Communications in Theoretical Physics ›› 2020, Vol. 72 ›› Issue (6): 065201. doi: 10.1088/1572-9494/ab7ed8

• Particle Physics and Quantum Field Theory • Previous Articles     Next Articles

Hidden analytic relations for two-loop Higgs amplitudes in QCD

Qingjun Jin1,2,(),Gang Yang1,3,()   

  1. 1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
    2Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
    3School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, China
  • Received: 2020-02-15 Revised: 2020-03-09 Accepted: 2020-03-09 Published: 2020-06-01


We compute the Higgs plus two-quark and one-gluon amplitudes ($H\to q\bar{q}g$) and Higgs plus three-gluon amplitudes ($H\to 3g$) in the Higgs effective theory with a general class of operators. By changing the quadratic Casimir CF to CA, the maximally transcendental parts of the $H\to q\bar{q}g$ amplitudes turn out to be equivalent to that of the $H\to 3g$ amplitudes, which also coincide with the counterparts in ${ \mathcal N }=4$ SYM. This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states, thus the full QCD theory. We further verify that the correspondence applies also to two-loop form factors of more general operators, in both QCD and scalar-YM theory. Another interesting relation is also observed between the planar $H\to q\bar{q}g$ amplitudes and the minimal density form factors in ${ \mathcal N }=4$ SYM.

Key words: scattering amplitudes, form factors, quantum chromodynamics, Higgs effective field theory