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SCET Insights Into Heavy-to-Light Form Factors

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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  1. SCET Insights Into Heavy-to-Light Form Factors Matthias Neubert - Cornell 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/0311345] • 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/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

  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

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