Forward Energy Flow, Central Charged-Particle Multiplicities, and Pseudorapidity Gaps in W and Z Boson Events from pp Collisions at 7 TeV

A study of forward energy flow and central charged-particle multiplicity in events with W and Z bosons decaying into leptons is presented. The analysis uses a sample of 7 TeV pp collisions, corresponding to an integrated luminosity of 36 inverse picobarns, recorded by the CMS experiment at the LHC. The observed forward energy depositions, their correlations, and the central charged-particle multiplicities are not well described by the available non-diffractive soft-hadron production models. A study of about 300 events with no significant energy deposited in one of the forward calorimeters, corresponding to a pseudorapidity gap of at least 1.9 units, is also presented. An indication for a diffractive component in these events comes from the observation that the majority of the charged leptons from the (W/Z) decays are found in the hemisphere opposite to the gap. When fitting the signed lepton pseudorapidity distribution of these events with predicted distributions from an admixture of diffractive (POMPYT) and non-diffractive (PYTHIA) Monte Carlo simulations, the diffractive component is determined to be (50.0 +/- 9.3 (stat.) +/- 5.2 (syst.))%.


Introduction
At high energies, proton-proton reactions are generally described in terms of a two-component outgoing system, pp → XY, where X is a state originating from a perturbative parton-parton interaction and Y consists of proton remnants carrying a large fraction of the total energy. The system Y represents the "underlying event" and consists of mostly low-transverse-momentum hadrons originating from parton showers, and non-perturbative multi-parton interactions. The latter are largely independent of the hard interaction, increase the particle multiplicity, and lead to correlations between the energy flows in the central and forward regions.
The currently available models of multi-parton interactions have mainly been tuned to minimumbias data and to final states including jets with large transverse momentum (p T ), using the observed central charged-particle multiplicities and the transverse momentum spectra of hadrons that are not associated with the hard jets. Models for a detailed simulation of multi-parton interactions are under rapid development and new features, including diffractive components in the energy flow, are being extensively investigated. A recent detailed CMS study of the underlying event structure at central rapidities is given in [1].
The analysis of the underlying event structure and energy flow correlations in hard processes with colorless final states, such as pp → W(Z)X → ν( )X, can provide insights into unexplored aspects of multi-parton interactions. In particular, processes with colorless final states allow a straightforward separation of the hard interaction and the underlying event. Correlations between the charged-particle multiplicity in the central rapidity range and energy depositions at large rapidities can give additional information about multi-parton interactions.
Furthermore, a fraction of these proton-proton interactions is expected to arise from singlediffractive (SD) reactions, where one of the colliding protons emerges intact from the interaction, having lost only a few percent of its energy. Such SD events may be ascribed to the exchange of vacuum quantum numbers (often called Pomeron exchange), which leads to the absence of hadron production over a wide region of rapidity adjacent to the outgoing proton direction. Experimentally, these large rapidity gaps will appear as regions of pseudorapidity, devoid of detected particles.
Soft-diffractive events can be described in the framework of Regge theory (see, e.g., [2]). Harddiffractive events, with the production of jets, heavy flavors, or W/Z bosons, have been observed at the SPS, HERA, and the Tevatron [3][4][5][6][7][8]. For electron-proton hard-diffractive interactions, a factorization theorem has been proven [9], allowing the introduction of diffractive parton distribution functions (dPDFs). In hadron-hadron diffractive interactions, factorization is however broken by soft multi-parton interactions [10,11], which fill the large rapidity gap and reduce the observed yields of hard-diffractive events. Such interactions are not yet simulated in the currently available Monte Carlo (MC) generators, and the reduction in the large rapidity gap hard-diffraction cross section is quantified by a suppression factor, the so-called rapidity gap survival probability. At the Tevatron, the observed hard-diffractive yields relative to the corresponding inclusive processes are approximately 1%. A recent study by CDF [12] indicates that the fractions of W and Z bosons produced diffractively are (1.00 ± 0.11)% and (0.88 ± 0.22)%, respectively.
The standard picture of W or Z boson production via hard parton-parton scattering is shown in Fig. 1a and combined with a multi-parton interaction in Fig. 1b. According to this picture, large rapidity gap events can only arise from multiplicity fluctuations. Figure 1c shows standard W(Z) production accompanied by multi-parton interactions with a diffractive component. Hard-diffractive production (Fig. 1d) leads to a large rapidity gap. Such contributions would result in almost unchanged central charged-particle multiplicity distributions with respect to Fig. 1b. However, a larger fraction of events with a relatively small energy deposition in the forward regions, and a smaller correlation of the energy flow in the central and forward regions, could be expected. The diffractive production mechanism with multi-parton interactions is shown in Fig. 1e. In this case, large rapidity gap events only survive if the multi-parton component is small. Finally, Fig. 1f indicates a possible combination of W(Z) production mechanisms with a diffractive component in both the hard process and the multi-parton interaction.
This paper presents an analysis of the underlying event structure and of events with a pseudorapidity gap of more than 1.9 units (in the following, referred to as LRG events for simplicity) in the processes pp → WX and pp → ZX, in 7 TeV pp collisions at the Large Hadron Collider (LHC), and recorded in 2010 with the Compact Muon Solenoid (CMS) detector. A data sample corresponding to an integrated luminosity of 36 pb −1 has been analyzed. Final states of the type WX and ZX are identified by the detection of electrons and muons with large transverse momentum p T . The underlying event structure is analyzed in terms of (i) the charged-particle multiplicity at central rapidities, (ii) the forward energy flow, and (iii) the correlations between these observables. The observed LRG events are expected to be sensitive to a diffractive production component.
The paper is structured as follows: after giving a short description of the models for inclusive and diffractive vector-boson production in pp collisions (Section 2) and the CMS detector (Section 3), the selection of W and Z bosons with leptonic decays, the rejection of pileup events, and the energy measurement in the forward calorimeters are described in Section 4. Section 5 summarizes the analysis of the underlying event structure in WX and ZX events in terms of the observed charged-particle multiplicity, the energy depositions in the forward calorimeters, and their correlations. The analysis of events with a LRG signature is discussed in Section 6.

Modeling of the underlying event structure in W and Z events
The simulation of non-diffractive processes, including multiple overlaid events within the same bunch crossing ("pileup"), was performed using the PYTHIA 6.420 and PYTHIA 8.145 event generators [13,14] with different tunes [15] for the underlying event structure and the multi-parton interactions. Several tunes were used for the simulation of the underlying event structure in W and Z events. In particular, the tunes developed before data from the LHC could be used were PYTHIA6 D6T [16], Pro-Q20 [17], Pro-PT0 [17], and P0 [18]. The newer tunes PYTHIA6 Z2 [19] and the PYTHIA6 2C [20] include already some information from the LHC data. It is relevant for the discussion in Section 5 that the older D6T and Pro-Q20 tunes are associated with virtuality-ordered showers, while the newer ones, P0, Pro-PT0, Z2, and 2C, are associated with p T -ordered showers. As shown in the recent CMS measurement of the underlying event structure Ref. [1], the Z2 tune provides a reasonably good description of the data in minimum-bias events.
Using the average instantaneous luminosity for each running period (discussed below), an average number of soft pileup minimum-bias MC events were superimposed on the simulated hard-interaction events. As discussed in detail in Section 5, the predicted pileup contribution to the forward energy flow from the simulation was found to be in good agreement with the one from a dedicated unbiased data sample.
The W and Z production cross sections were calculated using leading-order (LO) matrix elements for the process qq → W(Z), convolved with the CTEQ parton distribution functions (PDFs) [21]. Effects from higher-order QCD corrections were approximated with parton show- Figure 1: Sketches of the process pp → W(Z)X, where a W(Z) boson is produced in the hard interaction, combined with contributions from multi-parton interactions, with and without a diffractive component. The colored curly and straight lines are for gluons and quarks and the straight black lines are for W(Z). The symbol I P indicates the exchange of a state with the quantum numbers of the vacuum (Pomeron). (a) shows the standard hard interaction; (b) the same process with additional multi-parton interactions; (c) the hard process accompanied by multiparton interactions containing a diffractive component; (d) the hard-diffractive production of a W(Z) boson; (e) the hard-diffractive W(Z) production with multi-parton interactions, and (f) the hard-diffractive W(Z) production with multi-parton interactions containing a diffractive component. In the latter case, the diffractive component of the multi-parton interaction does not necessarily couple to the same proton as in the hard process (not shown here). ers from the initial and final-state partons.
Diffractive W and Z production was simulated with the POMPYT 2.6.1 [22,23] event generator. The hard processes responsible for the production of W and Z bosons were identical to those in non-diffractive models. For the simulation of diffractive processes, the dPDFs (fit B) measured by the H1 experiment at HERA were used [6,24]. This generator does not simulate multiparton interactions or the ensuing rapidity gap survival probability.

Selection of W and Z events with decays to electrons and muons
The identification of W and Z bosons is based on the presence of isolated electrons and muons with high transverse momentum. The selection criteria are given below. A more detailed description of the lepton selection, the efficiencies, and the associated systematic uncertainties is given in [26].
Events are selected online by requiring a high-transverse-momentum electron or muon with thresholds depending on the run period and varying between 10 and 17 GeV for electrons and between 9 and 15 GeV for muons. Thus, a small fraction of W → τν or Z → ττ events with leptonic decays of the τ is also included. The trigger efficiency for signal events with the selection conditions defined below is above 99% [26].
The offline selection of electrons is based on the matching of a reconstructed high-transversemomentum track candidate with energy depositions in the barrel and endcap calorimeters; shower shape requirements are applied to these clusters. Electron candidates are required to have |η| < 2.5 and transverse momenta larger than 25 GeV. Electrons from photon conversions are rejected. In order to suppress background from jets, the electrons are required to be isolated using a cone in η − φ space around the electron direction with ∆R < 0.3, where ∆R = ∆η 2 + ∆φ 2 and ∆η and ∆φ are the pseudorapidity and azimuthal angle difference between the electron and jet directions. The energy in the cone is calculated from the scalar sum of the transverse energies in the tracker and both calorimeters, and is required to be smaller than 10% of the lepton p T . More details are given in Ref. [26].
Two algorithms are used to identify muons. One is based on the matching of a reconstructed high-transverse-momentum silicon tracker candidate with a track candidate found in the muon system. The second is based on a global fit to tracker and muon system hits. Muons in this analysis have to pass both selection algorithms. The reconstructed muon candidates are required to be at |η| < 2.5 and to have transverse momentum larger than 25 GeV. The isolation criteria are similar to the ones used for electrons, and details about the muon identification are given in Ref. [26].
Jets and the missing transverse momentum in the event are determined from the four-vectors of reconstructed particles, which are measured from the combination of the tracker and the calorimeter informations [27]. For jets, the anti-k t algorithm with a cone size of 0.5 is used [28]. The transverse momentum of jets is required to be larger than 30 GeV with a pseudorapidity of |η| < 2.5.
An event is selected as a W → ν candidate if the following requirements are satisfied: (1) one isolated electron or muon with a transverse momentum greater than 25 GeV and |η| < 1.4; events with a second isolated electron or muon with a transverse momentum above 10 GeV are rejected; (2) the missing transverse momentum (ascribed to the neutrino) greater than 30 GeV; (3) the transverse mass = 2E T (ν)E T ( ) − 2 p T (ν) · p T ( ) of the charged lepton and the neutrino greater than 60 GeV.
Likewise, the following conditions are imposed to select Z(γ * ) → (called Z in the following) candidates: (1) two isolated electrons or muons with opposite charge and each with a minimum transverse momentum of 25 GeV; (2) at least one lepton with |η| < 1.4; (3) the reconstructed invariant mass of the dilepton system between 60 and 120 GeV.
This selection resulted into essentially background-free W and Z event samples. The background for the W sample is estimated to be less than 1% and even smaller for the Z sample, independent of any additional requirements on the energies in the HF calorimeters.
The main features of the W and Z event samples are found to be insensitive to small variations of the selection criteria. In the following, no efficiency corrections are applied, and only direct comparisons to MC predictions are shown.

Pileup rejection and single-vertex selection of W and Z events
As mentioned earlier, there can be several simultaneous pp interactions in the same bunch crossing in addition to the selected W and Z events, the so-called pileup. As the instantaneous luminosity increased steadily during the 2010 pp data taking, the analysis was affected by very different pileup conditions. For this analysis the data have been separated into three periods (P) with average instantaneous luminosities of L inst ≤ 0.17 µb −1 /s (P I), 0.17 < L inst ≤ 0.34 µb −1 /s (P II), and L inst > 0.34 µb −1 /s (P III), respectively. Assuming a total inelastic cross section of about 70 mb [29,30], an instantaneous luminosity of 0.17 µb −1 /s corresponds to an average of about one inelastic pileup event.
The selection efficiency for W and Z events is independent of the instantaneous luminosity. However, the charged-particle multiplicities and the energy depositions in the forward region of the detector (HF calorimeters), and thus especially the LRG signature, are strongly affected by the pileup (i.e., the gap is filled in).
The effects from pileup events for our analysis have been studied by means of zero-bias data samples where the only requirement was that of colliding beams in the detector. Such event samples were collected and analyzed for different instantaneous luminosities and the different periods. More details are given in Section 5.1.
In order to limit the consequences of pileup, events with more than one vertex are rejected. For this analysis a primary vertex, the W(Z)-vertex, is defined as the one which contains the lepton track(s). Events with additional vertices, formed by at least three tracks, are rejected. Details about the vertex reconstruction algorithm are given in Ref. [31]. The W-vertex z-position distribution is roughly Gaussian with a mean of 0.52 cm and a standard deviation of 5.9 cm.
The observed increase in the number of vertices has been studied using a zero-bias event sample and found to be in agreement with the number of pileup events expected on the basis of the luminosity increase (cf. Table 1). pileup events can be categorized as hard and soft events. Hard pp pileup interactions have some detectable charged particles in the central region of the detector and are removed by the multiple-vertex veto. The soft component has little or no detectable transverse activity in the central region and does not result in reconstructed vertices.
The efficiency to reconstruct pileup vertices (including vertex splitting) has been determined from MC simulations of minimum-bias and W → eν events. Based on the pileup conditions in the 2010 data, the efficiency to detect pp pileup interactions was found to be essentially constant within ±25 cm along the z direction of the nominal interaction point with an average of about 72%. The inefficiency essentially depends only on the amount of soft pileup interactions (e.g., events without detectable charged particles in the central region of the detector) in the MC simulation. The reconstruction efficiency for pileup vertices was found to be essentially independent for the different luminosity periods, as long as the vertices were separated by more than 0.1 cm. The corresponding inefficiency to detect the merged pileup vertex is estimated to be 3.3%. The uncertainties from the remaining soft pileup events on the results presented below are discussed in more detail in Section 5.1.
The numbers of single-vertex W and Z events are summarized in Table 1. The single-vertex event yields, compared to the inclusive event yields, decrease with increasing instantaneous luminosity and are in agreement with the expected numbers of vertices from the simulation, assuming Poisson distributions.

Central charged-particle multiplicity and forward energy flow
The observables used to study the underlying event structure in W and Z events are the chargedparticle multiplicity in the central detector, the energy depositions in both HF calorimeters (in the following designated as HF+ and HF− depending on the sign of the corresponding η coverage), and the correlations between them. In the following, only the distributions for W → ν events are discussed. No significant differences are observed between W events selected with decays to electrons or muons. The same analysis has been performed on the pp → ZX data sample and consistent results are obtained.
For the studies described below, the charged-particle multiplicity is measured in the range |η| < 2.5 for track momentum thresholds of p T > 0.5 GeV and p T > 1.0 GeV, excluding the tracks associated with W decays. Additionally, in order to study the underlying event structure, events with central jet activity (p T > 30 GeV, |η| < 2.5) are excluded from the multiplicity plots.
A detailed study of the pion track reconstruction within the acceptance of the tracker [31] determined that the efficiency rises from about 88% at a p T of 0.5 GeV to about 95% for p T between 1-10 GeV. Above 10 GeV, the efficiency decreases slowly to about 90% at 50 GeV. Furthermore, it was shown that the hadron track reconstruction efficiency in the data agrees within 1-2% with the one in the MC simulation. The total systematic uncertainty of the tracking efficiency was estimated to be less than 3.9%. The observed charged-particle multiplicities, excluding the lepton(s) from the W(Z) decays, vary between 0 and about 50, with an average of 11 and an r.m.s. of 8.2 for p T > 1.0 GeV. About twice as many tracks are found with the lower threshold, p T > 0.5 GeV, and about 0.15% of the events have more than 100 tracks. Nearly identical charged-particle multiplicity distributions are observed in electron-and muon-tagged events with the same p T thresholds. The charged-particle multiplicity distribution for W → eν events is shown in Fig. 2a for tracks with p T > 1.0 GeV, and for W → µν events with for p T > 0.5 GeV in Fig. 2b. The corresponding distributions for W → eν with p T > 0.5 GeV and W → µν with p T > 1.0 GeV are consistent with the displayed distributions in Figures 2a and 2b.
The PYTHIA6 generator with tune 2C provides the best overall description for the higher track p T threshold, and PYTHIA6 with tune Z2 provides a reasonable description for both track p T thresholds. However, both PYTHIA6 2C and PYTHIA6 Z2 predict too many events with very small charged-particle multiplicities. The PYTHIA6 D6T tune predicts a harder-p T spectrum for hadrons in the underlying event and thus a larger multiplicity in the case of the higher threshold. The Pro-Q20 tune of PYTHIA6 significantly underestimates the event yields with very high multiplicities (Fig. 2b).
The energy deposition in the HF+ and HF− calorimeters is determined from the sum of individual calorimeter towers with an energy threshold of 4 GeV, corresponding to a minimum transverse momentum of 0.07-0.4 GeV. The uncertainty on the energy scale of the HF calorimeter was estimated to be about ±10% (for details see [27]). This uncertainty was taken into account by a ±10% scaling of the single-tower energy, resulting in new estimates of the total energy deposition in HF for the data, while keeping the MC unchanged. The corresponding systematic uncertainty for the energy measurement in the HF is shown as a band in Fig. 2 and all the following figures. This uncertainty is much larger than the 3.5% difference between the reconstructed energy distributions in the HF+ and HF− calorimeters (cf. Table 2).
The observed HF energies vary between 0 GeV (i.e., no HF tower with an energy above 4 GeV) and more than 2 TeV. Only a few events have an energy deposition above 2 TeV (about 0.05% for electrons and muons combined) and the highest energy deposition is 2.7 TeV. All events with high-energy depositions also have large tower multiplicities. The average energies observed in HF+ and HF− are measured in 11 HF rings of calorimeter towers, each covering approximately a ∆|η| range of 0.175. The difference between the average energy deposition per ring (η bin) in the data and the different MC tunes is consistent for all tower rings. The average energy deposited per |η| ring predicted by the D6T (Z2) tune is too large (too small), while the Pro-Q20 tune provides a very good description of the data.
The distributions of the total HF+ and HF− energy sums (E HF+(−) ) are shown in Fig. 2c for the data and the PYTHIA6 D6T and Z2 tunes, with and without pileup (PU) in W → eν events. In order to take into account effects not included in the simulation (e.g., beam-gas interactions), the soft pileup contribution obtained from the zero-bias data is added to the MC simulation without pileup. It can be seen that the pileup contribution, as determined from the data, agrees very well with the one obtained from the luminosity-dependent MC simulation. Therefore, in the following analysis and all shown distributions, the pileup contribution is estimated from the MC simulation. Figure 2d shows the HF+ and HF− energy sums for W → µν events and  Figure 2: The charged-particle multiplicities and the summed HF+ and HF− energy distributions in a) and c) W → eνX and b) and d) W → µνX candidate events are shown for data and MC simulations, including pileup, with different tunes for the underlying event. The uncorrected charged-particle multiplicities are shown for electron-and muon-tagged W events, for two thresholds on track transverse momenta of (a) p T > 1.0 GeV and (b) p T > 0.5 GeV The band shown for the HF energy distributions indicates the uncertainty related to a ± 10% HF energy scale variation. The effects of the pileup on the MC simulation can be seen in (c) where the MC HF energy distributions are shown with pileup taken either from data or from the MC simulation and without pileup.
for several different MC tunes of the underlying event.
The mean values of the reconstructed HF energy and the tower multiplicities are given in Table  2, again for the three different instantaneous luminosity periods and separately for W → eν and W → µν events. The average HF energy deposition, averaging the energy deposits in the HF+ and HF-calorimeters, in the data is 310 GeV, with an r.m.s. of 235 GeV. On average, about 30 towers with more than 4 GeV are reconstructed in each HF calorimeter. The statistical uncertainties of the mean energy values (mean tower multiplicities), estimated from the r.m.s. of the distribution, amount to less than ±5 GeV (±0.4) in the data and even smaller in the MC simulation. The corresponding mean value obtained with PYTHIA6 D6T, including the HF energy depositions from simulated pileup, is 370 GeV, with a tower multiplicity of 35. The PYTHIA6 Z2 tune predicts a mean energy deposition of 270 GeV and a tower multiplicity of 27, whereas using the Pro-Q20 tune results in a simulated energy deposition of 311 GeV and a tower multiplicity of 29 towers, similar to the data.
As can be seen from Figs. 2c and 2d, besides the Pro-Q20 tune, none of the MC models considered provide a good description of the HF energy distribution observed in the data. For energy depositions between 10 and 150 GeV, large differences between the data and different tunes are observed. In particular, the number of events in the data is about 30 to 50% higher than predicted by the D6T tune, and 50% lower than predicted by the Z2 tune. For simplicity, the older P0 and Pro-PT0 tunes are omitted from the following more detailed studies.
In total, 287 W and Z events with no individual tower energy deposition above 4 GeV in one HF calorimeter, are observed. These events are defined as LRG events, i.e., events with "zero" energy depositions, and are discussed in detail in Section 6.

Soft pileup events and HF energy distributions
The observed mean energy values in the HF increased by about 10 ± 5 GeV from period I to period II and by about 15 ± 5 GeV from period II to period III (cf. Table 2), both in W → eν and W → µν events. This increase of HF energy depositions is interpreted as arising from soft pileup events, not identified by the vertex finder. A similar increase of the mean energy deposition in HF is also seen in the MC simulations, when events with and without pileup are compared.
The properties of such soft pileup events have been studied with the zero-bias data samples, where the only requirement was that of colliding beams in the detector, taken during the different running periods. In events from this sample with zero reconstructed vertices, three classes of events can be identified: (1) events with no energy deposition in either HF (hereafter referred to as quasi-elastic pp-scattering), (2) events with zero energy in only one of the HF calorimeters and non-zero energy in the other (soft scattering with a LRG signature), and (3) events with non-zero energy depositions in both HF calorimeters (soft inelastic pp-scattering).
The contributions of beam-gas events and other beam-related backgrounds to the HF energy dispositions were studied in randomly triggered events with non-colliding beams and were found to be negligible.
The relative fraction of quasi-elastic pp-scattering event candidates in the zero-bias samples decreases from about 50% in period I to 20% in period III, while the fraction of soft inelastic events increases from about 15% in period I to 40% in period III. The fraction of soft events with a LRG signature of about 40% is roughly constant across the three luminosity periods.
In conclusion, soft pileup events, not identified by the single-vertex requirement, can have an important effect on the HF energy distributions and on LRG events in particular. As discussed below, their contribution is well modeled by the MC simulations.

Correlations of the forward energy flow and the central charged-particle multiplicity
In the following, the correlation between the central charged-particle multiplicity and the forward energy flow is measured in the data and compared to MC models. For this study, events with energy depositions in the HF− calorimeter of 20-100 GeV (low), 200-400 GeV (medium), and above 500 GeV (high) are selected. The central charged-particle multiplicity distributions with track p T thresholds of 1 GeV (for W → eν events) and 0.5 GeV (for W → µν events) are shown in Fig. 3, while the HF+ energy distributions for the three HF− energy intervals are shown in Fig. 4 (for W → eν and W → µν events).
The charged-particle multiplicity distributions for the medium HF− energy range (Figs. 3c and 3d) are described reasonably well by the PYTHIA6 D6T and Z2 tunes. The agreement between the data and the D6T tune is poorer when a 1 GeV track p T threshold is applied. For the low HF energy range (Figs. 3a and 3b), the D6T tune fails to describe the charged-particle multiplicity distribution, whereas the Z2 tune is in good agreement with the data, after applying a 0.5 GeV track p T threshold. Finally, when requiring a large HF energy deposition (Figs. 3e and 3f), the Z2 tune provides a good description, whereas the D6T tune overestimates the charged-particle multiplicity.
The HF+ distributions for the medium HF− energy interval (Figs. 4c and 4d) are in better agreement with the predictions of the various tunes than the inclusive HF distributions (Figs.  2c and 2d). On the other hand, when requiring a low HF− energy deposition, the HF+ energy distribution is poorly modeled by all MC tunes (Figs. 4a and 4b). Finally, for events with highenergy depositions in HF−, the PYTHIA6 generator, which in the inclusive case underestimates the rate of events with large HF− energy depositions, provides a good description of the energy distribution in HF+. Conversely, all other tunes predict more events with large HF+ energy than observed in the data (Figs. 4e and 4f). → W ± X → e ± νX, for tracks with p T > 1.0 GeV, and those in the right column for pp → W ± X → µ ± νX, for p T > 0.5 GeV (different scales are used for the x-axes).

Interpretation of the observed HF energy and charged-particle multiplicity correlations
As seen in the previous section, the energy distributions in the two HF calorimeters and the central charged-particle multiplicities are strongly correlated: large energy depositions in one of the HF calorimeters correspond to large energy depositions in the other HF calorimeter, as well as to an increase in the central charged-particle multiplicity. Such correlations are also predicted by the various MC tunes, though with very different strengths. Our observations can be summarized as follows: D6T tune: The inclusive distribution of charged-particle multiplicities, with a minimum p T of 0.5 GeV, is reasonably well described, whereas raising this threshold to 1 GeV leads to an overestimation of the event rate with large multiplicities. Furthermore, on average much-larger HF energy depositions are predicted than observed. When selecting events with small energy depositions in the HF, the fraction of events in the data is 30-50% larger than predicted by the D6T tune. In terms of correlations, the D6T tune provides a reasonable description only for the charged-particle multiplicity in the medium HF− energy interval (track p T threshold of 0.5 GeV) and for HF+ energy distribution corresponding to the low HF− energy bin.

Z2 tune:
Overall, the Z2 tune provides a very good description of the inclusive chargedparticle multiplicities, but predicts too many events with very low charged-particle multiplicities. Concerning the HF energy distributions, too many events with low-energy depositions are predicted. The correlations between charged-particle multiplicity and HF− energy are well described. The HF+ energy distribution obtained for the low HF− energy interval is badly modeled, with the MC prediction much higher than the data at low energies. However, the correlations are well described for the higher HF− energy intervals.

Pro-Q20 tune:
This tune provides the best description of the HF energy distributions and the charged-particle multiplicities with the p T > 0.5 GeV threshold. However, the inclusive charged-particle multiplicity for the p T > 1.0 GeV threshold is not well described, though still closer to the data than the D6T tune. In terms of correlations, the central charged-particle multiplicities are reasonably well described, though the fraction of events with large multiplicity and a large HF− energy deposition is underestimated. Furthermore, too many events with low-energy depositions in HF+ are predicted when a low-energy deposition in HF− is selected. For the other HF− energy bins this tune provides a good description of the data.

PYTHIA6 2C tune:
In the inclusive case, this tune predicts too many events with low HF energy depositions, whereas the central charged-particle multiplicity distributions are well described. The HF+ energy distributions for the cases of low and medium HF− energy intervals are shifted towards lower values compared to data, whereas for the high-energy bin good agreement is found.
In summary, none of the analyzed MC tunes provides an overall consistent and reasonable description of the inclusive charged-particle multiplicities and the HF energy distributions in the W data sample, as well as correlations between them. It follows that the tunes, which provide a reasonable description of the underlying event structure for central rapidities in jet events, as presented in [1], require substantial modifications to describe the W data presented here. Similar, though statistically less significant results were obtained from the corresponding Z event samples.
As the next step, the subset of W and Z events with a single primary vertex and a LRG signature was analyzed.
A LRG event was defined by the requirement that none of the calorimeter towers had a measured energy of more than 4 GeV in at least one of the HF calorimeters, corresponding to a pseudorapidity interval of 1.9 units. This subset of events may be enhanced by a diffractive W/Z production mechanism. Table 3 shows the observed LRG event yields and their ratio to the number of inclusive W and Z single-vertex events for the three luminosity periods. This ratio decreases by roughly a factor of 2 to 4 when going from period I to period III. The decrease can be explained by the HF energy depositions coming from soft pileup events. As discussed in Section 5.1 (cf. Fig. 2c), adding pileup to the Monte Carlo simulation shifts some of the LRG events to the class of low-energy depositions in the HF.

Observed number of LRG events
The inefficiency to detect a vertex in an event with forward energy deposition depends on the instantaneous luminosity and is estimated from zero-bias events (Section 5.1). After correcting the observed number of LRG events in the data for pileup effects, using data, a constant fraction of LRG events, relative to the total number of W and Z events with a single primary vertex, is found for the three instantaneous luminosity periods. The corrected fraction of LRG events is given in Table 4. The uncertainties on this correction are small compared to the statistical errors and to the ±10% energy scale uncertainties of the HF calorimeters (for details see [27]). Indeed, this energy scale variation is the dominant systematic uncertainty for the estimated fraction of LRG events in the data, resulting in a change of about ±26% when varying the tower energy threshold between 3.6 and 4.4 GeV.  Combining the results obtained with electrons and muons, the percentage of W and Z events with LRG signature is (1.46 ± 0.09 (stat.) ± 0.38 (syst.))% and (1.57 ± 0.25 (stat.) ± 0.42 (syst.))%, respectively. In comparison, as can be seen from Figs. 2 and 5, the fraction of W LRG events predicted with the PYTHIA6 Z2 and Pro-Q20 and the PYTHIA6 2C tunes are larger than observed in the data. In contrast, for the D6T tune the number of LRG events is smaller than in the data.

Jet activity in W/Z events with a LRG signature and search for exclusive W/Z production
A further subset of W and Z events are those that show some jet activity, using the particle-flow algorithm with a cone size of 0.5. We find (11.1 ± 0.2)% of the selected W and Z events with a single vertex contain at least one reconstructed jet with a transverse momentum above 30 GeV and |η| < 2.5. Taking the subsample of 100 identified W → eν events with a LRG signature, 8 events are found with one or more jets above a 30 GeV threshold. The corresponding numbers for the muon channel are 145 identified LRG events and 8 of them with at least one jet. Thus, we find that (6.5±1.6)% of the LRG events have jet activity, which is smaller (but still consistent) with the fraction of events with jets observed in the inclusive W sample. No other particular features of the events with jet activities, when compared to the MC simulations, are observed.
Another potentially interesting class of LRG events consists of W and Z events with essentially no activity besides that from the vector-boson decays. Such candidate exclusive events are selected with the requirement that both HF calorimeters fulfill the LRG condition and that no particle-flow object besides the lepton(s) is reconstructed in the central detector, above a transverse momentum threshold of 0.5 GeV. For the electron selection no such events are found.
In the muon case, 2 W and 2 Z event candidates with zero energy in both HF calorimeters are found. All four events have some reconstructed tracks in the central detector. The number of observed events is consistent with expected number of non-exclusive W and Z events predicted from the MC simulations.

Size of the pseudorapidity gap and central gaps
For the study of events with large pseudorapidity gaps an interesting parameter is how far the size of the gap extends into the central detector. One might intuitively expect that the signal for diffractive events, compared to the effects from multiplicity fluctuations, would become stronger when the the gap size increases into the central detector. This intuitive view is confirmed when comparing diffractive W events simulated with POMPYT, where the decrease in event yields with increasing gap size is much smaller than in the different non-diffractive MC models.
Obviously, the definition of the gap is ambiguous, as the meaning of zero activity or zero energy depositions depends on the experimental criteria for the detection of particles in the data and in the MC simulation. For this study the size of the pseudorapidity gap was determined by using particle-flow objects with a minimum energy of 1.5 GeV for |η| < 1.5 (barrel), 2 GeV for 1.5 < |η| < 2.85 (endcaps), and 4 GeV for |η| > 2.85 (HF calorimeters). For charged particle-flow candidates a minimum transverse momentum of 0.5 GeV was required. The largest (η max ) and smallest (η min ) observed pseudorapidity values of the particles are used to determine the gap size between the maximum (minimum) η coverage of the experiment and the nearest detected particle on each side. In order to combine both hemispheres, we defineη as the minimum of η max and −η min . The size of the pseudorapidity gap is then ∆η 4.9 gap = 4.9 −η, where 4.9 is the largest η value covered by the HF .   Figures 6a and 6b show theη distribution in the data and MC simulation with different tunes, for the W decays to electrons and muons, respectively. The fraction of events with pseudorapidity gaps decreases rapidly when the gap size increases. A statistically significant excess of events atη values smaller than 3 is observed, compared to the predictions of the non-diffractive model implemented in PYTHIA6, tune D6T. However, the fraction of events with very large gaps and without a diffractive component in the PYTHIA6 Z2, Pro-Q20, and PYTHIA6 2C tunes and up to the largest observed gap size is larger than in the data.
The stability of theη distribution was tested by allowing a ±10% variation of the particle-flow candidate energy and momentum thresholds in the data. The resulting variations were found to be similar to the statistical uncertainties.
Ifη < 0, all the reconstructed particle-flow objects in the event are contained in one hemisphere. Combining the W events with LRG signature in both lepton channels, 4 events with one "empty" detector hemisphere, corresponding to a gap of at least ∆η 4.9 gap = 4.9 units in pseudorapidity, are observed. In comparison, 0.8, 3.5, and 2.2 such events are expected from the non-diffractive MC simulation based on the PYTHIA6 D6T, Z2, and Pro-Q20 tunes, respectively.
As discussed in Sections 4 and 5, soft pileup events without a detectable second vertex remain in the sample. However, since these events do not produce significant particle-flow in the central pseudorapidity regions, the effect on events with pseudorapidity gaps in the more central region, |η| < 2.85, is expected to be small. The number of pseudorapidity gap events in this detector region, when ignoring the information in the HF detectors, should mainly depend on the amount of very low multi-parton activity and thus on the number of low-multiplicity events. Theη distributions using only particle-flow objects with |η| < 2.85 and ignoring the information in the HF are shown for W events in Figs. 6c and 6d. Accordingly, the gap size is now defined as ∆η 2.85 gap = 2.85 −η. Again, when compared to the MC simulation with the D6T tune, the data show a large excess of events withη below 1, corresponding to a central pseudorapidity gap of ∆η 2.85 gap ≥ 1.85. The fraction of such gap events in the data is reasonably well described by the PYTHIA6 Z2 and Pro-Q20 tunes, and much larger fractions are predicted by the PYTHIA6 2C tune.
The limited number of LRG events, as well as the large uncertainties related to the modeling of the underlying event and multi-parton interactions, prevent any conclusions from being drawn on the possible presence of a diffractive W/Z-production component from the observed rate of events with a pseudorapidity gap in the central detector.

Charged-particle multiplicity and forward energy distributions in LRG events
The charged-particle multiplicity distribution in LRG events, from combining the W events in the electron and muon channels, is shown in Fig. 7a for a minimum track p T of 0.5 GeV. A slight excess of events with large charged-particle multiplicities is found in the data, compared to the various MC tunes. However, overall the track p T spectrum is well described. The number of LRG events with 20 and more tracks, combining the electron and muon channels, is 33 in the data. Only 13 (19) events with more than 20 tracks are expected from the D6T (Z2) tunes. A similar, but statistically less significant, excess of events with multiplicities larger than predicted by the different tunes is also observed when a track threshold of p T > 1.0 GeV is required. The POMPYT diffractive model, which does not include multi-parton interactions, predicts even smaller charged-particle multiplicities. However, the observed excess of events with relatively large charged-particle multiplicities in LRG events could be an indication of a diffractive component in the multi-parton interactions, as depicted in Figs. 1c and 1f.
The corresponding distribution for the energy sum in the HF calorimeter opposite to the gap is shown in Fig. 7b. The average total energy of 150 GeV with an r.m.s. of 160 GeV is about  a factor of two smaller than the one observed for the inclusive HF energy distribution, and is reasonably well described by the various MC tunes. In the data, we find 2 events with no towers above the energy threshold of 4 GeV in either HF calorimeters, in agreement with the expectation from the D6T tune. This number is slightly lower, but still consistent, with the expections from the Z2 and the PYTHIA6 2C tunes. The Pro-Q20 tune predicts 8 such events.   Figure 7: (a) Charged-particle multiplicity and (b) HF energy distributions (opposite to the gap) in pp → W ± X → ± νX events with a LRG signature, for the data and different MC tunes. The charged-particle multiplicity distribution is obtained for a track p T threshold of 0.5 GeV. Figure 8 shows the distribution of the signed charged lepton pseudorapidity η in W events with a LRG signature (electron and muon channels combined). The sign is defined to be positive when the gap and the lepton are in the same hemisphere and negative otherwise. The data show that charged leptons from W decays are found more often in the hemisphere opposite to the gap. Combining the electron and muon channels, 147 events are found with the charged lepton in the hemisphere opposite to the gap and 96 events with the lepton in the same hemisphere. Defining an asymmetry as the ratio of the difference between the numbers of LRG events in each hemisphere and the sum, the corresponding asymmetry is (-21.0 ± 6.4)%. In the case of Z candidates (the rapidity of the Z is used) with a LRG signature, 24 (16) events are in the opposite (same) hemisphere as the gap, resulting in an asymmetry of (-20 ± 16)%.

Hemisphere correlations between the gap and the W (Z) boson
In comparison, the various non-diffractive MC tunes predict a symmetric lepton pseudorapidity distribution in LRG events. On the other hand, events generated with the POMPYT generator, based on a diffractive production model, exhibit a strong asymmetry. This can be explained in terms of diffractive PDFs, which peak at smaller x (the parton momentum divided by the proton momentum) than the conventional proton PDFs. The produced W(Z) is thus boosted in the direction of the parton that had the larger x. This is typically the direction of the dissociated proton, i.e., opposite to the gap. The signed lepton pseudorapidity distribution in the data is fit to the predictions from the diffractive POMPYT and the non-diffractive PYTHIA event generators, with the relative fraction of the two as the free parameter. The fit results in a fraction of diffractive events in the LRG sample of (50.0 ± 9.3 (stat.) ± 5.2 (syst.))%, assuming the model of diffraction implemented in POMPYT and using the PYTHIA6 Pro-Q20 for the simulation of non-diffractive events. The fit results are shown in Fig. 8. The fits using the combination of POMPYT with other tunes give similar results, and only the non-diffractive contribution from the other tunes is shown in Fig. 8. The systematic uncertainty of 5.2% has been determined from the 10% HF energy scale variations and from the fits with the different tunes, using the maximal and minimal fractions obtained from the different fits.

Data
10% ± HF Energy Scale PYTHIA 6 D6T PYTHIA 6 Z2 PYTHIA 6 ProQ20 PYTHIA 8 2C PYTHIA 6 ProQ20 + POMPYT CMS Figure 8: Signed lepton pseudorapidity distribution in W events with a LRG signature, with the sign defined by the pseudorapidity of the lepton relative to the gap (positive for the lepton and gap in the same hemisphere, negative otherwise). Electron and muon channels are combined. The fit result for the combination of PYTHIA6 (Pro-Q20 tune) and POMPYT predictions is shown as a dotted black line. For the other PYTHIA tunes, only the non-diffractive component is shown.
The asymmetry in the signed η distribution for non-LRG events decreases when the forward energy deposition increases. For example, for HF energy depositions in the intervals 20-100 GeV, 200-400 GeV, and > 500 GeV, the asymmetry is (-3.5 ± 1.1)%, (-2.7 ± 1.0)%, and (0.9 ± 2.3)%. The small residual asymmetry in events with low HF energy depositions is in-significant in comparison to the one in LRG events. However, this could be explained by the presence of a small fraction of diffractively produced W bosons events in which the LRG signature is destroyed by the accompany multi-parton interaction or by the undetected pileup component. For higher energy depositions in the forward region, the asymmetry vanishes.

Conclusions
Central charged-particle multiplicities, forward energy flow, and correlations between them have been studied in W and Z events, identified by the vector-boson decays to electrons and muons, using the 2010 data sample of pp collisions at 7 TeV, corresponding to an integrated luminosity of 36 pb −1 .
None of the studied MC tunes provides simultaneously a satisfactory description of the chargedparticle multiplicity in the central pseudorapidity region (|η| < 2.5) and the forward energy flow (3 < |η| < 4.9). The PYTHIA6 Z2 and PYTHIA6 2C tunes give a reasonable description of the central charged-particle multiplicity, but predict too many events with relatively lowenergy depositions in the forward calorimeters. The PYTHIA6 D6T tune predicts too many events with high charged-particle multiplicities, too few events with low-energy depositions, and too many events with very large energy depositions in the forward calorimeters. The Pro-Q20 tune provides the best description of the forward energy distribution and a good description of the charged-particle multiplicity, when a track p T threshold of 0.5 GeV is applied. However, the charged-particle multiplicity with p T > 1.0 GeV is not well described, though the prediction is closer to the data than that for the D6T tune.
Strong positive correlations between the energy measured in the two forward calorimeters (i.e. at positive and negative rapidities) and the charged-particle multiplicity are observed in the data and in Monte Carlo models. However, the correlations in the various MC tunes are different from those seen in the data.
As far as the LRG events are concerned, the following observations can be made: • Out of a sample of about 40 000 W and Z events, almost 300 events with a LRG signature are found. According to the POMPYT model of diffractive W production, such events can be interpreted as diffractive. However, while the observed fraction of such events is significantly larger than predicted with the non-diffractive PYTHIA6 D6T tune, it is smaller than expected from the PYTHIA6 Z2, Pro-Q20, and PYTHIA6 2C tunes. Thus, no conclusions can be drawn from the presence of LRG events.
• The central charged-particle multiplicity in these events is somewhat larger than predicted by the various models.
• The HF energy distribution opposite to the gap peaks at much smaller values than in the inclusive events, and is reasonably well described by the MC generators.
• A large asymmetry is observed between the number of events with the charged lepton (from the W decay) in the opposite and with it in the same hemisphere as the pseudorapidity gap. Such an asymmetry is predicted by POMPYT, in contrast to the various non-diffractive PYTHIA MC tunes. When fitting the observed asymmetry in LRG events with an admixture of diffractive (POMPYT) and non-diffractive (PYTHIA) events, the diffractive component is determined to be (50.0 ± 9.3 (stat.) ± 5.2 (syst.))%, thus providing the first evidence for diffractive W production at the LHC. A comparable, but statistically less significant asymmetry is seen in Z events with large pseudorapidity gaps.
INFN Sezione di Pisa a , Università di Pisa b , Scuola Normale Superiore di Pisa c , Pisa, Italy