Dynamical Chirally Improved Quarks: First Results for Hadron MassesC.B. Lang : Dynamical Chirally Improved Quarks: First Results for Hadron Masses C. B. Lang Inst. f. Physik / FB Theoretische Physik Karl-Franzens-Universität Graz LAT 2007, Collaborators: R. Frigori, Ch. Gattringer, M. Limmer, T. Maurer, D. Mohler, A. Schäfer

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Approximate solution of the Ginsparg-Wilson equation Systematic expansion, parameterisation (© Gattringer, Hip, CBL.) CI (chirally improved) quarks Quenched simulation Various hadron operatoors, excited hadrons Further studies in progress (derivative sources), cf. Poster by D. Mohler Dynamical fermions CBL, Majumdar, Ortner (PR D 73 (2006) ) Eigenvalue spectrum (cf. Poster by M. Jörgler) Implementation Results: Hadron masses = +

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Study with dynamical CI fermions Lüscher-Weisz gauge action Chirally improved fermions, n f =2 light quarks Stout smearing 12 3 x24 (CBL, Majumdar, Ortner: PRD73(2006)034507) Lattice spacing 0.11 … 0.16 fm Eigenvalue spectrum cf. Poster by Martina Jörgler 16 3 x32 (in progress, here: first results) Lattice spacing 0.16 fm Hybrid Monte Carlo simulation: Each „trajectory“ (one unit HMC time): –Pseudofermion formulation –Molecular dynamics trajectory (100 steps) –Monte Carlo accept/reject step –Several 100 trajectories Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses MD fermion force term Dirac operator contains longer paths: the force term is technically more complicated Cyclically reorder terms such that p comes to the front = with coefficients products of links Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Equlibration signals plaquette CG it‘s for a/r step Single configuration pion mass Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Eigenvalues of D CI History: every 5th configuration Topological charge Histogram of top. charge Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Physical parameters Gauge coupling(s) D CI parameters Correlation functions, Wilson loops m AWI lattice spacing (or r 0 or m  or m N or …) Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Parameters: AWI-mass Implementation Results: Hadron masses Histogram of smallest Real modes (gap) for A m AWI

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Parameter landscape A B Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Run sequences (16 3 x32) A (  =4.65, m=-0.06): 65 „independent“ configurations (  int <5) a m AWI =0.025 (= 31 MeV) a=0.166 fm M  =440 MeV, M  /M  =0.54 B (  =4.7, m=-0.05): 50 „independent“ configurations a m AWI =0.039 (= 48 MeV) a=0.159 fm M  =495 MeV, M  /M  =0.59 Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Hadron propagators: „Variational“ analysis Use several interpolators Different quark source shapes Different interpolating fields, e.g., Compute all cross-correlations Solve the generalized eigenvalue problem The eigenvectors are „fingerprints“ of the state Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Meson results: pion Eff mass plots (from ratios of eigenvalues of C) „partially quenched“ Results: Hadron masses Implementation GMOR

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Vector mesons: rho Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Vector mesons: rho Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Vector mesons: a 1 Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Scalar meson a 0 Quenched: lowest state too high. Dynamical: Do we now see the ground state? Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Nucleon (pos. parity) Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Nucleon (pos. parity) Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Nucleon (neg. parity) Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Nucleon (neg. parity) Results: Hadron masses Implementation Like in quenched: two states (N(1535), N(1650)?)

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Delta (pos. parity) Results: Hadron masses Implementation

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Delta (pos. parity) Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Delta (neg. parity) Implementation Results: Hadron masses

C.B. Lang :Dynamical Chirally Improved Quarks: First Results for Hadron Masses Thank you !