Elastic scattering occurs at centre-of-mass energy

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

Elastic π+p→π+p\pi^+p \to \pi^+p scattering occurs at centre-of-mass energy s=1.400 GeV\sqrt{s} = 1.400\,\mathrm{GeV}, with centre-of-mass momentum p∗=0.367 GeVp^* = 0.367\,\mathrm{GeV} and scattering angle θ∗=60∘\theta^* = 60^\circ. Take mπ=0.1396 GeVm_\pi = 0.1396\,\mathrm{GeV} and mp=0.9383 GeVm_p = 0.9383\,\mathrm{GeV}. ((a)) Calculate tt using t=−2p∗2(1−cos⁡θ∗)t = -2p^{*2}(1-\cos\theta^*). ((b)) Use s+t+u=∑imi2s+t+u=\sum_i m_i^2 to obtain uu, and comment on its sign.

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