A design brief calls for twenty pairs per hour from an collider running at

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

Particle Physics, Ch Accelerators and colliders: energy, luminosity and reach

Problem

A design brief calls for twenty

W^+W^-

pairs per hour from an

e^+e^-

collider running at

\sqrt{s} = 180\,\mathrm{GeV}

, where the cross section for

e^+e^-\to W^+W^-

is about

16\,\mathrm{pb}

. The affordable synchrotron loss is taken to be

2\,\mathrm{GeV}

per beam per turn, the same budget used for the

ZH

ring. Take

M_Wc^2 = 80.37\,\mathrm{GeV}

, the loss-per-turn scaling

U_0\,[\mathrm{GeV}] = 8.85\times10^{-5}\,E^4\,[\mathrm{GeV}]/r\,[\mathrm{m}]

(with

E

the beam energy and

r

the bending radius), and the bending relation

B\,[\mathrm{T}] = p\,[\mathrm{GeV}/c]/(0.2998\,r\,[\mathrm{m}])

for a singly charged particle, with the electron and positron rest mass neglected against the beam energy. ((a)) Confirm that

\sqrt{s} = 180\,\mathrm{GeV}

clears the

W^+W^-

production threshold and state the beam energy per particle. ((b)) Find the luminosity needed to deliver twenty pairs per hour at the quoted cross section. ((c)) Find the bending radius that keeps the loss per turn to

2\,\mathrm{GeV}

. ((d)) Find the dipole field needed on that radius. ((e)) State briefly why an

e^+e^-

collider, rather than a fixed-target experiment, is the right choice for a clean measurement of

W^+W^-

pair production, and say which of luminosity, radius or field is the demanding number in this design. ((f)) A linear collider has no bending and so no synchrotron loss: each beam crosses its accelerating cavities once, in a straight line. If the cavities add

30\,\mathrm{MeV}

per metre, how long must each of the two straight accelerators be to reach the beam energy of part (a)? Compare this with the length of the same cavities that the ring of part (c) needs to replace its loss each turn, and say what the ring gains, and what it pays, by bending its beams.

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