett. 2018 Oct 26;121(17):172001. doi: 10.1103/PhysRevLett.121.172001.
We study inclusive processes involving two heavy quarkonia in nonrelativistic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay ϒ→χ_{cJ}+X via bbover ¯→ccover ¯+gg and the production process e^{+}e^{-}→J/ψ+χ_{cJ}+X via e^{+}e^{-}→ccover ¯+ccover ¯+g. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-leading order. As a solution to this problem, we introduce to NRQCD effective field theory new types of operators whose quantum corrections absorb these singularities.
我们研究了非相对论量子色动力学（NRQCD）中涉及两个重夸克偶素的包容过程，并证明，在存在两个 P 波 Fock 态的情况下，NRQCD 因子化会失效，留下不可约除的红外奇点。作为具有重要物理意义的例子，我们考虑通过 bbover ¯→ccover ¯+gg 衰变 Υ→χ_{cJ}+X 以及通过 e^{+}e^{-}→ccover ¯+ccover ¯+g 产生过程 e^{+}e^{-}→J/ψ+χ_{cJ}+X 来研究这种包含两个重夸克偶素的非相对论量子色动力学过程。我们推断，这些奇点将在下一个-leading 阶次出现在双夸克偶素强子产生过程中。为了解决这个问题，我们在 NRQCD 有效场理论中引入了新类型的算子，其量子修正吸收了这些奇点。
