Signs of /Delta//ital m/ and /Delta//gamma/ of the /ital B//sub /ital d//-/ital B/bar ///sub /ital d// system

Journal Article · Tue Aug 01 04:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.40.806· OSTI ID:6028811

Wu, D

The /ital B/-/ital B/bar // mixing system with two eigenstates called /ital B//sub +/ and /ital B//sub /minus// is considered. We have the well-defined quantities /Delta//ital m/=/ital m//sub +//minus/m/sub /minus//, /Delta//gamma/=/gamma//sub +//minus//gamma//sub /minus//, /eta//sub /lambda//=/l angle//lambda/, /ital CP/=+/vert bar//ital B//sub /minus///r angle///l angle//lambda/,/ital CP/ =+/vert bar//ital B//sub +//r angle/. The sign of /Delta//ital m/(1/minus//vert bar//eta//sub /lambda///vert bar/) is in principle measurable. We find, in the standard Kobayashi-Maskawa (KM) model, that this sign depends on the sign of the /ital B//sup /ital B// parameter, in addition to the sign of the relevant rephasing invariant of the KM matrix marked by Re/Delta//sub /ital i//alpha//. We suggest that a natural definition for /ital B//sub +/ is to take it as nearly the /ital CP/-even eigenstate of the effective Hamiltonian, in order to guarantee a ''correct'' behavior of /eta//sub /lambda//, /eta//sub /lambda///proportional to/Im/Delta//sub /ital i//alpha// other than (Im/Delta//sub /ital i//alpha//)/sup /minus/1/. The sign of /Delta//ital m/ gains an absolute meaning in this sense. A phase-convention-independent condition to determine the sign of /Delta//ital m/ is given. This condition involves some decay amplitudes in addition to /ital M//sub 12/ (or /Gamma//sub 12/). Some /eta//sub /lambda// may be larger than 1, depending on the values of unknown KM parameters. In addition, we explore the phase-convention dependence of the ''/ital CP/ impurity parameter,'' convenient phase conventions for the /ital B/ systems, similar to the Wu-Yang convention for the /ital K/ system, and a simplified formula to calculate the effect of /pi//sup 0-//eta/ mixing on the difference between /eta//sup +/minus// and /eta//sup 00/.

• Research Organization: Center of Theoretical Physics, Chinese Center of Advanced Science Technology (World Laboratory), Beijing, People's Republic of China Republic of China(CN)
• OSTI ID: 6028811
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 40:3; ISSN PRVDA
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTIBARYONS
ANTIMATTER
ANTINUCLEI
ANTINUCLEONS
ANTIPARTICLES
ANTIPROTONS
B MESONS
BARYONS
BOSONS
CP INVARIANCE
DECAY
EIGENSTATES
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
HADRONS
HAMILTONIANS
INVARIANCE PRINCIPLES
KAONS
KAONS NEUTRAL
KOBAYASHI-MASKAWA MATRIX
MATHEMATICAL OPERATORS
MATRICES
MESONS
NUCLEI
NUCLEONS
PIONS
PIONS MINUS
PIONS PLUS
PROTONS
PSEUDOSCALAR MESONS
QUANTUM OPERATORS
STRANGE MESONS
STRANGE PARTICLES
UNIFIED-FIELD THEORIES