Improving systematic uncertainties on precision two-body mass measurements

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 <i>ad hoc</i> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup><mml:mrow><mml:mtext>K</mml:mtext></mml:mrow> <mml:mtext>s</mml:mtext> <mml:mn>0</mml:mn></mml:msubsup> </mml:math> 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/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>c</mml:mi> <mml:mn>2</mml:mn></mml:msup> </mml:math> . This allows a total precision of 2.2 keV/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>c</mml:mi> <mml:mn>2</mml:mn></mml:msup> </mml:math> to be achieved, dominated by the knowledge of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup><mml:mrow><mml:mtext>K</mml:mtext></mml:mrow> <mml:mtext>s</mml:mtext> <mml:mn>0</mml:mn></mml:msubsup> </mml:math> mass used for calibration. This would improve the current knowledge of the Λ hyperon mass by a factor of three.