<p>We perform a global analysis of lattice and experimental data on negative-strangeness meson-baryon scattering using a large set of variations of the theoretical framework based on the chiral unitary approach. For the former, the Lüscher formalism is utilized taking into account all pertinent coupled-channel effects. Through this, systematic uncertainties related to data scarcity, potential ambiguities, and possible framework dependence are quantified for the first time. The implementation of information criteria and other statistical tools is discussed. As a final result we provide pole positions for isoscalar resonances at the physical and lattice points, including statistical and systematic uncertainties. Predictions for the isovector states are also provided, showing large uncertainties.</p>

Cyprus

Ferenc Pittler

Switzerland

United States

Maxim Mai

Germany

China

Ulf-G. Meißner

United Kingdom

Ryan F. Ferguson

Peter Hurck

David G. Ireland

Bryan McKinnon

Universal parameters of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1380</mn><mo stretchy="false">)</mo></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math>, and their isospin partners from a combined analysis of lattice QCD and experimental results

We investigate contributions of excited states to nucleon matrix elements computed in lattice QCD by employing, in addition to the standard nucleon interpolating operator, pion-nucleon (<math><mrow><mi>π</mi><mtext>−</mtext><mi>N</mi></mrow></math>) operators. We solve a generalized eigenvalue problem (GEVP) to obtain an optimal interpolating operator that minimizes overlap with the <math><mrow><mi>π</mi><mtext>−</mtext><mi>N</mi></mrow></math> states. We derive a variant of the standard application of the GEVP method, which allows for constructing 3-point correlation functions using the optimized interpolating operator without requiring the computationally demanding combination that includes <math><mrow><mi>π</mi><mtext>−</mtext><mi>N</mi></mrow></math> operators in both sink and source. We extract nucleon matrix elements using two twisted mass fermion ensembles, one ensemble generated using pion mass of 346 MeV and one ensemble tuned to reproduce the physical value of the pion mass. Especially, we determine the isoscalar and isovector scalar, pseudoscalar, vector, axial, and tensor matrix elements. We include results obtained using a range of kinematic setups, including momentum in the sink. Our results using this variational approach are compared with previous results obtained using the same ensembles and multistate fits without GEVP improvement. We find that for the physical mass point ensemble, the improvement, in terms of suppression of excited states using this method, is most significant for the case of the matrix elements of the isovector axial and pseudoscalar currents.

Constantia Alexandrou

Giannis Koutsou

Yan Li

Marcus Petschlies

Investigation of pion-nucleon contributions to nucleon matrix elements

We present an investigation of pion-nucleon elastic scattering in the <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>(</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>)</mo></math> channel using lattice QCD with degenerate up and down, strange and charm quarks with masses tuned to their physical values. We use an ensemble of twisted mass fermions with box size <math><mi>L</mi><mo>=</mo><mn>5.1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and lattice spacing <math><mi>a</mi><mo>=</mo><mn>0.08</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and we consider the <math><mi>π</mi><mi>N</mi></math> system in rest and moving frames up to total momentum <math><mrow><msup><mrow><mover><mrow><mi>P</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>3</mn><mo>(</mo><mn>2</mn><mi>π</mi><mo>/</mo><mi>L</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.17</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. We take into account the finite volume symmetries and <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave mixing, and use the Lüscher formalism to simultaneously constrain the <math><mi>J</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mo>ℓ</mo><mo>=</mo><mn>0</mn></math> and <math><mi>J</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo>,</mo><mo>ℓ</mo><mo>=</mo><mn>1</mn></math> scattering amplitudes. We estimate the <math><mi>Δ</mi></math> resonance pole in the <math><mi>P</mi></math>-wave channel as well as the <math><mi>S</mi></math>-wave isospin-<math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> scattering length.

Simone Bacchio

Theodoros Leontiou

Srijit Paul

Elastic nucleon-pion scattering amplitudes in the <math><mi>Δ</mi></math> channel at physical pion mass from lattice QCD

We calculate the double-virtual <math><mrow><mi>η</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> transition form factor <math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>η</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></msub><mo>(</mo><msubsup><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow></math> from first principles using a lattice QCD simulation with <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> quark flavors at the physical pion mass and at one lattice spacing and volume. The kinematic range covered by our calculation is complementary to the one accessible from experiment and is relevant for the <math><mi>η</mi></math>-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment <math><msub><mi>a</mi><mi>μ</mi></msub><mo>=</mo><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>/</mo><mn>2</mn></math> of the muon. From the form factor calculation we extract the partial decay width <math><mrow><mi>Γ</mi><mo>(</mo><mi>η</mi><mo>→</mo><mi>γ</mi><mi>γ</mi><mo>)</mo><mo>=</mo><mn>338</mn><mo>(</mo><mn>87</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>17</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> and the slope parameter <math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>=</mo><mn>1.34</mn><mo>(</mo><mn>28</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>14</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. For the <math><mi>η</mi></math>-pole contribution to <math><msub><mi>a</mi><mi>μ</mi></msub></math> we obtain <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>η</mi><mtext>-pole</mtext></mrow></msubsup><mo>=</mo><mn>13.8</mn><mo>(</mo><mn>5.2</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>1.5</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>.

Sebastian Burri

Jacob Finkenrath

Andrew Gasbarro

Kyriakos Hadjiyiannakou

Karl Jansen

Gurtej Kanwar

Bartosz Kostrzewa

Konstantin Ottnad

Carsten Urbach

Urs Wenger

<math><mrow><mi>η</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> transition form factor and the hadronic light-by-light <math><mi>η</mi></math>-pole contribution to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> from lattice QCD

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> scheme at 2 GeV. We find <math><mrow><mo>⟨</mo><mi>x</mi><msub><mrow><mo>⟩</mo></mrow><mrow><mi>u</mi><mo>+</mo><mi>d</mi></mrow></msub><mo>=</mo><mn>0.601</mn><mo>(</mo><mn>28</mn><mo>)</mo></mrow></math>, <math><mo>⟨</mo><mi>x</mi><msub><mo>⟩</mo><mi>s</mi></msub><mo>=</mo><mn>0.059</mn><mo>(</mo><mn>13</mn><mo>)</mo></math>, <math><mo>⟨</mo><mi>x</mi><msub><mo>⟩</mo><mi>c</mi></msub><mo>=</mo><mn>0.019</mn><mo>(</mo><mn>05</mn><mo>)</mo></math>, and <math><mo>⟨</mo><mi>x</mi><msub><mo>⟩</mo><mi>g</mi></msub><mo>=</mo><mn>0.52</mn><mo>(</mo><mn>11</mn><mo>)</mo></math> for the separate contributions, respectively, whose sum saturates the momentum sum rule.

Georg Bergner

Fernanda Steffens

CERN

Quark and Gluon Momentum Fractions in the Pion from <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> Lattice QCD

We present a lattice computation of ππ–scattering in the <math><mi>I</mi><mo>=</mo><mn>1</mn></math> channel with <math><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn></math> dynamical quark flavours obtained with ensembles bracketing the physical value of the pion mass. Employing a global fit to data at three values of the pion mass, we determine the universal parameters of the ρ-resonance. We carefully investigate systematic uncertainties by determining energy eigenvalues using different methods and by comparing inverse amplitude method and Breit-Wigner type parametrizations. Overall, exploring the complex energy plane we find mass <math><msub><mrow><mi>M</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>=</mo><mn>786</mn><mo>(</mo><mn>22</mn><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and width <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>=</mo><mn>180</mn><mo>(</mo><mn>6</mn><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>, including statistical and systematic uncertainties. In contrast to previous <math><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn></math> extrapolations from higher than physical pion mass results, our mass value is in good agreement with experiment, while the width is too high.

Matthias Fischer

Martin Ueding

Markus Werner

The -resonance From = 2 lattice QCD including the physical pion mass

The infamous strong <math><mi>C</mi><mi>P</mi></math> problem in particle physics can in principle be solved by a massless up quark. In particular, it was hypothesized that topological effects could substantially contribute to the observed nonzero up-quark mass without reintroducing <math><mi>C</mi><mi>P</mi></math> violation. Alternatively to previous work using fits to chiral perturbation theory, in this Letter, we bound the strength of the topological mass contribution with direct lattice QCD simulations, by computing the dependence of the pion mass on the dynamical strange-quark mass. We find that the size of the topological mass contribution is inconsistent with the massless up-quark solution to the strong <math><mi>C</mi><mi>P</mi></math> problem.

Canada

Lena Funcke

Ruling Out the Massless Up-Quark Solution to the Strong <math><mi>C</mi><mi>P</mi></math> Problem by Computing the Topological Mass Contribution with Lattice QCD

We study the problems of deconfinement, chiral symmetry restoration and localisation of the low Dirac eigenmodes in a toy model of QCD, namely unimproved staggered fermions on lattices of temporal extension N T = 4. This model displays a genuine deconfining and chirally-restoring first-order phase transition at some critical value of the gauge coupling. Our results indicate that the onset of localisation of the lowest Dirac eigenmodes takes place at the same critical coupling where the system undergoes the first-order phase transition. This provides further evidence of the close relation between deconfinement, chiral symmetry restoration and localisation of the low modes of the Dirac operator on the lattice.

Hungary

Matteo Giordano

Sándor Katz

Tamás Kovács

Deconfinement, chiral transition and localisation in a QCD-like model

We study the problems of chiral symmetry breaking and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We recast the staggered Dirac operator into an unconventional three-dimensional Anderson Hamiltonian (“Dirac-Anderson Hamiltonian”) carrying internal degrees of freedom, with disorder provided by the fluctuations of the gauge links. In this framework, we identify the features relevant to chiral symmetry restoration and localisation of the low-lying Dirac eigenmodes in the ordering of the local Polyakov lines, and in the related correlation between spatial links across time slices, thus tying the two phenomena to the deconfinement transition. We then build a toy model based on QCD and on the Dirac-Anderson approach, replacing the Polyakov lines with spin variables and simplifying the dynamics of the spatial gauge links, but preserving the above-mentioned relevant dynamical features. Our toy model successfully reproduces the main features of the QCD spectrum and of the Dirac eigenmodes concerning chiral symmetry breaking and localisation, both in the ordered (deconfined) and disordered (confined) phases. Moreover, it allows us to study separately the roles played in the two phenomena by the diagonal and the off-diagonal terms of the Dirac-Anderson Hamiltonian. Our results support our expectation that chiral symmetry restoration and localisation of the low modes are closely related, and that both are triggered by the deconfinement transition.

An Anderson-like model of the QCD chiral transition

We discuss a possible mechanism leading to localisation of the low-lying Dirac eigenmodes in high-temperature lattice QCD, based on the spatial fluctuations of the local Polyakov lines in the partially ordered configurations above T c . This mechanism provides a qualitative explanation of the dependence of localisation on the temperature and on the lattice spacing, and also of the phase diagram of QCD with an imaginary chemical potential. To test the viability of this mechanism we propose a three-dimensional effective, Anderson-like model, mimicking the effect of the Polyakov lines on the quarks. The diagonal, on-site disorder is governed by a three-dimensional Ising-like spin model with continuous spins. Our numerical results show that localised modes are indeed present in the ordered phase of the Ising model, thus supporting the proposed mechanism for localisation in QCD.

An Ising-Anderson model of localisation in high-temperature QCD