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Proof of factorization for B --> D pi.

C W Bauer1, D Pirjol, I W Stewart

  • 1Physics Department, University of California at San Diego, La Jolla, California 92093.

Physical Review Letters
|November 3, 2001
PubMed
Summary

Matrix elements for B decays to D and pion mesons can be factored. This involves a B to D transition form factor and a convolution of short-distance physics with pion wave functions, valid to all orders in alpha(s).

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Area of Science:

  • High Energy Physics
  • Quantum Chromodynamics (QCD)
  • Particle Physics Phenomenology

Background:

  • Understanding non-perturbative aspects of Quantum Chromodynamics (QCD) is crucial for interpreting B meson decays.
  • Factorization theorems simplify complex decay amplitudes into calculable components.

Purpose of the Study:

  • To demonstrate the factorization of matrix elements for B meson decays into a D meson and a pion.
  • To provide a theoretical framework for analyzing B -> D pi decays beyond leading order.

Main Methods:

  • Applying effective field theory techniques to analyze four-fermion operators.
  • Utilizing light-cone wave functions for the pion in QCD.
  • Performing calculations to all orders in the strong coupling constant, alpha(s).

Main Results:

  • The matrix elements for B -> D pi decays are shown to factorize into a product of a B -> D form factor and a convolution involving a short-distance coefficient and the pion light-cone wave function.
  • Corrections to this factorization are suppressed by inverse powers of heavy quark masses (m_b, m_c) and the pion energy (E_pi).
  • The result is independent of assumptions about the pion's Fock state dominance.

Conclusions:

  • The derived factorization provides a robust method for studying B -> D pi decays.
  • This framework allows for precise theoretical predictions and comparisons with experimental data.
  • The results contribute to a deeper understanding of non-perturbative QCD effects in weak decays.

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