Iain Stewart MIT Iain Stewart MIT Nonleptonic Decays and the Soft Collinear Effective Theory Super B Factory Workshop, Hawaii, 2004

Text 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: Outline ie. Factorization Theorem Hard vs. Jet: Polarization: Charming penguins, Power corrections in SCET

Two body nonleptonic decays. Simple? Note: Nonleptonic B-decays are not Gold Plated Observables for Lattice QCD

Electroweak Hamiltonian = 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 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 QCD,,,, form factor hard spectator Keum, Li, Sanda: pQCD Factorization Keum, Li, Sanda: pQCD Factorization

PP = decays PV = decays VV = decays PP = decays PV = decays VV = decays Chiang et al. SU(3) analysis QCDF analysis Beneke & Neubert 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 Theory

An effective field theory for energetic hadrons, Soft - Collinear Effective Theory Bauer, Pirjol, Stewart Fleming, Luke Bauer, Pirjol, Stewart Fleming, Luke

Soft Collinear Effective Theory eg.

Introduce fields for infrared degrees of freedom (in operators) Degrees of freedom in SCET Energetic jets Energetic hadrons

Factorization Bauer, Pirjol, I.S. Universal functions: Calculate T,

Universal hadronic parameters

SCET Expansion

Observed 2001 Large - not very predictive Naive Factorization - too small

(Cleo, Belle, Babar) Data 20-30% level

Color Suppressed Decays Mantry, Pirjol, I.S. ‘03 Factorization with SCET QCD new soft function - like generalized parton distributions QCD

Theory: Phenomenology:

is complex, new mechanism for rescattering with HQET for get not a convergent expansion

Tests and Predictions

All predictions so far are independent of the form of and ie. same Br and same strong phases

More 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

SCET Result

Chay, Kim Bauer, Pirjol, Rothstein, I.S. (to appear) operators, exponentiation of soft & collinear gluons hard spectator & form factor terms same operators long distance charming penguins analysis for PP, PV, VV unique function which is also in

Operators QCD Integrate out fluctuations...

Long Distance dangerous region near threshold,, NRQCD power suppression couple to b, spectator

Polarization... ie. SCET agrees with A. Kagan for polarization fraction: No power suppressed unless it is spoiled by charming penguins!

Same Jet function as New Nonperturbative Result in : : fit, calculate T’s

Hard Coefficients Note: have not used isospin here

can use SCET, but there is a lot of work left to do Open Issues in Factorization formula with charming penguins? Role of other degrees of freedom: messenger modes, Glaubers Role of other degrees of freedom: messenger modes, Glaubers ie. Power Corrections: expect nonperturbative phases “chirally” enhanced terms, annihilation Becher, Hill, Neubert

Factorization theorems usually do not try to untangle from 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: “Gell-Mann Okubo” all in

Outlook SCET We have only seen the tip of the iceberg