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 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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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

Separation of scalesand dimensional regularization: a simple example

Suppose we can’t

compute this:

expand


Precision tools for qcd scale separation and multi loop diagrams

Recurrence relations: integration by parts

Result: recurrence relations like


How does b quark decay

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

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

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

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 b sl

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 correction s on the bc line

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

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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