rpp2010-rev-dalitz-analysis-formalism

rpp2010-rev-dalitz-analysis-formalism - 1 DALITZ PLOT...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
–1– DALITZ PLOT ANALYSIS FORMALISM Written January 2006 by D. Asner (Pacifc Northwest National Laboratory) Introduction: Weak nonleptonic decays oF D and B mesons are expected to proceed dominantly through resonant two-body decays [1]; see ReF. [2] For a review oF resonance phenomenology. The amplitudes are typically calculated with the Dalitz-plot analysis technique [3], which uses the minimum number oF independent observable quantities. ±or three-body decays oF a spin-0 particle to all pseudo-scalar fnal states, D or B abc , the decay rate [4] is Γ= 1 (2 π ) 3 32 s 3 |M| 2 dm 2 ab dm 2 bc , (1) where m ij is the invariant mass oF particles i and j .The coefficient oF the amplitude includes all kinematic Factors, and |M| 2 contains the dynamics. The scatter plot in m 2 ab versus m 2 bc is the Dalitz plot. IF |M| 2 is constant, the kinematically allowed region oF the plot will be populated uniFormly with events. Any variation in the population over the Dalitz plot is due to dynamical rather than kinematical e²ects. It is straightForward to extend the Formalism beyond three-body fnal states. ±or N -body fnal states with only spin-0 particles, phase space has dimension 3 N 7. Other decays oF interest include one vector particle or a Fermion/anti-Fermion pair ( e.g. , B D ππ , B Λ c , B K±± ) in the fnal state. ±or the frst case, phase space has dimension 3 N 5, and For the latter two the dimension is 3 N 4. Formalism: The amplitude For the process, R rc, r ab where R is a D or B , r is an intermediate resonance, and a , b , c are pseudo-scalars, is given by M r ( J, L, l, m ab ,m bc )= X λ ± ab | r λ ² T r ( m ab ) ± cr λ | R J ² (2) = Z ( J, L, l, ²p, ² q ) B R L ( | ² p | ) B r L ( | ² q | ) T r ( m ab ) . The sum is over the helicity states λ oF r , J is the total angular momentum oF R (For D and B decays, J=0), L is the orbital CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
–2– angular momentum between r and c , l is the orbital angular momentum between a and b (the spin of r ), ± p and ± q are the momenta of c and of a in the r rest frame, Z describes the angular distribution of the Fnal-state particles, B R L and B r L are the barrier factors for the production of rc and of ab ,and T r is the dynamical function describing the resonance r .The amplitude for modeling the Dalitz plot is a phenomenological object. Di±erences in the parametrizations of Z , B L T r , as well as in the set of resonances r , complicate the comparison of results from di±erent experiments. Usually the resonances are modeled with a Breit-Wigner form, although some more recent analyses use a K -matrix for- malism [5,6,7] with the P -vector approximation [8] to describe the ππ S-wave. The nonresonant (NR) contribution to D abc is parametrized as constant (S-wave) with no variation in magni- tude or phase across the Dalitz plot. The available phase space is much greater for B decays, and the nonresonant contribu- tion to B abc requires a more sophisticated parametrization.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.

Page1 / 10

rpp2010-rev-dalitz-analysis-formalism - 1 DALITZ PLOT...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online