Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD

We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum. The required correlation functions, from which the spectrum is extracted, are computed using a newly implemented algorithm which speeds up the computation by more than an order of magnitude. On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the $1/L$ expansion of the three-particle quantization condition, which consistently describes all states at zero total momentum. The finite-volume spectrum is publicly available to facilitate further explorations within the available three-particle finite-volume approaches.Comment: 10 pages, 5 figures; added discussion of 1/L expansion, matches published versio

Multi-hadron spectroscopy in a large physical volume

We demonstrate the efficacy of the stochastic LapH method to treat all-to-all quark propagation on a $N_f = 2+1$ CLS ensemble with large linear spatial extent $L = 5.5$ fm, allowing us to obtain the benchmark elastic isovector p-wave pion-pion scattering amplitude to good precision already on a relatively small number of gauge configurations. These results hold promise for multi-hadron spectroscopy at close-to-physical pion mass with exponential finite-volume effects under control.Comment: 8 pages, 4 figures. Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June 201

Chiral perturbation theory for 2+1+1 flavor of Wilson quarks with twisted masses

Wir besprechen die Konstruktion der chiralen Störungstheorie (Chiral Perturbation Theory, ChPT) als effektive Theorie für das Niedrigenergieverhalten der Quantenchromodynamik (QCD). Wir fassen ihre Erweiterung zur Beschreibung von Cutoff-Effekten durch die Formulierung der QCD auf einer diskreten Raumzeit, so genannte Gitter-QCD, mit Wilson-Fermionen zusammen. Insbesondere können auch Wilson-Fermionen mit chiral verdrehtem Massenterm im Rahmen der twisted mass Wilson Chiral Perturbation Theory (tmWChPT) untersucht werden. Wir setzen dann die geeignete effektive Theorie zur Beschreibung aktueller Gitter-QCD-Simulationen mit 2+1+1 dynamischen Quarks mit separat getwisteten Massen im leichten und schweren Sektor auf. Insbesondere behandeln wir die Mesonen, die Charm-Quarks beinhalten, nicht als Pseudo-Goldstone-Bosonen der spontan gebrochenen näherungsweisen chiralen Symmetrie, um für die Phänomenologie nutzbare Formeln zu erhalten, die für schwere D-Mesonen gültig sind. Wir konstruieren den so genannten "charmless Lagrangian" und berechnen exemplarisch Pion- und Kaonmassen sowie -zerfallskonstanten zur Einschleifenordnung. Wir finden von den Kontinuumsresultaten abweichende Ausdrücke. Insbesondere finden wir zusätzliche chirale Logarithmen ohne Pendant in Kontinuums-ChPT, die die Ergebnisse anfällig für verstärkte Finite Volume-Korrekturen machen. Wir schätzen den systematischen Effekt durch Vernachlässigung dieser neuen Terme in der Analyse von Daten der European Twisted Mass Collaboration (ETMC) als vergleichbar groß wie die derzeitigen statistischen Unsicherheiten ein.We briefly review the construction of Chiral Perturbation Theory as an effective theory for the low-energy behavior of Quantum Chromodynamics (QCD). We then summarize its extension to describe cutoff effects induced by formulating QCD on a discrete space-time grid (Lattice QCD) with Wilson fermions. Particularly, Wilson fermions with twisted masses can be studied in the framework of twisted mass Wilson Chiral Perturbation Theory (tmWChPT). We then proceed to setting up the appropriate effective theory to describe recent lattice QCD simulations with 2+1+1 dynamical Wilson quark flavors and twisted masses in the light and heavy sector respectively. We avoid treating the pseudoscalar mesons including charm quark as pseudo Goldstone bosons of a spontaneously broken chiral symmetry to provide accurate formulae for phenomenological applications. After constructing the so-called charmless Lagrangian we exemplarily compute pion masses, kaon masses and decay constants to one loop. We find that the respective expressions differ from continuum ChPT results and that additional chiral logs predispose the results to exhanced finite volume corrections. We estimate the systematic effect of neglecting the novel terms in the analysis of data from the European Twisted Mass Collaboration (ETMC) to be of the same order of magnitude as current statistical uncertainties

The elastic I=3/2I=3/2 pp-wave nucleon-pion scattering amplitude and the Δ(1232)\Delta(1232) resonance from Nf=2+1N_{\mathrm{f}}=2+1 lattice QCD

We present the first direct determination of meson-baryon resonance parameters from a scattering amplitude calculated using lattice QCD. In particular, we calculate the elastic $I=3/2$, $p$-wave nucleon-pion amplitude on a single ensemble of $N_{\mathrm{f}}=2+1$ Wilson-clover fermions with $m_{\pi}=280\mathrm{MeV}$ and $m_{K}=460\mathrm{MeV}$. At these quark masses, the $\Delta(1232)$ resonance pole is found close to the $N-\pi$ threshold and a Breit-Wigner fit to the amplitude gives $g^{\mathrm{BW}}_{\Delta N\pi}=19.0(4.7)$ in agreement with phenomenological determinations.Comment: 7 pages, 2 figures. Agrees with published version, one additional phase shift point and clarification of different coupling convention

Scattering from finite-volume energies including higher partial waves and multiple decay channels

A new implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luescher formalism is described. The method includes higher partial waves and multiple decay channels, and the fitting procedure properly includes all covariances and statistical uncertainties. The method is also simpler than previously used procedures. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are presented.Comment: 8 pages. Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June 201

Estimating the two-particle KK-matrix for multiple partial waves and decay channels from finite-volume energies

An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the $K$-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are obtained for total momenta in several directions. First tests involving $\rho$-meson decay to two pions include the $L=3$ and $L=5$ partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.Comment: 32 pages, 1 figur