An electron-positron Higgs factory is to study by the recoil method

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

Symmetry and Flavour, Ch Four-vectors at work: boosts, invariants and the shape of a final state

Problem

An electron-positron Higgs factory is to study

e^+e^-\to ZH

by the recoil method, measuring only the

Z

through its decay to

\mu^+\mu^-

. Take

m_Z = 91.19\,\mathrm{GeV}

and

m_H = 125.2\,\mathrm{GeV}

, and neglect the beam-energy spread and radiation from the incoming beams. ((a)) Find the lowest centre-of-mass energy at which

ZH

can be produced at all. ((b)) The machine runs at

\sqrt s = 240\,\mathrm{GeV}

. Find the energy

E_Z

and momentum

|\mathbf p_Z|

of the

Z

in events where the recoiling system is a Higgs boson. ((c)) The

Z

energy is measured with an error

\delta E_Z = 0.10\,\mathrm{GeV}

. How large an error does this put on the recoil mass, and is the error in

E_Z

magnified or reduced? Would running at a higher

\sqrt s

help or hurt in this respect, for the same

\delta E_Z

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