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Precision tools for QCD: scale separation and multi-loop diagrams

Precision tools for QCD: scale separation and multi-loop diagrams. West Coast LHC Theory Network February 2006. Andrzej Czarnecki University of Alberta. Separation of scales and dimensional regularization : a simple example. Suppose we can’t compute this: expand.

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Precision tools for QCD: scale separation and multi-loop diagrams

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  1. Precision tools for QCD:scale separation and multi-loop diagrams West Coast LHC Theory Network February 2006 Andrzej Czarnecki University of Alberta

  2. Separation of scalesand dimensional regularization: a simple example Suppose we can’t compute this: expand

  3. Recurrence relations: integration by parts Result: recurrence relations like

  4. How does b quark decay? Semileptonic Semileptonic branching ratio (parton model without QCD) Nonleptonic 8% shift of the NL width shiftsBSLby 0.6 percentage points

  5. Missing in the theoretical bound:NNLO corrections to non-leptonic decays. Example: c b g g u d Four loop diagrams with masses – the limit of what has been done in QFT so far (only numerical for g-2) Our approach: reduction via recurrence; analytical determination of “master diagrams”

  6. Results Example for a single diagram: (with Maciek Ślusarczyk) Total correction for the non-leptonic width: About 5-8% increase of the NL width; lowers the theoretical lower bound on BSL

  7. Outlook • Methods of scale separation, recurrence relations, large-scale symbolic computation are versatile. • Progress in several areas: • New electron mass determination • Establishment of the running of the weak angle; • Solution of the b-decay branching puzzle. • Next challenge: QCD factorization for the LHC.

  8. What do experiments get for BSL? World average: hep-ex/0505100 Theoretical lower limit: Bigi et al, 1994 Voloshin, 2000 2.6σ difference Vbc = 0.04 << 1 Standard Model suppressed: good place to look for New Physics

  9. Known two-loop corrections on the bc line first calculation (1996) latest one (2004) mb (1) (mW/mt)2 = 0.2 mW/mb e b c Zero recoil line n Leptons’ invariant mass q – quark mass mc/mb mb (1)

  10. Summary of b decays: • “Fair agreement” reached between theory and experiment; • More important: we can further improve the theoretical prediction (account for charm mass); • With new data forthcoming, we want to use the branching ratio to help discover competitors to W bosons.

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