Hyperons and charmed baryons axial charges from lattice QCD. Christos Kallidonis

Transcription

1 Hyperons and charmed baryons axial charges from lattice QCD Christos Kallidonis Computation-based Science and Technology Research Center The Cyprus Institute with C. Alexandrou and K. Hadjiyiannakou Electromagnetic Interactions with Nucleons and Nuclei, 05 Paphos, Cyprus, -7 November 05 C. Kallidonis (CyI) Axial charges EINN05 / 0

2 Introduction Motivation Axial charges are important quantities probing hadron structure low energy effective theories chiral perturbation descriptions intrinsic spin carried by the quarks Nucleon g A (.695(9)) benchmark calculation Poor results available for hyperons and charmed baryons C. Kallidonis (CyI) Axial charges EINN05 / 0

3 Introduction Motivation Axial charges are important quantities probing hadron structure low energy effective theories chiral perturbation descriptions intrinsic spin carried by the quarks Nucleon g A (.695(9)) benchmark calculation Poor results available for hyperons and charmed baryons Simulation details R. Baron et al. (ETMC) arxiv: , A. Abdel-Rehim et al. (ETMC) gauge ensembles produced by ETMC with N f = + + dynamical twisted mass fermions a = 0.06 fm, L = 3. fm and a = 0.08 fm, L =.6 fm pion masses MeV gauge ensemble with N f = at the physical pion mass by ETMC, a = fm C. Kallidonis (CyI) Axial charges EINN05 / 0

4 Hyperons and charmed baryons - Spectrum 4 quark flavors baryons (qqq) SU(3) subgroups of SU(4) 0plet of spin-/ baryons 0 = plet of spin-3/ baryons 0 = C. Kallidonis (CyI) Axial charges EINN05 3 / 0

5 Hyperons and charmed baryons - Spectrum.8 ETMC N f = with CSW.7 ETMC N f =++ BMW N f =+.6 PACS-CS N f =+ QCDSF-UKQCD N.5 f =+ M (GeV) N Λ Σ Ξ Δ Σ* Ξ* Ω M (GeV) ETMC N f = with CSW ETMC N f =++ PACS-CS N f =+ Na et al. N f =+ Briceno et al. N f =++ Liu et al. N f =+ G. Bali et al. N f =+ 5 ETMC N f = with CSW ETMC N f = PACS-CS N f =+ M (GeV) Na et al. N f =+ Briceno et al. N f =++ 4 G. Bali et al. N f = Λ c Σ c Ξ c Ξ ' c Ω c Ξ cc Ω cc.5 Σ* c Ξ* c Ω* c Ξ* cc Ω* cc Ω ccc C. Alexandrou et al. arxiv: , S. Durr et al. arxiv: , A. Aoki et al. arxiv: , W. Bietenholz et al. arxiv:0.5300, R. A. Briceno et al. arxiv: , H. Na et al. arxiv:08.35, H. Na et al. arxiv:070.4, L. Liu et al. arxiv: , G. Bali et al. arxiv: , Particle Data Group C. Kallidonis (CyI) Axial charges EINN05 4 / 0

6 Calculation of Axial matrix element Axial matrix element B(p f, s f ) A µ B(p i, s i ) three-point functions, G( p = 0, t f t i, A µ (x)) with the axial vector current A µ (x) = q(x)γ µ γ 5 q(x) (using the fixed current method) two-point functions, C( p = 0, t f t i ) Axial charge obtained directly as R(t f t i ) (t ti) (t f t) g A R(t f t i ) = G( p = 0, t f t i, A µ ) C( p = 0, t f t i ) (neglect disconnected diagrams) Flavor combinations: Isovector, π-coupling: ūu dd Isoscalar: ūu + dd η 8 -coupling: ūu + dd ss η 5 -coupling: ūu + dd + ss 3 cc g + g 0 g + c 5 g + cc t/a = 5 t/a = (t f t)/a C. Kallidonis (CyI) Axial charges EINN05 5 / 0

7 m π-dependence g N A Nucleon N f = + + Fix Sink N f = Fix Sink N f = + + Fix Curr. (this work) Experiment C. Alexandrou et al. arxiv:0.0857, C. Alexandrou et al. arxiv: , A. Abdel-Rehim et al. (ETMC) arxiv: g N A (Talk by G. Koutsou on Thursday) N f = + + Fix Sink N f = Fix Sink N f = +CSW Fix Sink N f = + + Fix Curr. Experiment C. Kallidonis (CyI) Axial charges EINN05 6 / 0

8 m π-dependence Nucleon Σ, Ξ baryons g N A N f = + + Fix Sink N f = Fix Sink N f = + + Fix Curr. (this work) Experiment C. Alexandrou et al. arxiv:0.0857, C. Alexandrou et al. arxiv: , A. Abdel-Rehim et al. (ETMC) arxiv: g /g N g /g N A A DWF N f = + Clover N f = (QCDSF/UKQCD) Clover N f = (CP-PACS) TMF N f = + + (this work) g N A (Talk by G. Koutsou on Thursday) N f = + + Fix Sink N f = Fix Sink N f = +CSW Fix Sink N f = + + Fix Curr. Experiment H. Lin et al. arxiv:07.4, G. Erkol et al. arxiv:09.447, M. Göckeler et al. arxiv: C. Kallidonis (CyI) Axial charges EINN05 6 / 0.4

9 m π-dependence Decuplet g ++ g + g 0 g g + c 5 g ++ c 5 g + cc g ++ cc 5 g ++ ccc 5 Charm sector g + C. Kallidonis (CyI) Axial charges. EINN05 7 / 0.6.4

10 m π-dependence Decuplet g ++ g + g 0 g g + c 5 g ++ c 5 g + cc g ++ cc 5 g ++ ccc 5 Charm sector weak pion mass dependence g + C. Kallidonis (CyI) Axial charges. EINN05 7 / 0.6.4

11 m π-dependence Decuplet g ++ g + g 0 g g + c 5 g ++ c 5 g + cc g ++ cc 5 g ++ ccc 5 Charm sector weak pion mass dependence no noticeable cut-off effects g + C. Kallidonis (CyI) Axial charges. EINN05 7 / 0.6.4

12 SU(3) symmetry breaking Octet exact SU(3) symmetry: gπ N = F + D gπ Σ = F gπ Ξ = F D gn π g Σ π + g Ξ π = 0 δ SU(3) π = g N π g Σ π + g Ξ π = x c nx n, x = m K m π 4π f π Fit to ETMC ETMC Lin et al SU(3) 0. 0 Physical Point x breaking 4% at x phys = C. Kallidonis (CyI) Axial charges EINN05 8 / 0

13 SU(3) symmetry breaking 0. SU(3) = g g g Octet exact SU(3) symmetry: gπ N = F + D gπ Σ = F gπ Ξ = F D gn π g Σ π + g Ξ π = 0 SU(3) 0 Decuplet -0. g π = H -0.4 g Σ π = 3 H gπ Ξ = 3 H Physical Point gπ 3 gσ π = 0 gπ 3gπ Ξ = 0 gπ x gπ Σ gπ Ξ = δ SU(3) π = g N π g Σ π + g Ξ π = x c nx n, x = m K m π 4π f π Fit to ETMC ETMC Lin et al g g g 3g g g g SU(3) 0. SU(3) 0 0 Physical Point x breaking 4% at x phys = Physical Point x breaking consistent with zero x 0.3 C. Kallidonis (CyI) Axial charges EINN05 8 / 0

14 Sum rule J q = Σq + L q, Σ q = g q proton Contributions to proton spin N f = N f = + + (this work) Experiment u+d u+d+s u s C. Kallidonis 0.05 (CyI) Axial charges EINN05 9 / 0

15 0.30 Sum rule J q = Σq + L q, Σ q = g q proton Contributions to proton spin u+d cc Λ, baryons u+d+s u s+c 0.60 s c c.4 u+s+c.08 N f = N f = + + (this work) Experiment c u+c u+d+s u C. Kallidonis 0.05 (CyI) Axial charges EINN05 9 / 0

16 0.30 Sum rule J q = Σq + L q, Σ q = g q proton Contributions to proton spin u+d cc Λ, baryons u+d+s u s+c 0.60 s c c.4 u+s+c.08 N f = N f = + + (this work) Experiment c u+c u+d+s u Charm baryons 0.8 u+c C. Kallidonis 0.05 (CyI) Axial charges EINN05 9 / s+c.4 u+s+c u+c ++ c 0 c + c ++ cc weak m π -dependence intrinsic spin carried by quarks 40 60% of total particle spin

17 Conclusions good agreement with existing results for the nucleon and the octet hyperons axial charges weak m π -dependence of the axial charges estimates for decuplet baryons and charmed baryons small SU(3) breaking effects for the octet - consistent with zero for decuplet estimates on intrinsic spin carried by quarks for hyperons and charmed baryons Future Work finalize results for N f = at the physical pion mass calculate baryon spectrum, axial charges,(etc...) for N f = + + at the physical pion mass C. Kallidonis (CyI) Axial charges EINN05 0 / 0

18 Conclusions good agreement with existing results for the nucleon and the octet hyperons axial charges weak m π -dependence of the axial charges estimates for decuplet baryons and charmed baryons small SU(3) breaking effects for the octet - consistent with zero for decuplet estimates on intrinsic spin carried by quarks for hyperons and charmed baryons Future Work finalize results for N f = at the physical pion mass calculate baryon spectrum, axial charges,(etc...) for N f = + + at the physical pion mass Thank you C. Kallidonis (CyI) Axial charges EINN05 0 / 0