A meson ( , mean decay length ) is produced in a collision with rapidity and…

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Symmetry and Flavour, Ch The collider experiment: from bunch populations to a measured cross section

Problem

A D+D^+ meson (m=1.870 GeVm = 1.870\,\mathrm{GeV}, mean decay length cτ=311.8 μmc\tau = 311.8\,\mu\mathrm{m}) is produced in a pppp collision with rapidity y=3.0y = 3.0 and transverse momentum pT=3.0 GeVp_T = 3.0\,\mathrm{GeV}. ((a)) Using the transverse mass mT=m2+pT2m_T = \sqrt{m^2 + p_T^2} and E=mTcosh⁡yE = m_T\cosh y, pz=mTsinh⁡yp_z = m_T\sinh y, find the meson's total momentum pp and its Lorentz factor product βγ=p/m\beta\gamma = p/m in the laboratory frame. ((b)) Find the mean laboratory decay length ⟨ℓ⟩=βγ cτ\langle\ell\rangle = \beta\gamma\,c\tau and the Lorentz factor γ\gamma. ((c)) A daughter leaves at a laboratory angle of order 1/γ1/\gamma to the parent's direction. Estimate the transverse impact parameter of a daughter track, b≈⟨ℓ⟩/γb \approx \langle\ell\rangle/\gamma, and compare it in order of magnitude with cτc\tau itself. Someone argues that because βγ=19\beta\gamma = 19 the impact parameter must be about nineteen times cτc\tau: say why this is wrong. ((d)) A displaced-vertex-tagged sample of charm production gives Nobs=6400N_{\rm obs} = 6400 candidates with an estimated background of Nbkg=400N_{\rm bkg} = 400, an acceptance A=0.22A = 0.22, a tagging-and-selection efficiency ε=0.75\varepsilon = 0.75, and an integrated luminosity ∫L dt=100 pb−1\int\mathcal{L}\,\mathrm{d}t = 100\,\mathrm{pb^{-1}}. Compute the measured σ×B\sigma\times\mathcal{B} in nb\mathrm{nb}.

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