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Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD

We determine the energy-dependent amplitude for elastic ππ P-wave scattering in isospin-1 by computing part of the discrete energy spectrum of QCD in finite cubic boxes. We observe a rapidly rising phase shift that can be well described by a single ρ resonance. The spectrum is obtained from hadron correlators computed using lattice QCD with light quark masses corresponding to mπ ~ 400 MeV. Variational analyses are performed with large bases of hadron interpolating fields including, as well as fermion bilinears that resemble q-qbar constructions, also operators that resemble pairs of pions with definite relative and total momentum. We compute the spectrum for a range of center-of-mass momenta and in various irreducible representations of the relevant symmetry group. Hence we determine more than thirty values of the isospin-1 P-wave scattering phase shift in the elastic region, mapping out its energy dependence in unprecedented detail.