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

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

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

West Coast LHC Theory Network

February 2006

Andrzej Czarnecki University of Alberta

Separation of scalesand dimensional regularization: a simple example

Suppose we can’t

compute this:

expand

Recurrence relations: integration by parts

Result: recurrence relations like

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

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”

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

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.

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

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)

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.