J un 2 01 9 CERN-TH-2019-087 , ZU-TH 30 / 19 Physical projectors for multi-leg helicity amplitudes

We present a method for building physical projector operators for multi-leg helicity amplitudes. For any helicity configuration of the external particles, we define a physical projector which singles out the corresponding helicity amplitude. For processes with more than four external legs, these physical projectors depend on significantly fewer tensor structures and exhibit a remarkable simplicity compared with projector operators defined with traditional approaches. As an example, we present analytic formulas for a complete set of projectors for five-gluon scattering. These have been validated by reproducing known results for five-gluon amplitudes up to one-loop.

[1]  Tiziano Peraro,et al.  FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , 2019, Journal of High Energy Physics.

[2]  T. Peraro,et al.  Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude. , 2019, Physical review letters.

[3]  Long-Bin Chen.  A prescription for projectors to compute helicity amplitudes in D dimensions , 2019, The European Physical Journal C.

[4]  B. Page,et al.  Analytic form of the planar two-loop five-parton scattering amplitudes in QCD , 2019, Journal of High Energy Physics.

[5]  T. Gehrmann,et al.  The two-loop five-particle amplitude in N$$ \mathcal{N} $$ = 8 supergravity , 2019, Journal of High Energy Physics.

[6]  T. Gehrmann,et al.  Analytic Result for a Two-Loop Five-Particle Amplitude. , 2018, Physical review letters.

[7]  B. Page,et al.  Analytic Form of Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD. , 2018, Physical review letters.

[8]  H. Hartanto,et al.  Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case , 2018, Journal of High Energy Physics.

[9]  P. Mastrolia,et al.  Feynman integrals and intersection theory , 2018, Journal of High Energy Physics.

[10]  H. Hartanto,et al.  First Look at Two-Loop Five-Gluon Scattering in QCD. , 2017, Physical review letters.

[11]  L. Tancredi,et al.  Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph , 2017, 1704.05465.

[12]  Yang Zhang,et al.  Maximal cuts in arbitrary dimension , 2017, Journal of High Energy Physics.

[13]  C. Papadopoulos,et al.  Cuts of Feynman Integrals in Baikov representation , 2017, Journal of High Energy Physics.

[14]  L. Tancredi,et al.  On the maximal cut of Feynman integrals and the solution of their differential equations , 2016, 1610.08397.

[15]  T. Peraro.  Scattering amplitudes over finite fields and multivariate functional reconstruction , 2016, 1608.01902.

[16]  S. Badger.  Automating QCD amplitudes with on-shell methods , 2016, 1605.02172.

[17]  R. Schabinger,et al.  Computation of form factors in massless QCD with finite master integrals , 2015, 1510.06758.

[18]  H. Ita.  Two-loop integrand decomposition into master integrals and surface terms , 2015, 1510.05626.

[19]  S. Badger,et al.  A two-loop five-gluon helicity amplitude in QCD , 2013, 1310.1051.

[20]  J. Henn.  Multiloop integrals in dimensional regularization made simple. , 2013, Physical review letters.

[21]  P. Mastrolia,et al.  Scattering Amplitudes from Multivariate Polynomial Division , 2012, 1205.7087.

[22]  Yang Zhang.  Integrand-level reduction of loop amplitudes by computational algebraic geometry methods , 2012, Journal of High Energy Physics.

[23]  S. Badger,et al.  Hepta-cuts of two-loop scattering amplitudes , 2012, 1202.2019.

[24]  P. Mastrolia,et al.  On the integrand-reduction method for two-loop scattering amplitudes , 2011, 1107.6041.

[25]  A. Hodges.  Eliminating spurious poles from gauge-theoretic amplitudes , 2009, 0905.1473.

[26]  Z. Kunszt,et al.  Full one-loop amplitudes from tree amplitudes , 2008, 0801.2237.

[27]  Z. Kunszt,et al.  A numerical unitarity formalism for evaluating one-loop amplitudes , 2007, 0708.2398.

[28]  R. Pittau,et al.  Reducing full one-loop amplitudes to scalar integrals at the integrand level , 2006, hep-ph/0609007.

[29]  F. Cachazo,et al.  Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills , 2004, hep-th/0412103.

[30]  L. Dixon,et al.  Supersymmetric regularization, two-loop QCD amplitudes, and coupling shifts , 2002, hep-ph/0202271.

[31]  S. Laporta,et al.  HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS , 2000, hep-ph/0102033.

[32]  T. Gehrmann,et al.  Differential Equations for Two-Loop Four-Point Functions , 1999, hep-ph/9912329.

[33]  E. Remiddi.  Differential equations for Feynman graph amplitudes , 1997, Il Nuovo Cimento A.

[34]  L. Dixon,et al.  Fusing gauge theory tree amplitudes into loop amplitudes , 1994, hep-ph/9409265.

[35]  L. Dixon,et al.  One-loop n-point gauge theory amplitudes, unitarity and collinear limits , 1994, hep-ph/9403226.

[36]  P. Nogueira.  Automatic Feynman graph generation , 1993 .

[37]  L. Dixon,et al.  One-loop corrections to five-gluon amplitudes. , 1993, Physical review letters.

[38]  A. Kotikov.  NEW METHOD OF MASSIVE FEYNMAN DIAGRAMS CALCULATION , 1991 .

[39]  W. Giele,et al.  Recursive calculations for processes with n gluons , 1988 .

[40]  M. Mangano,et al.  Duality and Multi - Gluon Scattering , 1988 .

[41]  F. Tkachov,et al.  Integration by parts: The algorithm to calculate β-functions in 4 loops , 1981 .

[42]  F. Tkachov.  A theorem on analytical calculability of 4-loop renormalization group functions , 1981 .