Hyperon Physics from Mixed Action Huey-Wen Lin* and Kostas Orginos Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 *presenter Lattice QCD Axial Coupling Constants Vus from Hyperon Semi-leptonic Decays • First-principles calculation of nonpertur- • Important applications such as in hyperon scattering and non-leptonic decays • Vus can be obtained from the semileptonic decay (B1 ! B2lν) width via bative physics in QCD • Only existing predictions are from chiral perturbation theory and large-N calcula- ) c ∆m5 • Lattice QCD is a discrete version of con- tions [3]: Γ = G2 jV j2 (1 + δ ) F us 60π3 rad tinuum QCD theory 3 2 2 6 2 2 2 ∗ 2 2 • Use Monte Carlo integration to calculate physical observables directly from path integral 0:18 < −g < 0:36 × 1 − β jf j + jg j + β jf j + 2jg j + Re(f f ) + jf j + δ 2 ΞΞ 2 1 1 7 1 1 1 2 3 2 q Z 0:30 < gΣΣ < 0:55 1 i R d4x LQCD( ; ;A) h0jO( ; ; A)j0i = [dA][d ][d ] O( ; ; A)e with ∆m = m − m , β = ∆m=m , the radiative corrections δ , and δ 2(f ; g ) Z B1 B2 B1 rad q 1 1 • Poor fit into the formulation of SU(3) χPT[4] even with large-Nc constraints taking into account the transfer-momentum dependence of f and g [7] for quantity of interest 1 1 2 − 0 • Naive linear extrapolation against (mπ=fπ) . • In this work, only Σ ! n is analyzed. (Ξ ! Σ underway) • Take V ! 1 and a ! 0 to continuum limit We find gΣΣ = 0:441(14) and gΞΞ = −0:277(11). • Ademollo-Gatto (AG) theorem [8]: SU(3)-breaking corrections start at second order Gauge action SU(3) 2 f1(0) = f1(0) + O(λ ) • One-loop Symanzik O(a2)-improved action b • Dipole form fit to the q2 = 0 point at each pion ensemble Sg ReTr c0 1 - + c1 1 - + c2 1 - 3 • Construct a ratio f SU(3) − jf 0(0)j R(m ; m ) = ; K π a4(m2 − m2 )2 J Z ^ Z x ^ Z ^N K π m f coupling between walls and linearly extrapolate it to the physical Fermion action • Simultaneous SU(3) fit in the near future (8 parameters) [5] point 2 2 2 • Domain-wall fermion formulation Hyperon Form Factors R(mK; mπ) = c0 + c1a (mK + mπ): y x, s ? k • A proxy for studying the strangeness of the nucleon D 0 0 = δ 0D 0 + δ 0D 0 x;s;x ;s x;x s;s s;s x;x • Very weak constraint to the fit from the last point; hence, this is not an ideal solution H L 0 • Many experiments are devoted to understanding strange quark contributions to the Ls 2 Ls for our data. s elctromagnetic form factors of the nucleon: HAPPEX and G0 at JLab, SAMPLE at ? 1 D 0 = (1 − γ )δ 0 + (1 + γ )δ 0 − 2δ 0 s;s 2 5 s+1;s 5 s−1;s s;s MIT-BATES, and A4 at Mainz. mf − (1 − γ5)δs;L −1δ0;s0 + (1 + γ5)δs;0δL −1;s0 ; s 2 s s Strange Magnetic Moment GM 1 4 h i s k X y 0 • Quenched approximation in lattice QCD gives values of GM ranging from −0:28(10) to Dx;x0 = (1 − γµ)Uµ(x)δx+µ,x0 + (1 + γµ)Uµ(x )δx−µ,x0 + (M5 − 4)δx;x0 • Improvement: a single simultaneous fit (left) 2 µ=1 +0:05(6) 2 { Controllable chiral symmetry breaking with L 1 + M 2 − M 2 A + A M 2 + M 2 s • Adelaide-JLab Collaboration used an indirect approach with the help of charge symmetry 2 K π 1 2 K π f1(q ) = ) No complicated operator mixing and chiral perturbation theory to correct for quenching effects, obtaining −0:046(19) q2 2 1 − 2 2 M0+M1(M +M ) { Automatic O(a) off-shell improvement • Charge symmetry gives K π ) Easy to implement RI/MOM NPR • Our preliminary result: f1 = −0:88(15). s " N # ) No extra O(a) off-shell improvement on the action nor the operators s Rd p n u Ξ0 Σ− GM = s µ + 2µ − Ξ (µ − µ ) { Expensive in computational resources 1 − Rd u • (Improved) Staggered fermions (asqtad): no tree-level a2 effect uN { Relatively cheap for dynamical fermions (good) • uΞ : Linear ansatz chiral extrapolation to the physical pion mass (right) { Mixing among parities and tastes Conclusion and Outlook { Baryonic operators a nightmare | not suitable • Preliminary dynamical results for hyperon three-point data analysis • Mixed action: Match the sea Goldstone pion mass to the DWF pion { First lattice hyperon axial coupling constants: • (left) The pink band is the constraint for the g = 0:441(14) and g = −0:277(11) Numerical Parameters/Ensembles proton strangeness magnetic moment from ΣΣ ΞΞ • MILC 2+1-flavor staggered lattices [1] (lattice spacing a ≈ 0:125 fm with volume fixed our data, and the grey band indicates the { Stangeness in the proton: s s 2 s s at 2.6 fm) Rd given by Adelaide-JLab Collaboration GM = −0:066(12)stat(23)R , GE(Q = 0:1 GeV) = 0:022(61) • Mixed action: staggered sea (cheap) with DWF fermion (chiral symmetry) with Ls = 16, { First dynamical hyperon semileptonic decays: M5 = 1:7 [2] f1 = −0:88(15) • Ensemble parameters: s • More statistics needed since the pion mass is low Label mπ (MeV) mK (MeV) Σ conf. 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Orginos, in preparation. s 2 s ! ! • G (Q = 0:1 GeV) = 0:022(61), if taking r = 0:16(4) from χPT [6] ! X ip·x abc h T i E d 6. D. B. Leinweber, Phys. Rev. D53, 5115 (1996); D. B. Leinweber and A. W. Thomas, Jα p; t = e ua (y1; t)Cγ5db(y2; t) uc,α(y3; t)φ(y1 − x)φ(y2 − x)φ(y3 − x) !x;a;b;c Phys. Rev. D62, 074505 (2000); D. B. Leinweber et al., Phys. Rev. Lett. 94, 212001 (2005); D. B. Leinweber et al., Phys. Rev. Lett. 97, 022001 (2006). • Gs -Gs plane: • Two-point correlation function M E 7. A. Garcia et al., Lect. Notes Phys. 222, 1 (1985). Pink: experimental result ! X 1 + γ4 D ! ! E Purple: our preliminary result from mixed 8. M. Ademollo and R. Gatto, Phys. Rev. Lett. 13, 264 (1964). C2pt p; t = Jβ(p; t)J α(p; 0) α,β 2 αβ action 9. R. G. Edwards and B. Joo (SciDAC), Nucl. Phys. Proc. Suppl. 140, 832 (2005) Green: Adelaide-JLab Collaboration [6] us- • Three-point correlation function ing a quenched simulation but with quench- Acknowledgements ing corrections Γ;O ! X α,β D ! ! E This work was done on the clusters at Jefferson Laboratory using time awarded under C3pt p; t; τ = Γ Jβ(p; t)O(τ)J α(p; 0) α,β the SciDAC Initiative. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177..