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, 30.7.-4.8. 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 equationSystematic expansion, parameterisation (© Gattringer, Hip, CBL.)

CI (chirally improved) quarks

Quenched simulationVarious hadron operatoors, excited hadronsFurther studies in progress (derivative sources), cf. Poster by D. Mohler

Dynamical fermionsCBL, Majumdar, Ortner (PR D 73 (2006) 034507) 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 actionChirally improved fermions, nf=2 light quarksStout smearing

123x24 (CBL, Majumdar, Ortner: PRD73(2006)034507)Lattice spacing 0.11 … 0.16 fmEigenvalue spectrum cf. Poster by Martina Jörgler

163x32 (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 fora/r step

Single configuration pion mass

Implementation Results: Hadron masses

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

Eigenvalues of DCI

History: every 5th configuration

Topologicalcharge

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)DCI parameters

Correlation functions,Wilson loops

mAWI

lattice spacing (or r0 or m or mN or …)

† (0) ( )Op Op t

Implementation Results: Hadron masses

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

Parameters: AWI-mass

4 ( 0, ) (0)12 ( 0, ) (0)

tA p t PAWIP p t Pm

Implementation Results: Hadron masses

Histogram of smallestReal modes (gap) for A

mAWI

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

Parameter landscape

AB

Implementation Results: Hadron masses

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

Run sequences (163x32)

A (=4.65, m=-0.06):65 „independent“ configurations (int <5)

a mAWI=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 mAWI=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 interpolatorsDifferent quark source shapesDifferent 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 massesImplementation

GMOR

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

Vector mesons: rho

Results: Hadron massesImplementation

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

Vector mesons: rho

Results: Hadron massesImplementation

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

Vector mesons: a1

Results: Hadron massesImplementation

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

Scalar meson a0

Quenched: lowest state too high.Dynamical: Do we now see the ground state?

Results: Hadron massesImplementation

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

Nucleon (pos. parity)

Results: Hadron massesImplementation

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

Nucleon (pos. parity)

Results: Hadron massesImplementation

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

Nucleon (neg. parity)

Results: Hadron massesImplementation

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

Nucleon (neg. parity)

Results: Hadron massesImplementation

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 massesImplementation

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 !