Huey-Wen Lin* and Kostas Orginos Lattice QCD Numerical Parameters

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 |V |2 (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 |f | + |g | + β |f | + 2|g | + Re(f f ) + |f | + 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(ψ,ψ,A) h0|O(ψ, ψ, A)|0i = [dA][dψ][dψ] O(ψ, ψ, 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 → ∞ 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 Β • 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) − |f 0(0)| 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). Ψ 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 † 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. Ξ conf. Strange Electric Moment GE m010 358(2) 605(2) 600 600 • Similarly, charge symmetry connects us to a References m020 503(2) 653(2) 420 436 strange quantity through hr2iu: 1. C. W. Bernard et al., Phys. Rev. D 64, 054506 (2001). m030 599(1) 688(2) 561 561 s 2. D. B. Renner et al., Nucl. Phys. Proc. Suppl. 140, 255(2005); R. G. Edwards et al., PoS 2 s rd h 2 p 2 n 2 u i m040 689(2) 730(2) 306 319 hr i = s 2hr i + hr i − hr i ) . LAT2005, 056 (2005). 1 − rd • HYP (hypercubic)-smeared gauge and Gaussian-smeared fermion fields 3. M. J. Savage and J. Walden, Phys. Rev., D55:5376 (1997); R. Flores-Mendieta, et al., • Source-sink separation fixed at 10 • Chiral extrapolation for proton u- Phys. Rev., D58:094028 (1998). • Unitary sea quark mass only component charge radius shown on the 4. W. Detmold and C.-J. D. Lin, Phys. Rev. D71, 054510 (2006). • Interpolating field right 5. H-W. Lin and K. 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.