Boundary contributions of on-shell recursion relations with multiple-line deformation
- PDF / 583,284 Bytes
- 13 Pages / 595.276 x 790.866 pts Page_size
- 68 Downloads / 150 Views
Regular Article - Theoretical Physics
Boundary contributions of on-shell recursion relations with multiple-line deformation Chang Hua , Xiao-Di Lib , Yi Lic Department of Physics, Zhejiang Institute of Modern Physics, Zhejiang University, No. 38 Zheda Road, Hangzhou 310027, People’s Republic of China
Received: 3 September 2020 / Accepted: 3 October 2020 © The Author(s) 2020
Abstract The on-shell recursion relation has been recognized as a powerful tool for calculating tree-level amplitudes in quantum field theory, but it does not work well ˆ when the residue of the deformed amplitude A(z) does not vanish at infinity of z. However, in such a situation, we still can get the right amplitude by computing the boundary contribution explicitly. In Arkani-Hamed and Kaplan (JHEP 04:076. https://doi.org/10.1088/1126-6708/2008/04/ 076. arXiv:0801.2385, 2008), the background field method was first used to analyze the boundary behaviors of amplitudes with two deformed external lines in different theories. The same method has been generalized to calculate the explicit boundary operators of some amplitudes with BCFWlike deformation in Jin and Feng (JHEP 04:123. https://doi. org/10.1007/JHEP04(2016)123. arXiv:1507.00463, 2016). In this paper, we will take a step further to generalize the method to the case of multiple-line deformation, and to show how the boundary behaviors (even the boundary contributions) can be extracted in the method.
Contents 1 Introduction . . . . . . . . . . . . . . . . . 2 Boundary term of on-shell recursion relation 3 Real scalar field theory . . . . . . . . . . . . 4 Yukawa theory . . . . . . . . . . . . . . . . 5 Yang–Mills theory . . . . . . . . . . . . . . 6 Conclusion . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .
a e-mail:
[email protected]
b e-mail:
[email protected] (corresponding author)
c e-mail:
[email protected]
. . . . . . .
. . . . . . .
. . . . . . .
0123456789().: V,-vol
. . . . . . .
. . . . . . .
1 Introduction Recent decades have witnessed the prosperity in the area of scattering amplitudes, including the discovery of new mathematical structures, the new formalisms of scattering amplitudes, and even more important, the new methods for calculating the scattering amplitude more efficiently. Among these methods the on-shell recursion relations, pioneered by the BCFW recursion relations [3,4], have been proved to be very powerful tools, which can be used to construct higher-point tree-level amplitudes from lower-point ones. After the idea of deforming two external momenta to capture the analytic structures of tree-level amplitudes was introduced, quickly the deformation of multiple lines and even all lines was used in [5–7] to discuss on-shell constructibility or other aspects of the amplitudes. The on-shell recursion relations are based on the Cauchy theorem. It says that under an appropriate deformation of a subset of n momenta, pi → pˆ i (z) = pi + zqi , with z being a complex parameter, the residue of Aˆ n (z)/z at z = 0,
Data Loading...
