# New Measurement of A{sub b} at the Z{sup 0} Resonance Using a Vertex Charge Technique Page: 4 of 9

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where we have assumed both vertices have the same correct-sign probability Pb. In general

this is not the case, so we use the MC to determine the mass-dependent shape pb(MtX) and

correct the above equation appropriately. Uncertainties in the mass-dependence of pb are

included in our systematic error estimate (see below). When applied to our MC simulation,

this self-calibration technique gives an average correct-sign probability < pb(Mvt > 2.0) >=

(73.6 0.5)%, in good agreement with the MC "true" value quoted above. The error here

is due only to the limited statistics of the self-calibration technique. The same technique

applied to the data yields < pb(Mvt, > 2.0) >= (75.6 0.9)%, and we use this value in

the analysis. The MC mass dependence pb(Mvt,) is used to extrapolate this value to other

masses.

Final-state gluon radiation reduces the observed asymmetry from its Born-level value.

This effect is incorporated in our analysis by applying a correction AQCD ( cos 0) to the

maximum likelihood function (Eq. 3). This correction is based on the o(a,) calculation for

massive final state quarks of Stav and Olsen [13], which ranges from AsoCD( cos 0) - 0.05

at I cos 0 = 0 to ~ 0.01 at I cos 0 = 1. However, QCD radiative effects are mitigated by the

use of the thrust axis to estimate the b-quark direction, the Z0 -+ bb enrichment algorithm,

the self-calibration procedure, and the cut on the number of jets. A MC simulation of

the analysis chain indicates that these effects can be represented by a cos 0-independent

suppression factor, XQCD 0.50 0.25, such that AQCD XQCDAQCD. The effects of o(a2)

QCD radiation [14], which are dominated by gluon splitting to bb, lead to an additional

correction 6'Ab/Ab = +0.004 0.002.

The dependence of the b-tagging efficiency upon the secondary vertex mass is taken from

the simulation, with the overall tagging efficiency derived from the single- and double-tagging

rates [8] observed in the data. Tagging efficiencies for charm and uds events are estimated

using the MC simulation, as is the charm correct-signing probability pc. The value of A,

is set to its Standard Model value of 0.67, and the value of Abk9 is set to zero. After a

small (+0.2%) correction [15] for initial state radiation and Z-7 interference, the value of Ab

extracted from the fit is Ab = 0.897 0.027 Statt). This result is found to be insensitive to

the value of the b-tag mass cut.

We have investigated a number of systematic effects which can change the measured

value of Ab; these are summarized in Table 1. The uncertainty in pb due to the statistical

uncertainties in the data self-calibration technique corresponds to a +3.4/-3.2% uncertainty

in Abt. We have estimated the effects of possible biases in the self-calibration technique by

comparing the MC true value of pb(Mvtx) with the self-calibrated value of the same quantity

determined using the same MC as a trial dataset. We observe no bias, and assign a 1.0%

systematic uncertainty in Ab due to our limited MC statistics. The uncertainty in the MC

modelling of the Mvtx dependence of pb is included in the tracking efficiency corrections (see

below). In addition, while the mean value of the self-calibration parameter pb is constrained

by the data, it has a cos 0 dependence due to the fall-off of the tracking efficiency at high

cos 0 which must be estimated using the simulation, leading to a 0.6% uncertainty in Ab.

We also rely on the MC to correctly model the vertex charge distribution of the light-flavor

background (dominantly Z0 -+ cc ) which is subtracted from the raw counts N++ and N+;

we conservatively take a 50% relative uncertainty on this subtraction, which results in a

tThe error in the self-calibrated PA is symmetric, but the corresponding error in the event weight (the

"analyzing power", = 2pb - 1) is asymmetric.3

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### Reference the current page of this Report.

Abe, K. New Measurement of A{sub b} at the Z{sup 0} Resonance Using a Vertex Charge Technique, report, July 20, 1999; Menlo Park, California. (digital.library.unt.edu/ark:/67531/metadc624411/m1/4/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.