Scalar QED, NLO and PHOTOS Monte Carlo

Abstract

Recently, QED bremsstrahlung in $B$-meson decays into pair of scalars (π's and/or K's) is of interest. If experimental acceptance must be taken into account, PHOTOS Monte Carlo is often used in experimental simulations. We will use scalar QED to benchmark PHOTOS, even though this theory is of limited use for complex objects. We present the analytical form of the kernel used in the older versions of PHOTOS, and the new, exact (scalar QED) one. Matrix element and phase-space Jacobians are separated in the final weight and future extensions based on measurable electromagnetic form-factors are thus possible. The massive phase-space is controlled in the the program with no approximations. Thanks to the iterative solution all leading and next to leading logarithmic terms are properly reproduced by the Monte Carlo simulation. Simultaneously, full differential distributions over complete multiple body phase-space are provided. An agreement of better than 0.01% with independent calculations of scalar QED is demonstrated.

Figures (11)

• Figure 1: Results from PHOTOS, standard version, and SANC for $B^- \to \pi^0 K^-(\gamma)$ decay are superimposed on the consecutive plots. Standard distributions, as defined in the text, and logarithmic scales are used. The distributions from the two programs overlap almost completely. Samples of $10^9$ events were used. The ultraviolet scale, $\mu_{_{UV}}$, was chosen to leave total decay width unchanged by QED.
• Figure 2: Results from PHOTOS, standard version, and SANC for ratios of the $B^- \to \pi^0 K^-(\gamma)$ distribution in fig.\ref{['P0Km_distr_NotCorrected_p']} are presented. Differences between PHOTOS and SANC are small, but are clearly visible now.
• Figure 3: Results from PHOTOS with the exact matrix element, and SANC for ratios of the $B^- \to \pi^0 K^-(\gamma)$ distributions. Differences between PHOTOS and SANC are below statistical error for samples of $10^9$ events.
• Figure 4: Results from PHOTOS, standard version, and SANC for $B^0 \to \pi^- K^+(\gamma)$ decay are superimposed on the consecutive plots. Standard distributions, as defined in the text and logarithmic scales are used. The distributions from the two programs overlap almost completely. Samples of $10^9$ events were used. The ultraviolet scale, $\mu_{_{UV}}$, was chosen to leave total decay width unchanged by QED.
• Figure 5: Results from PHOTOS, standard version, and SANC for ratios of the $B^0 \to \pi^- K^+(\gamma)$ distributions in fig.\ref{['PmKp_distr_NotCorrected_p']} are presented. Differences between PHOTOS and SANC are small, but are clearly visible now.