Infrared singularities in one-loop amplitudes

Abstract

In this talk we discuss a purely numerical approach to next-to-leading order calculations in QCD. We present a simple formula, which provides a local infrared subtraction term for the integrand of a one-loop amplitude. In addition we briefly comment on local ultraviolet subtraction terms and on the required deformation of the contour of integration.Comment: 6 pages, talk given at the conference "Loops and Legs", Woerlitz, 201

Efficiency improvements for the numerical computation of NLO corrections

“…This will be discussed in detail in section 3. The soft and collinear subtraction terms for QCD amplitudes with massive partons are also known [2][3][4]. The soft and collinear subtraction terms are formulated at the amplitude level and are proportional to the corresponding Born amplitudes.…”

“…The calculation has been performed with a method, which uses numerical Monte Carlo integration for the computation of the one-loop amplitude. To render this part finite, the subtraction method [2][3][4][5] and a contour deformation [2,3,[6][7][8][9][10][11] have been used. Also, it has been the first time ever that the numerical method has been applied to a cutting-edge process.…”

“…The basic principles how the virtual corrections are calculated within the numerical method have already been discussed in the literature [2][3][4][5][6][7][8][9][10][11]. What is missing in the literature is information on how this can be done efficiently.…”

Random polarizations of the dipoles

“…Secondly, techniques based on unitarity or cuts have made a major contribution to the field [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Finally purely numerical methods for the computation of the virtual one-loop part were shown to be competitive in the multi-parton domain [32][33][34][35][36][37][38]. With the help of these techniques several multi-parton processes have been computed [39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

Direct contour deformation with arbitrary masses in the loop

“…Within the numerical approach the ideas of the subtraction method and Monte Carlo integration are carried over to the virtual part. One subtracts from the one-loop amplitude suitable approximation terms for the soft, collinear and ultraviolet singularities [11][12][13][14][15]. The difference is integrable and the integration over the loop momentum can be combined with the integration over the phase space of the final state particles in one Monte Carlo integration.…”