Helicity methods for high multiplicity subleading soft and collinear limits
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Springer
Received: April 26, 2019 Accepted: May 23, 2019 Published: May 28, 2019
Arindam Bhattacharya,a Ian Moult,b,c Iain W. Stewarta and Gherardo Vitaa a
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. b Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, U.S.A. c Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity variables in collinear limits with consistency relations derived from the soft collinear effective theory, we show how to efficiently extract the subleading power leading logarithms of N -jet event shape observables directly from known spinor-helicity amplitudes. At subleading power, we observe the presence of power law singularities arising solely from the expansion of the amplitudes, which for hadron collider event shapes lead to the presence of derivatives of parton distributions. The techniques introduced here can be used to efficiently compute the power corrections for N -jettiness subtractions for processes involving jets at the LHC. Keywords: Effective Field Theories, Perturbative QCD, Scattering Amplitudes, Resummation ArXiv ePrint: 1812.06950
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)192
JHEP05(2019)192
Helicity methods for high multiplicity subleading soft and collinear limits
Contents 1 Introduction
1
2 Subleading power expansions of spinors 2.1 Subleading power collinear limit ¯ 2.2 Example: H → q¯q QQ
2 3 5 10 13 15 19 19 20
4 Power law divergences in subleading power matrix elements
21
5 Conclusions
24
1
Introduction
The factorization properties of multi-leg gauge theory amplitudes in the soft and collinear limits are essential for our theoretical understanding of these amplitudes, as well as for the calculation of multi-jet observables at hadron colliders. While the leading power soft and collinear limits have been extensively studied, very little is known about the subleading power factorization properties of multi-leg amplitudes, or multi-jet observables. There has recently been significant progress in understanding the structure of power corrections in the soft and collinear limits [1–39], including the first all order resummation of power suppressed logarithms for collider observables with soft and collinear radiation [40]
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