Model for the curvature response of the CDF II drift chamber

Abstract

The CDF II experiment at the Fermilab Tevatron used a drift chamber to measure the momenta of charged particles. We present a model for the response of the drift chamber to the curvature of a charged particle's trajectory. Constraints on the model parameters are obtained from cosmic-ray data and from information published by CDF in the context of the W boson mass measurement. Implications for the calibration of the drift chamber measurement of momentum are discussed. The robustness of the CDF calibration procedure is demonstrated. The model provides a framework for the analysis of precision magnetic trackers of high-momentum particles.

Figures (9)

• Figure 1: Schematics of the CDF II experiment's cylindrical drift chamber (COT) in the transverse (azimuthal) view (left) and longitudinal view (right). The beam line is along the longitudinal axis of the tracker, which is also the direction of the magnetic field. The green-shaded region shows the active gas-filled volume, between radii of 40 cm and 138 cm from the cylinder (and beam) axis cotNim. The eight darker-green annuli depict the superlayers (rings of supercells) as shown in Fig. . The grey shading indicates the region occupied by the silicon tracking detector. The red and blue trajectories illustrate two oppositely charged cosmic-ray muons propagating downward in azimuth, each of $p_T = 10$ GeV. Their impact parameter of $\pm 1$ cm is typical of the cosmic-ray sample analyzed in this paper and in cosmicAlignment. Also shown as the black trajectory is a muon with $p_T = 40$ GeV emanating from a decaying $W$ boson. The arrows indicate the direction of propagation. The complete cosmic-ray trajectory is referred to as the dicosmic because it is comprised of the incoming (pointing towards the beam axis) and outgoing (pointing away from the beam axis) legs of the cosmic-ray path.
• Figure 2: The measurement of $\Delta^+_c$ as a function of $c_{\rm d}$, the measured curvature of the COT dicosmic helix, in cosmic-ray data collected in situ during collider operation. The requirement $| z_0 | < 60$ cm ensures that the cosmic-ray tracks have similar trajectories as the particles selected for physics analysis. Also shown are the fits to Eq. and the values and statistical uncertainties of the fitted parameters (left) $a_0$ (in PeV$^{-1}$), $b_1$ (in ), $a_2$ and $\epsilon$ (both in MeV), and $b_3$ (in GeV$^2$), and (right) $b_1$, $a_2$ and $\epsilon$, and $b_3$. The error bars indicate the statistical uncertainties on the data points. The horizontal arrows indicate the range of $q/p_T$ of the leptons originating from $W^\pm \to \ell^\pm \nu$ and $Z \to \ell^+ \ell^-$ decays that are used in the $m_W$ analysis CDF2022.
• Figure 3: The measurement of $\Delta^+_c$ as a function of $c_{\rm d}$, the measured curvature of the COT dicosmic helix, in cosmic-ray data collected in situ during collider operation. The requirement $| z_0 | < 60$ cm ensures that the cosmic-ray tracks have similar trajectories as the particles selected for physics analysis. The data have been corrected for the known energy loss $\epsilon$. Also shown are the fits to Eq. and the values and statistical uncertainties of the fitted parameters (left) $a_2$ (in MeV), and $b_3$ (in GeV$^2$), and (right) $b_3$. The error bars indicate the statistical uncertainties on the data points. The horizontal arrows indicate the range of $q/p_T$ of the leptons originating from $W^\pm \to \ell^\pm \nu$ and $Z \to \ell^+ \ell^-$ decays that are used in the $m_W$ analysis CDF2022.
• Figure 4: End view of a section of the CDF COT end plate. The sense wires are organized into eight concentric "superlayers". Each superlayer is partitioned azimuthally into cells, and each cell contains 12 sense wires separated from adjacent cells by field sheets. Precision-machined slots in the end plates hold each cell's sense wires and field sheets under tension. The radius at the center of each superlayer is shown in cm. Figure reproduced with permission from Fig. 2 of cotNim.
• Figure 5: (Left) The fraction of the maximum possible number of COT hits contributing to the cosmic-ray tracks. (Right) The fraction of the maximum possible number of superlayers contributing to the cosmic-ray tracks, when a superlayer is required to contribute at least 5 (out of 12) hits. The fit is intended to guide the eye. The superlayer efficiency is constant at 99.95% at low curvature and lower by 0.02% for $|c_{\rm th}^{-1}| = p_T \lesssim 25$ GeV when a different trigger is used. The fit function is $y = \varepsilon + \Delta \varepsilon/(1 + e^{-\xi}) + \frac{q}{2}\kappa/(1 + e^{\xi})$ where $\xi = (|x|-|c_{\rm th}|)/\beta$. The parameter $\kappa = (0.002 \pm 0.004)$% describes the difference in superlayer efficiency as $c \to 0^+$ versus $c \to 0^-$.