$e^+ e^- \to e^- {\bar ν_e} u {\bar d}$ from LEP to linear collider energies

TL;DR

The paper computes the complete tree-level cross section for $e^+e^- \to e^- \bar{\nu}_e u \bar{d}$ using the GRACE system, addressing gauge-violation issues from finite $W$ width with a preserved gauge scheme. It demonstrates that including all diagram classes (double-, single-, non-resonant) is essential for reliable predictions from LEP energies to linear colliders, and provides an electron-angle-cut-free generator to estimate backgrounds for jets and missing energy. Threshold and high-energy behavior are analyzed, showing the impact of $t$-channel diagrams and the importance of precise electron tagging for $W$ mass measurements. The work also connects to LEP monojet observations, illustrating the generator’s relevance for background modeling and collider phenomenology.

Abstract

The complete tree level cross section for the process $e^+e^- \to e^- \barν_e u \bar{d}$ is computed using the GRACE system, a program package for automatic amplitude calculation. Special attention is brought to the gauge violation problem induced by the finite width of the $W$-boson. The {\it preserved gauge scheme} is introduced and an event generator which includes double-resonant, single-resonant and non-resonant diagrams with no need for a cut on the electron polar angle is presented. Since no cut needs to be applied to the electron, the generator can be used to estimate background for searches involving jets and missing energy. A monojet event rate estimation based on this process at LEP-I energy is discussed.

Figures (9)

• Figure 1: The $s$-channel diagrams of the $e^+e^- \to e^- \bar{\nu}_e u \bar{d}$ process in unitary gauge. The first three diagrams in the first row are double-resonant diagrams.
• Figure 2: The $t$-channel diagrams of $e^+e^- \to e^- \bar{\nu}_e u \bar{d}$ process in unitary gauge. The first and second columns show the single-resonant diagrams and the rest shows the non-resonant diagrams. Diagrams in first row($\gamma$-$W$ processes) give the dominant contribution among $t$-channel diagrams.
• Figure 3: The cross-section vs. electron cut angle for the sub-set of $\gamma$-$W$ diagrams only at $\surd s =180$ GeV. The left half of the figure is a magnified view of the small angle region. The dashed line shows a result with a naive Breit-Wigner form for the $W$-propagator and the solid line corresponds to the introduction of the width in a gauge-invariant way using the so-called preserved gauge scheme as explained in the text. The arrow shows the cross-section using the second method described in the section 3.
• Figure 4: The cross-section vs. the $e^-$ cut angle at $\surd s =180$ GeV. The solid line represents the contribution from all diagrams, the dashed line from the double-resonant diagrams, and the dotted line from the $\gamma$-$W$ diagrams.
• Figure 5: The threshold behavior of the total cross-section of the $e^+e^- \to e^- \bar{\nu}_e u \bar{d}$ process. Cuts described in section 2 are applied on $u$ and ${\bar{d}}$ quarks, a) no cut on the final electron (case-a), and b) $\theta_e > 8^\circ$ (case-b). The solid line shows the cross-section from all diagrams, the dashed line from the double-resonant diagrams, and the dotted line from the $t$-channel diagrams. Results at $\surd s =500$ GeV are shown by solid arrows (all diagrams) and dashed arrows (double-resonant diagrams).