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Next to Leading Logarithms and the PHOTOS Monte Carlo

P. Golonka, Z. Was

Abstract

With the approaching start-up of the experiments at LHC, the urgency to quantify systematic uncertainties of the generators, used in the interpretation of the data, is becoming pressing. The PHOTOS Monte Carlo program is often used for the simulationof experimental, selection-sensitive, QED radiative corrections in decays of Z bosons and other heavy resonances and particles. Thanks to its complete phase-space coverage it is possible, with no approximations for any decay channel, to implement the matrix-element. The present paper will be devoted to those parts of the next-to-leading order corrections for Z decays which are normally missing in PHOTOS. The analytical form of the exact and truncated (standard) kernel used in PHOTOS will be explicitly given. The correction, being the ratio of the exact to the approximate kernel, can be activated as an optional contribution to the internal weight of PHOTOS. To calculate the weight, the information on the effective Born-level Z/gamma* couplings and even directions of the incoming beams, is needed. A universal implementation would have made the PHOTOS solution less modular and less convenient for the users. That is why, for the time being, we will keep the correcting weight as an extra option, available for special tests only. We will quantify the numerical effect of the approximation with the help of a multitude of distributions. The numerical size of the effect is in general below 0.1%; however, in some corners of the phase-space (well defined and contributing less than 0.5% to the total rate), it may reach up to about 20% of their relative size.

Next to Leading Logarithms and the PHOTOS Monte Carlo

Abstract

With the approaching start-up of the experiments at LHC, the urgency to quantify systematic uncertainties of the generators, used in the interpretation of the data, is becoming pressing. The PHOTOS Monte Carlo program is often used for the simulationof experimental, selection-sensitive, QED radiative corrections in decays of Z bosons and other heavy resonances and particles. Thanks to its complete phase-space coverage it is possible, with no approximations for any decay channel, to implement the matrix-element. The present paper will be devoted to those parts of the next-to-leading order corrections for Z decays which are normally missing in PHOTOS. The analytical form of the exact and truncated (standard) kernel used in PHOTOS will be explicitly given. The correction, being the ratio of the exact to the approximate kernel, can be activated as an optional contribution to the internal weight of PHOTOS. To calculate the weight, the information on the effective Born-level Z/gamma* couplings and even directions of the incoming beams, is needed. A universal implementation would have made the PHOTOS solution less modular and less convenient for the users. That is why, for the time being, we will keep the correcting weight as an extra option, available for special tests only. We will quantify the numerical effect of the approximation with the help of a multitude of distributions. The numerical size of the effect is in general below 0.1%; however, in some corners of the phase-space (well defined and contributing less than 0.5% to the total rate), it may reach up to about 20% of their relative size.

Paper Structure

This paper contains 8 sections, 9 equations, 1 figure.

Table of Contents

  1. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma$
  2. Decay Channel: $Z^{0} \rightarrow \mu^{+} \mu^{-} \gamma$
  3. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma$
  4. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma$
  5. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma$
  6. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma \gamma$
  7. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma$
  8. Decay Channel: $Z^{0} \rightarrow \mu^{-} \mu^{+} \gamma \gamma$

Figures (1)

  • Figure 1: A typical plot for comparisons, as described in ref. Hamilton:2006xz. We use it to illustrate our method. The histograms presented in the left and right plots have identical content, and show a comparison of KKMC kkcpc:1999 and PHOTOS used in $Z$ decay. The total energy carried out by all final-state photons is presented. Red (darker grey) colour represents the results of KKMC, green (lighter grey) of PHOTOS with the NLO weight activated. Samples of $10^7$ events were used in this comparison. The results are overwhelmed by the collinear/soft content of the predictions. If the $W$ instead of $Z$ decay was chosen, it would not be the case. There, NLO effects would be dominant for the part of the spectrum above $M_W/2$. However, in that case, we would not profit from the second-order matrix element Monte Carlo, available for tests.