Beam-Beam Backgrounds for the Cool Copper Collider

TL;DR

This work provides a comprehensive end-to-end study of beam-beam backgrounds for the Cool Copper Collider (C$^3$) using a Key4hep-based pipeline that couples Guinea-Pig/Guinea-Pig++ for beam-beam effects with Whizard/Circe and Geant4 for background propagation in the SiD detector. It quantifies beamstrahlung, incoherent pair production, and hadron photoproduction across baseline, sustainability-update, and high-luminosity scenarios at 250 and 550 GeV, translating these processes into time profiles, hit rates, and occupancy metrics. The analysis demonstrates that the existing SiD design remains compatible with C$^3$ operation, while providing a detailed framework and mitigation strategies (buffered readout, timing strategies, and targeted reconstruction algorithms) to preserve physics performance. The modular, open-source pipeline offers a versatile platform for background studies applicable to other future collider concepts, fostering a common methodological ground for detector design and accelerator optimization.

Abstract

In this paper, we present a comprehensive characterization of beam-beam backgrounds for the Cool Copper Collider (C$^3$), a proposed linear $e^{+}e^{-}$ collider designed for precision Higgs studies at center-of-mass energies of 250 and 550 GeV. Using a simulation pipeline based on the Key4hep framework, we evaluate incoherent pair production and hadron photoproduction backgrounds through the SiD detector for baseline, power-efficiency, and high-luminosity C$^3$ operating scenarios. The occupancy induced by the beam-beam background is evaluated for each scenario, validating the compatibility of the existing SiD detector design with operations at C$^3$ without substantial modifications. At the same time, the modular simulation framework and analysis methodology presented in this paper offer a versatile toolkit for background studies in future collider proposals, contributing to a common platform for different machine designs.

Figures (14)

• Figure 1: Simulation pipeline used in this paper from the background generation to the detector hits simulation. Nodes in red, blue and green represent simulation inputs, tools and outputs, respectively. Typical diagnostic plots obtained at various stages of the pipeline are also provided for reference.
• Figure 2: View of the SiD detector in the $r-z$ plane showing the expected number of hits from the IPC and HPP backgrounds in each subdetector system per bunch crossing, assuming the C$^{3}$-250 PS1 parameter scenario.
• Figure 3: Normalized luminosity spectra of the relative center-of-mass energy $\sqrt{s'}/\sqrt{s}=\sqrt{xy}$ where $x,y$ the relevant energy fractions compared to the nominal beam energy of the colliding particles in the electron and positron beam, respectively, for $e^{+}e^{-}$, $e^{-}\gamma/\gamma e^{+}$, and $\gamma \gamma$ collisions for the four different C$^{3}$ parameter sets of \ref{['tab:C3_beam_params_PS1_PS2']}.
• Figure 4: (a) Distribution of the IPC particles for C$^{3}$-250 PS1 in the $p_{\mathrm{T}}-\theta$ plane. The accumulation zone due to the beam-beam deflection effect is highlighted in red and is fitted with a power law in brown. (b) Deflection zones for all C$^{3}$ beam parameter sets, restricted to larger values of $p_{\mathrm{T}}$ and $\theta$. The grey area represents the $p_{\mathrm{T}}$ and $\theta$ values necessary for the particles to reach the first vertex barrel layer. Information on how this area is derived is given in \ref{['app:reachability']}.
• Figure 5: Lab-frame $r-z$ distributions, and corresponding envelopes at various percentiles, of the trajectories of the IPC particles under the influence of the detector solenoid magnetic field for C$^{3}$ operating at 250 GeV (top) and 550 GeV (bottom) and for PS1 (left) and PS2 (right) beam parameter configurations.