How to use SANC to improve the PHOTOS Monte Carlo simulation of bremsstrahlung in leptonic W-Boson decays

TL;DR

This work leverages the SANC framework to compute complete one-loop electroweak corrections with real photon emission for leptonic W decays and uses these results to identify non-leading terms missing in the PHOTOS Monte Carlo. By deriving an analytic correcting weight δ from the full SANC matrix elements and applying it to PHOTOS, the authors achieve substantially improved agreement with SANC predictions across key observables, reducing discrepancies from up to ~40% to predominantly 5–10%. The approach provides a practical means to quantify and reduce PHOTOS uncertainties for LEP2 and future collider studies and suggests avenues for further refinement, such as exponentiation. Overall, the work demonstrates how exact matrix-element information can be leveraged to enhance widely used MC tools in particle phenomenology.

Abstract

Using the SANC system we study the one-loop electroweak standard model predictions, including virtual and real photon emission, for the decays of the on-shell vector boson, W --> L ANTI-NU (GAMMA). The complete one-loop corrections and exact photon emission matrix element are taken into account. For the phase-space integration, the Monte Carlo technique is used. This provides a useful element, first for the evaluation of the theoretical uncertainty of PHOTOS. Later we analyse the source of the differences between SANC and PHOTOS and we calculate the additional weight, which once installed, improves predictions of PHOTOS simulations. We can conclude that, after the correction of the weight is implemented, the theoretical uncertainty of PHOTOS simulations due to an incomplete first-order matrix element is reduced to below alpha/pi, for observables not tagging the photon in a direct way, and to 10% otherwise. This is interesting for applications in the phenomenology of the ongoing LEP2 and future LC and LHC experimental studies.

Figures (5)

• Figure 1: Feynman diagrams
• Figure 2: Comparisons (ratios) of the PHOTOS, truncated SANC and complete SANC predictions for the $W$ decay. Ratio of the $\mu^-\bar{\nu}$ acollinearity distribution from PHOTOS and complete SANC (left-hand side) and ratio of the $\mu^-\bar{\nu}$ acollinearity distribution from truncated SANC and complete SANC (right-hand side) are given. The dominant contribution is of non-leading nature, the observable D.
• Figure 3: Comparison (ratio) of the predictions for the $W$ decay from SANC truncated and corrected with the function $\delta$ and from the complete SANC. Ratio of the $\mu^-\bar{\nu}$ acollinearity distribution is given. The dominant contribution is of non-leading nature, the observable D.
• Figure 4: Comparisons (ratios) of the complete SANC and corrected PHOTOS predictions for the $W$ decay. Observables A and B: ratios of the photon energy (left-hand side) and muon energy (right-hand side) distributions from the two programs. The dominant contribution is of leading-log (collinear) nature. In the lower part of the plots similar comparisons for the complete SANC and truncated--corrected with $\delta$SANC predictions are given.
• Figure 5: Comparisons (ratios) of the complete SANC and corrected PHOTOS predictions for the $W$ decay. Observables C and D: ratios of the photon angle with respect to $\mu^-$ (left-hand side) and $\mu^-\bar{\nu}$ acollinearity (right-hand side) distributions from the two programs. The dominant contribution is of infrared non-leading-log nature for the left-hand side plot, and non-infrared non-leading-log nature for the right-hand side one. In the lower part of the plots similar comparisons for the complete SANC and truncated--corrected with $\delta$SANC predictions are given.