2\beta + \gamma from B^0 to D^\mp K^0 \pi^\pm Decays at BaBar: aSimulation Study Page: 2 of 4
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2
m(__-) F( 5) a(Vc6) a(va6) 3(Vc6) 3(Vw6)
Ds2-+ (2573)* 2.572 0.015 - 0.02 - 70
D2+(2460) 2.461 0.046 0.12 0.048 30 30
D*+ (2308)" 2.308 0.276 0.12 0.048 70 0
K*_ (892)* 0.89166 0.0508 1 - 0 -
K*+(1430)+ 1.412 0.294 0.6 - 80 -
K*+(1430)* 1.4256 0.0985 0.2 - 0 -
K*_ (1680)+ 1.717 0.322 0.3 - 30 -
Non resonant - - 0.07 0.028 0 30
TABLE I: Masses and widths of the resonances considered in
the model. The last four columns present the chosen values of
the coefficients a and b in Eq. 2 for the Cabibbo allowed and
Cabibbo suppressed decays respectively.
with:Ak2 (A- Ak&(/ q)m(o
DI) AAk A A
k 2Im(AceAsa e (+ry+ 7 (e -La)>N
5 10 15 20 2 3
m (DKs)FIG. 2: Dalitz distribution of the very high statistics Monte-
Carlo sample of signal events (black dots). Each event is
weighted with the second derivative with respect to 2$ + y of
( A3 the log-likelihood (colored squares).where e= +1 (-1) if the tagged initial state is a B0 (B ),
rl +1 (-1) if the final state contains a D+ (D-), and
At is the proper time interval between the reconstructed
B (B~ec) and the tagging B (Brag). FB and Amd are
respectively the B0 decay width and its mixing frequency.
Thanks to the presence of the terms BWk (m, F, s) which
vary over the Dalitz plot, we can fit the amplitudes (a )
and the phases (3g) of Eq. 2, together with 2/3 + y with
only a two-fold ambiguity.
III. THE B0 -> DTK% r+ DALITZ MODEL
The decay mode under study is assumed to proceed
through the resonances listed in Table I. The K r+ res-
onances (K* like) can only come from Vcb mediated pro-
cesses, while both Vcb and Vu5 transitions contribute to
D-+ resonances (D** like). Finally the D-K reso-
nances (D*-like) come only through Vub mediated pro-
cesses. Contributions coming from very wide resonances
like higher K excited states or higher D** excited states
will be taken into account by a generic "non resonant"
term.
The total phase and amplitude are arbitrary, so we
can chose amplitude unity and phase zero for the mode
K*+(892) decaying into K r+. All the other amplitudes
and phases values are referred to the K*+(892) ones.
Since the strong phases are not known experimentally,
their values are chosen arbitrarily, while the values of
the amplitudes comes from the available measurements
of related B decay modes and some theoretical consid-
erations [5]. In agreement with the Standard Model we
assume for the sensitivity study 2/3 + y 2 rad.
The total number of DTK r signal events is esti-
mated using the measured branching fraction and ob-served yield [7]: we expect about 250 signal events per
unit of 100 fb-1 .
IV. SENSITIVITY TO 2$ + y
In order to show the regions of the Dalitz plot that
mostly contribute to the determination of 2/3 + y, a very
high statistics Monte-Carlo sample of signal events has
been generated according to the nominal model described
in Section III. Since the uncertainty on 2/3 +'y is:1
Z+r = 2Q~ (5)nwe can weight each event by the quantity weight, the sec-
ond derivative with respect to 2/3+y of the log-likelihood
constructed according to Eq.3:.2lnL
weight = +(6)
Note that this likelihood considers only signal contribu-
tion and does not take into account tagging and resolu-
tion effects.
In Figure 2, the weighted distribution expressing the sen-
sitivity (colored squares) is superimposed to the distri-
bution of the Monte Carlo events in the m2%Ko versus
mLo0_ plane (black dots). The regions with interfer-
ence between B0 - D**0K0 and B0 -> D**0K0 color
suppressed processes (diagonal side of the Dalitz) show
the greater sensitivity to 2/3 + y. A particularly sensitive
zone is at the intersection between B0 -> D-K*+ andS"
A2 + A2
(5)
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Polci, Francesco; Schune, Marie-Helene; Stocchi, Achille & /Orsay, LAL. 2\beta + \gamma from B^0 to D^\mp K^0 \pi^\pm Decays at BaBar: aSimulation Study, article, April 16, 2007; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc890271/m1/2/?rotate=270: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.