Scet insights into heavy to light form factors
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SCET Insights Into Heavy-to-Light Form Factors. Matthias Neubert - Cornell. 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?

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SCET Insights Into Heavy-to-Light Form Factors

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Scet insights into heavy to light form factors

SCET Insights Into Heavy-to-Light Form Factors

Matthias Neubert - Cornell

Vxb Workshop - SLAC


Some open issues

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


Soft overlap

Soft Overlap

  • Have used SCET to define the soft overlap term: [Lange, Neubert: hep-ph/0311345]

  • Combination of soft, collinear and messenger contributions


More artistic view

More Artistic View

  • Messenger exchange:

soft

collinear

messenger sector


Sudakov resummation

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


Importance of non valence fock states

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/mbas 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


Toy model

Toy Model

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


Result

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)?


Summary

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


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