Measure the Lifetime of D⁰ · RMPH 2021 #2

Physics · modern-physics

Problem

Context: You will use a data sample of about 50,000 events to measure the lifetime of the D⁰ particle. The D⁰ decays according to an exponential distribution, and fitting this exponential to a distribution of D⁰ decay times gives the lifetime as the slope parameter. Variables available: - D⁰ mass: invariant mass (1816-1914 MeV range), signal described by Gaussian distribution - D⁰ TAU: distribution of decay times, signal described by single exponential - D⁰ IP: distance of closest approach to primary vertex (plotted as log₁₀) - D⁰ PT: momentum transverse to LHC beamline Method: Background subtraction using signal region and sidebands in mass distribution. Tasks: 2.1 Define a range for the D⁰ mass which should be your 'signal region'. Comment on the criterion you used. 2.2 Perform the fit and obtain the value and the statistical error for D⁰ lifetime. 2.3 Repeat your fit for the lifetime of the D⁰ while varying the maximum allowed D⁰ impact parameter. The allowed values range from -4.0 to 1.5 in the original fit. Move this upper value down, at least 10 points and make the plot of the lifetime obtained. Save the plot (name it 2.3_YOURCODE). Create a table:
IPτ (lifetime)error (statistical)
1.5......
.........
2.4 The sigma-shaped plot you obtained is the indication of the presence of a systematic effect, which once identified can be removed. Make a hypothesis on what causes this systematic effect. 2.5 Seeing the shape of the lifetime as a function of the upper cut on the impact parameter where would you consider to be 'correct' value of the lifetime? Give a criterion for where on the plot you would choose this 'correct' value to lie. 2.6 Based on the criterion found above choose your best value for D⁰ lifetime the nominal value, and a range around this point. 2.7 Repeat the steps 2.3 and 2.6 for the D⁰ TAU variable such that you 'improve' the correct value of the lifetime. Create the table suggested above. 2.8 Repeat the steps 2.3 and 2.6 for the D⁰ PT variable. 2.9 Quote the final value of the D⁰ lifetime, called the nominal value and the statistical error associated with it.

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