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
Qingjun Jin1,2,(),Gang Yang1,3,()
Received:
2020-02-15
Revised:
2020-03-09
Accepted:
2020-03-09
Published:
2020-06-01
Qingjun Jin, Gang Yang, Commun. Theor. Phys. 72 (2020) 065201.
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Table 1.
The universal maximally transcendental properties for Higgs amplitudes or form factors of length-2 and 3 operators with three partons, and minimal form factors with higher length operators are summarized. The color-singlet operators are classified according to their lengths and representative examples are provided. We also indicate the external on-shell partons."
Length-2 | Length-3 | Higher length | |||||
---|---|---|---|---|---|---|---|
Operators | |||||||
Examples | $\mathrm{tr}({F}^{2})$ | $\bar{\psi }\psi $ | $\bar{\phi }\phi $ | $\begin{array}{c}\mathrm{tr}({F}^{3}),\\ \mathrm{tr}({F}_{\mu }^{\,\nu }{D}_{\sigma }{F}_{\nu }^{\,\rho }{D}^{\sigma }{F}_{\rho }^{\,\mu })\end{array}$ | $\begin{array}{c}{F}_{\mu \nu }{D}^{\mu }(\bar{\psi }{\gamma }^{\nu }\psi ),\\ {F}_{\mu \nu }(\bar{\psi }{\gamma }^{\mu \nu }\psi )\end{array}$ | $\mathrm{tr}({F}^{L}),L\geqslant 4$ | $\bar{\psi }({F}^{L})\psi ,L\geqslant 2$ |
External Partons | $(g,g,g),(\bar{\psi },\psi ,g)$ | $(\bar{\psi },\psi ,g)$ | $(\bar{\phi },\phi ,g)$ | $(g,g,g)$ | $(\bar{\psi },g,\psi )$ | $({g}_{1},\ldots ,{g}_{L})$ | $(\bar{\psi },{g}_{1},\ldots ,{g}_{L},\psi )$ |
$\begin{array}{c}{\rm{Max.}}\,{\rm{Trans.}}\\ {\rm{Remainder}}\\ ({\rm{with}}\ {C}_{F}\to {C}_{A})\end{array}$ | ${R}_{{\rm{L}}2;4}(u,v,w)$ | ${R}_{\mathrm{len}-3;4}(u,v,w)$ | ${\sum }_{i}{{ \mathcal R }}_{{\rm{density}};4}^{(2)}({u}_{i},{v}_{i},{w}_{i})$ |
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