Measurements of longitudinal and transverse momentum distributions for neutral pions in the forward-rapidity region with the LHCf detector

The differential cross sections for inclusive neutral pions as a function of transverse and longitudinal momentum in the very forward-rapidity region have been measured at the LHC with the LHC forward detector in proton-proton collisions at $\sqrt{s}=2.76$ and 7 TeV and in proton-lead collisions at nucleon-nucleon center-of-mass energies of $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$. Such differential cross sections in proton-proton collisions are compatible with the hypotheses of limiting fragmentation and Feynman scaling. Comparing proton-proton with proton-lead collisions, we find a sizable suppression of the production of neutral pions in the differential cross sections after subtraction of ultraperipheral proton-lead collisions. This suppression corresponds to the nuclear modification factor value of about 0.1–0.3. The experimental measurements presented in this paper provide a benchmark for the hadronic interaction Monte Carlo simulation codes that are used for the simulation of cosmic ray air showers.

Figure 1

Observation of ${\pi }^0$ decay by a LHCf detector. Left: Type-I ${\pi }^0$ event having one photon entering each calorimeter. Right: Type-II ${\pi }^0$ event having two photons entering one calorimeter, here entering the small calorimeter.

Figure 2

Reconstructed invariant mass distributions in $p+p$ collisions at $\sqrt{s}=7\mathrm{TeV}$. Left: Type-II ${\pi }^0$ events in the Arm2 small calorimeter. Right: Type-II ${\pi }^0$ events in the Arm2 large calorimeter. The solid curves show the best-fit composite physics model to the invariant mass distributions.

Figure 3

Diagrams of all multihit events that are rejected. Panels (a) and (b) show the multihit Type-I ${\pi }^0$ events, and panels (c) and (d) show the multihit Type-II ${\pi }^0$ events. Red and green arrows indicate a background particle not originating in a ${\pi }^0$ decay and two photons originating in a ${\pi }^0$ decay, respectively.

Figure 4

The acceptance map of ${\pi }^0$ detection by the LHCf detectors in $p_{\mathrm{z}}–p_{\mathrm{T}}$ phase space: Arm1 Type I (left top), Arm1 Type II (right top), Arm2 Type I (left bottom), and Arm2 Type II (right bottom). The fiducial area cuts and energy threshold ($E_{\text{photon}}>100\mathrm{GeV}$) are taken into account. Dashed curves indicate lines of constant rapidity ${\pi }^0\mathrm{s}$, $y=8.8$, 9.0, and 10.0 reading from top to bottom.

Figure 5

LHCf $p_{\mathrm{T}}$ distributions (filled circles) in $p+p$ collisions at $\sqrt{s}=7\mathrm{TeV}$. Error bars indicate the total statistical and systematic uncertainties. The predictions of hadronic interaction models are shown for comparison: dpmjet (solid red line), qgsjet (dashed blue line), sibyll (dotted green line), epos (dashed-dotted magenta line), and pythia (dashed-double-dotted brown line).

Figure 6

Ratios of LHCf $p_{\mathrm{T}}$ distributions to the $p_{\mathrm{T}}$ distributions predicted by hadronic interaction models in $p+p$ collisions at $\sqrt{s}=7\mathrm{TeV}$ are shown by solid red line (dpmjet), dashed blue line (qgsjet), dotted green line (sibyll), dashed-dotted magenta line (epos), and dashed-double-dotted brown line (pythia). Shaded areas indicate the range of total uncertainties of the LHCf $p_{\mathrm{T}}$ distributions.

Figure 7

LHCf $p_{\mathrm{z}}$ distributions (filled circles) in $p+p$ collisions at $\sqrt{s}=7\mathrm{TeV}$. Error bars indicate the total statistical and systematic uncertainties. The predictions of hadronic interaction models are shown for comparison: dpmjet (solid red line), qgsjet (dashed blue line), sibyll (dotted green line), epos (dashed-dotted magenta line), and pythia (dashed-double-dotted brown line).

Figure 8

Ratios of LHCf $p_{\mathrm{z}}$ distributions to the $p_{\mathrm{z}}$ distributions predicted by hadronic interaction models in $p+p$ collisions at $\sqrt{s}=7\mathrm{TeV}$ are shown by solid red line (dpmjet), dashed blue line (qgsjet), dotted green line (sibyll), dashed-dotted magenta line (epos), and dashed-double-dotted brown line (pythia). Shaded areas indicate the range of total uncertainties of the LHCf $p_{\mathrm{z}}$ distributions.

Figure 9

LHCf $p_{\mathrm{T}}$ distributions (filled circles) in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$. Error bars indicate the total statistical and systematic uncertainties. The predictions of hadronic interaction models are shown for comparison: dpmjet (solid red line), qgsjet (dashed blue line), sibyll (dotted green line), epos (dashed-dotted magenta line), and pythia (dashed-double-dotted brown line).

Figure 10

Ratios of LHCf $p_{\mathrm{T}}$ distributions to the $p_{\mathrm{T}}$ distributions predicted by hadronic interaction models in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ are shown by solid red line (dpmjet), dashed blue line (qgsjet), dotted green line (sibyll), dashed-dotted magenta line (epos), and dashed-double-dotted brown line (pythia). Shaded areas indicate the range of total uncertainties of the $p_{\mathrm{T}}$ spectra.

Figure 11

LHCf $p_{\mathrm{z}}$ distributions (filled circles) in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$. Error bars indicate the total statistical and systematic uncertainties. The predictions of hadronic interaction models are shown for comparison: dpmjet (solid red line), qgsjet (dashed blue line), sibyll (dotted green line), epos (dashed-dotted magenta line), and pythia (dashed-double-dotted brown line).

Figure 12

Ratios of LHCf $p_{\mathrm{z}}$ distributions to the $p_{\mathrm{z}}$ distributions predicted by hadronic interaction models in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ are shown by solid red line (dpmjet), dashed blue line (qgsjet), dotted green line (sibyll), dashed-dotted magenta line (epos), and dashed-double-dotted brown line (pythia). Shaded areas indicate the range of total uncertainties of the $p_{\mathrm{z}}$ distributions.

Figure 13

LHCf $p_{\mathrm{T}}$ distributions (filled circles) in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$. Error bars indicate the total statistical and systematic uncertainties. The predictions of hadronic interaction models are shown for comparison: dpmjet (solid red line), qgsjet (dashed blue line), and epos (dashed-dotted magenta line).

Figure 14

Ratios of LHCf $p_{\mathrm{T}}$ distributions to the $p_{\mathrm{T}}$ distributions predicted by hadronic interaction models in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ are shown by solid red line (dpmjet), dashed blue line (qgsjet), and dashed-dotted magenta line (epos). Shaded areas indicate the range of total uncertainties of the $p_{\mathrm{T}}$ distributions.

Figure 15

LHCf $p_{\mathrm{z}}$ distributions (filled circles) in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$. Error bars indicate the total statistical and systematic uncertainties. The predictions of hadronic interaction models are shown for comparison: dpmjet (solid red line), qgsjet (dashed blue line), and epos (dashed-dotted magenta line).

Figure 16

Ratios of LHCf $p_{\mathrm{z}}$ distributions to the $p_{\mathrm{z}}$ distributions predicted by hadronic interaction models in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ are shown by solid red line (dpmjet), dashed blue line (qgsjet), and dashed-dotted magenta line (epos). Shaded areas indicate the range of total uncertainties of the $p_{\mathrm{T}}$ distributions.

Figure 17

LHCf $p_{\mathrm{T}}$ distributions (filled black circles), the best-fit Gaussian distributions (dotted red curve), and the best-fit Hagedorn functions (dashed blue curve). Left: the data for $p+p$ collisions at $\sqrt{s}=7\mathrm{TeV}$. Right: the data for $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$.

Figure 18

Average $p_{\mathrm{T}}$ as a function of rapidity loss $\mathrm{\Delta }y=y_{\mathrm{beam}}-y$. Open red circles and filled black circles indicate LHCf data in $p+p$ collisions at $\sqrt{s}=2.76$ and 7 TeV, respectively. The results of the UA7 experiment (open magenta box) at $\mathrm{Sp}\overline{\mathrm{p}}\mathrm{S}$ ($p+\overline{p}$ collisions at $\sqrt{s}=630\mathrm{GeV}$) and the predictions from dpmjet (thick lines) and qgsjet (thin lines) are added for reference.

Figure 19

The ${\pi }^0$ yield in each rapidity interval as a function of rapidity loss $\mathrm{\Delta }y=y_{\mathrm{beam}}-y$. Open red circles and filled black circles indicate LHCf data in $p+p$ collisions at $\sqrt{s}=2.76$ and 7 TeV, respectively. The results of the UA7 experiment (open magenta squares) at $\mathrm{Sp}\overline{\mathrm{p}}\mathrm{S}$ ($p+\overline{p}$ collisions at $\sqrt{s}=630\mathrm{GeV}$) and the predictions by dpmjet (thick red line) and qgsjet (thin blue line) are added for reference.

Figure 20

The ${\pi }^0$ yield at $0.0<p_{\mathrm{T}}<0.4\mathrm{GeV}$ as a function of $x_F$. Open red circles and filled black circles indicate LHCf data in $p+p$ collisions at $\sqrt{s}=2.76$ and 7 TeV, respectively.

Figure 21

The ${\pi }^0$ yield in each $p_{\mathrm{T}}$ range as a function of $x_F$. Left: the distributions for $0.0<p_{\mathrm{T}}<0.2\mathrm{GeV}$. Right: the distributions for $0.2<p_{\mathrm{T}}<0.4\mathrm{GeV}$. Open red circles and filled black circles indicate LHCf data in $p+p$ collisions at $\sqrt{s}=2.76$ and 7 TeV, respectively.

Figure 22

The best-fit leading exponent of (1-$x_F$) as a function of $p_{\mathrm{T}}$. Open red circles and filled black circles indicate LHCf data in $p+p$ collisions at $\sqrt{s}=2.76$ and 7 TeV, respectively. Filled blue triangles indicate LHCf data in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$.

Figure 23

The nuclear modification factor for ${\pi }^0\mathrm{s}$. Filled circles indicate the factors obtained from LHCf data. Error bars indicate the total uncertainties incorporating both statistical and systematic uncertainties. Other lines are the predictions from hadronic interaction models: dpmjet (solid red line), qgsjet (dashed blue line), and epos (dashed-dotted magenta line).