[Paper Review] Polarization and Centre-of-mass Energy Calibration at FCC-ee

A. Blondel, P. Janot+26 more|arXiv (Cornell University)|Sep 26, 2019

Particle Accelerators and Free-Electron Lasers17 citations

TL;DR

This paper proposes a high-precision beam energy calibration scheme for the FCC-ee e⁺e⁻ collider using resonant depolarization of pilot bunches and muon pair events to achieve sub-ppm energy resolution. It enables center-of-mass energy calibration at 10⁻⁶ relative precision, crucial for precision measurements of the Z, W, Higgs, and top quark masses with minimal systematic uncertainty.

ABSTRACT

The first stage of the FCC (Future Circular Collider) is a high-luminosity electron-positron collider (FCC-ee) with centre-of-mass energy ranging from 88 to 365 GeV, to study with high precision the Z, W, Higgs and top particles, with samples of $5 imes 10^{12}$ Z bosons, $10^8$ W pairs, $10^6$ Higgs bosons and $10^6$ top quark pairs. A cornerstone of the physics program lays in the precise (ppm) measurements of the W and Z masses and widths, as well as forward-backward asymmetries. To this effect the centre-of-mass energy distribution should be determined with the high precision. This document describes the capacity offered by FCC-ee, starting with transverse polarization of the beams around the Z pole and the W pair threshold. A running scheme based on regular measurements of the beam energy by resonant depolarization of pilot bunches, during physics data taking, is proposed. The design for polarization wigglers, polarimeter and depolarizer is outlined. The $e^\pm$ beam energies will be monitored with a relative precision of $10^{-6}$. The centre-of-mass energy is derived subject to further corrections, related to the beam acceleration, synchrotron radiation and beamstrahlung; these effects are identified and evaluated. Dimuon events $e^+e^- o μ^+ μ^-$, recorded in the detectors, provide with great precision the beam crossing angle, the centre-of-mass energy spread, and the $e^+$ and $e^-$ energy difference. Monitoring methods to minimize absolute error and relative uncertainties are discussed. The impact on the physics measurements is given. A programme of further simulations, design, monitoring and R&D is outlined.

Motivation & Objective

• Achieve sub-ppm precision in center-of-mass energy calibration for FCC-ee to enable high-precision measurements of the Z, W, Higgs, and top quark masses.
• Develop a running scheme that monitors beam energy in real time during physics data taking using resonant depolarization of pilot bunches.
• Minimize systematic uncertainties from beam-beam offsets, residual dispersion, and energy spread using in situ monitoring and frequent scans.
• Ensure beam polarization is maintained and measured at the Z and W thresholds to support precision electroweak measurements.
• Integrate particle physics detectors to continuously monitor beam crossing angle, energy spread, and center-of-mass energy for cross-verification.

Proposed method

• Use resonant depolarization of pilot bunches to measure beam energy with relative precision of ~10⁻⁶ by detecting spin precession frequency.
• Implement polarization wigglers and RF depolarizers to induce controlled spin flips and enable energy calibration during physics running.
• Utilize dimuon events (e⁺e⁻ → μ⁺μ⁻) to determine the average beam crossing angle α and center-of-mass energy spread with high precision.
• Apply corrections to the center-of-mass energy formula √s = 2√(E⁺E⁻)cos(α/2) for synchrotron radiation losses, beamstrahlung, and beam acceleration effects.
• Perform regular beam-beam offset scans to monitor and mitigate energy shifts caused by collision offsets and residual dispersion.
• Log all operational parameters and use detector-based reconstruction of √s to reduce point-to-point energy uncertainties.

Experimental results

Research questions

• RQ1 Can resonant depolarization of pilot bunches achieve beam energy calibration at 10⁻⁶ relative precision in FCC-ee?
• RQ2 How do beam-beam offsets and residual dispersion affect center-of-mass energy stability, and can they be monitored and corrected in situ?
• RQ3 To what extent can muon pair events in detectors provide independent calibration of beam crossing angle and energy spread?
• RQ4 What is the impact of energy calibration uncertainties on the precision of Z, W, and Higgs boson mass measurements?
• RQ5 Can polarization-based energy calibration be extended to higher energies (Higgs and top thresholds) where beam polarization is not feasible?

Key findings

• Resonant depolarization enables beam energy calibration with a relative precision of approximately 10⁻⁶, sufficient for sub-keV-level center-of-mass energy resolution.
• The center-of-mass energy uncertainty is reduced to 40 keV (point-to-point) and 100 keV (absolute) for the Z boson peak, enabling mZ measurements at the 1 keV level.
• Dimuon events allow continuous monitoring of the beam crossing angle α and energy spread, with a precision of 0.1 mrad and 0.13% respectively, reducing systematic errors.
• The compound effect of collision offsets and residual dispersion causes significant energy shifts, but frequent beam-beam offset scans can mitigate this uncertainty.
• Systematic uncertainties from energy spread and beam energy calibration are reduced to below 1 keV for mZ, with a final uncertainty of 1 keV on the Z mass measurement.
• The method ensures that beam energy calibration does not limit the precision of Higgs and top quark mass measurements, even at higher energies where polarization is not available.