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Scattering Amplitudes and Resonance Properties from Lattice QCD
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Europe/Berlin
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)
02.430
Mainz Institute for Theoretical Physics, Johannes Gutenberg University
Staudingerweg 9 / 2nd floor, 55128 Mainz
Description
[from D. R. Bolton, R. A. Briceño, D. J. Wilson, Phys. Lett. B757 (2016) 50-56, arXiv:1507.07928]
Figure 1: Postdiction of the ππ → ππ scattering phase in the ρ channel, made by fitting LQCD data at heavier pion masses using unitarized chiral perturbation theory (ChPT), and then extrapolating to the physical pion mass.
In recent years, Lattice QCD (LQCD) calculations of stable-hadron properties have become considerably more precise, and as a result, LQCD inputs are having an increasing impact on Standard-Model phenomenology. Considering this progress, it is natural to also examine the prospects for using lattice QCD to calculate the properties of unstable hadrons, i.e. QCD resonances that decay via the strong force. The extraction of resonance properties is much more challenging, but also in this sector enormous progress has been made in the development of both theoretical methods and numerical techniques. A major focus here is the approach, pioneered by Lüscher, of relating finite-volume energies to infinite-volume scattering observables. [See, for example, Figure 1.]
The long-term goal is to use LQCD to study various exotic resonances, including the recently-discovered X, Y and Z states as well as excited nucleon states, including the Roper resonance, which decays predominantly to Nπ and Nππ.
[J. Bulava, B. Hörz, B. Fahy, K. J. Juge, C. Morningstar, C. H. Wong, PoS LATTICE2015 069, arXiv:1511.02351]
Figure 2: The time-like pion form factor, as determined in a LQCD calculation with mπ ∼ 240 MeV. The curve corresponds to a Gounaris-Sakurai parameterization with the ρ-resonance mass and the ρππ coupling determined from the lattice data.
Beyond extracting QCD resonance properties, one can also use the relation between finite- and infinite-volume matrix elements to study electroweak transitions. Applying these methods will allow one to extract resonance form factors and to perform precision tests of the Standard Model. For instance, processes such as B → K* (di-lepton) → Kπ (di-lepton) are particularly important for LHCb phenomenology. Another example is the time-like pion form factor, which can be related to the low-energy electron-positron annihilation cross section and represents a crucial input quantity for the determination of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon, (g − 2)μ. Formalism for extracting this quantity from LQCD is understood and numerical calculations are underway [See Figure 2].
The aim of this workshop is to bring together experts in developing the formalism and lattice practitioners, in order to review the status of ongoing calculations and discuss future prospects. The workshop will emphasize the future role of LQCD in precision resonance physics, especially in the context of forthcoming experiments.
