Iain StewartMIT

Iain StewartMIT

Nonleptonic Decays and the Soft Collinear Effective Theory

Nonleptonic Decays and the Soft Collinear Effective Theory

Super B Factory Workshop, Hawaii, 2004

• Introduction: What is the Soft-Collinear EFT?

•1) Lessons from

•2) Factorization for

•Outlook and Open Issues

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

• Introduction: What is the Soft-Collinear EFT?

•1) Lessons from

•2) Factorization for

•Outlook and Open Issues

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

•Clean:

•Color Suppressed:

•Baryons:

•CP violation:

OutlineOutline

ie.ie.

Factorization Theorem

Factorization TheoremHard vs. Jet:

Hard vs. Jet:

Polarization:

Polarization: Charming penguins, Power

corrections Charming penguins, Power

corrections

in SCETin SCET

Two body nonleptonic decays. Simple?

Two body nonleptonic decays. Simple?

B

B

π

π

Note: Nonleptonic B-decays are not Gold Plated

Observables for Lattice QCD

Note: Nonleptonic B-decays are not Gold Plated

Observables for Lattice QCD

Electroweak HamiltonianElectroweak Hamiltonian

b u

d

u

W

b u

u

d

u

u

b

W

d

g

db

uu

db

uu

u,c

QuickTime™ and aGIF decompressorare needed to see this picture.QuickTime™ and aGIF decompressorare needed to see this picture.

QuickTime™ and aGIF decompressorare needed to see this picture.

= CKM factors= CKM factors

1.Use SU(2) or SU(3) to relate amplitudes so data can be used to reduce uncertainties.

• Flavor symmetries of QCD,

2.Factorization from QCD to reduce the amplitudes to simple universal nonperturbative parameters.

• Expand in

1.Use SU(2) or SU(3) to relate amplitudes so data can be used to reduce uncertainties.

• Flavor symmetries of QCD,

2.Factorization from QCD to reduce the amplitudes to simple universal nonperturbative parameters.

• Expand in

Measuring CP violation in “unclean” decays requires

Measuring CP violation in “unclean” decays requires

These two possibilities are not exclusive.These two possibilities are not exclusive.

The important thing to keep in mind is “what are the uncertainties”.

The important thing to keep in mind is “what are the uncertainties”.

• Beneke, Buchalla, Neubert, Sachrajda proposed a QCD factorization theorem for , QCDF .

• Amplitude is reduced to simpler matrix elements

• At LO in strong phases are perturbative,

, and therefore small.

• Beneke, Buchalla, Neubert, Sachrajda proposed a QCD factorization theorem for , QCDF .

• Amplitude is reduced to simpler matrix elements

• At LO in strong phases are perturbative,

, and therefore small.

Factorization in QCDFactorization in QCD

,, ,,

form factorform factor hard spectatorhard spectator

Keum, Li, Sanda:pQCD FactorizationKeum, Li, Sanda:

pQCD Factorization

PP = 21 + 13 decays

PV = 40 + 23 decays

VV = 21 + 13 decays

PP = 21 + 13 decays

PV = 40 + 23 decays

VV = 21 + 13 decays

Chiang et al.Chiang et al.SU(3) analysis SU(3) analysis

QCDF analysisQCDF analysisBeneke & NeubertBeneke & Neubert

eg.eg.

• Separate physics at different momentum scales

• Power expansion

• Make symmetries explicit

• Model independent, systematically improvable

• Separate physics at different momentum scales

• Power expansion

• Make symmetries explicit

• Model independent, systematically improvable

Effective Field TheoryEffective Field Theory

• An effective field theory for energetic hadrons,

• An effective field theory for energetic hadrons,

Soft - Collinear Effective Theory

Soft - Collinear Effective Theory

Bauer, Pirjol, StewartFleming, Luke

Bauer, Pirjol, StewartFleming, Luke

Soft Collinear Effective TheorySoft Collinear Effective Theory

eg.eg.

Introduce fields for infrared degrees of freedom (in operators)Introduce fields for infrared degrees of freedom (in operators)

Degrees of freedom in SCETDegrees of freedom in SCET

Energetic jetsEnergetic jets

Energetic hadronsEnergetic hadrons

FactorizationFactorization

Bauer, Pirjol, I.S. Bauer, Pirjol, I.S.

Universal functions:Universal functions: Calculate T, Calculate T,

Universal hadronic parameters

Universal hadronic parameters

SCET Expansion SCET Expansion

Observed 2001Observed 2001Large - not very predictiveLarge - not very predictiveNaive Factorization - too smallNaive Factorization - too small

(Cleo, Belle, Babar)(Cleo, Belle, Babar)Data

20-30% level20-30% level

Color Suppressed DecaysColor Suppressed Decays

Mantry, Pirjol, I.S. ‘03

Mantry, Pirjol, I.S. ‘03

Factorization with SCET Factorization with SCET

QCDQCD

new soft functionnew soft function

- like generalized parton distributions

- like generalized parton distributions

QCDQCD

Theory: Theory:

Phenomenology:

Phenomenology:

is complex, new mechanism for rescatteringis complex, new mechanism for rescattering

with HQET forwith HQET for getget

not a convergent expansionnot a convergent expansion

Tests and PredictionsTests and Predictions

Tests and PredictionsTests and Predictions

All predictions so far are independent of the form of All predictions so far are independent of the form of

and and

ie. same Br and same strong phases

ie. same Br and same strong phases

More PredictionsMore Predictions

• nonperturbative strong phases are natural

• Nonperturbative J vs. Perturbative J

• With the entire amplitude power suppressed the polarization issue in B to VV is non-trivial

• nonperturbative strong phases are natural

• Nonperturbative J vs. Perturbative J

• With the entire amplitude power suppressed the polarization issue in B to VV is non-trivial

Lessons

Lessons

SCET ResultSCET Result

Chay, KimChay, Kim

Bauer, Pirjol, Rothstein, I.S. (to appear)

Bauer, Pirjol, Rothstein, I.S. (to appear)

operators, exponentiation of soft & collinear gluonsoperators, exponentiation of soft & collinear gluons

hard spectator & form factor terms hard spectator & form factor terms same operatorssame operators

long distance charming penguinslong distance charming penguins

analysis for PP, PV, VVanalysis for PP, PV, VV

unique functionunique function which is also in which is also in

Operators

OperatorsQCDQCD

Integrate out Integrate out fluctuationsfluctuations

......

......

Long Distance Long Distance

dangerous region near threshold

dangerous region near threshold ,,

NRQCD NRQCD

power suppressionpower suppression

couple to b, spectatorcouple to b, spectator

Polarization

Polarization

......

......

......

ie. SCET agrees with A. Kagan for polarization fraction:

ie. SCET agrees with A. Kagan for polarization fraction:

NoNo

power suppressedpower suppressed

unless it is spoiled by charming penguins!

unless it is spoiled by charming penguins!

Same Jet function as Same Jet function as

New Nonperturbative Result in New Nonperturbative Result in ::

fit fit , calculate T’s, calculate T’s

Hard CoefficientsHard Coefficients

Note: have not used isospin hereNote: have not

used isospin here

can use SCET, but there is a lot of work

left to do

can use SCET, but there is a lot of work

left to do

Open Issues inOpen Issues inFactorization formula with charming

penguins?Factorization formula with charming

penguins?Role of other degrees of freedom: messenger modes, Glaubers

Role of other degrees of freedom: messenger modes, Glaubers

ie. ie.

Power Corrections:Power Corrections:

expect nonperturbative phasesexpect nonperturbative phases

“chirally” enhanced terms, annihilation“chirally” enhanced terms, annihilation

Becher, Hill, NeubertBecher, Hill, Neubert

Factorization theorems usually do not try to untangle Factorization theorems usually do not try to untangle

fromfrom left in nonperturbative functions

left in nonperturbative functions

• Non-analytic terms vanish

• With all NLO operators, ie all the leading SU(3) violation:

• Non-analytic terms vanish

• With all NLO operators, ie all the leading SU(3) violation:

Using chiral perturbation theory we find:

Using chiral perturbation theory we find:

“Gell-Mann Okubo”

“Gell-Mann Okubo”

all in all in

OutlookOutlook

SCETSCET

We have only seen the tip of the

iceberg

We have only seen the tip of the

iceberg