Scattering amplitudes Scattering amplitudes

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The Perturbative QCD Amplitudes
 
We are currently in the era of the Large Hadron Collider (LHC). The unprecedented energy of LHC will reach an new level of experimental precision. As a major theoretical challenge, there are huge Standard Model backgrounds along with any potential signals of new physics. Therefore, computing loop amplitudes efficiently is extremely important. A major bottleneck of computing one-loop QCD amplitudes comes from the so-called "rational terms", which are usually referred to as the non-cut-constructible part.
 
One-loop QCD Amplitudes = (easy) Cut-constructible part + (hard) Rational terms
 
With Zhi-Guang Xiao and Chuan-Jie Zhu, we developed a systematic method to compute the rational parts. As a non-trivial application, we calculated for the first time the full rational part of one-loop six-gluon amplitudes. While five-gluon one-loop QCD amplitude had been computed in 1993 by Bern, Dixon and Kosower, the six-gluon case had remained an open problem for a long time. Our results fully solved this longstanding problem. (See our paper and paper for further details.) With Ruth Britto and Bo Feng, we also developed the D-dimensional unitarity methods to compute the full one-loop QCD amplitudes. (See our paper and paper.)
 
'Higgs-gluons' amplitudes in N=4 SYM and QCD
 
An interesting class of observables are form factors, which are a mixture of operators and on-shell particles. Despite being partially on-shell and partially off-shell, form factors share many nice properties of amplitudes, such as Parke-Taylor formulae, supersymmetric generalizations, dual MHV rules, and the dual Wilson lines picture at one-loop. (See our paper and paper.)
 
A special class of form factors we considered also have relations to Higgs-gluon amplitudes in QCD, in the sense that the operator in the form factors is related to the Higgs-gluon effective vertex. With Brandhuber and Travaglini, I studied the three-point two-loop form factor in N=4 SYM. We applied the unitarity methods and the so-called symbol techniques. Surprisingly, the form factor result in N=4 SYM matches exactly the leading transcendental part of two-loop Higgs to three-gluon amplitudes in QCD. (See our paper.) This result implies some new hidden relations between N=4 SYM and QCD, which are still to be understood.
 
Does N=4 SYM give the maximally transcendental part of QCD?
 
Sudakov form factors at four loops
 
Our knowledge about non-planar sector of N=4 SYM is very limited. For example, even for one of the simplest quantities, the so-called cusp anomalous dimension, its leading non-planar corrections are still not known. One way to compute this quantity is by calculating Sudakov form factors, where the non-planar corrections only start to appear at four loops.
 
To attack this challenging problem, Boels, Kniehl, Tarasov and I introduced the color-kinematic duality method into the computation of form factors in N=4 SYM. Using this method, we are able to address the challenging four-loop Sudakov form factor computation, which would be very hard otherwise. In particular, we obtained a very compact four-loop integrand. (See our paper.) Recently, we are working on the evaluation of the relevant integrals with the hope of finally fixing explicitly the leading non-planar correction of cusp anomalous dimension. (See paper and paper for recent progress.)