Observation of exclusive dijet production at the Fermilab Tevatron $\overline{p}p$ collider

We present the first observation and cross section measurement of exclusive dijet production in $\overline{p}p$ interactions, $\overline{p}p\to \overline{p}+\mathrm{dijet}+p$. Using a data sample of $310{\mathrm{pb}}^{-1}$ collected by the Run II Collider Detector at Fermilab at $\sqrt{s}=1.96\mathrm{TeV}$, exclusive cross sections for events with two jets of transverse energy $E_T^{\mathrm{jet}}\ge 10\mathrm{GeV}$ have been measured as a function of minimum $E_T^{\mathrm{jet}}$. The exclusive signal is extracted from fits to data distributions based on Monte Carlo simulations of expected dijet signal and background shapes. The simulated background distribution shapes are checked in a study of a largely independent data sample of $200{\mathrm{pb}}^{-1}$ of $b$-tagged jet events, where exclusive dijet production is expected to be suppressed by the $J_z=0$ total angular momentum selection rule. Results obtained are compared with theoretical expectations, and implications for exclusive Higgs boson production at the $pp$ Large Hadron Collider at $\sqrt{s}=14\mathrm{TeV}$ are discussed.

Figure 1

Illustration of event topologies in pseudorapidity, $\eta$, and associated Pomeron exchange diagrams for dijet production in (a) single diffraction and (b) double Pomeron exchange. The shaded areas on the left side represent “underlying event” particles not associated with the jets (from Ref. [2]).

Figure 2

Leading order diagrams for (a) exclusive dijet and (b) exclusive Higgs boson production in $\overline{p}p$ collisions.

Figure 3

Schematic drawing (not to scale) of the CDF II detector.

Figure 4

Schematic cross sectional view of one of the two forward MiniPlug calorimeters installed in CDF II.

Figure 5

(a) ${\xi }_{\overline{p}}^X$ distribution of DPE events passing the ${\mathrm{LRG}}_p$ requirement (solid histogram), with the shaded area representing events in the region $0.01<{\xi }_{\overline{p}}^X<0.12$; the dashed histogram shows the ${\xi }_{\overline{p}}^X$ distribution for ND events passing the same ${\mathrm{LRG}}_p$ requirement and normalized to the solid histogram in the plateau region of $0.22<{\xi }_{\overline{p}}^X<0.50$; (b) MPCAL hit multiplicity, ${\mathrm{N}}_{\mathrm{MP}}^p$, vs ${\mathrm{BSC}1}_p$ hit counter multiplicity, ${\mathrm{N}}_{\mathrm{BSC}1}^p$, in SD events with $0.01<{\xi }_{\overline{p}}^X<0.12$.

Figure 6

(a) Mean $E_T$, (b) mean $\eta$ of the two leading jets, and (c) azimuthal angle difference between the two leading jets of $E_T>10\mathrm{GeV}$ in IDPE (circles), SD (solid histograms), and ND (dashed histograms) dijet events.

Figure 7

(a) Sum of the BSC1 hit counter multiplicity and MPCAL hit multiplicity, ${\mathrm{N}}_{\mathrm{BSC}1}^p+{\mathrm{N}}_{\mathrm{MP}}^p$, versus CLC hit multiplicity, ${\mathrm{N}}_{\mathrm{CLC}}^p$, in SD events with dijets of $E_T^{\mathrm{jet}1,2}>10\mathrm{GeV}$ and $0.01<{\xi }_{\overline{p}}^X<0.12$; (b) multiplicity distribution along the diagonal line in the left plot, ${\mathrm{N}}_{\mathrm{diag}}$, defined by ${\mathrm{N}}_{\mathrm{BSC}1}^p+{\mathrm{N}}_{\mathrm{MP}}^p={\mathrm{N}}_{\mathrm{CLC}}^p$, with the solid line representing a linear fit in the region $2\le {\mathrm{N}}_{\mathrm{diag}}\le 9$, and the dashed line the extrapolation of the fit to the ${\mathrm{N}}_{\mathrm{diag}}=0$ bin.

Figure 8

(a) Mean transverse energy $E_T^{*}$ and (b) mean pseudorapidity ${\eta }^{*}$ of the two highest $E_T$ jets in IDPE data (points) and pomwig MC events (thick solid histograms) composed of pomwig DPE signal (thin solid histograms) and the sum of SD and ND background events (dashed histograms). The data and $\mathrm{POMWIG}+\mathrm{\text{background}}$ distributions are normalized to unit area. The pomwig generated distributions in the plots (a) and (b) correspond to the four different diffractive/Pomeron structure functions used: $\mathrm{CDF}\oplus \mathrm{H}1$, CDF, H1-fit2, and ZEUS-LPS.

Figure 9

(a) Dijet mass $M_{jj}$ and (b) central hadronic system mass, $M_X$ in IDPE data (points) and pomwig MC events (thick solid histograms) composed of pomwig generated DPE dijet events (thin solid histograms) and the sum of SD and ND generated background events (dashed histograms). The data and $\mathrm{POMWIG}+\mathrm{\text{background}}$ distributions are normalized to unit area. The pomwig DPE distributions in each set of four plots correspond to the four different diffractive/Pomeron structure functions used: $\mathrm{CDF}\oplus \mathrm{H}1$, CDF, H1-fit2, and ZEUS-LPS.

Figure 10

Dijet mass fraction, $R_{jj}$, in IDPE data (points) and pomwig MC events (upper histograms), composed of pomwig DPE signal and the sum of SD and ND background events (lower dashed histogram) normalized to the background fraction in the data. The upper four histograms correspond to the four different diffractive/Pomeron structure functions used in pomwig: $\mathrm{CDF}\oplus \mathrm{H}1$ (solid), CDF (dashed), H1-fit2 (dotted), and ZEUS-LPS (dot-dashed histogram). These four histograms and the data distribution are normalized to unit area.

Figure 11

Second jet $\eta$ vs leading jet $\eta$ for events with two jets of $E_T^{\mathrm{jet}1,jet2}>10\mathrm{GeV}$ satisfying all IDPE requirements plus the additional requirements of $LR{G}_{\overline{p}}$ and $E_T^{\mathrm{jet}3}<5\mathrm{GeV}$ (third jet veto): (a) data, (b) pomwig generated events, (c) exclusive ExclDPE generated events, and (d) exclusive ExHuME generated events. The solid lines represent the ${\eta }^{\mathrm{jet}}$-cuts of ${\eta }^{\mathrm{jet}1}$ and/or ${\eta }^{\mathrm{jet}2}$ $<-0.5$ used to divide the ${\eta }^{\mathrm{jet}1}$-${\eta }^{\mathrm{jet}2}$ space into the exclusive signal-enriched region A and the nonexclusive dominated region B.

Figure 12

Comparison of IDPE data distributions of (a) $E_T^{*}$, (b) $M_{jj}$, (c) ${\eta }^{*}$, and (d) $M_X$ for the background-rich region B with corresponding pomwig distributions obtained using the $\mathrm{CDF}\oplus \mathrm{H}1\mathrm{DSF}$; the events plotted are those used in plots (a) and (b) of Fig. 11.

Figure 13

(a) Mean $E_T^{\mathrm{jet}}$ of the two leading jets, $E_T^{*}$, (b) mean ${\eta }^{\mathrm{jet}}$, ${\eta }^{*}$, and (c) dijet mass fraction, $R_{jj}$ for pomwig DPE dijet events generated using the $\mathrm{CDF}\oplus \mathrm{H}1\mathrm{DSF}$ diffractive/Pomeron structure function (solid histograms), and for exclusive dijet events generated with the ExclDPE (dashed histograms) and ExHuME MC simulations (dotted histograms). All distributions are normalized to unit area.

Figure 14

Dijet mass fraction in IDPE data (points) and best fit (solid histograms) with a mixture of (i) pomwig generated events composed of pomwig DPE signal and SD plus ND background events (dashed histogram), and (ii) exclusive dijet MC events (shaded histogram). The data and the MC events are selected from the respective IDPE samples after applying the additional veto cuts of ${\mathrm{LRG}}_{\overline{p}}$ and $E_T^{\mathrm{jet}3}<5\mathrm{GeV}$. Plots (a) and (c) [(b) and (d)] present fits using ExHuME [ExclDPE] generated exclusive dijet events, while a requirement of $E_T^{\mathrm{jet}2}>10\mathrm{GeV}$ [25 GeV] is applied to plots (a) and (b) [(c) and (d)].

Figure 15

Dijet mass fraction for IDPE data (points) and for pomwig generated events (dashed histogram) composed of pomwig DPE plus SD and ND background events, and for ExHuME generated exclusive dijet events (shaded histograms). The solid histogram is the sum of $\mathrm{POMWIG}\oplus \mathrm{EXHUME}$ events. Plot (a) shows distributions for event sample B, and plot (b) for event sample A. The events plotted pass all other selection cuts. The MC events are normalized using the results of the fits shown in Fig. 14, scaled according to the actual number of events that pass the ${\eta }^{\mathrm{jet}}$-cut requirement.

Figure 16

Dijet mass fraction for IDPE data (points) and best fit (solid histogram) to the data obtained from a combination of pomwig events (dashed histogram) composed of pomwig DPE plus SD and ND background events, and exclusive dijet MC events (shaded histogram) generated using (a) ExclDPE or (b) ExHuME. The data and the MC events are from sample A and are required to pass all other selection cuts.

Figure 17

Comparison of mean pseudorapidity distributions ${\eta }^{*}$ between the IDPE data of sample A and the mixture of pomwig and (a) ExclDPE or (b) ExHuME simulated events normalized by the fit presented in Fig. 16.

Figure 18

The number of calorimeter towers per event with $E_T>100\mathrm{MeV}$ which are outside the jet cones versus tower detector $\eta$ for IDPE data (points) and pomwig MC events (thick line) composed of pomwig DPE signal (thin line) and the sum of SD and ND background events (dashed line) normalized to the background fraction per event.

Figure 19

Calorimeter tower multiplicity and tower $E_T$ distributions in the transverse region with respect to the leading jet axis ($60°<\Delta \varphi <120°$ or $240°<\Delta \varphi <300°$) for four $R_{jj}$ bins in the region of $0.5<R_{jj}<0.9$. The tower multiplicity and tower $E_T$ distributions are normalized to unit area and to the number of transverse towers per event, respectively.

Figure 20

Exclusive dijet cross sections for events with two jets of $E_T^{\mathrm{jet}}>10\mathrm{GeV}$ plotted vs the minimum $E_T^{\mathrm{jet}}$ of the two jets in the kinematic range denoted in the figures: (a) total exclusive cross sections compared with ExHuME and ExclDPE predictions; (b) exclusive cross sections for events with $R_{jj}>0.8$ compared with ExHuME (solid curve) and with the LO analytical calculation from Ref. [6] (see also Ref. [42]) scaled down by a factor of 3 (dashed lines)—the shaded area represents uncertainties in the calculation due to hadronization effects; and (c) the ratio of total exclusive to inclusive DPE cross sections.

Figure 21

Displaced secondary vertex mass distribution for jets tagged by the secvtx algorithm in DPE data (points). The solid histogram shows the result of a three-component binned maximum likelihood fit to the data, using Monte Carlo templates of distribution shapes, consisting of $b$-jets (shaded histogram), $c$-jets (dashed histogram), and other jets (dotted histogram) obtained from pythia dijet events.

Figure 22

(a) Measured ratio $F_{HF/\mathrm{incl}}$ of heavy flavor jets to all inclusive jets of $E_T^{\mathrm{jet}}>10\mathrm{GeV}$ and $|{\eta }^{\mathrm{jet}}|<1.5$ as a function of dijet mass fraction $R_{jj}$, normalized to the weighted average value in the region of $R_{jj}<0.4$, with systematic uncertainties represented by the shaded band; (b) values of $F_{\mathrm{excl}\leftarrow HF}=1-F_1$ (filled circles) and $F_{\mathrm{excl}\leftarrow MC}=1-F_2$ (open squares) as a function of $R_{jj}$, where $F_1=F_{HF/\mathrm{incl}}/<F_{HF/\mathrm{incl}}>{|}_{R_{jj}<0.4}$, plotted in (a) vs $R_{jj}$, and $F_2$ is the ratio of pomwig MC to inclusive dijet events obtained from the studies presented in Sec. 6—the error bars (shaded band) represent statistical ($F_{\mathrm{excl}\leftarrow HF}$ systematic) uncertainties.

Figure 23

ExHuME exclusive dijet differential cross section at the hadron level vs dijet mass $M_{jj}$. The filled points show cross sections derived from the measured ${\sigma }_{jj}^{\mathrm{excl}}$ values shown in Fig. 20 (top) using the procedure described in the text. The vertical error bars on the points and the shaded band represent statistical and systematic uncertainties, respectively, obtained by propagating the corresponding uncertainties to the measured values of ${\sigma }_{jj}^{\mathrm{excl}}$. The solid curve is the cross section predicted by ExHuME using the default settings.