A baryon ( , mean decay length ) is produced with rapidity and transverse momentum…

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

\Lambda_b^0

baryon (

m = 5.620\,\mathrm{GeV}

, mean decay length

c\tau = 441\,\mu\mathrm{m}

) is produced with rapidity

y = 2.0

and transverse momentum

p_T = 8.0\,\mathrm{GeV}

. ((a)) Using

m_T = \sqrt{m^2+p_T^2}

E = m_T\cosh y

and

p_z = m_T\sinh y

, find the laboratory momentum

p

and

\beta\gamma = p/m

. ((b)) Find the mean laboratory decay length

\langle\ell\rangle

and the Lorentz factor

\gamma

. ((c)) A daughter leaves at a laboratory angle of order

1/\gamma

to the parent's direction. Estimate the daughter impact parameter

b\approx\langle\ell\rangle/\gamma

and compare it, in order of magnitude, with

c\tau

. State in one sentence why a vertex detector's required spatial resolution does not have to keep pace with

\beta\gamma

. ((d)) A displaced-vertex

b

-tagged dimuon sample gives

N_{\rm obs} = 15\,200

N_{\rm bkg} = 1200

, acceptance

A = 0.30

, efficiency

\varepsilon = 0.65

, and

\int\mathcal{L}\,\mathrm{d}t = 5.0\,\mathrm{fb^{-1}}

. Compute

\sigma\times\mathcal{B}

\mathrm{pb}

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