Advances in High Energy Physics

Volume 2016, Article ID 1615081, 9 pages

http://dx.doi.org/10.1155/2016/1615081

## Comparison of HORACE and PHOTOS Algorithms for Multiphoton Emission in the Context of Boson Mass Measurement

^{1}Physics Department, Duke University, Durham, NC 27708, USA^{2}Scientific Computing Division, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA

Received 21 October 2015; Accepted 24 December 2015

Academic Editor: Smarajit Triambak

Copyright © 2016 Ashutosh V. Kotwal and Bodhitha Jayatilaka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

boson mass measurement is sensitive to QED radiative corrections due to virtual photon loops and real photon emission. The largest shift in the measured mass, which depends on the transverse momentum spectrum of the charged lepton from the boson decay, is caused by the emission of real photons from the final-state lepton. There are a number of calculations and codes available to model the final-state photon emission. We perform a detailed study, comparing the results from HORACE and PHOTOS implementations of the final-state multiphoton emission in the context of a direct measurement of boson mass at Tevatron. Mass fits are performed using a simulation of the CDF II detector.

#### 1. Introduction

The measurement of boson mass () is one of the most interesting precision electroweak observables. In the standard model (SM), the mass of boson can be calculated with higher precision [1] than the existing measurement uncertainty [2–6], thus providing motivation for improving the statistical and systematic uncertainties on the measurement. The comparison between the theoretical prediction and the measurement provides a stringent test of the SM and constrains beyond-standard model (BSM) theories.

At hadron colliders, the mass of boson is extracted from inclusively produced bosons decaying to electrons or muons and the associated neutrinos. At the Tevatron, almost pure samples of such candidate events have been identified with backgrounds typically smaller than 1%. The momenta of the decay electrons and muons have been measured with a precision of ~0.01%, allowing a boson mass measurement with precision of 0.02% [6].

The calibration of the electron and muon momenta is the single most important aspect of the measurement. In the approximation that boson undergoes a two-body decay, the distribution of the transverse momentum (, defined as the component of the momentum perpendicular to the beam axis) of the charged lepton has the characteristic Jacobian edge at half the mass of boson. In practice, electroweak radiative corrections modify the lepton spectrum, mainly due to the emission of photons from the decay lepton. If no correction was applied for this radiative process, the measurement would be biased by ≈200 MeV [7]. Throughout this paper, we use the convention .

In the first Run II measurement [7] of boson mass, WGRAD [8] and ZGRAD [9] programs were used to calculate the QED radiative correction. WGRAD and ZGRAD are exact next-to-leading order (NLO) electroweak matrix element calculations of the and processes, respectively. The effect of higher-order radiative corrections has been estimated to be about 10% [7, 10] of boson mass shift estimated from these NLO calculations. In order to increase the precision of the QED radiative correction for boson mass measurement, higher-order calculations were used, as implemented in HORACE [10–14] and PHOTOS [15, 16] programs. These programs calculate the emission of multiple photons with the appropriate rates, energy, and angular distributions.

PHOTOS uses the exact first-order matrix element of and boson decay for the photon emission kernel. For multiphoton radiation, PHOTOS uses an iterative solution for this kernel, developed on the basis of an exact and complete phase space parametrization. This ensures not only resummation of leading-logarithm contributions of higher orders but also the infrared region of the phase space being accurately simulated [16] (Z. Was, private communication).

HORACE is a parton-level electroweak Monte Carlo generator for precision simulations of charged-current and neutral-current Drell-Yan processes. HORACE uses the full phase space for each radiated photon and there is no ordering of the photons (i.e., in angle or transverse momentum) in multiphoton emission (C. M. Carloni Calame, G. Montagna, and A. Vicini, private communication). Two versions of the HORACE program are available. The OLD version [10, 11] implements a multiphoton emission QED parton shower algorithm for the simulation of final-state radiation (FSR) in the leading-logarithmic approximation, without initial-state radiation (ISR) and without interference between ISR and FSR. In this sense the OLD HORACE program is similar to the PHOTOS program, which also implements multiphoton FSR. OLD HORACE does not include full one-loop electroweak corrections, but it mimics the real radiation matrix element for the description of the photon radiation in and boson decays, in the leading-logarithmic approximation (C. M. Carloni Calame, G. Montagna, and A. Vicini, private communication). There is also a NEW HORACE program [12, 13], which implements multiphoton ISR and FSR with interference and also matches each photon to the exact matrix element calculation of one-loop electroweak corrections and single-photon emission (C. M. Carloni Calame, G. Montagna, and A. Vicini, private communication).

The PHOTOS program provides a generic interface to any other event generator such that all charged leptons produced by the latter can be passed through the PHOTOS FSR algorithm. We use this feature as follows. We generate and boson events for Tevatron collisions at TeV, including higher-order QCD matrix elements and QCD resummation effects, but without loops or emission of electroweak bosons. We interface these events to PHOTOS such that the events from the chain contain the QED-FSR photons added by PHOTOS. We save photons with MeV and the events are processed with a detector simulation [6, 7] to make the pseudodata and the mass-fitting templates. Lowering the photon threshold further has negligible effect on the results presented here, within the uncertainties quoted.

In this paper we present comparisons between the distributions and the mass-fitting results obtained from the OLD HORACE and PHOTOS programs.

#### 2. Electron Channel Comparisons

To make direct comparisons between quantities sensitive to QED physics, we need to ensure that the underlying boson and lepton distributions are identical between OLD HORACE and PHOTOS. For this purpose we use the “Born” mode of OLD HORACE to generate Born-level and events, which are then processed through PHOTOS. The Born mode generates these purely parton processes with no radiative photons. These events are compared with events from OLD HORACE run in the QED multiphoton emission FSR mode. Both OLD HORACE and PHOTOS are run in the “exponentiation” mode, which exercises their full physics content. All of the events used in these comparisons have unit weights. For all generated events we make a generator-level cut on the partonic center-of-mass energy GeV to remove the contribution of the photon pole for neutral-current events. For consistency, we also apply this cut on the charged-current events.

In Figure 1 we compare the distributions for photon emission rates as well as the energy and angular distributions for the process. For these comparisons we consider photons with energy MeV; photons with lower energy than this threshold are not counted and ignored in the distributions. In addition to the number of photons emitted, we find that the distributions of the following quantities are useful to compare: , the fractional photon energy (where is the energy of the final-state lepton), and (the angular separation between a photon and the final-state lepton, where the pseudorapidity , being the polar angle with respect to the beam axis, and is the azimuthal angle about the beam axis).