Understanding how momentum anisotropies arise in small collision systems is important for a quantitative understanding of collectivity in terms of QCD dynamics in small and large collision systems. In this letter we present results for small collision systems from the newly developed parton cascade Alpaca, which faithfully encodes the AMY effective kinetic theory. Alpaca reproduces quantitatively previously known results from a calculation in the single-hit approximation for small values of the coupling. We discuss in detail how such a comparison is to be carried out. Particularly at larger coupling a generic difference between the two approaches becomes apparent, namely that in parton cascades particles interact over a finite distance while in direct integrations of the Boltzmann equation the interactions are local. This leads to quantitative differences in the extracted values for the elliptic flow coefficient. These discrepancies appear in situations where the mean free path is not large compared to the interaction time and the applicability of kinetic theory is thus questionable.

Sweden

Robin Törnkvist

Korinna Zapp

Small systems and the single-hit approximation in the AMY parton cascade

A lattice QCD computation of the coupled channel <math><mi>π</mi><mi>Σ</mi><mi>–</mi><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> scattering amplitudes in the <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> region is detailed. Results are obtained using a single ensemble of gauge field configurations with <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> dynamical quark flavors and <math><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math><msub><mi>m</mi><mi>K</mi></msub><mo>≈</mo><mn>487</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering <math><mi>K</mi></math>-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the <math><mi>π</mi><mi>Σ</mi></math> threshold and a resonance pole just below the <math><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> threshold.

Germany

John Bulava

Bárbara Cid-Mora

United States

Andrew D. Hanlon

Ben Hörz

Daniel Mohler

Colin Morningstar

Joseph Moscoso

Amy Nicholson

Fernando Romero-López

Sarah Skinner

André Walker-Loud

Lattice QCD study of <math><mi>π</mi><mi>Σ</mi><mo>−</mo><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> scattering and the <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> resonance

This Letter presents the first lattice QCD computation of the coupled channel <math><mrow><mi>π</mi><mi>Σ</mi><mtext>−</mtext><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>N</mi></mrow></math> scattering amplitudes at energies near 1405 MeV. These amplitudes contain the resonance <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> with strangeness <math><mi>S</mi><mo>=</mo><mo>−</mo><mn>1</mn></math> and isospin, spin, and parity quantum numbers <math><mrow><mi>I</mi><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow></math>. However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≈</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> and <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>≈</mo><mn>487</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, this study finds the amplitudes exhibit a virtual bound state below the <math><mi>π</mi><mi>Σ</mi></math> threshold in addition to the established resonance pole just below the <math><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> threshold. Several parametrizations of the two-channel <math><mi>K</mi></math> matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity.

Two-Pole Nature of the <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> Resonance from Lattice QCD

We introduce the parton cascade Alpaca, which evolves parton ensembles corresponding to single events according to the effective kinetic theory of QCD at high temperature formulated by Arnold, Moore and Yaffe by explicitly simulating elastic scattering, splitting and merging. By taking the ensemble average over many events the phase space density (as evolved by the Boltzmann equation) is recovered, but the parton cascade can go beyond the evolution of the mean because it can be turned into a complete event generator that produces fully exclusive final states including fluctuations and correlations. The parton cascade does not require the phase space density as input (except for the initial condition at the starting time). Rather, effective masses and temperature, which are functions of time and are defined as integrals over expressions involving the distribution function, are estimated in each event from just the parton ensemble of that event. We validate the framework by showing that ensembles sampled from a thermal distribution stay in thermal equilibrium even after running the simulation for a long time. This is a non-trivial result, because it requires all parts of the simulation to intertwine correctly.

Norway

Aleksi Kurkela

AMY Lorentz invariant parton cascade: the thermal equilibrium case

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with <math><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> dynamical quark flavors and <math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><mn>200</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>. The s-wave scattering lengths with both total isospins <math><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> and <math><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> are inferred from the finite-volume spectrum below the inelastic threshold together with the <math><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> p-wave containing the <math><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></math> resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels, enabling a determination of the <math><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> scattering length with statistical errors below 5%, while the <math><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> scattering length is somewhat less precisely evaluated. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a step toward future computations down to physical light quark masses with multiple lattice spacings and volumes.

Pavlos Vranas

Elastic nucleon-pion scattering at = 200 MeV from lattice QCD

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations <math><mrow><mo>≳</mo><mn>1</mn></mrow></math> fm are commonly used to combat these issues. In this work, focusing on <math><msub><mi>g</mi><mi>A</mi></msub></math>, we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2–1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

China

Jinchen He

David A. Brantley

Japan

Chia Cheng Chang

Ivan Chernyshev

Evan Berkowitz

Dean Howarth

Christopher Körber

Aaron S. Meyer

Costa Rica

Henry Monge-Camacho

Enrico Rinaldi

United Kingdom

Chris Bouchard

M.A. Clark

Arjun Singh Gambhir

Christopher J. Monahan

Detailed analysis of excited-state systematics in a lattice QCD calculation of <math><msub><mi>g</mi><mi>A</mi></msub></math>

We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of <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> highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Möbius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of <math><msub><mi>t</mi><mrow><mi>gf</mi></mrow></msub><mo>=</mo><mn>1</mn></math> in lattice units. The ensembles span four lattice spacings in the range <math><mn>0.06</mn><mo>≲</mo><mi>a</mi><mo>≲</mo><mn>0.15</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, six pion masses in the range <math><mn>130</mn><mo>≲</mo><msub><mi>m</mi><mi>π</mi></msub><mo>≲</mo><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and multiple lattice volumes. On each ensemble, the gradient-flow scales <math><msub><mi>t</mi><mn>0</mn></msub><mo>/</mo><msup><mi>a</mi><mn>2</mn></msup></math> and <math><msub><mi>w</mi><mn>0</mn></msub><mo>/</mo><mi>a</mi></math> and the omega baryon mass <math><mi>a</mi><msub><mi>m</mi><mi>Ω</mi></msub></math> are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of <math><msqrt><msub><mi>t</mi><mn>0</mn></msub></msqrt><mo>=</mo><mrow><mn>0.1422</mn><mo>(</mo><mn>14</mn><mo>)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and <math><msub><mi>w</mi><mn>0</mn></msub><mo>=</mo><mrow><mn>0.1709</mn><mo>(</mo><mn>11</mn><mo>)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for <math><msqrt><msub><mi>t</mi><mn>0</mn></msub></msqrt></math> there are comparable continuum extrapolation uncertainties. For <math><msub><mi>w</mi><mn>0</mn></msub></math>, there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.

Nolan Miller

Logan Carpenter

M. A. Clark

Scale setting the Möbius domain wall fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales <math><msub><mi>t</mi><mn>0</mn></msub></math> and <math><msub><mi>w</mi><mn>0</mn></msub></math>

We report on the first application of the stochastic Laplacian Heaviside method for computing multiparticle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a set of positive-definite two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the SU(3)-flavor-symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of <math><mrow><mi>a</mi><mo>≈</mo><mn>0.086</mn></mrow></math> fm, lattice volume of <math><mrow><mi>L</mi><mo>=</mo><mn>48</mn><mi>a</mi><mo>≈</mo><mn>4.1</mn></mrow></math> fm and pion mass <math><mrow><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>714</mn></mrow></math> MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

Andrew Hanlon

Denmark

Wayne Tai Lee

Two-nucleon <math><mi>S</mi></math>-wave interactions at the SU(3) flavor-symmetric point with <math><mrow><msub><mi>m</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo>≈</mo><msubsup><mi>m</mi><mi>s</mi><mtext>phys</mtext></msubsup></mrow></math>: A first lattice QCD calculation with the stochastic Laplacian Heaviside method

We report the results of a lattice quantum chromodynamics calculation of <math><msub><mi>F</mi><mi>K</mi></msub><mo>/</mo><msub><mi>F</mi><mi>π</mi></msub></math> using Möbius domain-wall fermions computed on gradient-flowed <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> highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from <math><mn>130</mn><mo>≲</mo><msub><mi>m</mi><mi>π</mi></msub><mo>≲</mo><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, four lattice spacings of <math><mrow><mi>a</mi><mo>∼</mo><mn>0.15</mn></mrow></math>, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the <math><mi>a</mi><mo>∼</mo><mn>0.06</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> ensemble is helpful, but not necessary to achieve a subpercent determination of <math><msub><mi>F</mi><mi>K</mi></msub><mo>/</mo><msub><mi>F</mi><mi>π</mi></msub></math>. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of <math><msub><mi>F</mi><msup><mover><mi>K</mi><mo>^</mo></mover><mo>+</mo></msup></msub><mo>/</mo><msub><mi>F</mi><msup><mover><mi>π</mi><mo>^</mo></mover><mo>+</mo></msup></msub><mo>=</mo><mn>1.1942</mn><mo>(</mo><mn>45</mn><mo>)</mo></math> with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>s</mi></mrow></msub><mo>|</mo><mo>/</mo><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>0.2311</mn><mo>(</mo><mn>10</mn><mo>)</mo></math>.

Bálint Joó

Thorsten Kurth

Kostas Orginos

<math><msub><mi>F</mi><mi>K</mi></msub><mo>/</mo><msub><mi>F</mi><mi>π</mi></msub></math> from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

We present a determination of nucleon-nucleon scattering phase shifts for ââ¥0 . The S , P , D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For â&gt;0 , this is the first lattice QCD calculation using the LÃ¼scher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3) -flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to mÏ=mKâ800Â MeV . In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of Vâ(3.5Â fm)3 and Vâ(4.6Â fm)3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the LÃ¼scher formalism for two-nucleon systems.

Mark Strother

Pavlos M. Vranas

Two-nucleon higher partial-wave scattering from lattice QCD