Fitting Results N + − − $_{2}$√$_{N}$$_{++}$$_{N}$$_{−−}$ 80.9 Υ counts 59 ± 20 Bin-by-bin Counting N + − − $_{2}$√$_{N}$$_{++}$$_{N}$$_{−−}$ 82.7 Υ counts 61 ± 20 Single-bin Counting N + − − $_{2}$√$_{N}$$_{++}$$_{N}$$_{−−}$ 75 ± 20 Υ counts 54 18 TABLE III: Extraction of Υ(1S+2S+3S) yield by bin count- ing and fitting. The sums are done in the range 8 < m < 11 GeV /c $^{2}$. tour the allowed range for the sum of cross sections is ( σ$_{DY}$ + σ$_{b}$$_{-}$ ¯ $_{b}$) | | y | < 0 . 5 , 8 <m< 11 GeV /c 2 = 38 ± 24 pb. This variation is taken into account in the fit to extract the Υ yield, and is included in the quoted uncertainty. C. Υ yield and cross section The quoted uncertainty in N$_{+}$$_{−}$ − 2 √ N$_{++}$N$_{−−}$ is listed for the single-bin counting method, which is obtained from a straightforward application of the statistical er- rors of the corresponding yields ( N$_{+}$$_{−}$ = 230, N$_{++}$ = 92, N$_{−−}$ = 65). It amounts to a contribution of 26% to the uncertainty, and originates only from counting statistics. In addition to this purely statistical uncertainty, we must also take into account the uncertainty of the continuum subtraction. This part of the uncertainty is obtained from the fitting method in all the quoted Υ counts in the Table. It should be noted that one cannot use count- ing statistics to estimate the uncertainty on the Υ yield due to the continuum subtraction. The reason is that the Υ and continuum yields are obtained from the same data, namely the invariant mass dielectron spectrum in Fig. 11. The two yields are therefore anti-correlated: a larger continuum yield reduces the extracted Υ counts. One must take this anti-correlation into account in the es- timation of the uncertainty on the Υ yield. The best way to do this is to use the fitting method. In the fit, both the statistical precision of the invariant mass spectrum and the anti-correlation between the Υ and continuum yields in the estimation of the uncertainty are taken into ac- count when varying the Υ yield and the continuum yield to minimize the χ $^{2}$. We find the uncertainty from the fit to be 33% of the Υ yield, and we hence use this fitting- method result to estimate the uncertainty in all the Υ yields quoted in Table III. We quote this as the “stat. + fit” uncertainty in our cross section result. It should be noted that with the statistics of the present analysis, we find that the allowed range of variation of the continuum yield in the fit is still dominated by the statistical error bars of the invariant mass distribution, and so the size of the 33% uncertainty is mainly statistical in nature. However, we prefer to denote the uncertainty as “stat. + fit” to clarify that it includes the estimate of the anti- correlation between the Υ and continuum yields obtained by the fitting method. A systematic uncertainty due to the continuum subtraction can be estimated by varying the model used to produce the continuum contribution from b - ¯ b . These variations produce a negligible change in the extracted yield with the current statistics. When comparing different counting methods in Ta- ble III, we see that the difference between the bin-by- bin counting method and the fitting method is negligible. The single-bin counting method yield is lower than the one from the bin-by-bin counting method by 9%, and we assign this as a component of the systematic uncertainty. Table III also lists the yield of Υ(1S+2S+3S). In the fitting method, the yield and the quoted uncertainty is obtained directly from the fit, as well as the contribu- tion from Drell-Yan and b - ¯ b discussed in the previous sec- tion. This has the advantage that the uncertainty due to the continuum subtraction and the correlations between the Υ, Drell-Yan and b - ¯ b contributions are automatically taken into account when exploring the parameter space. The disadvantage is that there is a model dependence on the line-shapes used for the fit. In the counting methods, to extract the Υ yield we subtract the continuum con- tribution obtained from the fit. This reduces the model dependence on the Υ line shape. However, we must still account for the uncertainty in the estimate of the con- tinuum contribution in the determination of the Υ yield uncertainty. Since this uncertainty should include simi- lar correlations between the Υ yield and continuum yields as found in the fitting method, the relative uncertainties The fitting function in Fig. 11 includes a total of three free parameters: the Υ yield, the Drell-Yan yield and the b - ¯ b yield. This allows us to extract the Υ yield di- rectly, automatically including ( i ) the statistical uncer- tainty for each mass bin in Fig. 11, and ( ii ) the uncer- tainty due to the anti-correlation between the continuum contributions and the Υ contribution. To compare the yield extraction using a different method, one can also perform bin counting. There are two ways to do this. One method is to take the background-subtracted unlike- sign yield directly from the data shown in Fig. 11, where the background subtraction is done for each mass bin. We then sum the resulting histogram in the mass re- gion of the Υ peak, 8–11 GeV /c $^{2}$. This sum includes the Υ yield and the continuum contribution, so we sub- tract from it the contribution from the Drell-Yan and b - ¯ b continuum obtained in the fit. A second method is to sum the yield of the unlike-sign ( N$_{+}$$_{−}$ ) in the region 8– 11 GeV /c $^{2}$, do the same for the like-sign positive ( N$_{++}$ ), and like-sign negative ( N$_{−−}$ ), and then do the subtrac- tion N$_{+}$$_{−}$ − 2 √ N$_{++}$N$_{−−}$ . In other words, in the first method we do the subtraction bin-by-bin and then do the sum, in the second method we do the sum first to get a single bin and then we do the subtraction. The results for estimating N$_{+}$$_{−}$ − 2 √ N$_{++}$N$_{−−}$ from the combined fit, the bin-by-bin counting method, and the single-bin counting method, are shown in Table III. 14