1 / 17

SCET Approaches for Factorization in Nonleptonic Decays: Outlines

Explore the factorization approaches in SCET for nonleptonic decays, focusing on B! form factor, charming penguin, and matching at different scales. Learn the application of SCET to charming penguin and the implications for amplitude parameterization.

candice-cross
Télécharger la présentation

SCET Approaches for Factorization in Nonleptonic Decays: Outlines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture III Factorization approaches SCET

  2. Outlines • Introduction • B! form factor • Nonleptonic decays • Charming penguin • Summary

  3. Introduction • An effective theory by integrating out high energy (E) modes. • Effective degrees of freedom: collinear fields, soft fields,… • Express an amplitude in 1/E in terms of the effective operators. • The Wilson coefficients of these operators are the hard kernels. • The (nonlocal) matrix element of the operators are DAs (or form factors). • Convenient for deriving factorization theorem.

  4. B! form factor • Kinematics • Soft spectator in B, r» • If p2» mb, pg2=(p2-r)2=-2r¢ p2»O(mb) • Then the internal quark is off-shell by (mbv+k+pg)2-mb2»O(mb2 ) • SCET is careful in matching at different scales.

  5. Matching • Demonstrate the matching in SCET • Full theory! SCETI: integrating out the lines off-shell by mb2 Power scaling mb-3/2 from HQET Wilson coeff at SCETI W 2 b C()J(0)()!C()() J(0) T(0)J(1)(0) g mb2 mb 1/mb suppressed current

  6. Jet=Wilson coeff at SCETII =hard kernel in PQCD • SCETI! SCETII: integrating out the lines off-shell by mb J(0,)O() 2 ! T(0)J(0,)M()B() Power scaling mb-1/2 Two terms have the same power scaling.

  7. Comparison • The fundamental inputs, B meson transition forjm factors, are treated differently in different approaches. • fNF is not calculable, so FB is not in QCDF. No matching at mb. Just input it from sum rules. • FNF is factorizable in kT factorization theorem, so FB is in PQCD. No matching at mb. Input B from sum rules, and compute FB. • FB contains both fNF and fF, so it is a mixture in SCET. They are determined from the fit to the B! data.

  8. Nonleptonic decays • SCET can be applied to nonleptonic decays. The result for B! MM’ is

  9. Charming penguin • SCET gives another example that the leading amplitude in a nonleptonic decay does not need to be in the BSW form. • At leading power, no alrge source of strong phases in SCET (no annihilation) . • Long-distance charming penguin is then introduced, parameterized as Acc.

  10. Decay amplitude • SCET factotrization formula for B! M1M2 Wilson coeff Color-allowed Color-suppressed factorizable Wilson coeff

  11. Comment on charming penguin • Charming penguin is factorizable at leading power (see BBNS). • Compute one-loop correction to the charm loop, and see no IR divergence. • No need for additional nonperturbative parameter at leading power. • IR divergence could appear at next-to-leading power. • Then annihilation should be also formulated into SCET.

  12. Fit to data • Do not compute the jet function J(s(mb)) • Determine complex Acc, real B, real JB=s dz JB(z) from the B! data, Absorb JB+,  from somewhere

  13. Results • Small FB • Acc dominates penguin contribution • Predict Why is P so large?

  14. Amplitude parameterization • I can get the same “prediction” using T, C, P, assuming C to be real, same as in SCET---4 parameters with 4 inputs. • The 00 amplitude is fixed by the isospin relation. • A stringent test will be B! K modes. Need more parameters. +-: T+P p200: P-C p2+0: T+C

  15. Amplitude topologies

  16. Summary (Beneke at CKM 2005) SCET QCDF/PQCD QCDF/SCET PQCD

  17. Summary • QCDF, PQCD, SCET go beyond FA. • They have different assumptions, whose verification or falsification may not be easy. • They all have interesting phenomenological applications. • Huge uncertainty from QCDF is annoying. Input from time-like form factor for annihilation? • NLO correction in PQCD needs to be checked. • SCET should be applied to explore heavy quark decay dynamics more.

More Related