Improving systematic uncertainties on precision two-body mass measurements

TL;DR

The paper develops a data-driven formalism that links biases in two-body invariant-mass measurements to detector calibration parameters by analyzing mass shifts as functions of the sum and difference of daughter momenta. It demonstrates a $\Lambda$ mass measurement at LHCb with tracking-system systematic control to about $0.7\,\mathrm{keV}/c^2$ and a total precision near $2.2\,\mathrm{keV}/c^2$, limited by the $m_{K_S^0}$ calibration, and it extends the method to multibody decays and CPT tests. The approach decomposes biases into physically interpretable components ($\alpha$, $\delta$, $\Delta\theta$, $\Delta\omega$) and uses calibration channels to extract them, enabling high-precision mass determinations and robust cross-checks with lattice QCD. This framework provides a practical path to greatly improve $\Lambda$ mass measurements and CPT tests at LHCb and can be adapted to other two-body and selected multibody decays.

Abstract

To make precision particle mass measurements in charged spectrometers detailed understanding of the influence of detector effects is critical. In this paper the influence of detector-related uncertainties on the determination of the parent particle mass in two-body decays is investigated. It is shown how the dependence of observed mass shifts on the sum and difference of the daughter particle momenta can be used to determine the physical causes of a bias more rigorously than the \textit{ad hoc} rules that are often adopted. The approach is illustrated using the case of measuring the $Λ$ hyperon mass. This observable is of interest because our current knowledge relies on information from a single experiment that has not been updated to account for changes in the value of the $\textrm{K}_{\textrm{s}}^0$ mass used for calibration. With the approach developed in the paper it shown that the LHCb experiment has the capability to make a measurement of the $Λ$ mass with systematic uncertainties from the tracking system controlled to $0.7\,$keV/$c^2$. This allows a total precision of $2.2\,$keV/$c^2$ to be achieved, dominated by the knowledge of the $\textrm{K}_{\textrm{s}}^0$ mass used for calibration. This would improve the current knowledge of the $Λ$ hyperon mass by a factor of three.

Figures (5)

• Figure 1: (a) Distribution of the $R_{p}$ variable for the two ${{\mathrm{K}\xspace}\xspace^0_{\mathrm{S}}}\xspace\!\rightarrow\xspace {{\pi\xspace}\xspace^+}\xspace{{\pi\xspace}\xspace^-}\xspace$ and ${\Lambda\xspace}\xspace\!\rightarrow\xspace {\mathrm{p}\xspace}\xspace{{\pi\xspace}\xspace^-}\xspace$ simulation samples. b) Invariant mass calculated under the two-pion mass hypothesis for the two simulation samples versus $R_{p}$, taken here to be the maximum of $p_1/p_2$ and $p_2/p_1$. Under the $\pi^+\pi^-$ hypothesis, $\hbox{${\Lambda\xspace}\xspace\!\rightarrow\xspace {\mathrm{p}\xspace}\xspace{{\pi\xspace}\xspace^-}\xspace$}\xspace$ decays give a characteristic curved band versus $R_{p}$. This illustrates how the two decays can be separated kinematically using $R_{p}$ even if particle identification information is unavailable.
• Figure 2: (a) Distribution of $\Delta m_{{{\mathrm{K}\xspace}\xspace^0_{\mathrm{S}}}\xspace}$ in pseudoexperiments determined from a fit of a Crystal Ball function to the full sample. (b) Distribution of $\Delta m_{{\Lambda\xspace}\xspace}$ in pseudoexperiments from a Crystal Ball function fit. Note the change in scale on the $x-$axis.
• Figure 3: Distribution of $\Delta m_{{{\mathrm{K}\xspace}\xspace^0_{\mathrm{S}}}\xspace}$ in an example pseudoexperiment with $\alpha = 1.5 \times 10^{-4}, \delta = 2.6 \, \textrm{MeV}$ and $\Delta \theta = 5 \times 10^{-6} \, \textrm{rad}$. (a) Before calibration, a fit to Equation \ref{['eq:master']} is superimposed. (b) After calibration, a fit to a constant is superimposed. The probability of $\chi^2$ of the fit is 0.66. Note the change of scale on the $y-$axis.
• Figure 4: (a) Distribution of $\Delta m_{{{\mathrm{K}\xspace}\xspace^0_{\mathrm{S}}}\xspace}$ in an example pseudoexperiment with $\alpha = 1.5 \times 10^{-4}, \delta = 2.6 \, \textrm{MeV}$, $\Delta \theta = 5\times 10^{-6} \, \textrm{rad}$ and $\Delta \omega = -1.5 \times 10^{-5} \textrm{c/GeV}$. (b) After the first calibration step. A fit to linear form is superimposed (b) After the full calibration. A fit to a constant is superimposed. The probability of $\chi^2$ for the fit is 0.66. Note the change of scale on the $y-$axis.
• Figure 5: (a) Mass shift, $\Delta m_{\psi(2S)}$ verus $p_{\pi^+\pi^-}$. The points are a simulation sample generated with RapidSim. In the simulation, the values $\alpha = 2 \times 10^{-4}$ and $\delta = 2 \, \textrm{MeV}/c$ were used. The dotted line shows the expectation for the mass shift with these values and the functional form given in Equation \ref{['eq:psi']}. (b) Mass shift, $\Delta m_{\psi(2S)}$ verus $p_{\pi^+\pi^-}$ for a simulation sample with the opening angle between the pion pair increased by $5 \times 10^{-6}\mu$rad. The resulting bias is compared to the linear form expected from Equation \ref{['eq:psi2']}.