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Model independent analysis of B meson light-cone wavefunction

Model independent analysis of B meson light-cone wavefunction. Hiroyuki Kawamura (RIKEN). BNM08 in Atami Jan.24-26 2008. Work in collaboration with K.Tanaka (Juntendo Univ.). Beneke et al. (’99) Bauer, Pirjol, Stewart (’01) Keum, Li, Sanda (’01). Introduction.

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Model independent analysis of B meson light-cone wavefunction

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  1. Model independent analysis of B meson light-cone wavefunction Hiroyuki Kawamura (RIKEN) BNM08 in Atami Jan.24-26 2008 Work in collaboration with K.Tanaka (Juntendo Univ.)

  2. Beneke et al. (’99) Bauer, Pirjol, Stewart (’01) Keum, Li, Sanda (’01) Introduction QCD Factorization for Exclusive B decays: B →ππ, πlν, γlν… → systematic framework to calculate QCD effects in the mb →∞ limit • successful to describe the hadronic B decays. BBNS vs. data Beneke (Beauty06) • In some cases, the ignorance of B meson wavefunction gives • a major theoretical uncertainty. ex. hard spectator interactionsin B→π0π0 etc.

  3. B meson LCWF • B meson light-cone wavefunction in HQET light-cone vector: HQET field: In momentum space momentum of light quark • UV structure (radiative tail) Radiative corrections generate a hard negative tail. ↔ pion LCWF

  4. IR structure Kodaira, Tanaka, Qiao, HK (’01) HQ symmetry + E.O.M. → “Wandzura-Wilczek” part — “twist = dimension - spin” is not a good quantum number — Contributions from higher dim. Operators in the IR region.

  5. Radiative corrections Lange & Neubert (’03), Braun et al. (03), Li & Liao (’04), Lee & Neubert (’05) • cusp singularity → radiative tail CUSP • non-analytic at . • UV & IR structures are different! RG evolution

  6. Operator product expansion correlated • gives a natural scale to separate UV & IR behaviors ⇒ OPE • B meson LCWF in terms of HQET parameters UV RG evolution for LCWF OPE at expansion in with higher dim. ops. IR

  7. OPE at NLO • Lee & Neubert PRD72(’05)094028 cut-off scheme, up to dim-4 ops. • This work MS-bar scheme, up to dim-5 ops. +

  8. Calculation • 1-loop matching of the non-local operator for B meson LCDA • with non-local ops. up to dim.5 many dim. 5 ops. → calculation in x-space keeping gauge invariance explicitly. • Background field method • Fock-Schwinger gauge for → decouple from Wilson line

  9. OPE up to dim.5 (NLO in MS-bar scheme) dim.3 dim.4 dim.5

  10. Matrix elements dim.3 ← decay constant dim.4 dim.5 (covariant tensor formalism) “Chromo-electronic” “Chromo-magnetic”

  11. B meosn LCWF from OPE dim.3 dim.4 dim.5 • Dim.3&4 terms reproduce the results in cut-off schemeby Lee & Neubert (’05) • Expressed in terms of 3 HQET parameters: • in on-shell scheme suffers IR renormalon ambiguities. → “distribution amplitude” scheme

  12. LCWF from OPE at Inputs: Lee,Neubert (’05) Grozin,Neubert (’97) (QCD sum rule) real part imaginary part • Contributions from dim. 5 operators are important. • Effects from are very small. • Evolution effects must be included.

  13. Summary • Knowledge of B meson LCWF is important to reduce the theory error • for exclusive B decays. • Radiative correction to B meson LCWF — different UV & IR structures — → • OPE for B meson LCWF • — up to dim.5 • — NLO corrections to Wilson coefficient • expressed in terms of 3 HQET parameters at • Model-independent study including RG evolution is underway. • Similar analysis for shape function is possible.

  14. LCWF with analytic continuation

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