Measurement of the relative $B^{\pm}_{c}/B^{\pm}$ production cross section with the ATLAS detector at $\sqrt{s}=8$ TeV

The total cross section and differential cross sections for the production of $B_{c}^{\pm}$ mesons, times their branching fraction to $J/\psi \pi^{\pm}$, are measured relative to those for the production of $B^{\pm}$ mesons, times their branching fraction to $J/\psi K^{\pm}$. The data used for this study correspond to an integrated luminosity of $20.3\,\mathrm{fb}^{-1}$ of $pp$ collisions recorded by the ATLAS detector at the Large Hadron Collider in 2012 at a center-of-mass energy of $\sqrt{s} = 8$ TeV. The measurement is performed differentially in bins of transverse momentum $p_{\mathrm{T}}$ for $13$ GeV $22$ GeV and in bins of rapidity $y$ for $|y|<0.75$ and $0.75<|y|<2.3$. The relative cross section times branching fraction for the full range $p_{\mathrm T}>13$ GeV and $|y|<2.3$ is $(0.34\,\pm\,0.04_{\text{stat}}\,^{+0.06}_{-0.02}\,_{\text{sys}}\,\pm\,0.01_{\text{lifetime}})\%$. The differential measurements suggest that the production cross section of the $B^{\pm}_c$ decreases faster with $p_{\mathrm T}$ than the production cross section of the $B^{\pm}$, while no significant dependence on rapidity is observed.


Introduction
The ± meson is a bound state of the two heaviest distinct quarks able to form a stable state, andf or + or¯and for − . Measurements of its production can provide unique insight into heavy-quark hadronization: unlike lighter -states, production of a ± meson requires collinear production of two distinct heavy quarks.
A measurement of the production cross section times branching fraction for ± → / ± , relative to that for ± → / ± , at √ = 8 TeV of collisions and differential in transverse momentum T and in rapidity 1 , has not yet been reported for the fiducial region considered in this article and defined below, although measurements of the individual cross sections have been published. At √ = 7 TeV, the LHCb Collaboration reported [1] a relative cross section times branching fraction of (0.68 ± 0.10 stat ± 0.03 syst ± 0.05 lifetime )% for T ( ± ) > 4 GeV in the pseudorapidity 2 range 2.5 < < 4.5. LHCb reported [2] for the same differential relative + cross-section at √ = 8 TeV a measurement of (0.683 ± 0.018 stat ± 0.009 syst )% in the rapidity range 2.0 < < 4.5 for the interval 0 < T ( + ) < 20 GeV. The measurement [2] by the LHCb Collaboration at √ = 8 TeV has a very slight overlap with the fiducial region (defined below) of this one. In the fiducial region 13 < T ( ) < 20 GeV and 2.0 < ( ) < 2.3, where the two experiments are both sensitive, the LHCb data show no trend in the ratio as a function of T . However, the LHCb dataset is dominated by candidates with T lower than those in this ATLAS analysis. The CMS Collaboration measured the same quantity in the rapidity range | | < 1.6 for T ( ± ) > 15 GeV to be (0.48 ± 0.05 stat ± 0.03 syst ± 0.05 lifetime )% [3] at √ = 7 TeV. The values reported here by ATLAS are smaller than those obtained by the other experiments at different energies and with different fiducial volumes, and evidence of dependence of this relative production cross section on transverse momentum is shown here for the first time.
Theoretical predictions for the hadronic ± production cross section have been reported by several authors [4][5][6][7][8][9][10] and this study is motivated by the range of predicted values. Theoretical calculations predict that the total production cross section is in the range of 1 nb to 31.5 nb at √ = 1.8 TeV and 44 nb to 190 nb at √ = 14 TeV, but no published calculation for the relative cross section at √ = 8 TeV is available at this time. These calculations depend on the square of the decay constant ± [4,11,12], which in the non-relativistic approach is proportional to the absolute value of the wave function at the origin.
In this measurement of the cross section times branching fraction for ± → / ± relative to that for ± → / ± , the / mesons are reconstructed from their decays into + − . The relative cross-section measurement is differential in two bins of the transverse momentum T of the ± , 13 GeV < T ( ± ) < 22 GeV and T ( ± ) > 22 GeV, for rapidity | | < 2.3, and in two bins of rapidity y of the ± , | | < 0.75 and 0.75 < | | < 2.3, for T ( ± ) > 13 GeV.
The relative cross section is also measured for the inclusive dataset with T > 13 GeV and | | < 2.3. The fiducial volume is defined by the requirements on T ( ± ) and ( ± ). The bins are selected to equalize yields of the ± . The same bin sizes are used for the ± and the ± . The data were recorded in 2012 by the ATLAS [13] experiment at a center-of-mass energy of The article is organized as follows. After this introduction, Section 2 provides an overview of the ATLAS detector including the trigger system and the objects used. Section 3 describes the simulation, reconstruction, and event selection. Section 4 shows the relative cross-section calculation. Section 5 presents the fits to the mass distributions. Section 6 describes the calculation of the efficiency and acceptance ratios. Section 7 reports the systematic uncertainties. Section 8 presents the results of the measurements. Conclusions are drawn in Section 9.

The ATLAS detector, trigger, and basic track selections
ATLAS is a general-purpose particle detector [13] consisting of several subsystems including the inner detector (ID), the electromagnetic and hadronic calorimeters, and the muon spectrometer (MS). Muons pass through the calorimeters and reach the MS if their momentum is above approximately 3 GeV. The ID features a three-component tracking system, consisting of two silicon-based detectors, the pixel detector and the microstrip semiconductor tracker (SCT), and the transition radiation tracker (TRT).
ID tracks are reconstructed if their transverse momentum is greater than 400 MeV and if the magnitude of their pseudorapidity, | |, is less than 2.5. Muon candidates are either formed from a stand-alone MS track that is matched to an ID track (so-called combined muons) or from an ID track extrapolated to the MS and matched to track segments in the MS (so-called tagged muons) [14]. The ID and MS subsystems are of particular importance to this study. Only the data taken when both of these subsystems were properly operational and when LHC beams were stable are used, corresponding to an integrated luminosity of 20.3 fb −1 . Although both the ID and the MS provide momentum measurements, in the T range relevant to this analysis, the MS momentum resolution is worse than that of the ID due to energy loss in the calorimeters. Therefore, the MS is used only to identify muons, and the T measurement is taken from the ID. The muon candidates are required to have the number of pixel hits plus the number of crossed dead pixel sensors greater than zero, the number of SCT hits plus the number of crossed dead SCT sensors greater than four, and the number of pixel holes 3 plus the number of SCT holes on the track less than three.
ID tracks from charged hadrons are required to have at least two pixel hits and at least six hits in the SCT (eight hits in total). If a track crosses a dead sensor, it is not counted as a hit in the corresponding subdetector; the number of pixel+SCT holes is required to be less than three. For tracks with 0.1 < | | < 1.9 it is required that > 5 and out TRT < 0.9 , where = TRT + out TRT , and TRT ( out TRT ) stands for the number of TRT hits (outliers [14]) on the track.
The trigger system [15] for data collected up to and including 2012 comprises three levels: the hardwarebased first-level (L1) trigger and the high-level triggers (HLT), consisting of the second-level trigger and the event filter. The L1 trigger uses resistive plate chambers and thin gap chambers to trigger on muons in the pseudorapidity ranges of | | < 1.05 and 1.05 < | | < 2.5, respectively. One or more regions-of-interest (RoI), identified by the L1 muon trigger, seed the HLT muon reconstruction algorithms, where the tracks from both the ID and the MS are combined. For this analysis the HLT selection of the / requires two oppositely charged muons, originating at a common vertex, with the invariant mass of the muon pair lying between 2.5 GeV and 4.3 GeV. The individual muon T thresholds are both 4 GeV. The pseudorapidity range of the muon selection is | | < 2.5.

Simulation, reconstruction, and event selection
Another significant source of background which is especially important for the ± is the partially reconstructed semileptonic decays of the ± such as ± → / ± . This background is reduced by removing combinations in which one of the hadronic candidates is identified as a muon by the MS.
Reconstructed candidates are required to satisfy the following selection criteria: • The 2 /( d.o.f. = 4) of the fit of the vertex must be below 1.8.
• The T of the hadron candidate must be above 2.0 GeV.
• To suppress combinatorial background due to prompt 5 / candidates, the impact parameter significance 0 / ( 0 ) of the hadron candidate must exceed 1.2. MC studies demonstrated that this criterion is more efficient for the ± candidate selection than a requirement on the lifetime.
In events with multiple candidates, the candidate with the best 2 from the vertex fits is used. The fraction of multiple-candidate events is negligible for this analysis, as observed in data and confirmed by MC studies. This analysis uses all the ground-state candidates including those produced directly and those produced from the cascade decay of excited states.

Relative cross-section calculation
The relative cross section times branching fraction is given by: The notation reco ( ) refers to the number of reconstructed collision data events, where is either ± or ± . The ( ± ) and ( ± ) are the efficiencies of ± and ± reconstruction that correct the numbers reco ( ± ) and reco ( ± ) for detector effects, selection criteria, differences between interactions of ± and ± with the detector material, as well as efficiencies associated with the trigger.

Fit to the mass distributions
Extended unbinned maximum-likelihood fits to the mass distributions of the ± and the ± are performed to extract reco ( ± ) and reco ( ± ) from the data in each bin in T and | |. This involves calculating the parameters that maximize the likelihood function, defined as where is the total number of / ℎ candidates, ℎ represents the corresponding hadron, sig is the total number of signal events, and bkg is the total number of background events. The contribution from the signal F signal is modeled by a Gaussian probability density function with event-by-event errors. It is given for the ± by and for the ± by where ± and ± are the masses of the ± and ± , respectively. The variables ± and ± are taken as free parameters in the fit. The widths 1 / ± and 2 / ± are the products of the corresponding scale factors 1 and 2 and the event-by-event mass resolution. The event-by-event mass uncertainty is calculated from the tracking covariance matrices by error propagation. The scale factors are free parameters of the fit which account for imperfection in estimates of the mass errors. Ideally the value of 1,2 is one. The mass resolution is obtained from the fits and appears in the relevant tables below. It is defined as the half-width of the region of the / mass distribution for which the integral of the sum of F signal ( / ℎ , ( / ℎ )) over all candidates contains 68.27% of sig .
The background to ± production is modeled with an exponential function plus a constant term, In the ± mass region, partially reconstructed -hadron decays populate the lower part of the ± mass spectrum. Their contributions are estimated with a complementary error function , and 0 and 0 determine the position and the slope of the error function, respectively.
The Cabibbo-suppressed decay ± → / ± populates the high part of the ± mass spectrum. It is modeled by a Gaussian function where 3 is the corresponding scale factor. The variable ± , ± is the median of the mass distribution in the data for ± → / ± events when the kaon mass instead of the pion mass is assumed for the charged-hadron track.
The remaining background is mostly due to production of / mesons from decays of -hadrons other than the ± , which are combined with a random hadron track. They are described with an exponential function where is a constant.
The models for the background contributions are combined with different fractions, which are fitted to the data. The relative fractions are left free in the fit, as ( × F (1) bkg + × F (2) bkg + (1 − ( + )) × F (3) bkg ), where and are free parameters of the fit.
5200 5300 5400 5500 (Data -fit)/err.  Figure 1: The projection of the fit of the invariant mass distribution for the ± meson. "Signal" stands for the signal component of the fit, "Comb. bkg" stands for the combinatorial background component of the fit, and "Total fit" stands for the fit to the sum of the signal and all background components. The fit for the low transverse momentum bin (13 GeV < T ( ± ) < 22 GeV) is shown at the top, and that for the high transverse momentum bin ( T ( ± ) > 22 GeV) is shown at the bottom. The rapidity requirement is | ( ± )| < 2.3. The fits are used to extract reco ( + ) + reco ( − ) and its uncertainty in each bin. The inset below each plot shows the bin-by-bin difference between the data point and the value obtained from the fit function divided by the quadrature sum of the statistical uncertainty and the systematic uncertainties obtained from varying the fit model.
The projections of the results of the invariant-mass fits of the ± and the ± for the various T and bins considered in this measurement are given in Figures 1-6. The inset below each plot shows the bin-by-bin difference between each data point and the value obtained from the fit function divided by the quadrature sum of the statistical uncertainty and the systematic uncertainties obtained from varying the fit model and discussed in Section 7. Tables 1 and 2 show a summary of the main parameters of the fits.
5200 5300 5400 5500 (Data -fit)/err.  Figure 2: The projection of the fit of the invariant mass distribution for the ± meson. "Signal" stands for the signal component of the fit, "Comb. bkg" stands for the combinatorial background component of the fit, and "Total fit" stands for the fit to the sum of the signal and all background components. The fit for the inner rapidity bin (| ( ± )| < 0.75) is shown at the top, and that for the outer rapidity bin (0.75 < | ( ± )| < 2.3) is shown at the bottom. The T requirement is T ( ± ) > 13 GeV. The fits are used to extract reco ( + ) + reco ( − ) and its uncertainty in each bin. The inset below each plot shows the bin-by-bin difference between the data point and the value obtained from the fit function divided by the quadrature sum of the statistical uncertainty and the systematic uncertainties obtained from varying the fit model.
5200 5300 5400 5500 (Data -fit)/err.   Figure 4: The projection of the fit of the invariant mass distribution for the ± meson. "Signal" stands for the signal component of the fit, "Background" stands for the combinatorial background component of the fit, and "Total fit" stands for the fit to the sum of the signal and background components. The fit for the low transverse momentum bin (13 GeV < T ( ± ) < 22 GeV) is shown at the top, and that for the high transverse momentum bin ( T ( ± ) > 22 GeV) at the bottom. The rapidity requirement is | ( ± )| < 2.3. The fits are used to extract reco ( + ) + reco ( − ) and its uncertainty in each bin. The inset below each plot shows the bin-by-bin difference between the data point and the value obtained from the fit function divided by the quadrature sum of the statistical uncertainty and the systematic uncertainties obtained from varying the fit model.  Figure 5: The projection of the fit of the invariant mass distribution for the ± meson. "Signal" stands for the signal component of the fit, "Background" stands for the combinatorial background component of the fit, and "Total fit" stands for the fit to the sum of the signal and background components. The fit for the inner rapidity bin (| ( ± )| < 0.75) is shown at the top, and that for the outer rapidity bin (0.75 < | ( ± )| < 2.3) at the bottom. The T requirement is T ( ± ) > 13 GeV. The fits are used to extract reco ( + ) + reco ( − ) and its uncertainty in each bin.
The inset below each plot shows the bin-by-bin difference between the data point and the value obtained from the fit function divided by the quadrature sum of the statistical uncertainty and the systematic uncertainties obtained from varying the fit model.  Figure 6: The projection of the fit of the invariant mass distribution for the ± meson using the complete dataset ( T ( ± ) > 13 GeV, | ( ± )| < 2.3). "Signal" stands for the signal component of the fit, "Background" stands for the combinatorial background component of the fit, and "Total fit" stands for the fit to the sum of the signal and background components. The fit is used to extract reco ( + ) + reco ( − ) and its uncertainty in each bin. The inset below each plot shows the bin-by-bin difference between the data point and the value obtained from the fit function divided by the quadrature sum of the statistical uncertainty and the systematic uncertainties obtained from varying the fit model.

Determination of the / ± efficiency and acceptance ratio
In order to correct the MC distributions to match the observed data, a sPlot-based MC reweighting technique [23] is exploited. This procedure is applied separately to the ± and ± candidates. The following MC variables are reweighted: T of the candidate, of the candidate, 2 of the secondary vertex, and the transverse impact parameter significance 0 / ( 0 ).
The reconstruction efficiencies are determined using the MC samples for the ± and ± signals. The efficiencies are averaged over each bin in T and each bin in | |. They are calculated from the ratio of the number of reconstructed MC events reco MC to the number of generated MC events gen MC in the associated bins in the fiducial region. Bin-to-bin migration is included and found to be less than 0.1%, and the associated systematic uncertainties are significantly smaller than uncertainties from other sources.
The efficiencies can be factorized into the product of the efficiency of the / trigger trigger , the efficiency of the muon spectrometer MS , the efficiency of the inner detector ID , the efficiency of fitting the muon and hadron tracks to a common decay vertex vertex , and the efficiency of the selection criteria selection [24]: where ( ℎ ) is the ± efficiency in the ± channel and ± efficiency in the ± channel, while stands for the ± and ± candidates. Muon trigger efficiencies are calculated using the method outlined in Ref.
[25], which can be briefly summarized as follows. The single-muon trigger efficiency is determined from a tag-and-probe study of the / and Υ dimuon decays in Ref. [26]. The efficiency map is calculated as a function of T ( ) and × ( ), where = ±1 is the electric charge of the ± , expressed in units of .
Besides the product of two single-muon terms, the trigger efficiency includes components that account for reductions in efficiency due to closely spaced muons firing only a single RoI, for vertex quality and opposite-sign charge requirements.
For the calculation of MS ( ± ), the muon reconstruction maps [27] are used. These maps are based on a sample of about two million / → + − events collected with unbiased triggers (single muonic and "muon + track"). The efficiency is measured in bins of T and using the same tag-and-probe method. Combined muons are used as the tag muons and the ID tracks with the standard quality requirements are used as probes. The efficiency ID ( ± ) of the muon track reconstruction with the ID is conservatively taken to be (99 ± 1)% [28,29].
The vertexing efficiency vertex is estimated with data and MC simulation for the ± and the ± . The efficiency ratio vertex ( ± )/ vertex ( ± ) is found to be 1.01 ± 0.01 stat .
The MC samples ( ± → / ± and ± → / ± ) were generated with requirements on hadron T of T > 500 MeV and | | < 2.5. The requirements on muons were T > 2.5 GeV and | | < 2.7. These are called the minimal selection criteria (MSC). To determine corrections to the efficiencies due to MSC, a dedicated MC sample was produced for each channel with no selection on pion, kaon, and muon momenta and with a requirement that their absolute rapidity be less than 10. The MC samples are corrected to take into account the MSC, and these correction factors are propagated to the analysis results. The following values are computed: cor ( ± ) = ( ± ) MSC / ( ± ) no MSC , and cor ( ± ) = ( ± ) MSC / ( ± ) no MSC , where ( ) no MSC and ( ) MSC stand for the numbers of decays before and after applying the MSC, respectively, in the T and | | bins used in the analysis. These correction factors range from 8% to 22% depending on the T and | | of the candidates. The value of the ratio cor ( ± )/ cor ( ± ) is propagated as a correction factor to the relative ± / ± cross section. The corrections obtained, along with their uncertainties, are summarized in Table 3. Each entry in the rightmost column in Table 3 is then multiplied by the corresponding value of the ratio of efficiencies ( ± )/ ( ± ). The systematic uncertainty on the MSC procedure is estimated as the difference between the raw MC prediction and the one reweighted using the sPlot-based technique. The uncertainties in these corrections and each of the uncertainties contributing to the final efficiency ratios are added in quadrature. Table 3: Summary of corrections due to the minimal selection criteria in the MC simulation. The first uncertainty is statistical, the second one is systematic.

Analysis bin
Correction to the ± Correction to the ± Ratio of the corrections The efficiency of the analysis selection criteria, selection , derived from MC simulation, is incorporated into the final efficiency ratios given below. The efficiency ratios ( ± )/ ( ± ), excluding the MSC corrections, are found to be 2.19 ± 0.05 for 13 GeV < T < 22 GeV, 1.22 ± 0.03 for T > 22 GeV, 1.75 ± 0.03 for T > 13 GeV, 1.74 ± 0.05 for | | < 0.75, and 1.76 ± 0.04 for 0.75 < | | < 2.3 (see Section 7). Here and below, when the range of a single variable is specified, it is implicitly understood that the full range is selected for the other variable, namely T > 13 GeV and | | < 2.3. The reason for the efficiency ratios being larger than one is primarily that the ± has a longer lifetime than the ± . Due to the shorter ± lifetime, the combination of the 0 / ( 0 ) and T (hadron) selections criteria affects the ± more than the ± , this fact explains the factor two difference in the relative analysis efficiency between the T bins.

Systematic uncertainties
A summary of all sources of uncertainty that contribute to the analysis efficiency values is given in Table 4. These are absolute values, not percentages. The absolute values for the efficiency ratios are presented in Section 6. They propagate directly to the final results via Eq. (1). The uncertainty in the ratio of efficiencies of detecting a kaon versus a pion is shown in Table 4 in the row titled "Tracking uncertainty". Tables 5, 6, and 7 contain the systematic uncertainties related to the number of signal events.
The systematic uncertainties of the efficiency ratios are primarily given by the systematic uncertainties of ID ( ℎ ). They are dominated by the material description in the simulation of the detector [30]. The material density affects the ± and ± detection in different ways.
The uncertainty in the efficiencies is due to the size of the MC sample and systematic uncertainties in the event counting. The precision of the efficiencies due to the size of the MC sample is calculated according to Bernoulli statistics. The uncertainty in the probability of generated events to fall into a specific bin in T or | | and the uncertainty in the probability of reconstructing these events are added in quadrature.
The sPlot-based MC reweighting procedure produces an additional systematic uncertainty that is estimated by varying the reweighted distributions while preserving agreement with the data at the 1 level. The maximum deviation for the analysis efficiency is taken as the systematic uncertainty of the analysis efficiency derived from the sPlot-based MC reweighting procedure. The uncertainties in the efficiency ratios are found to be 0.03 for 13 GeV < T < 22 GeV, 0.03 for T > 22 GeV, 0.04 for T > 13 GeV, 0.05 for | | < 0.75, and 0.06 for 0.75 < | | < 2.3.
convolved with a Gaussian function. All the parameters in the convolution are free and their values are obtained from the fit itself. The resulting uncertainty in reco ( + ) + reco ( − ) is 2.4% for 13 GeV < The uncertainty due to the choice of background model is estimated as the maximum deviation from the nominal signal yield reco ( ± ) when the default model is replaced by fourth-order Chebychev polynomials of the second kind. The result is 1.7% for 13 GeV < T ( ± ) < 22 GeV, 1.2% for T ( ± ) > 22 GeV, 2.8% for | | < 0.75, 1.3% for 0.75 < | | < 2.3, and 2.9% for the inclusive bin T ( ± ) > 13 GeV.
To estimate the effect of neglecting the contributions of the Cabibbo-suppressed (CS) decays ± → / ± , the nominal fit model is adapted to include a CS contribution and the difference with respect to the nominal result is taken as a systematic uncertainty. In addition, to estimate the effect of neglecting both the CS contribution and the partially reconstructed ± decays (PRD), MC pseudo-experiments have been used. They are generated starting from the default yield results of the fits and adding CS and PRD components. The CS component is estimated based on its branching fraction and efficiency ratio to be 8.6% of the signal yield [21], while a conservative estimation of the PRD component is obtained from a fit to the data.
The generated samples are then fit both with the default configuration (no CS and no PRD) and with a fit including the CS and PRD components and the differences on the signal yields are recorded.
The uncertainty in the number of reconstructed ± events due to the choice of signal model, estimated in the same way as for the ± , is found to be 0.1% for 13 GeV < T ( ± ) < 22 GeV, 0.2% for T ( ± ) > 22 GeV, 0.1% for | | < 0.75, 0.2% for 0.75 < | | < 2.3, and 0.1% for the combined bin T ( ± ) > 13 GeV. The total systematic uncertainty of the ± fit is calculated by adding the uncertainties associated with the mass range, the signal model, and the background model in quadrature.
To determine the systematic uncertainty due to the choice of background model for the ± fit, the exponential function in Eq. (2) is replaced by fourth-order Chebychev polynomials of the second kind. The result is 0.2% for 13 GeV < T ( ± ) < 22 GeV, 0.2% for T ( ± ) > 22 GeV, 0.2% for | | < 0.75, 0.2% for 0.75 < | | < 2.3, and 0.1% for the inclusive bin T ( ± ) > 13 GeV. All these contributions are summarized in Tables 5, 6, and 7 in the row labeled "Background model of the fit." The CS contribution to the ± fit is estimated by considering two extreme scenarios: no contribution and one that is twice the nominal fraction obtained from the fit. The difference between these scenarios is taken as the uncertainty in the number of candidates. As a cross-check, the functional form of the ± → / ± component is varied to the sum of a Gaussian and an asymmetric Johnson function [33,34] and the resulting effects are found to be covered by the quoted systematic uncertainty.
Dimuon trigger efficiencies are calculated for both decay modes, and relative trigger efficiencies for both channels considered are identical within the systematic uncertainty. The residual minor uncertainty is propagated to the final combined uncertainty of the result.
The current world average uncertainty in the ± lifetime of 0.507 ps is 0.009 ps [21], which corresponds to about 2%, while the uncertainty in the ± lifetime is four times smaller. To analytically estimate the upper limit on the uncertainty due to the lifetime, the 0 significance is studied and treated as 100% correlated with the lifetime. Using the limiting value for the selection criterion, which is 0 / ( 0 ) = 1.2, the uncertainty is obtained by multiplying 1.2 by 2% to yield 0.024. Applying ±0.024 to the 0 significance, the resulting change in the number of ± signal events is taken as the uncertainty due to the lifetime.
The absolute values of this uncertainty are shown in Tables 5-7. As a cross-check, the ± MC exclusive signal sample is reweighted in order to reflect the ±2% lifetime uncertainty mentioned above. The analysis efficiencies are recalculated and the maximum deviations are found to have smaller impact than those from the main method, so the largest deviations obtained from the main method are used as an estimator of the uncertainty.
The central values of the integrated luminosity for the two -meson datasets are exactly the same, so the integrated luminosity cancels out completely in the ratio and the luminosity uncertainty does not contribute to the uncertainty of this measurement. Removing combinations in which one of the hadronic candidates is identified as a muon contributes an uncertainty that is very small compared with the total systematic uncertainty and is consequently neglected.
A summary of all sources of systematic uncertainties that contribute to the number of signal events is given in Tables 5-7. The different components of the systematic uncertainty are added in quadrature. The components of uncertainties correlated between the ± and the ± are subtracted for the relative production cross section times branching fractions presented in Section 8.

Results
The yields reco ( ± ) and reco ( ± ), and their statistical uncertainties are extracted from the maximumlikelihood fits of the respective invariant mass distributions. The differential relative production cross sections times branching fractions are calculated according to Eq. (1) for all bins in T and | |.
The differential relative production cross section for the inclusive selection containing all events in the range T > 13 GeV and | | < 2.3 is ( ± ) · B ( ± → / ± ) ( ± ) · B ( ± → / ± ) = (0.34 ± 0.04 stat    The differential measurement suggests a dependence on the transverse momentum: the production cross section of the ± decreases faster with T than the production cross section of the ± . No significant dependence on rapidity is observed.

Conclusion
The production cross section of the ± meson relative to the production cross section of the ± meson is measured using ± → / ± and ± → / ± decays reconstructed by the ATLAS detector analyzing collisions at √ = 8 TeV delivered by the LHC in 2012. The data used for this study correspond to an integrated luminosity of 20.3 fb −1 . The relative cross section times branching fraction for the full range T > 13 GeV and | | < 2.3 is (0.34 ± 0.04 stat +0.06 −0.02 sys ± 0.01 lifetime )%. The ratio of the to ± cross sections is measured in two intervals of transverse momentum and rapidity of the -meson candidates. The differential measurement suggests a dependence on the transverse momentum: the production cross section of the ± meson decreases faster with T than the production cross section of the ± meson. No significant dependence on rapidity is observed.

Acknowledgments
This paper is dedicated to the memory of Konstantin Toms who has been the main force behind this analysis and did not live to see it published.
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.  [24] ATLAS Collaboration, Measurement of the differential cross-section of + meson production in collisions at √ = 7 TeV at ATLAS, JHEP 10 (2013) 042, arXiv: 1307.0126 [hep-ex].