An automated subtraction of NLO EW infrared divergences

TL;DR

The paper extends the Catani–Seymour dipole subtraction framework to NLO electroweak accuracy, incorporating photon emissions and splittings for massless and massive partons with both massless and massive spectators. It develops differential and integrated subtraction terms, reorganised into I, K, and P operators, and implements them in SHERPA/AMEGIC to automate mixed QCD/QED NLO calculations. Key contributions include handling external photons, multiple recoil schemes for photon splittings, process mappings to reduce computational load, and infrared-safe fiducial phase-space definitions with flavour-scheme conversions. The work is validated against independent implementations and extensive internal checks, establishing a practical, robust path to precise NLO EW predictions in a Monte Carlo framework.

Abstract

In this paper a complete generalisation of the Catani-Seymour dipole subtraction method to next-to-leading order electroweak calculations is presented. All singularities due to photon and gluon radiation off both massless and massive partons in the presence of both massless and massive spectators are accounted for. Particular attention is paid to the simultaneous subtraction of singularities of both QCD and electroweak origin which are present in the next-to-leading order corrections to processes with more than one perturbative order contributing at Born level. Similarly, embedding non-dipole-like photon splittings in the dipole subtraction scheme discussed. The implementation of the formulated subtraction scheme in the framework of the Sherpa Monte-Carlo event generator is detailed and numerous internal consistency checks validating the obtained results are presented.

Figures (7)

• Figure 1: Classification of the four dipole types in Catani-Seymour-type dipole subtraction.
• Figure 2: $\{\alpha_\text{dip}\}$-dependence of the sum of integrated subtraction term and differentially subtracted real emission for $\nu_e\bar{\nu}_e\to jj$, $\nu_e p\to \nu_e j$ and $pp\to \nu_e\bar{\nu}_e$.
• Figure 3: Left and centre:$\{\alpha_\text{dip}\}$-dependence of the sum of integrated subtraction term and differentially subtracted real emission for $\nu_e\bar{\nu}_e\to e^+e^-$ and $pp\to e^+e^-$. Right: Dependence of the sum of the integrated subtraction term and differentially subtracted real emission for $pp\to e^+e^-$ in the $\gamma q$/$\gamma\bar{q}$ channel on the choice of recoil partner for the initial state photon splittings $c_{\tilde{k}}^\gamma$. The invariant mass of the electron pair is raised to increase the contribution of the photon induced channels. The $q\bar{q}$ and $\gamma\gamma$ channels comprise no dipoles with splitting photons.
• Figure 4: $\{\alpha_\text{dip}\}$-dependence of the sum of integrated subtraction term and differentially subtracted real emission for $\nu_e\bar{\nu}_e\to t\bar{t}$ and $\nu_e p\to\nu_e t$. For the latter the Standard Model is extended by a $u\bar{t}Z$ interaction with the structure and coupling as the existing $u\bar{u}Z$ interaction.
• Figure 5: Left:$\kappa$-dependence of the sum of integrated subtraction term and differentially subtracted real emission for $\nu_e\bar{\nu}_e\to t\bar{t}j$. Right: Dependence of the sum of the integrated subtraction term and differentially subtracted real emission for $\nu_e\bar{\nu}_e\to t\bar{t}j$ at $\mathcal{O}(\alpha^4)$ on the choice of recoil partner for the final state photon splittings $c_{\tilde{k}}^\gamma$.