# Presentation: 098158

## Semileptonic Hyperon Decays in Full QCD

- Huey-Wen Lin

- in collaboration with Kostas Orginos

- Huey-Wen Lin — DWF@10 Workshop

## Outline

- Motivation/Background
- Quick Review of Lattice Calculations
- Lattice Techniques/Parameters
- Numerical Results
- Summary and Outlook

- Huey-Wen Lin — DWF@10 Workshop

## 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

## |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

## Lattice Calculation of |Vus| — Meson

- Calculate                matrix element
- Lorentz invariance
-     with

- Calculate the scalar form factor
- Extrapolate to *q* = 0 point in dipole
- Obtain |*V**us*| from

- Huey-Wen Lin — DWF@10 Workshop

## Lattice Calculation of |Vus| — Meson

- Lattice Calculation of |*V**us*| — Meson

- Multiple *K**l*3 decay calculations:

- Twisted-BC approach			*Guadagnoli et. al. (2004)*
-     momentum changes by
- Tune *θ**j* to cancel out the mass difference.
-  No extrapolation in momentum is needed!

- Huey-Wen Lin — DWF@10 Workshop

## Baryon Matrix Elements

- Matrix element of hyperon *β* decay process
-    with

- The decay rate is

- Huey-Wen Lin — DWF@10 Workshop

## Baryon Matrix Elements

- Matrix element of hyperon *β* decay process
-    with

- The vector form factor *f*1(0) links to |*V**us*|
- More than just an alternative way to get |*V**us*|!
*g*1(0)/*f*1(0) gives information about strangeness content.
*g*2(0) and *f*3(0) vanish in the SU(3) limit → Symmetry-breaking measure

- Huey-Wen Lin — DWF@10 Workshop

## Hyperon Experiments

- Experiments: CERN WA2, Fermilab E715,  BNL AGS,
-     Fermilab KTeV, CERN NA48
- Summary

- Ξ* *measurements are still active!

- Huey-Wen Lin — DWF@10 Workshop

## Lattice Calculation of |Vus| — Baryon

-    * Pion mass > 700 MeV
-    * *f*1(0) = −0.988(29)stat.
-    * |*V**us*| = 0.230(8)
*Guadagnoli et al.*
-   * Pion mass ≈ 530–650 MeV
-   * *f*1(0) = −0.953(24)stat
-    * |*V**us*| = 0.219(27)
*Sasaki et al.*

- Lattice Calculation of |*V**us*| — Baryon

- Two quenched calculations, different channels

- 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

- 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: 2.6–3.5 fm
- Free light quark propagators

- Huey-Wen Lin — DWF@10 Workshop

## Parameters

- This calculation:
- Pion mass range: 360–700 MeV
- Strange-strange Goldstone fixed at 763(2) MeV
- Volume fixed at 2.6 fm
*a* ≈ 0.125 fm, *L**s*= 16, *M*5 = 1.7
-  HYP-smeared gauge, box size of 203×32

- Huey-Wen Lin — DWF@10 Workshop

## Effective Mass Plots

- The worst set

- The best set

- Huey-Wen Lin — DWF@10 Workshop

## Octet Spectrum

- Summary

- Huey-Wen Lin — DWF@10 Workshop

## Octet Spectrum

- Summary and extrapolation

- Huey-Wen Lin — DWF@10 Workshop

## Octet Spectrum

- Summary and extrapolation

- Disappointed 

- Huey-Wen Lin — DWF@10 Workshop

## Octet Spectrum

- Alternative extrapolations

- Better agreement with experiments

- Huey-Wen Lin — DWF@10 Workshop

## Constructions

- Two–point function

- Three–point function

- Huey-Wen Lin — DWF@10 Workshop

## Constructions

- Two–point function

- Three–point function

- Ratio cancels out *t* and *Z* dependence

- Huey-Wen Lin — DWF@10 Workshop

## Constructions

- Two–point function

- Three–point function

- Ratio cancels out *t* and *Z* dependence

- Huey-Wen Lin — DWF@10 Workshop

## Solve for From factors

-  Redefine matrix element as
- Use “mixed” projection operator
- Solve the following:

- Huey-Wen Lin — DWF@10 Workshop

## Solve for From factors

-  Redefine matrix element as
- Use “mixed” projection operator
- Solve the following:

- Huey-Wen Lin — DWF@10 Workshop

## Three-Point Plateau

*m*π = 358(2) MeV

- Huey-Wen Lin — DWF@10 Workshop

## Three-Point Plateau

*m*π = 358(2) MeV

*m*π = 503(2) MeV

*m*π = 599(2) MeV

*m*π = 689(2) MeV

- Huey-Wen Lin — DWF@10 Workshop

## Momentum Extrapolation

- Fit to the dipole form

- Huey-Wen Lin — DWF@10 Workshop

## Momentum Extrapolation

- Fit to the dipole form

- Huey-Wen Lin — DWF@10 Workshop

## Ademollo-Gatto Theorem

- Symmetry-breaking Hamiltonian
-  Long story short,
-    There is no first order correction O(*H′ *) to *f*1(0); thus

- Huey-Wen Lin — DWF@10 Workshop

## Ademollo-Gatto Theorem

- Symmetry-breaking Hamiltonian
-  The theorem tells us that
-    There is no first order correction O(*H′ *) to *f*1(0); thus
-  Choices of observable for *H’ *:

*m**K*2 – *m**π*2
- (*m*Σ – *m**N* )/ *m*Σ
- Others...

- Huey-Wen Lin — DWF@10 Workshop

## 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

## Mass Dependence — II

- Use                                      to describe the SU(3) symmetry breaking

*f*1(0) = 0.90(7) (Preliminary)

- Huey-Wen Lin — DWF@10 Workshop

## Axial Coupling Constants: gΞΞ and gΣΣ 

- Cannot be determined by exp.
- Existing predictions from χPT and large *N**c* calculations

- Applications such as hyperon scattering, non-leptonic decays, etc.

- 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 |*V**us*| (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

- Huey-Wen Lin — DWF@10 Workshop