arXiv subjects

Jozef J. Dudek

Publications and source records attributed to Jozef J. Dudek.

At least 37 records · Page 2Linked to original sources

arXiv2018

Recent progress on hadron spectroscopy from lattice QCD

Lattice QCD has matured to a degree where it is now possible to study excited hadrons as they truly appear in nature, as short-lived resonant enhancements decaying into multiple possible final states. Through variational analysis of matrices of correlation functions computed with large bases of interpolating fields it has proven possible to extract many excited state energy levels, and these can be used to constrain the hadron-hadron scattering amplitudes in which hadron resonances can be observed. Recent progress is illustrated with several examples including coupled-channel scattering in the $πη, K\overline{K}$ and $ππ, K\overline{K}, ηη$ systems in which the $a_0, f_0$ scalar mesons appear.

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arXiv2018

Dynamically-coupled partial-waves in $ρπ$ isospin-2 scattering from lattice QCD

We present the first determination of $ρπ$ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 $ρπ$, we calculate partial-wave amplitudes with $J \le 3$ and determine the degree of dynamical mixing between the coupled $S$ and $D$-wave channels with $J^P=1^+$. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that $m_π\sim 700$ MeV, ensuring that the $ρ$ is stable against strong decay. This work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.

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arXiv2018

Searching for the rules that govern hadron construction

Just as Quantum Electrodynamics describes how electrons are bound in atoms by the electromagnetic force, mediated by exchange of photons, Quantum Chromodynamics (QCD) describes how quarks are bound inside hadrons by the strong force, mediated by exchange of gluons. At face value, QCD allows hadrons constructed from increasingly many quarks to exist, just as atoms with increasing numbers of electrons exist, yet such complex constructions seemed, until recently, to not be present in nature. In what follows we describe advances in the spectroscopy of mesons that are refining our understanding of the rules for building hadrons from QCD.

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arXiv2017

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector

We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_π=$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Therefore, there is no strong indication for any bound state or narrow resonance in the channels we study.

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arXiv2017

Isoscalar $ππ, K\overline{K}, ηη$ scattering and the $σ, f_0, f_2$ mesons from QCD

We present the first lattice QCD study of coupled isoscalar $ππ,K\overline{K},ηη$ $S$- and $D$-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the quark mass corresponding to $m_π\sim391$ MeV. In the $J^P=0^+$ sector we find analogues of the experimental $σ$ and $f_0(980)$ states, where the $σ$ appears as a stable bound-state below $ππ$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $ππ$ cross section in the vicinity of the $K\overline{K}$ threshold. For $J^P=2^+$ we find two states resembling the $f_2(1270)$ and $f_2'(1525)$, observed as narrow peaks, with the lighter state dominantly decaying to $ππ$ and the heavier state to $K\overline{K}$. The presence of all these states is determined rigorously by finding the pole singularity content of scattering amplitudes, and their couplings to decay channels are established using the residues of the poles.

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arXiv2017

Scattering processes and resonances from lattice QCD

The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

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arXiv2016

Isoscalar $ππ$ scattering and the $σ$ meson resonance from QCD

We present for the first time a determination of the energy dependence of the isoscalar $ππ$ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the $S$-wave phase-shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_π= 236, 391$ MeV and the resulting amplitudes are described in terms of a $σ$ meson which evolves from a bound-state below $ππ$ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.

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arXiv2016

The $ππ\toπγ^\star$ amplitude and the resonant $ρ\toπγ^\star$ transition from lattice QCD

We present a determination of the $P$-wave $ππ\toπγ^\star$ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Lüscher formalism. We determine the amplitude for a range of discrete values of the $ππ$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $ρ$ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the $ρ$ pole extract the $ρ\to πγ^\star$ transition form factor. This calculation, at $m_π\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

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arXiv2016

An $a_0$ resonance in strongly coupled $πη$, $K\overline{K}$ scattering from lattice QCD

We present the first calculation of coupled-channel meson-meson scattering in the isospin $=1$, $G$-parity negative sector, with channels $πη$, $K\overline{K}$ and $πη'$, in a first-principles approach to QCD. From the discrete spectrum of eigenstates in three volumes extracted from lattice QCD correlation functions we determine the energy dependence of the $S$-matrix, and find that the $S$-wave features a prominent cusp-like structure in $πη\to πη$ close to $K\overline{K}$ threshold coupled with a rapid turn on of amplitudes leading to the $K\overline{K}$ final-state. This behavior is traced to an $a_0(980)$-like resonance, strongly coupled to both $πη$ and $K\overline{K}$, which is identified with a pole in the complex energy plane, appearing on only a single unphysical Riemann sheet. Consideration of $D$-wave scattering suggests a narrow tensor resonance at higher energy.

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arXiv2015

The resonant $π^+γ\toπ^+π^0$ amplitude from Quantum Chromodynamics

We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for $ππ\to πγ^\star$, as a function of the energy of the $ππ$ pair and the virtuality of the photon, in the kinematic regime where $ππ$ couples strongly to the unstable $ρ$ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to $m_π\approx 400$~MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the $ρ$ pole and identify from its residue the $ρ\to πγ^\star$ form factor.

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arXiv2015

Coupled $ππ, K\overline{K}$ scattering in $P$-wave and the $ρ$ resonance from lattice QCD

We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_π= 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $ππ$, $K\overline{K}$ and $q\bar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $ππ$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $ρ$ resonance, and we extend the analysis into the coupled-channel $K\overline{K}$ region for the first time, finding a small coupling between the channels.

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arXiv2015

Resonances in coupled $πK, ηK$ scattering from lattice QCD

Coupled-channel $πK$ and $ηK$ scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a $q\bar{q}$ construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at ${m_π=391\,\mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $πK$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $πK$ and weakly to $ηK$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $κ$ resonance. A bound state with $J^P=1^-$ is found very close to the $πK$ threshold energy, whose coupling to the $πK$ channel is compatible with that of the experimental $K^\star(892)$. Evidence is found for a narrow resonance in $J^P=2^+$. Isospin--3/2 $πK$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.

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arXiv2015

Excited meson radiative transitions from lattice QCD using variationally optimized operators

We explore the use of optimized operators, designed to interpolate only a single meson eigenstate, in three-point correlation functions with a vector-current insertion. These operators are constructed as linear combinations in a large basis of meson interpolating fields using a variational analysis of matrices of two-point correlation functions. After performing such a determination at both zero and non-zero momentum, we compute three-point functions and are able to study radiative transition matrix elements featuring excited state mesons. The required two- and three-point correlation functions are efficiently computed using the distillation framework in which there is a factorization between quark propagation and operator construction, allowing for a large number of meson operators of definite momentum to be considered. We illustrate the method with a calculation using anisotopic lattices having three flavors of dynamical quark all tuned to the physical strange quark mass, considering form-factors and transitions of pseudoscalar and vector meson excitations. The dependence on photon virtuality for a number of form-factors and transitions is extracted and some discussion of excited-state phenomenology is presented.

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arXiv2014

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.

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arXiv2014

Resonances in coupled πK,ηK scattering from quantum chromodynamics

Using first-principles calculation within Quantum Chromodynamics, we are able to determine a pattern of strangeness=1 resonances which appear as complex singularities within coupled $πK$, $ηK$ scattering amplitudes. We make use of numerical computation in the lattice discretized approach to the quantum field theory with light quark masses corresponding to $m_π\sim 400\, \textrm{MeV}$ and at a single lattice spacing. The energy dependence of scattering amplitudes is extracted through their relationship to the discrete spectrum in a finite-volume, which we map out in unprecedented detail.

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arXiv2013

Toward the excited isoscalar meson spectrum from lattice QCD

We report on the extraction of an excited spectrum of isoscalar mesons using lattice QCD. Calculations on several lattice volumes are performed with a range of light quark masses corresponding to pion masses down to about 400 MeV. The distillation method enables us to evaluate the required disconnected contributions with high statistical precision for a large number of meson interpolating fields. We find relatively little mixing between light and strange in most JPC channels; one notable exception is the pseudoscalar sector where the approximate SU(3)F octet, singlet structure of the η, η' is reproduced. We extract exotic JPC states, identified as hybrid mesons in which an excited gluonic field is coupled to a color-octet qqbar pair, along with non-exotic hybrid mesons embedded in a qqbar-like spectrum.

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arXiv2012

S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD

The isospin-2 pi pi system provides a useful testing ground for determining elastic hadron scattering parameters from finite-volume spectra obtained using lattice QCD computations. A reliable determination of the excited state spectrum of two pions in a cubic box follows from variational analysis of correlator matrices constructed using a large basis of operators. A general operator construction is presented which respects the symmetries of a multi-hadron system in flight. This is applied to the case of pi pi and allows for the determination of the scattering phase-shifts at a large number of kinematic points, in both S-wave and D-wave, within the elastic region. The technique is demonstrated with a calculation at a pion mass of 396 MeV, where the elastic scattering is found to be well described by a scattering length parameterisation.

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arXiv2012

Excited and exotic charmonium spectroscopy from lattice QCD

We present a spectrum of highly excited charmonium mesons up to around 4.5 GeV calculated using dynamical lattice QCD. Employing novel computational techniques and the variational method with a large basis of carefully constructed operators, we extract and reliably identify the continuum spin of an extensive set of excited states, states with exotic quantum numbers (0+-, 1-+, 2+-) and states with high spin. Calculations are performed on two lattice volumes with pion mass approximately 400 MeV and the mass determinations have high statistical precision even for excited states. We discuss the results in light of experimental observations, identify the lightest 'supermultiplet' of hybrid mesons and comment on the phenomenological implications of the spectrum of exotic mesons.

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