D spectroscopy 2+1+1 Setup Martin Kalinowski in collaboration - PowerPoint PPT Presentation

D ∗∗ spectroscopy 2+1+1 Setup Martin Kalinowski in collaboration with Marc Wagner November 26 , 2012 pic/Goethe-Logo lattice D ∗∗ Martin Kalinowski

Aims Long term project to compute spectra of mesons with strange and charm quark content using lattice QCD methods. Extrapolation to the physical pion mass and the continuum limit. Here: First steps focussing on tuning valence s and c quark masses and computing low-lying D mesons. pic/Goethe-Logo lattice D ∗∗ Martin Kalinowski

Wilson twisted mass action � D [ U ] + m 0 , l + i µ l γ 5 τ 3 � S l = a 4 � χ l ( x ) ¯ χ l ( x ) x � D [ U ] + m 0 , h + i µ σ γ 5 τ 1 + µ δ τ 3 � S h = a 4 � χ h ( x ) ¯ χ h ( x ) x � χ u � � χ s � � 0 � � 1 � 1 0 τ 1 = τ 3 = χ l = , χ h = , χ d χ c 1 0 0 − 1 ψ phys i ψ phys i ¯ 2 ω h γ 5 τ 1 ¯ 2 ω h γ 5 τ 1 χ h , = e = e χ h . diff. masses h h i ψ phys i ψ phys 2 ω l γ 5 τ 3 ¯ ¯ 2 ω l γ 5 τ 3 χ l , = e = e χ l mass degenerated l l Tuned to ’maximal’ twist: m 0 , l = m 0 , h → m crit ⇒ ω h = ω l → π pic/Goethe-Logo 2 ⇒ automatic O ( a ) improvement for physical observables. lattice D ∗∗ Martin Kalinowski

ETMC 2 + 1 + 1 ensembles Available 2 + 1 + 1 configurations. Mismatch of strange and charm mass. Idea: different valence action for s and c quarks. � χ c + � χ c := , D W + m crit ± i µ c γ 5 χ c − pic/Goethe-Logo lattice D ∗∗ Martin Kalinowski

Switching the basis assuming maximal twist � ψ up � � ψ s 1 � � ψ c 1 � Mass degenerated doublets , , ψ dn ψ s 2 ψ c 2 � χ up + � � χ s + � � χ c + � Twisted basis , , χ dn − χ s − χ c − ¯ ψ = exp ( i γ 5 τ 3 ω/ 2 ) χ, ψ = ¯ χ exp ( i γ 5 τ 3 ω/ 2 ) ¯ ψ Γ ψ = ¯ χ ( 1 + i γ 5 τ 3 )Γ( 1 + i γ 5 τ 3 ) χ ∝ ¯ χ Γ twm χ Γ phys Γ twm Γ phys Γ twm γ i γ i γ i γ 5 γ i γ i γ j γ 5 γ i γ j γ i γ j γ i γ j γ 5 γ 5 γ 5 1 γ 5 1 1 1 ¯ ¯ ψ u Γ ψ u ψ u Γ ψ d Example: D - meson ¯ ¯ ψ up γ 5 ψ c 1 → ¯ χ up χ c + , ψ up γ 5 ψ c 2 → ¯ χ up γ 5 χ c − pic/Goethe-Logo Two numbers for every mass. lattice D ∗∗ Martin Kalinowski

Introduction of strange and charm valence quarks unitary setup valence quark setup 2.8 A1- A1+ linear extrapolations from lattice calculations 2.7 T1 T1 2.6 2.5 D * 1 (2420) effective mass [GeV] 2.4 D * 0 (2400) 2.3 2.2 2.1 D * (2010) 2 1.9 D(exp.) 1.8 0.22 0.23 0.24 0.25 0.26 0.27 0.28 valence mass charm Introduction of mass degenerated doublets for charm and strange quarks(Valence sector). � χ c + � χ c := , D W + m crit ± i µ c γ 5 χ c − Calculation at different bare masses and extrapolation to pic/Goethe-Logo the ’physical’ point ( c : m D , s : 2 m 2 K − m 2 PS ) lattice D ∗∗ Martin Kalinowski

Example operators Continuum J P Irrep Operators ¯ A 1 − 0 − , 4 − , ... q γ 5 q ¯ q γ 5 γ i q D i ¯ A 1 + 0 + , 4 + , ... qq ¯ q γ i q D i ¯ T 1 − 1 − , 3 − , ... q γ i q ¯ qq D i ¯ q ǫ ijk γ j q D k T 1 + 1 + , 3 + , ... ¯ q γ 5 γ i q ¯ q γ 5 q D i ¯ q γ 5 ǫ ijk γ j q D k q D i means a derivative source in direction i. All operators q Γ q D stay in the same irrep when Γ is multiplied by γ 0 . pic/Goethe-Logo lattice D ∗∗ Martin Kalinowski

Setup Gauge link configurations with 2 + 1 + 1 dynamical quark flavors (ETMC). Tuning charm valence quark mass to reproduce physical m D mass. Tuning strange valence quark mass to reproduce physical value of 2 m 2 K − m 2 π mass. Weak dependence on the pion mass. Mixed action setup to avoid mixing of strange and charm flavor and repair mismatch in the sea. Gaussian distributed spin diluted timeslice sources with APE smeared gauge links. Parameters of the ensemble: ( L / a ) 3 × ( T / a ) = 32 3 × 64 , β = 1 . 9 , µ = 0 . 004 , µ δ = 0 . 19 , µ σ = 0 . 15 , pic/Goethe-Logo a = 0 . 0859 ( 5 ) fm , m π ≈ 325MeV lattice D ∗∗ Martin Kalinowski

Desults D D s D s mesons D mesons 2.7 2.7 lattice lattice pp lattice pp lattice 2.6 2.6 PDG PDG 2.5 2.5 2.4 2.4 mass [GeV] mass [GeV] 2.3 2.3 2.2 2.2 2.1 2.1 2 2 1.9 1.9 1.8 1.8 D * D * D * D * D * D D * D S 0 1 S0 S S1 Results for a single ensemble Discrepancies for D ∗ s 0 and at the pion mass D ∗ s 1 . Similar findings in other m π ≈ 325MeV . lattice studies and Rather good agreement with phenomenological model experiment, even without calculations. chiral and continuum extrapolation. pic/Goethe-Logo lattice D ∗∗ Martin Kalinowski

quality of the T 2 ( J = 2 , 3 , 4 , ... ) channel effective masses T 2 2 1.5 am effective 1 0.5 am = 1.4141 ± 0.0324 ( χ 2 /dof = 0.23) am = 1.2416 ± 0.0136 ( χ 2 /dof = 0.57) 0 0 2 4 6 8 10 12 T pic/Goethe-Logo Thank you for your attention. lattice D ∗∗ Martin Kalinowski