The low-energy spectrum and phenomenology of strongly-interacting particles is well described by Quantum Chromodynamics (QCD). Ab initio results have been obtained using Monte Carlo simulations of QCD regularized on the lattice, with a very good agreement with experiments. In particular, the mass pattern of an octet of light pseudoscalar mesons is well understood identifying them as pseudo Nambu–Goldstone bosons of spontaneous chiral symmetry breaking. A ninth pseudoscalar meson—the ′—evades this classification. It is associated to flavoursinglet axial U(1) transformations, but it is too heavy to be a pseudo Nambu–Goldstone boson. This is known as the U(1) problem. A solution to this problem was proposed by Witten and Veneziano in 1979. Their proposal links the ′ mass to the anomaly in the flavour-singlet axial Ward–Takahashi identities. They predict an anomalous contribution to the mass proportional to the topological susceptibility computed in Yang–Mills (YM) theory. The verification of the Witten–Veneziano formula requires the computation of the YM topological susceptibility and the ′ meson mass from first principles. This is possible only solving QCD at the non-perturbative level, as for instance in lattice simulations. This thesis is a step toward the implementation and verification of the Witten–Veneziano formula on the lattice. In the first part of the thesis, we computed the topological susceptibility with percent-level accuracy in the SU(3) YM theory and for the first time in the c → ∞ limit. The computation was done on the lattice implementing a naïve discretization of the topological charge evolved with the YM gradient flow. We provided a field-theoretical proof that the cumulants of the topological charge distribution computed using this definition coincide, in the continuum limit, with those of the universal definition appearing in the anomalous Ward–Takahashi identities. We performed a range of high statistics Monte Carlo simulations with different lattice spacings and c values. The coverage of parameter space allowed us to extrapolate the topological susceptibility to the continuum and c → ∞ limits with confidence, keeping all systematic effects under control. As a by-product, we measured the non-Gaussianity of the topological charge distribution in SU(3) YM theory. This result is compatible with the expectations from the large-c expansion, while it rules out the behaviour of the vacuum energy predicted by the dilute instanton gas model. In the last part of the thesis, we focused on the direct lattice determination of the mass of the ′ meson. With state-of-the-art techniques, it is still not possible to compute this mass with an adequate accuracy. The root of the issue is the exponential worsening with distance of the signal-to-noise ratio of correlation functions. This is a very general unsolved problem, which is currently limiting the accuracy of a broad class of Monte Carlo computations. We proposed to address this problem generalising the multilevel Monte Carlo algorithm to theories with dynamical fermions. We devised the first step of this program, namely the factorization of hadronic two-point functions, focusing on the disconnected contribution which is relevant to the ′ meson.

Solving the U(1) problem of QCD: new computational strategies and results / Ce', Marco; relatore: Giusti, Leonardo; Scuola Normale Superiore, 27-Feb-2017.

Solving the U(1) problem of QCD: new computational strategies and results

Ce', Marco
2017

Abstract

The low-energy spectrum and phenomenology of strongly-interacting particles is well described by Quantum Chromodynamics (QCD). Ab initio results have been obtained using Monte Carlo simulations of QCD regularized on the lattice, with a very good agreement with experiments. In particular, the mass pattern of an octet of light pseudoscalar mesons is well understood identifying them as pseudo Nambu–Goldstone bosons of spontaneous chiral symmetry breaking. A ninth pseudoscalar meson—the ′—evades this classification. It is associated to flavoursinglet axial U(1) transformations, but it is too heavy to be a pseudo Nambu–Goldstone boson. This is known as the U(1) problem. A solution to this problem was proposed by Witten and Veneziano in 1979. Their proposal links the ′ mass to the anomaly in the flavour-singlet axial Ward–Takahashi identities. They predict an anomalous contribution to the mass proportional to the topological susceptibility computed in Yang–Mills (YM) theory. The verification of the Witten–Veneziano formula requires the computation of the YM topological susceptibility and the ′ meson mass from first principles. This is possible only solving QCD at the non-perturbative level, as for instance in lattice simulations. This thesis is a step toward the implementation and verification of the Witten–Veneziano formula on the lattice. In the first part of the thesis, we computed the topological susceptibility with percent-level accuracy in the SU(3) YM theory and for the first time in the c → ∞ limit. The computation was done on the lattice implementing a naïve discretization of the topological charge evolved with the YM gradient flow. We provided a field-theoretical proof that the cumulants of the topological charge distribution computed using this definition coincide, in the continuum limit, with those of the universal definition appearing in the anomalous Ward–Takahashi identities. We performed a range of high statistics Monte Carlo simulations with different lattice spacings and c values. The coverage of parameter space allowed us to extrapolate the topological susceptibility to the continuum and c → ∞ limits with confidence, keeping all systematic effects under control. As a by-product, we measured the non-Gaussianity of the topological charge distribution in SU(3) YM theory. This result is compatible with the expectations from the large-c expansion, while it rules out the behaviour of the vacuum energy predicted by the dilute instanton gas model. In the last part of the thesis, we focused on the direct lattice determination of the mass of the ′ meson. With state-of-the-art techniques, it is still not possible to compute this mass with an adequate accuracy. The root of the issue is the exponential worsening with distance of the signal-to-noise ratio of correlation functions. This is a very general unsolved problem, which is currently limiting the accuracy of a broad class of Monte Carlo computations. We proposed to address this problem generalising the multilevel Monte Carlo algorithm to theories with dynamical fermions. We devised the first step of this program, namely the factorization of hadronic two-point functions, focusing on the disconnected contribution which is relevant to the ′ meson.
27-feb-2017
FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI
Fisica
fermions
lattice QCD
mesons
particle physics
Physics
Quantum Chromodynamics (QCD)
Witten–Veneziano formula
YM theory
Scuola Normale Superiore
Giusti, Leonardo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/85885
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