Two Photon Radiation in W and Z Boson Production at the Tevatron Collider

TL;DR

The work addresses how real two-photon radiation at $O(\alpha^2)$ affects $W$ and $Z$ resonance parameters in hadronic collisions. It computes full tree-level matrix elements for $\ell\nu\gamma\gamma$ and $\ell^+\ell^-\gamma\gamma$ with finite lepton masses, using a gauge-invariant finite-$W$ width treatment and a multiconfiguration Monte Carlo (MCMC) phase-space integration to handle sharp, multi-dimensional peaks. Numerical results for the Tevatron show non-negligible two-photon fractions, with notably larger rates in $Z$ decays, and significant distortions in $m_T$ and $m_{\ell\ell}$ distributions, indicating potential shifts in $M_W$, $M_Z$, and $\Gamma_W$ that require soft/virtual corrections and detector modeling. The study also demonstrates a general, automated MCMC framework that can be applied to other processes with complex peak structures, representing an important methodological step toward a complete $O(\alpha^2)$ EW treatment in hadron-collider phenomenology.

Abstract

We present a calculation of two photon radiation in W and Z boson production in hadronic collisions, based on the complete matrix elements for the processes q\bar q'\to\ell^\pmνγγand q\bar q\to\ell^+\ell^-γγ, including finite charged lepton masses. In order to achieve stable numerical results over the full phase space, multiconfiguration Monte Carlo techniques are used to map the peaks in the differential cross section. Numerical results are presented for the Fermilab Tevatron.

Figures (3)

• Figure 1: The Feynman diagrams contributing to $\nu_\mu\bar{\nu}_\mu\to e^+e^-\gamma\gamma$ at tree level, as generated by MadGraph. $A$ ($Z$) represents a photon ($Z$ boson), $e$ an electron or positron, and $nu\_ mu$ a muon neutrino, $\nu_\mu$.
• Figure 2: The distribution of the separation between the two photons, $\Delta R_{\gamma\gamma}$, for a) $p\bar{p}\to\ell^+\ell^-\gamma\gamma$ and b) $p\bar{p}\to\ell^+\nu\gamma\gamma$ at $\sqrt{s}=1.8$ TeV. The solid and dashed histograms show the differential cross sections for electrons and muons, respectively. The cuts imposed are described in the text.
• Figure 3: Ratio of a) the $p\bar{p}\to\ell^+\ell^-\gamma\gamma$ and the lowest order $p\bar{p}\to\ell^+\ell^-$ cross sections as a function of the $\ell^+\ell^-$ invariant mass, and b) the $p\bar{p}\to\ell^+\nu\gamma\gamma$ and the lowest order $p\bar{p}\to\ell^+\nu$ cross section versus $m_T(\ell p\hbox{/}_T)$ at $\sqrt{s}=1.8$ TeV. The solid and dashed histograms show the cross section ratios for electrons and muons, respectively. The cuts imposed are described in the text.