Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO

Abstract

Within the framework of local analytic sector subtraction, we present the full analytic integration of double-real and real-virtual local infrared counterterms that enter NNLO QCD computations with any number of massless final-state partons. We show that a careful choice of phase-space mappings leads to simple analytic results, including non-singular terms, that can be obtained with conventional integration techniques.

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

“…For this reason a lot of theoretical effort has been invested in their evaluation and in the development of ever-more efficient methods for their calculation. A number of gauge theories are being studied, starting from string and supersymmetric theories [1][2][3][4][5][6][7][8][9][10][11][12][13], to gravity [14][15][16], to Yang-Mills [17,18], to QED [19] and QCD [20][21][22][23][24][25][26][27][28][29][30][31][32] and ultimately to the full Standard Model [33][34][35][36][37][38][39][40][41][42]. Research on generic methods for solving multi-loop integrals is also ongoing [43][44][45][46][47][48]…”

May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

“…The lack of such ingredients obviously affects the possibility to test the method for arbitrary processes. Efforts are ongoing to tackle the above mentioned missing ingredients, towards a general validation of the scheme [115].…”

“…Thus, the cancellation of singularities proportional to tripolecolour-correlated matrix elements is a crucial step of the method, whose treatment is detailed in Ref. [115].…”

“…For the gg case (and for the collinear contributions) the integration is much more involved. However, in our approach it can be carried out with standard techniques [115]. Similar integrals have been computed in the context of other NNLO schemes, for instance by means of integration by parts identities and differential equations machinery [120,121].…”

Dual subtractions

“…Several techniques have been developed to address this problem, such as q T [8] and N -jettiness [9,10] slicing methods, subtraction schemes like antenna [11][12][13][14][15][16][17][18][19], CoLoRFulNNLO [20][21][22][23][24][25][26][27][28][29], residue-improved [30][31][32][33], nested soft-collinear [34][35][36][37][38] and projection-to-Born [39]. Also, other approaches are under development [40][41][42][43]. Although there is still not the same level of automation as for the NLO, progress on the subtraction of the singularities is going quite fast.…”