Measurement of the mass and lifetime differences between the heavy and light B/sub s/ eigenstates Page: 2 of 11
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I. Introduction
This report concerns measurements of the mass and lifetime differences
of the B5 - Bs system, A large mass difference, (Am/y)^ > 5, Is predicted in the
Kobayasht-Maskawa (KM) model with three generations of quarks.% This
prediction follows from two factors. The first is the ARGUS collaboration report
of a large Bd - mixing,2 (Am/y)^ - 1. The second is the unitarity of the 3X3
KM matrix. The prediclion does ggi depend whether the KM model is relevant
for CP violation. Thus, a much smaller (Am/y)Bj« 5 would indicate new
physics. An argument lor an observable litetime difference will be given. This
report discusses time-dependent ways to extract the mass difference and
lifetime deference of the neutral B5 system,
II. Formalism
An arbitrary neutral B-meson slate
a [ 8° > + b l 8°> (2/i)
is governed by the time-dependent Schrbdinger equation
*!r(S)=H(bM“-JrKb)
Here M and f are 2X2 matrices, with M=M+, r«=r+- CPT invariance
guarantees M11=Ma2 and f't 1=1*22- Wo assume CPT throughout to obtain the
eigenstates of the mass matnx as
| Bl > = p | B° > + q ( B° >, (2.3)
IBH > = p | B6 > - q | B° >, (2.4)
with eigenvalues (L=Tight,“ H="heavy‘)
^l.h = mi.n " 2 Vh (2 ^
Here mLH and yL H denote the masses and decay widths of BL H. Furthermore,
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Dunietz, I. Measurement of the mass and lifetime differences between the heavy and light B/sub s/ eigenstates, article, November 1, 1987; Menlo Park, California. (https://digital.library.unt.edu/ark:/67531/metadc1093296/m1/2/: accessed March 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.