1. SCET Insights Into Heavy-to-Light Form Factors
Matthias Neubert - Cornell
December 13, 2003
Vxb Workshop - SLAC

2. Some Open Issues
Field-theoretic understanding of the “soft overlap” contribution
Systematic separation of short- and long-distance contributions
Sudakov suppression of the soft contribution?
pQCD vs. QCD factorization

3. Soft Overlap
Have used SCET to define the soft overlap term: [Lange, Neubert: hep-ph/ ]
Combination of soft, collinear and messenger contributions

4. More Artistic View
Messenger exchange:
soft
collinear
messenger sector

5. Sudakov Resummation
Can use SCET to systematically resum all short-distance Sudakov logarithms:
for physical values of the B-meson mass, there is no sizable Sudakov suppression
E-dependence of the low-energy matrix element remains, which can only be controlled using a truly non-perturbative approach (lattice?)
0.5
0.75
αs(μ) = 1

6. Importance of Non-Valence Fock States ?
SCET shows that 3-particle Fock states (in both B and π) contribute at the same order in Λ/mb as the leading Fock states
Not suppressed by any small parameter
A puzzle (to us) is why their effect appears to be tiny (<3%) in the light-cone sum rule approach

7. Toy Model
Regularize endpoint singularities using cut-offs adjusted such that the leading Fock states reproduce LCSR (crude):

8. Result
Find potentially large effects, which tend to reduce the values of the form factors
Effects tend to be larger for B V form factors
Is this effect real? Could it indicate a problem with light-cone sum rules (continuum model)?

9. Summary Physics of heavy-to-light form factors is subtle:
Transformation of soft collinear partons
Subleading quantities in SCET power counting (vanish at leading order)
This physics is not captured in quark models (ISGW, BSW, …) based on wave-function overlap integrals