1 / 33

Semileptonic Hyperon Decays in Full QCD

This workshop provides an in-depth exploration of lattice techniques in semileptonic hyperon decays. Topics covered include motivation, lattice calculations, numerical results, and implications on the CKM matrix. Insight from past experiments and current studies is presented, offering valuable information for researchers in the field. The workshop also delves into baryon matrix elements, hyperon experiments, and momentum extrapolation techniques. Attendees gain a thorough understanding of the complexities involved in these decays and the methodologies used for precise calculations.

normanmcdaniel
Download Presentation

Semileptonic Hyperon Decays in Full QCD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related