IX. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties are assessed by varying the values of a specific parameter in the modeling of the data, and determining the effect on the distributions or MC templates of the combined MVA or the b-ID MVA. Compared to the earlier D0 measurement [3] we employ a more refined strategy for systematic uncertainties includ- ing the newly added hadronization uncertainty. Unless otherwise stated, the magnitude of the parameter modi- fications is obtained from alternative calibrations of the MC simulation. Each of the modified MVA distributions is used to determine the effect of systematic uncertainties. As described in Sec. VIII all nuisance parameters are fit- ted simultaneously with the nominal MVA distributions to measure the t¯ t production **cross** **section**. Systematic uncertainties are constrained by the data and are mini- mized since we use the full shape information of the MVA templates. A further reduction of correlated systematic uncertainties is achieved when combining the ℓ+jets and ℓℓ decay channels, since systematic uncertainties are then **cross**-calibrated.

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(Dated: July 17, 2018)
The PHENIX experiment presents results from the RHIC 2006 run with polarized **p** + **p** collisions at √ s = 62.4 GeV, for inclusive π 0
production at mid-rapidity. Unpolarized **cross** **section** results are measured for transverse momenta **p** T = 0.5 to 7 GeV/c. Next-to-leading order perturbative quantum chromodynamics calculations are compared with the data, and while the calculations are consistent with the measurements, next-to-leading logarithmic corrections improve the agreement. Double helicity asymmetries A LL are presented for **p** T = 1 to 4 GeV/c and probe the higher range of Bjorken x of the gluon (x g ) with better statistical precision than our previous measurements at √ s = 200 GeV. These measurements are sensitive to the gluon polarization in the proton for 0.06 < x g < 0.4.

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constructed, the discriminant function peaks near zero for the background, and near unity for the signal. We modeled it using simulated t¯ t and W +jets events, and a data sample selected by requiring that the leptons fail the tight selection criterion, representative of the mul- tijet background. A Poisson maximum-likelihood fit of the modeled discriminant function distribution to that of the data yielded the top quark **cross** **section** σt¯ t and the numbers of W +jets and multijet background events in the selected data sample. The multijet background was constrained within errors to the level determined by the matrix method.

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VI. CONCLUSION
We have measured the **cross** **section** and single trans- verse spin asymmetry, A N , for very forward neutron production in polarized **p**+**p** collisions at √ s=200 GeV. The results from the PHENIX experiment at RHIC were based on a zero degree hadronic calorimeter (ZDC) aug- mented by a shower maximum detector, covering neu- tron production angles to θ n =2.2 mrad. A large A N for neutron production had been observed in a polarimeter development experiment at RHIC, using an electromag- netic calorimeter to identify neutrons, with coarse neu- tron energy resolution[1]. The PHENIX experiment then outfitted existing ZDC detectors to act as polarimeters to monitor the beam polarizations and polarization direc- tions at the experiment. The results presented here are based on studies with the ZDC polarimeter, which due to a much better measurement of the neutron energy, pro- vide first measurements of the neutron production **cross** **section** at RHIC energy, and the dependence of A N on the neutron energy.

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diction (line histogram) and the signal+background dis- tribution (dashed histogram) [9, 14].
The **cross** **section** was calculated from the number of t¯ t and background candidates above a cut value of the N N discriminant. The cut value was chosen to maxi- mize the expected statistical significance s/ √ s + b, where s and b were the number of expected signal and back- ground events. The signal and background distributions were estimated using the trf prediction and t¯ t Monte Carlo events [15]. For both analyses, the expected sta- tistical significance was about two standard deviations.

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Since hadrons are slower than photons, an additional time of flight cut is used for photon identification. Fur- thermore, the cluster must not be associated with a hit from a charged particle in the Pad Chamber (PC3) just in front of the EMCal; an exception is made if the hit position in the EMCal and in the PC3 are aligned in such a way that the particle could have come from the vertex on a straight line, i.e., it was not bent in the cen- tral magnetic field. In this case, the cluster is accepted as a photon candidate since it is likely that the original photon converted into an e + e − pair before the PC3 but outside the magnetic field. The latter two selection cuts are used in the analysis of the double helicity asymmetry but not in the extraction of the **cross** sections, leading to a smaller signal to background ratio in the **cross** **section** measurements. In order to exclude clusters with poten- tially incorrectly reconstructed energies due to leakage effects, the tower with the largest energy deposition in a cluster must not be in the outermost two columns or rows of an EMCal sector. In addition, there must not be a noisy or dead tower in the eight towers surrounding the central one.

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D. Observed and Predicted Numbers of Tagged
Events
The numbers of observed and predicted single and dou- ble tagged events are summarized in Tables IX and X, respectively. Figure 11 shows the observed number of tagged events in data compared to the total SM back- ground predictions, excluding tt. The background in the first jet multiplicity bin is dominated by W +light and W c events. The contribution from heavy flavor produc- tion, particularly from W b¯b, dominates for events with three or more jets. Very good agreement between ob- servation and background prediction is observed in the background-dominated first and second jet multiplicity bins, which gives confidence in the background estimate of the analysis. A clear excess of observed events over background is seen in the third and fourth jet multiplicity bins. The excess events are attributed to tt production and are used to extract the **cross** **section**. Figure 12 shows the observed number of tagged events in data compared to the total SM predictions including tt. The number of tt events shown is calculated based on the measured **cross** **section**.

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1 9.7% normalization uncertainty is not included
FIG. 1: The neutral pion production **cross** **section** at √s = 200 GeV as a function of pT (squares) and the results of NLO pQCD calculations for theory scales µ = pT /2 (dotted line), pT (solid line) and 2pT (dashed line), see text for details; note that the error bars are smaller than the points. The inset shows, in addition to π 0

are based on data corresponding to an integrated lumi- nosity of 8.7 ± 0.5 fb −1 [10] collected with the D0 detec- tor from June 2006 to September 2011 at the Fermilab Tevatron Collider at √ s =1.96 TeV. The large data sam- ple and use of advanced photon and b-jet identification tools [11–13] enable us to measure the γ + 2 b-jet pro- duction **cross** **section** differentially as a function of **p** γ T for photons with rapidities |y γ | < 1.0 and transverse mo- menta 30 < **p** γ T < 200 GeV, while the b jets are required to have **p** jet T > 15 GeV and |y jet | < 1.5. This allows for probing the dynamics of the production process over a wide kinematic range not studied before in other mea- surements of a vector boson + b-jet final state. The ratio of differential **cross** sections for γ + 2 b-jet production rel- ative to γ + b-jet production is also presented in the same kinematic region and differentially in **p** γ T . The measure- ment of the ratio of **cross** sections leads to cancellation of various experimental and theoretical uncertainties, al- lowing a more precise comparison with the theoretical predictions.

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The efficiency for W W signal events to pass the ac- ceptance and kinematic criteria is determined using the pythia 6.2 [8] event generator followed by a detailed geant -based [9] simulation of the DØ detector. All trig- ger and reconstruction efficiencies are derived from the data. For the ee channel, the overall detection efficiency is (8.76 ± 0.13)%. The overall efficiencies for the µµ and eµ channels are (6.22 ± 0.15)% and (15.40 ± 0.20)%, re- spectively. Using an NLO **cross** **section** of 13.5 pb [3] and branching fractions B of 0.1072 ±0.0016 for W → eν and 0.1057 ±0.0022 for W → µν [10], the expected number of events for the pair production of W bosons combined for all three channels is 16.6 ±0.1(stat)±0.6(syst)±1.1(lum) events, where the statistical error is given by the statis- tics of the MC sample. The signal breakdown for the three channels is given by the first line of Table I.

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C. Optimization of the discriminant function
The optimization procedure, determining which com- bination of topological input variables will form the fi- nal discriminant function, is performed by estimating the expected combined statistical and systematic uncer- tainty of the measured t¯ t **cross** **section**. The expected uncertainty is calculated for all discrimination functions that can be constructed from the selected input variables by using all possible subsets of the 13 variables in turn as input. Pseudo-experiments are performed by draw- ing pseudo-data discriminant output distributions from the output discriminant distributions of simulated events. The composition of such a pseudo-dataset is taken ac- cording to the expected sample composition for N jet ≥ 4 and σ t¯ t = 7 pb and allowing Poisson fluctuations. 3, 000 pseudo-experiments are built for each source of statisti- cal or systematic uncertainty and discriminant function under consideration. We select the discriminant function which provides the smallest expected total uncertainty, including all sources of systematic uncertainties that af- fect the shape of the discriminant function.

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5 Systematic uncertainties
The systematic uncertainties on the **cross**-**section** ratios are determined as follows. A systematic uncertainty on the signal extraction is determined by varying the models used in the mass-difference fits. Several different signal and background models are tested. The signal shapes are varied between Gaussian functions and Voigtian functions (a convolution of a Breit-Wigner and a Gaussian function), and the background shape is varied between second- and third-order Chebyshev polynomials. The natural widths of the χ c1 and χ c2 states are narrow compared to the resolution, the Breit-Wigner widths are therefore fixed to the known values [24]. The fit range is varied between 100 (150) < ∆M < 900 MeV/c 2 and 200 < ∆M < 800 (850) MeV/c 2 for the converted candidates at forward (backward) rapidity. For the calorimetric candidates, the fit range is varied between 250 < ∆M < 650 MeV/c 2 and 300 < ∆M < 600 MeV/c 2 in the two rapidity intervals. The various choices of signal shape, background parametrization, and range give a total of eight fits to each of the mass-difference spectra in each rapidity interval. In all cases, the χ c0 peak is also included in the fit; however, no significant χ c0 yield is observed. The systematic uncertainty on the yield ratios due to the fitting procedure is assigned as the standard deviation between the values returned by the eight individual fits. For the converted sample, this systematic uncertainty amounts to 4.9% (3.2%) at forward (backward) rapidity. For the calorimetric sample it is 2.6% (6.8%) at forward (backward) rapidity. The residual background from the nonprompt χ c1,2 production is verified as negligible and shown to cancel out in the ratio, hence no related uncertainty is assigned. The systematic uncertainty on the acceptance and efficiency corrections includes contributions from the limited size of the simulated samples used to compute the ε acc and ε reco factors, and the uncertainty due to the discrepancy of the χ

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sources. Processes with light-quark (u, d or s) initi- ated jets recoiling against the W boson can produce a small fraction of charge-correlated µ-tagged jets owing to leading particle effects [15]. Background from W W production contributes only a small amount to the signal sample. The W Z and ZZ processes only rarely pro- duce charge-correlated jets. Other final states that can produce charge-correlated jets (t¯ t, t¯b, W +b¯ c and W +b) are suppressed by small production **cross** sections or tiny CKM matrix elements. These considerations allow a measurement of the W +c-jet production rate from OS events with the backgrounds determined in situ from SS events, up to small weakly model-dependent theory cor- rections.

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have at least three lepton candidates with **p** T > 15 GeV that originate from the same vertex and separated from each other by at least ∆R = **p**(∆φ) 2 + (∆η) 2 > 0.5. The event must also have a significant E / T to account for the unobserved neutrino. We require E / T to be above 20 GeV. Events are selected using triggers based on elec- trons and muons. Since there are multiple high **p** T lep- tons from the decay of the heavy gauge bosons the trigger efficiency is measured to be 98% ± 2% for all signatures. In the W Z candidate selection, we first identify the leptons from the Z boson decay. We consider all pairs of electrons or muons, additionally requiring opposite elec- trical charge in the cases of muon pairs or electron pairs including an ICR electron. The pair that has an invariant mass closest to and consistent with the Z boson nominal mass is selected as coming from the Z boson decay. If such pair is not found the event is rejected. The lepton from the W boson decay is selected as the one with the highest transverse momentum from the remaining unas- signed muons and CC or EC electrons in the event. This assignment is studied in the simulation and found to be 100% correct for eeµ and µµe channels. It is found to be correct in about 92% and 89% of cases for eee and µµµ signatures, respectively. The effects of misassign- ment on the product of acceptance and efficiency of the selection criteria, A × ǫ, are estimated in the signal sim- ulation. Values of A × ǫ measured using the assignment method described above differ from those obtained us- ing MC generator-level information by less than one per cent. Therefore, the systematic uncertainty on A × ǫ due to the misassignment is neglected in this analysis.

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In order to determine the longitudinal spin asymmetry with a sample of W decays with minimal background con- tamination, two additional requirements were imposed on the candidate events. An isolation cut requiring the sum of cluster energies in the calorimeter and transverse mo- menta measured in the drift chamber be less than 2 GeV in a cone with a radius in η and φ of 0.5 around the candi- date track was used to remove remaining events with jets. About 80% of the signal is kept, while the background is reduced by a factor ∼ 4 as shown in Fig. 1. The sec- ond cut is to reject tracks with |α| < 1 mr, which reduces charge misidentification to negligible levels. There are 42 candidate W + + Z 0 decays to positrons with a back- ground of 1.7 ± 1.0 and 13 candidate W − + Z 0 decays to electrons with a background of 1.6 ± 1.0 events within 30 < **p** T < 50 GeV/c after these two additional cuts.

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The next step weights the reconstructed and generated η mesons in **p** T and pseudorapidity to mimic the measured
data distribution. This accounts for **p** T smearing effects on an exponential spectrum, and for the falling pseudorapidity
dependence in the forward region. As the weighting is dependent on the shape of the corrected spectrum, an iterative procedure is used to ensure the efficiency correction converges to a stable value. The reconstruction efficiency is calculated as the ratio of reconstructed η mesons divided by the number generated. The reconstruction efficiency for the South and North MPC for both triggers is shown in Fig. 4. The North MPC has a lower reconstruction efficiency than the South, due to a more restrictive noisy/inactive tower map in the North. The reconstruction efficiency shape is predominantly due to the geometric acceptance coupled to the narrowing γγ opening angle from low to higher momenta. At low momenta, wider opening angles can prohibit the measurement of both γs in the detector. At high momenta, cluster merging increasingly inhibits the detection of distinct γ pairs. Significant cluster merging effects occur when the cluster separation is less than 1.5 times the tower width (∆R < 3.3 cm).

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the time window for the protons which have undergone elastic scattering usually passes through the diagonally opposite antiproton detector at an earlier time (and vice versa). Therefore, the time information can be used to veto events with early time hits, consistent with halo pro- tons and antiprotons in the elastic sample. The veto is not 100% efficient due to a combination of scintillator efficiency and positioning of the detectors with respect to the beam (a closer detector position both increases a detector’s signal acceptance and its ability to reject halo). Consequently, it is necessary to subtract the re- maining background. We consider an event to be caused by **p** (**p**) halo if one or both of the two **p** (**p**) detectors of an elastic combination have hits in their early time interval. We require events to have no activity in either the **p** halo or the **p** halo timing window. We select back- ground samples by requiring hits consistent with **p** halo and **p** halo simultaneously. First, we verify that outside the elastic correlation band between the coordinates of a proton and antiproton detector the signal tagged events have the same |t| dependence as the background tagged ones (see Fig. 5). Next, assuming that signal and back- ground tagged events also have the same |t| dependence inside the correlation band, we use the ratio of these two distributions and use it to estimate the percentage of background events inside the signal tagged correlation band. This background is subtracted from all events in- side the correlation band to obtain dN /dt as a function of |t|. The amount of background subtracted inside the elastic correlation band varies from 1% at low |t| to 5% at high |t|. The absolute uncertainty of the background, which is propagated as a statistical uncertainty to dσ/dt, varies from 0.3% at low |t| to 5.0% at high |t|. As a **cross** check, we vary the detector band cuts from 3.0σ to 3.5σ and to 6.0σ, to allow more background, and obtain sim- ilar dN /dt results after applying the same background subtraction procedure (within 1%).

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J.M. Otalora Goicochea 2 , **P**. Owen 53 , A. Oyanguren 64 , B.K. Pal 59 , A. Palano 13,c , F. Palombo 21,u , M. Palutan 18 , J. Panman 38 , A. Papanestis 49,38 , M. Pappagallo 51 , L.L. Pappalardo 16,f ,
C. Parkes 54 , C.J. Parkinson 9,45 , G. Passaleva 17 , G.D. Patel 52 , M. Patel 53 , C. Patrignani 19,j ,
A. Pazos Alvarez 37 , A. Pearce 54 , A. Pellegrino 41 , M. Pepe Altarelli 38 , S. Perazzini 14,d , E. Perez Trigo 37 , **P**. Perret 5 , M. Perrin-Terrin 6 , L. Pescatore 45 , E. Pesen 66 , K. Petridis 53 , A. Petrolini 19,j , E. Picatoste Olloqui 36 , B. Pietrzyk 4 , T. Pilaˇ r 48 , D. Pinci 25 , A. Pistone 19 ,

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In addition to the MSTW2008NLO PDFs, Fig. 2 shows also predictions for CT10 PDFs [9] and the correspond- ing value of α s (M Z ) = 0.118, normalized by the pre- dictions for MSTW2008NLO and represented by the solid lines. To compare the CT10 PDF uncertainties (which have been published at the 90% C.L.) with the experimental uncertainties (corresponding to one stan- dard deviation), the former have been scaled by a fac- tor of 1/1.645 [28]. The resulting 68% C.L. uncertain- ties are displayed around the CT10 central values by the dark band. The CT10 PDFs predict a different shape for the M 3jet dependence of the **cross** **section**. For M 3jet < 0.6 TeV, the central results for CT10 PDFs agree with those for MSTW2008NLO, while the CT10 predictions at M 3jet = 1.2 TeV are up to 30% higher. These discrepancies at highest M 3jet are larger than the combined 68% C.L. uncertainty bands of the CT10 and MSTW2008NLO PDFs.

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The assumption of the equality of the pp and **p**¯ **p** elastic **cross** sections at the OP could be modified if an odderon exists [1, 2]. A reduction of the significance of a difference between pp and **p**¯ **p** **cross** sections would only occur if the pp total **cross** **section** were larger than the **p**¯ **p** total **cross** **section** at 1.96 TeV. This is the case only in maximal odd- eron scenarios [21], in which a 1.19 mb difference of the pp and **p**¯ **p** total **cross** sections at 1.96 TeV would correspond to a 2.9% effect for the OP. This is taken as an additional systematic uncertainty and added in quadrature to the quoted OP uncertainty estimated from the TOTEM to- tal **cross** **section** fit. The effect of additional (Reggeon) exchanges [9, 26, 27], different methods for extrapolation to the OP, and potential differences in ρ for pp and **p**¯ **p** scattering are negligible compared with the uncertain- ties in the experimental normalization. The comparison between the extrapolated and rescaled TOTEM pp **cross** **section** at 1.96 TeV and the D0 **p**¯ **p** measurement is shown in Fig. 6 over the interval 0.50 ≤ |t| ≤ 0.96 GeV 2 .

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