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Semileptonic Hyperon Decays in Full QCD

Semileptonic Hyperon Decays in Full QCD. Huey-Wen Lin. in collaboration with Kostas Orginos. Outline. Motivation/Background Quick Review of Lattice Calculations Lattice Techniques/Parameters Numerical Results Summary and Outlook. Semileptonic Decays and CKM Matrix.

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Semileptonic Hyperon Decays in Full QCD

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  1. Huey-Wen Lin — DWF@10 Workshop Semileptonic Hyperon Decays in Full QCD Huey-Wen Lin in collaboration with Kostas Orginos

  2. Huey-Wen Lin — DWF@10 Workshop Outline • Motivation/Background • Quick Review of Lattice Calculations • Lattice Techniques/Parameters • Numerical Results • Summary and Outlook

  3. Semileptonic Decays and CKM Matrix • 1963: Cabibbo proposes current theory to explain semileptonic decays. • 1973: Kobayashi and Maskawa add mixing of three generations of quarks: before the discovery of the b quark. • Cabibbo angle in CKM matrix: Huey-Wen Lin — DWF@10 Workshop

  4. |Vus| in CKM Matrix • Unitarity constraint: • PDG 2006 gives • Well determined • Very small • Less known • Experimentally, • Hyperon decay • Leptonic decay ratios: • Hadronic τ decays: Huey-Wen Lin — DWF@10 Workshop

  5. Lattice Calculation of |Vus| — Meson • Calculate matrix element • Lorentz invariance with • Calculate the scalar form factor • Extrapolate to q=0 point in dipole • Obtain |Vus| from Huey-Wen Lin — DWF@10 Workshop

  6. Lattice Calculation of |Vus| — Meson Multiple Kl3 decay calculations: • Twisted-BC approach Guadagnoli et. al. (2004) momentum changes by Tune θj to cancel out the mass difference. No extrapolation in momentum is needed! Huey-Wen Lin — DWF@10 Workshop

  7. Baryon Matrix Elements • Matrix element of hyperon β decay process with The decay rate is Huey-Wen Lin — DWF@10 Workshop

  8. Baryon Matrix Elements • Matrix element of hyperon β decay process with The vector form factor f1(0) links to |Vus| More than just an alternative way to get |Vus|! g1(0)/f1(0) gives information about strangeness content. g2(0) and f3(0) vanish in the SU(3) limit → Symmetry-breaking measure Huey-Wen Lin — DWF@10 Workshop

  9. Huey-Wen Lin — DWF@10 Workshop Hyperon Experiments Experiments: CERN WA2, Fermilab E715, BNL AGS, Fermilab KTeV, CERN NA48 Summary Ξmeasurements are still active!

  10. Lattice Calculation of |Vus| — Baryon Two quenched calculations, different channels * Pion mass > 700 MeV * f1(0) = −0.988(29)stat. * |Vus| = 0.230(8) Guadagnoli et al. * Pion mass ≈ 530–650 MeV * f1(0) = −0.953(24)stat * |Vus| = 0.219(27) Sasaki et al. Huey-Wen Lin — DWF@10 Workshop

  11. Huey-Wen Lin — DWF@10 Workshop Lattice Actions • (Improved) Staggered fermions (asqtad): • Relatively cheap for dynamical fermions (good) • Mixing among parities and flavors or tastes • Baryonic operators a nightmare — not suitable • Chiral fermions (e.g., Domain-Wall/Overlap): • Automatically O(a) improved, suitable for spin physics and weak matrix elements • Expensive

  12. Huey-Wen Lin — DWF@10 Workshop Lattice Actions • (Improved) Staggered fermions (asqtad): • Relatively cheap for dynamical fermions (good) • Mixing among parities and flavors or tastes • Baryonic operators a nightmare — not suitable • Chiral fermions (e.g., Domain-Wall/Overlap): • Automatically O(a) improved, suitable for spin physics and weak matrix elements • Expensive • Mixed actions: • Match the sea Goldstone pion mass to the DWF pion • Pion masses as low as 260 MeV • Volume: 2.6–3.5fm • Free light quark propagators

  13. Parameters • This calculation: • Pion mass range: 360–700 MeV • Strange-strange Goldstone fixed at 763(2) MeV • Volume fixed at 2.6fm • a ≈ 0.125 fm, Ls= 16, M5 = 1.7 • HYP-smeared gauge, box size of 203×32 Huey-Wen Lin — DWF@10 Workshop

  14. Effective Mass Plots • The worst set • The best set Huey-Wen Lin — DWF@10 Workshop

  15. Octet Spectrum • Summary Huey-Wen Lin — DWF@10 Workshop

  16. Octet Spectrum • Summary and extrapolation Huey-Wen Lin — DWF@10 Workshop

  17. Octet Spectrum • Summary and extrapolation • Disappointed  Huey-Wen Lin — DWF@10 Workshop

  18. Octet Spectrum • Alternative extrapolations • Better agreement with experiments Huey-Wen Lin — DWF@10 Workshop

  19. Constructions Two–point function Three–point function Huey-Wen Lin — DWF@10 Workshop

  20. Constructions Two–point function Three–point function Ratio cancels out t and Z dependence Huey-Wen Lin — DWF@10 Workshop

  21. Constructions Two–point function Three–point function Ratio cancels out t and Z dependence Huey-Wen Lin — DWF@10 Workshop

  22. Solve for From factors Redefine matrix element as Use “mixed” projection operator Solve the following: Huey-Wen Lin — DWF@10 Workshop

  23. Solve for From factors Redefine matrix element as Use “mixed” projection operator Solve the following: Huey-Wen Lin — DWF@10 Workshop

  24. Three-Point Plateau • mπ = 358(2) MeV Huey-Wen Lin — DWF@10 Workshop

  25. Three-Point Plateau • mπ = 358(2) MeV mπ = 503(2) MeV mπ = 599(2) MeV mπ = 689(2) MeV Huey-Wen Lin — DWF@10 Workshop

  26. Momentum Extrapolation • Fit to the dipole form Huey-Wen Lin — DWF@10 Workshop

  27. Momentum Extrapolation • Fit to the dipole form Huey-Wen Lin — DWF@10 Workshop

  28. Ademollo-Gatto Theorem • Symmetry-breaking Hamiltonian • Long story short, There is no first order correction O(H′ ) to f1(0); thus Huey-Wen Lin — DWF@10 Workshop

  29. Ademollo-Gatto Theorem • Symmetry-breaking Hamiltonian • The theorem tells us that There is no first order correction O(H′ ) to f1(0); thus • Choices of observable for H’: mK2 – mπ2 (mΣ– mN)/ mΣ Others… Huey-Wen Lin — DWF@10 Workshop

  30. Mass Dependence — I What has been done in the past… • Guadagnoli et al. construct an AG ratio and extrapolate mass dependence as Huey-Wen Lin — DWF@10 Workshop

  31. Mass Dependence — II • Use to describe the SU(3) symmetry breaking f1(0) = 0.90(7) (Preliminary) Huey-Wen Lin — DWF@10 Workshop

  32. Axial Coupling Constants: gΞΞand gΣΣ Cannot be determined by exp. Existing predictions from χPT and large Nc calculations Applications such as hyperon scattering, non-leptonic decays, etc. Huey-Wen Lin — DWF@10 Workshop

  33. Huey-Wen Lin — DWF@10 Workshop Summary/Outlook • First non-quenched calculation of hyperon semileptonic decays • Lighter pion masses as low as 350 MeV • Preliminary results show |Vus| (from Σ →n) * Consistent with the previous lattice measurement * Larger error due to lighter pion mass * More statistics needed for lightest point! In the near future: • Finish the semileptonic form factor analysis, including Ξ→ Σ channel • Σ and Ξ structure-function form factors • Possibly take Λ→p data, if time allows

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