Search for charged Higgs bosons produced in vector boson fusion processes and decaying into vector boson pairs in proton-proton collisions at $\sqrt{s} =$ 13 TeV

The CMS collaboration Sirunyan, Albert M ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
CMS-HIG-20-017, 2021.
Inspire Record 1857811 DOI 10.17182/hepdata.102461

A search for charged Higgs bosons produced in vector boson fusion processes and decaying into vector bosons, using proton-proton collisions at $\sqrt{s}=$ 13 TeV at the LHC, is reported. The data sample corresponds to an integrated luminosity of 137 fb$^{-1}$ collected with the CMS detector. Events are selected by requiring two or three electrons or muons, moderate missing transverse momentum, and two jets with a large rapidity separation and a large dijet mass. No excess of events with respect to the standard model background predictions is observed. Model independent upper limits at 95% confidence level are reported on the product of the cross section and branching fraction for vector boson fusion production of charged Higgs bosons as a function of mass, from 200 to 3000 GeV. The results are interpreted in the context of the Georgi-Machacek model.

8 data tables

Summary of the impact of the systematic uncertainties on the extracted signal strength; for the case of a background-only simulated data set, i.e., assuming no contributions from the $\mathrm{H}^{\pm}$ and $\mathrm{H}^{\pm\pm}$ processes, and including a charged Higgs boson signal for values of $s_{\mathrm{H}}=1.0$ and $m_{\mathrm{H}_{5}}=500$ GeV in the GM model.

Expected signal and background yields from various SM processes and observed data events in all regions used in the analysis. The expected background yields are shown with their normalizations from the simultaneous fit for the background-only hypothesis, i.e., assuming no contributions from the $\mathrm{H}^{\pm}$ and $\mathrm{H}^{\pm\pm}$ processes. The expected signal yields are shown for $s_{\mathrm{H}}=1.0$ in the GM model. The combination of the statistical and systematic uncertainties is shown.

Distributions for signal, backgrounds, and data for the bins used in the simultaneous fit. The bins 1--32 (4$\times$8) show the events in the WW SR ($m_{\mathrm{jj}} \times m_{\mathrm{T}}$), the bins 33--46 (2$\times$7) show the events in the WZ SR ($m_{\mathrm{jj}} \times m_{\mathrm{T}}$), the 4 bins 47--50 show the events in the nonprompt lepton CR ($m_{\mathrm{jj}}$), the 4 bins 51--54 show the events in the tZq CR ($m_{\mathrm{jj}}$), and the 4 bins 55--58 show the events in the ZZ CR ($m_{\mathrm{jj}}$). The predicted yields are shown with their best fit normalizations from the simultaneous fit for the background-only hypothesis, i.e., assuming no contributions from the $\mathrm{H}^{\pm}$ and $\mathrm{H}^{\pm\pm}$ processes. Vertical bars on data points represent the statistical uncertainty in the data. The histograms for tVx backgrounds include the contributions from ttV and tZq processes. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from tt, tW, $\mathrm{W}^{+}\mathrm{W}^{-}$, and Drell--Yan processes. The overflow is included in the last bin in each corresponding region. The lower panels show the ratio of the number of events observed in data to that of the total SM prediction. The hatched gray bands represent the uncertainties in the predicted yields. The solid lines show the signal predictions for values of $s_{\mathrm{H}}=1.0$ and $m_{\mathrm{H}_{5}}=500$ GeV in the GM model.

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Measurement of the production cross section of 31 GeV/$c$ protons on carbon via beam attenuation in a 90-cm-long target

The NA61/SHINE collaboration Acharya, A. ; Adhikary, H. ; Aduszkiewicz, A. ; et al.
Phys.Rev.D 103 (2021) 012006, 2021.
Inspire Record 1824424 DOI 10.17182/hepdata.100512

The production cross section of 30.92 GeV/$c$ protons on carbon is measured by the NA61/SHINE spectrometer at the CERN SPS by means of beam attenuation in a copy (replica) of the 90-cm-long target of the T2K neutrino oscillation experiment. The employed method for direct production cross-section estimation minimizes model corrections for elastic and quasi-elastic interactions. The obtained production cross section is $\sigma_\mathrm{prod}~=~227.6~\pm~0.8\mathrm{(stat)}~_{-~3.2}^{+~1.9}\mathrm{(sys)}~{-~0.8}\mathrm{(mod)}$ mb. It is in agreement with previous NA61/SHINE results obtained with a thin carbon target, while providing improved precision with a total fractional uncertainty of less than 2$\%$. This direct measurement is performed to reduce the uncertainty on the T2K neutrino flux prediction associated with the re-weighting of the interaction rate of neutrino-yielding hadrons.

2 data tables

Production cross section in p+C interactions at different incident beam momenta.

Production cross section in p+C interactions at different beam momenta. The total uncertainty is the statistical, systematic and model uncertainties added in quadrature.


Measurements of $\pi^-$ production in $^7$Be+$^9$Be collisions at beam momenta from 19$A$ to 150$A$GeV/$c$ in the NA61/SHINE experiment at the CERN SPS

The NA61/SHINE collaboration Acharya, A. ; Adhikary, H. ; Aduszkiewicz, A. ; et al.
Eur.Phys.J.C 80 (2020) 961, 2020.
Inspire Record 1811793 DOI 10.17182/hepdata.98673

The NA61/SHINE collaboration studies at the CERN Super Proton Synchrotron (SPS) the onset of deconfinement in hadronic matter by the measurement of particle production in collisions of nuclei with various sizes at a set of energies covering the SPS energy range. This paper presents results on inclusive double-differential spectra and mean multiplicities of $\pi^{-}$ mesons produced in the 5\% most \textit{central} $^7$Be+$^9$Be collisions at beam momenta of 19$A$, 30$A$, 40$A$, 75$A$ and 150$A$ GeV/$c$ obtained by the so-called $h^-$ method which does not require any particle identification. The shape of the transverse mass spectra differs from the shapes measured in central Pb+Pb collisions and inelastic p+p interactions. The normalized width of the rapidity distribution decreases with increasing collision energy and is in between the results for inelastic nucleon-nucleon and central Pb+Pb collisions. The mean multiplicity of pions per wounded nucleon in \textit{central} $^7$Be+$^9$Be collisions is close to that in central Pb+Pb collisions up to 75$A$GeV/$c$. However, at the top SPS energy the result is close to the one for inelastic nucleon-nucleon interactions. The results are discussed in the context of predictions for the onset of deconfinement at the CERN SPS collision energies.

10 data tables

Transverse momentum spectra of PI− in rapidity slices produced in the 5% most central Be+Be collisions at 19A GeV/c.

Transverse momentum spectra of PI− in rapidity slices produced in the 5% most central Be+Be collisions at 30A GeV/c.

Transverse momentum spectra of PI− in rapidity slices produced in the 5% most central Be+Be collisions at 40A GeV/c.

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Investigation of the linear and mode-coupled flow harmonics in Au+Au collisions at $\sqrt {S_{NN}}$ = 200 GeV

The STAR collaboration Adam, J. ; Adamczyk, L. ; Adams, J.R. ; et al.
Phys.Lett.B 809 (2020) 135728, 2020.
Inspire Record 1802752 DOI 10.17182/hepdata.95353

Flow harmonics ($\textit{v}_{n}$) of the Fourier expansion for the azimuthal distributions of hadrons are commonly employed to quantify the azimuthal anisotropy of particle production relative to the collision symmetry planes. While lower order Fourier coefficients ($\textit{v}_{2}$ and $\textit{v}_{3}$) are more directly related to the corresponding eccentricities of the initial state, the higher-order flow harmonics ($\textit{v}_{n>3}$) can be induced by a mode-coupled response to the lower-order anisotropies, in addition to a linear response to the same-order anisotropies. These higher-order flow harmonics and their linear and mode-coupled contributions can be used to more precisely constrain the initial conditions and the transport properties of the medium in theoretical models. The multiparticle azimuthal cumulant method is used to measure the linear and mode-coupled contributions in the higher-order anisotropic flow, the mode-coupled response coefficients, and the correlations of the event plane angles for charged particles as functions of centrality and transverse momentum in Au+Au collisions at nucleon-nucleon center-of-mass energy \roots = 200 GeV. The results are compared to similar LHC measurements as well as to several viscous hydrodynamic calculations with varying initial conditions.

5 data tables

3-particle integrated correlators

The integrated $v_{4}$ and $v_{5}$

The integrated $\chi_{4,22}$, $\rho_{4,22}$, $\chi_{5,23}$ and $\rho_{5,23}$

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Measurements of $\Xi^{-}$ and $\overline{\Xi}^{+}$ production in proton-proton interactions at $\sqrt{s_{NN}}$ = 17.3 GeV in the NA61/SHINE experiment

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Antićić, T. ; et al.
Eur.Phys.J.C 80 (2020) 833, 2020.
Inspire Record 1799187 DOI 10.17182/hepdata.98674

The production of $\Xi(1321)^{-}$ and $\overline{\Xi}(1321)^{+}$ hyperons in inelastic p+p interactions is studied in a fixed target experiment at a beam momentum of 158 GeV/textit{c}. Double differential distributions in rapidity y and transverse momentum $p_{T}$ are obtained from a sample of 33M inelastic events. They allow to extrapolate the spectra to full phase space and to determine the mean multiplicity of both $\Xi^{-}$ and $\overline{\Xi}^{+}$. The rapidity and transverse momentum spectra are compared to transport model predictions. The $\Xi^{-}$ mean multiplicity in inelastic p+p interactions at 158~\GeVc is used to quantify the strangeness enhancement in A+A collisions at the same centre-of-mass energy per nucleon pair.

6 data tables

Transverse momentum spectra in rapidity slices of Xi- produced in inelastic p+p interactions at 158 GeV/c. Rapidity values given in the legends correspond to the middle of the corresponding interval.

Transverse momentum spectra in rapidity slices of bar{Xi+} produced in inelastic p+p interactions at 158 GeV/c. Rapidity values given in the legends correspond to the middle of the corresponding interval.

Rapidity spectra of Xi- and XIBAR+ produced in inelastic p+p interactions at 158 GeV/c.

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Measurement of jet-medium interactions via direct photon-hadron correlations in Au$+$Au and $d$ $+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV

The PHENIX collaboration Acharya, U. ; Adare, A. ; Afanasiev, S. ; et al.
Phys.Rev.C 102 (2020) 054910, 2020.
Inspire Record 1798493 DOI 10.17182/hepdata.101752

We present direct photon-hadron correlations in 200 GeV/A Au+Au, d+Au, and p+p collisions, for direct photon pT from 5–12 GeV/c, collected by the PHENIX Collaboration in the years from 2006 to 2011. We observe no significant modification of jet fragmentation in d+Au collisions, indicating that cold nuclear matter effects are small or absent. Hadrons carrying a large fraction of the quark's momentum are suppressed in Au+Au compared to p+p and d+Au. As the momentum fraction decreases, the yield of hadrons in Au+Au increases to an excess over the yield in p+p collisions. The excess is at large angles and at low hadron pT and is most pronounced for hadrons associated with lower momentum direct photons. Comparison to theoretical calculations suggests that the hadron excess arises from medium response to energy deposited by jets.

14 data tables

Per-trigger yield of hadrons associated to direct photons in Au+Au collisions for direct photon $p_T$ 5-9 GeV/$c$, compared with p+p baseline, in various $\xi$ bins.

Per-trigger yield of hadrons associated to direct photons in d+Au collisions for direct photon $p_T$ 7-9 GeV/$c$, compared with p+p baseline, in various $\xi$ bins.

Integrated away-side $\gamma_{dir}$-h per-trigger yields of Au+Au, d+Au, and p+p, as a function of $\xi$.

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Measurement of charged pion double spin asymmetries at midrapidity in longitudinally polarized $p+p$ collisions at $\sqrt {s}$ = 510 GeV

The PHENIX collaboration Acharya, U.A. ; Adare, A. ; Aidala, C. ; et al.
Phys.Rev.D 102 (2020) 032001, 2020.
Inspire Record 1789851 DOI 10.17182/hepdata.95883

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the longitudinal double spin asymmetries, $A_{LL}$, for charged pions at midrapidity ($|\eta|<0.35$) in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510$ GeV. These measurements are sensitive to the gluon spin contribution to the total spin of the proton in the parton momentum fraction $x$ range between 0.04 and 0.09. One can infer the sign of the gluon polarization from the ordering of pion asymmetries with charge alone. The asymmetries are found to be consistent with global quantum-chromodynamics fits of deep-inelastic scattering and data at $\sqrt{s}=200$ GeV, which show a nonzero positive contribution of gluon spin to the proton spin.

1 data table

Double-spin asymmetries $A_{LL}$ as a function of transverse momentum for positive and negative pions.


$K^{*}(892)^0$ meson production in inelastic p+p interactions at 158 GeV/$c$ beam momentum measured by NA61/SHINE at the CERN SPS

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Antićić, T. ; et al.
Eur.Phys.J.C 80 (2020) 460, 2020.
Inspire Record 1775731 DOI 10.17182/hepdata.94255

The measurement of $K^{*}(892)^0$ resonance production via its $K^{+}\pi^{-}$ decay mode in inelastic p+p collisions at beam momentum 158 GeV/$c$ ($\sqrt{s_{NN}}=17.3$ GeV) is presented. The data were recorded by the NA61/SHINE hadron spectrometer at the CERN Super Proton Synchrotron. The $\textit{template}$ method was used to extract the $K^{*}(892)^0$ signal and double differential transverse momentum and rapidity spectra were obtained. The full phase-space mean multiplicity of $K^{*}(892)^0$ mesons was found to be $(78.44 \pm 0.38 \mathrm{(stat)} \pm 6.0 \mathrm{(sys)) \cdot 10^{-3}}$. The NA61/SHINE results are compared with the E$_{POS}$1.99 and Hadron Resonance Gas models as well as with world data from p+p and nucleus-nucleus collisions.

11 data tables

Numerical values of mass and width of $K^{∗}(892)^0$ mesons fitted in 0<y<0.5 and presented in Fig.8. The first uncertainty is statistical, while the second one is systematic.

Numerical values of double-differential yields $d^{2}n/dydp_{T}$ presented in Fig. 10, given in units of $10^{−3} (GeV/c)^{−1}$. The first uncertainty is statistical, while the second one is systematic

Numerical values of double-differential yields $d^{2}n/dydp_{T}$ presented in Fig. 10, given in units of $10^{−3} (GeV/c)^{−1}$. The first uncertainty is statistical, while the second one is systematic

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Search for an Exotic $S=-2, Q=-2$ baryon resonance in proton-proton interactions at $\sqrt{s_{NN}}$ = 17.3 GeV

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Antićić, T. ; et al.
Phys.Rev.D 101 (2020) 051101, 2020.
Inspire Record 1773266 DOI 10.17182/hepdata.94256

Pentaquark states have been extensively investigated theoretically in the context of the constituent quark model. In this paper experimental searches in the $Xi^{-}\pi^{-}$, $Xi^{-}\pi^{+}$, $Xi^{+}\pi^{-}$ and $Xi^{+}\pi^{+}$ invariant mass spectra in proton-proton interactions at $\sqrt{s}$=17.3 GeV are presented. Previous possible evidence from the NA49 collaboration of the existence of a narrow $Xi^{-}\pi^{-}$ baryon resonance in p+p interactions is not confirmed with almost 10 times greater event statistics. The search was performed using the NA61/SHINE detector which reuses the main components of the NA49 apparatus. No signal was observed with either the selection cuts of NA49 or a newly optimised set.

5 data tables

Invariant mass spectra of XI-PI-, XI-PI+, XI+PI-, XI+PI+.

Sum of invariant mass spectra of XI-PI-, XI-PI+, XI+PI-, XI+PI+.

Invariant mass spectra of XI-PI-, XI-PI+, XI+PI-, XI+PI+.

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Proton-Proton Interactions and Onset of Deconfinement

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Anticic, T. ; et al.
Phys.Rev.C 102 (2020) 011901, 2020.
Inspire Record 1772241 DOI 10.17182/hepdata.95182

The NA61/SHINE experiment at the CERN SPS is performing a uniqe study of the phase diagram of strongly interacting matter by varying collision energy and nuclear mass number of colliding nuclei. In central Pb+Pb collisions the NA49 experiment found structures in the energy dependence of several observables in the CERN SPS energy range that had been predicted for the transition to a deconfined phase. New measurements of NA61/SHINE find intriguing similarities in p+p interactions for which no deconfinement transition is expected at SPS energies. Possible implications will be discussed.

12 data tables

K+/PI+ at y=0.

K+/PI+ at y=0.

<K+>/<PI+>.

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Measurement of the $\eta_c(1S)$ production cross-section in $pp$ collisions at $\sqrt{s} = 13$ TeV

The LHCb collaboration Aaij, Roel ; Abellán Beteta, Carlos ; Ackernley, Thomas ; et al.
Eur.Phys.J.C 80 (2020) 191, 2020.
Inspire Record 1763898 DOI 10.17182/hepdata.90457

Using a data sample corresponding to an integrated luminosity of $2.0\,fb^{-1}$, collected by the LHCb experiment, the production of the $\eta_c(1S)$ state in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13 \text{ TeV}$ is studied in the rapidity range ${2.0 < y < 4.5}$ and in the transverse momentum range ${6.5 < p_{T} < 14.0\text{ GeV}}$. The cross-section for prompt production of $\eta_c(1S)$ mesons relative to that of the $J/\psi$ meson is measured using the ${p\bar{p}}$ decay mode and is found to be ${\sigma_{\eta_c(1S)}/\sigma_{J/\psi} = 1.69 \pm 0.15 \pm 0.10 \pm 0.18}$. The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the ${J/\psi\to p \bar{p}}$ and ${\eta_c\to p \bar{p}}$ decays. The prompt $\eta_c(1S)$ production cross-section is determined to be ${\sigma_{\eta_c(1S)} = 1.26 \pm 0.11\pm 0.08 \pm 0.14 \,\mu b}$, where the last uncertainty includes that on the ${J/\psi}$ meson cross-section. The ratio of the branching fractions of $b$-hadron decays to the $\eta_c(1S)$ and ${J/\psi}$ states is measured to be ${\mathcal{B}_{b\to\eta_c X}/\mathcal{B}_{b\to J/\psi X} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$, where the last uncertainty is due to those on the branching fractions of the ${J/\psi \to p \bar{p}}$ and ${\eta_c\to p \bar{p}}$ decays. The difference between the ${J/\psi}$ and $\eta_c(1S)$ masses is also determined to be ${113.0 \pm 0.7 \pm 0.1\text{ MeV}}$, which is the most precise single measurement of this quantity to date.

4 data tables

Relative $\eta_c$ to $J/\psi$ differential production cross-sections for prompt production. The uncertainties are statistical, systematic, and due to the ${\eta_c\to p\bar{p}}$ and ${J/\psi\to p\bar{p}}$ branching fractions, respectively.

Differential production cross-sections of $\eta_c$ for prompt production. The uncertainties are statistical, systematic, and due to the $\eta_c\to p \bar{p}$ and $J/\psi\to p \bar{p}$ branching fractions and $J/\psi$ production cross-section.

Relative $\eta_c$ to $J/\psi$ differential production cross-sections for production in $b$-hadron inclusive decays. The uncertainties are statistical, systematic, and due to the ${\eta_c\to p\bar{p}}$ and ${J/\psi\to p\bar{p}}$ branching fractions, respectively.

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Measurement of $J/\psi$ at forward and backward rapidity in $p+p$, $p+A$l, $p+A$u, and $^3$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200~{\rm GeV}$

The PHENIX collaboration Acharya, U. ; Adare, A. ; Aidala, C. ; et al.
Phys.Rev.C 102 (2020) 014902, 2020.
Inspire Record 1762446 DOI 10.17182/hepdata.98626

Charmonium is a valuable probe in heavy-ion collisions to study the properties of the quark gluon plasma, and is also an interesting probe in small collision systems to study cold nuclear matter effects, which are also present in large collision systems. With the recent observations of collective behavior of produced particles in small system collisions, measurements of the modification of charmonium in small systems have become increasingly relevant. We present the results of J/ψ measurements at forward and backward rapidity in various small collision systems, p+p, p+Al, p+Au and 3He+Au, at √sNN =200 GeV. The results are presented in the form of the observable RAB, the nuclear modification factor, a measure of the ratio of the J/ψ invariant yield compared to the scaled yield in p+p collisions. We examine the rapidity, transverse momentum, and collision centrality dependence of nuclear effects on J/ψ production with different projectile sizes p and 3He, and different target sizes Al and Au. The modification is found to be strongly dependent on the target size, but to be very similar for p+Au and 3He+Au. However, for 0%–20% central collisions at backward rapidity, the modification for 3He+Au is found to be smaller than that for p+Au, with a mean fit to the ratio of 0.89±0.03(stat)±0.08(syst), possibly indicating final state effects due to the larger projectile size.

36 data tables

J/psi invariant yields in p+p collisions as a function of pT at forward and backward rapidity. The statistical and systematic uncertainties vary point-to-point and are listed for each measured value. An additional global systematic uncertainty is provided in each column heading, which applies to all data points per column.

J/psi nuclear modification in p+Al, p+Au and 3He+Au collisions as a function of centrality and rapidity. The statistical and systematic uncertainties vary point-to-point and are listed for each measured value. An additional global systematic uncertainty is provided in each column heading, which applies to all data points per column.

J/psi nuclear modification in p+Al collisions as a function of centrality and rapidity. The statistical and systematic uncertainties vary point-to-point and are listed for each measured value. An additional global systematic uncertainty is provided in each column heading, which applies to all data points per column.

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Measurements of hadron production in $\pi^{+}$ + C and $\pi^{+}$ + Be interactions at 60 GeV/$c$

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Antićić, T. ; et al.
Phys.Rev.D 100 (2019) 112004, 2019.
Inspire Record 1754136 DOI 10.17182/hepdata.91220

Precise knowledge of hadron production rates in the generation of neutrino beams is necessary for accelerator-based neutrino experiments to achieve their physics goals. NA61/SHINE, a large-acceptance hadron spectrometer, has recorded hadron+nucleus interactions relevant to ongoing and future long-baseline neutrino experiments at Fermi National Accelerator Laboratory. This paper presents three analyses of interactions of 60 GeV/$c$ $\pi^+$ with thin, fixed carbon and beryllium targets. Integrated production and inelastic cross sections were measured for both of these reactions. In an analysis of strange, neutral hadron production, differential production multiplicities of $K^0_{S}$, $\Lambda$ and anti-$\Lambda$ were measured. Lastly, in an analysis of charged hadron production, differential production multiplicities of $\pi^+$, $\pi^-$, $K^+$, $K^-$ and protons were measured. These measurements will enable long-baseline neutrino experiments to better constrain predictions of their neutrino flux in order to achieve better precision on their neutrino cross section and oscillation measurements.

16 data tables

Doubly differential multiplicity measurements of produced pi+ from 60 GeV/c pi+ + C interactions. Statistical and systematic uncertainties are shown. Additionally, a normalization uncertainty of [-1.1%,+1.9%] applies to all of the measurements for this reaction.

Doubly differential multiplicity measurements of produced pi- from 60 GeV/c pi+ + C interactions. Statistical and systematic uncertainties are shown. Additionally, a normalization uncertainty of [-1.1%,+1.9%] applies to all of the measurements for this reaction.

Doubly differential multiplicity measurements of produced K+ from 60 GeV/c pi+ + C interactions. Statistical and systematic uncertainties are shown. Additionally, a normalization uncertainty of [-1.1%,+1.9%] applies to all of the measurements for this reaction.

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Measurements of production and inelastic cross sections for p+C , p+Be , and p+Al at 60 GeV/c and p+C and p+Be at 120 GeV/c

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Antićić, T. ; et al.
Phys.Rev.D 100 (2019) 112001, 2019.
Inspire Record 1753094 DOI 10.17182/hepdata.95181

This paper presents measurements of production cross sections and inelastic cross sections for the following reactions: 60 GeV/$c$ protons with C, Be, Al targets and 120 GeV/$c$ protons with C and Be targets. The analysis was performed using the NA61/SHINE spectrometer at the CERN SPS. First measurements were obtained using protons at 120 GeV/$c$, while the results for protons at 60 GeV/$c$ were compared with previously published measurements. These interaction cross section measurements are critical inputs for neutrino flux prediction in current and future accelerator-based long-baseline neutrino experiments.

2 data tables

Results of production cross section measurements on proton beams. Measured channeles are p+C/Be/Al at 60 GeV and p+C/Be at 120 GeV.

Results of inelastic cross section measurements on proton beams. Measured channeles are p+C/Be/Al at 60 GeV and p+C/Be at 120 GeV.


Measurement of $\phi $ meson production in $p + p$ interactions at 40, 80 and $158 \, \hbox {GeV}/c$ with the NA61/SHINE spectrometer at the CERN SPS

The NA61/SHINE collaboration Aduszkiewicz, A. ; Andronov, E.V. ; Antićić, T. ; et al.
Eur.Phys.J.C 80 (2020) 199, 2020.
Inspire Record 1749613 DOI 10.17182/hepdata.93228

Results on $\phi$ meson production in inelastic p+p collisions at CERN SPS energies are presented. They are derived from data collected by the NA61/SHINE fixed target experiment, by means of invariant mass spectra fits in the $\phi \to K^+K^-$ decay channel. They include the first ever measured double differential spectra of $\phi$ mesons as a function of rapidity $y$ and transverse momentum $p_T$ for proton beam momenta of 80 GeV/c and 158 GeV/c, as well as single differential spectra of $y$ or $p_T$ for beam momentum of 40 GeV/c. The corresponding total $\phi$ yields per inelastic p+p event are obtained. These results are compared with existing data on $\phi$ meson production in p+p collisions. The comparison shows consistency but superior accuracy of the present measurements. The emission of $\phi$ mesons in p+p reactions is confronted with that occurring in Pb+Pb collisions, and the experimental results are compared with model predictions. It appears that none of the considered models can properly describe all the experimental observables.

17 data tables

Double differential multiplicity of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 158 GeV/c, as a function of transverse momentum $p_T$ and rapidity $y$.

Double differential multiplicity of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 80 GeV/c, as a function of transverse momentum $p_T$ and rapidity $y$.

Transverse momentum $p_T$ spectrum of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 40 GeV/c, in a broad rapidity $y$ bin of (0, 1.5).

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Observation of a narrow pentaquark state, $P_c(4312)^+$, and of two-peak structure of the $P_c(4450)^+$

The LHCb collaboration Aaij, Roel ; Abellán Beteta, Carlos ; Adeva, Bernardo ; et al.
Phys.Rev.Lett. 122 (2019) 222001, 2019.
Inspire Record 1728691 DOI 10.17182/hepdata.89271

A narrow pentaquark state, $P_c(4312)^+$, decaying to $J/\psi p$ is discovered with a statistical significance of $7.3\sigma$ in a data sample of ${\Lambda_b^0\to J/\psi p K^-}$ decays which is an order of magnitude larger than that previously analyzed by the LHCb collaboration. The $P_c(4450)^+$ pentaquark structure formerly reported by LHCb is confirmed and observed to consist of two narrow overlapping peaks, $P_c(4440)^+$ and $P_c(4457)^+$, where the statistical significance of this two-peak interpretation is $5.4\sigma$. Proximity of the $\Sigma_c^+\bar{D}^{0}$ and $\Sigma_c^+\bar{D}^{*0}$ thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.

4 data tables

Distribution of $(J/\psi p)$ system invariant mass from the decay of $\Lambda_{b}^{0}$ candidates in the channel $\Lambda_{b}^{0} \to J/\psi p K^{-}$.

Distribution of $(J/\psi p)$ system invariant mass from the decay of $\Lambda_{b}^{0}$ candidates in the channel $\Lambda_{b}^{0} \to J/\psi p K^{-}$. $\Lambda_{b}^{0}$ candidates are selected after the suppression of the dominant $\Lambda^{*} \to p K^{-}$ contributions using the $m_{Kp} > 1.9$ GeV$/c^2$ requirement.

$\cos \theta_{P_c}$-weighted ditribution of $(J/\psi p)$ system invariant mass from the decay of $\Lambda_{b}^{0}$ candidates in the channel $\Lambda_{b}^{0} \to J/\psi p K^{-}$. Here $\theta_{P_c}$ is the helicity angle of the pentaquark exotic state (the angle between $K^-$ and $J/\psi$ in the pentaquark state rest frame).

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Study of $\Upsilon$ production in $p$Pb collisions at $\sqrt{s_{NN}}=8.16$ TeV

The LHCb collaboration Aaij, Roel ; Abellán Beteta, Carlos ; Adeva, Bernardo ; et al.
JHEP 11 (2018) 194, 2018.
Inspire Record 1699106 DOI 10.17182/hepdata.93070

The production of $\Upsilon (nS)$ mesons ($n=1,2,3$) in $p$Pb and Pb$p$ collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{NN}}=8.16$ TeV is measured by the LHCb experiment, using a data sample corresponding to an integrated luminosity of 31.8 nb$^{-1}$. The $\Upsilon (nS)$ mesons are reconstructed through their decays into two opposite-sign muons. The measurements comprise the differential production cross-sections of the $\Upsilon (1S)$ and $\Upsilon (2S)$ states, their forward-to-backward ratios and nuclear modification factors, performed as a function of the transverse momentum $p_{\mathrm{T}}$ and rapidity in the nucleon-nucleon centre-of-mass frame $y^*$ of the $\Upsilon (nS)$ states, in the kinematic range $p_{\rm{T}}<25$ GeV/$c$ and $1.5<y^*<4.0$ ($-5.0<y^*<-2.5$) for $p$Pb (Pb$p$) collisions. In addition, production cross-sections for $\Upsilon (3S)$ are measured integrated over phase space and the production ratios between all three $\Upsilon (nS)$ states are determined. The measurements are compared to theoretical predictions and suppressions for quarkonium in $p$Pb collisions are observed.

17 data tables

$\Upsilon(1S)$ production cross-section in $p$Pb, as a function of $p_{T}$ and $y*$. The uncertainty is the sum in quadrature of the statistical and systematic components.

$\Upsilon(1S)$ production cross-section in Pb$p$, as a function of $p_{T}$ and $y^*$. The uncertainty is the sum in quadrature of the statistical and systematic components.

$\Upsilon(1S)$ production cross-section in $p$Pb and Pb$p$, as a function of $p_{T}$. The uncertainty is the sum in quadrature of the statistical and systematic components.

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Measurement of Antiproton Production in ${\rm p He}$ Collisions at $\sqrt{s_{NN}}=110$ GeV

The LHCb collaboration Aaij, Roel ; Abellán Beteta, Carlos ; Adeva, Bernardo ; et al.
Phys.Rev.Lett. 121 (2018) 222001, 2018.
Inspire Record 1688924 DOI 10.17182/hepdata.84584

The cross-section for prompt antiproton production in collisions of protons with an energy of $6.5$ TeV incident on helium nuclei at rest is measured with the LHCb experiment from a data set corresponding to an integrated luminosity of $0.5\,nb^{-1}$. The target is provided by injecting helium gas into the LHC beam line at the LHCb interaction point. The reported results, covering antiproton momenta between $12$ and $110\,\mathrm{GeV/}c$, represent the first direct determination of the antiproton production cross-section in ${\rm p He}$ collisions, and impact the interpretation of recent results on antiproton cosmic rays from space-borne experiments.

1 data table

Double-differential cross-section in antiproton momentum and transverse momentum for antiproton production in collisions of 6.5 TeV protons on He nuclei at rest. The antiproton momentum is defined in the laboratory frame. Results are averaged over the given kinematic range of each bin. The uncertainty is split into an uncertainty delta_uncorr, uncorrelated among the kinematic bins, and an uncertainty delta_corr, fully correlated among the kinematic bins. For both uncertainties, the systematic uncertainty, dominant for most bins, and the statistical uncertainty, are added in quadrature. The average value within each bin is also reported for the antiproton momentum, the transverse momentum, and x-Feynman xF=2 p_Z*/SQRT(S), where p_Z* is the longitudinal antiproton momentum in the center-of-mass system and SQRT(S) the nucleon-nucleon center-of-mass energy. These average values are obtained from simulation (based on EPOS LHC), to avoid biases from reconstruction effects and given the good agreement with data observed for the simulated kinematic spectra.


Measurements of $\pi ^\pm $ , $K^\pm $ and proton double differential yields from the surface of the T2K replica target for incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS

The NA61/SHINE collaboration Abgrall, N. ; Aduszkiewicz, A. ; Andronov, E.V. ; et al.
Eur.Phys.J.C 79 (2019) 100, 2019.
Inspire Record 1687433 DOI 10.17182/hepdata.88360

Measurements of the $\pi^{\pm}$, $K^{\pm}$, and proton double differential yields emitted from the surface of the 90-cm-long carbon target (T2K replica) were performed for the incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS using data collected during 2010 run. The double differential $\pi^{\pm}$ yields were measured with increased precision compared to the previously published NA61/SHINE results, while the $K^{\pm}$ and proton yields were obtained for the first time. A strategy for dealing with the dependence of the results on the incoming proton beam profile is proposed. The purpose of these measurements is to reduce significantly the (anti)neutrino flux uncertainty in the T2K long-baseline neutrino experiment by constraining the production of (anti)neutrino ancestors coming from the T2K target.

272 data tables

Double differential yiedls of positively charged pions emitted from the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and in the longitudinal range from 0 to 18cm, as a function of momentum. The normalization is per proton on target.

Double differential yiedls of positively charged pions emitted from the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and in the longitudinal range from 0 to 18cm, as a function of momentum. The normalization is per proton on target.

Double differential yiedls of positively charged pions emitted from the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and in the longitudinal range from 0 to 18cm, as a function of momentum. The normalization is per proton on target.

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Measurement of $D_s^{\pm}$ production asymmetry in $pp$ collisions at $\sqrt{s} =7$ and 8 TeV

The LHCb collaboration Aaij, Roel ; Adeva, Bernardo ; Adinolfi, Marco ; et al.
JHEP 08 (2018) 008, 2018.
Inspire Record 1674916 DOI 10.17182/hepdata.82715

The inclusive $D_s^{\pm}$ production asymmetry is measured in $pp$ collisions collected by the LHCb experiment at centre-of-mass energies of $\sqrt{s} =7$ and 8 TeV. Promptly produced $D_s^{\pm}$ mesons are used, which decay as $D_s^{\pm}\to\phi\pi^{\pm}$, with $\phi\to K^+K^-$. The measurement is performed in bins of transverse momentum, $p_{\rm T}$, and rapidity, $y$, covering the range $2.5

6 data tables

Values of the $D_s^+$ production asymmetry in percent, including, respectively, the statistical and systematic uncertainties for each of the $D_s^+$ kinematic bins using the combined $\sqrt{s} =7$ and 8 TeV data sets. The statistical and systematic uncertainties include the corresponding contributions from the detection asymmetries, and are therefore correlated between the bins. ASYM is defined as ASYM = ((SIG(D/S+)-SIG(D/S-))/(SIG(D/S+)+SIG(D/S+)).

Values of the $D_s^+$ production asymmetry in percent, including, respectively, the statistical and systematic uncertainties for each of the $D_s^+$ kinematic bins using the $\sqrt{s} =7$ TeV data set. The statistical and systematic uncertainties include the corresponding contributions from the detection asymmetries, and are therefore correlated between the bins. ASYM is defined as ASYM = ((SIG(D/S+)-SIG(D/S-))/(SIG(D/S+)+SIG(D/S+)).

Values of the $D_s^+$ production asymmetry in percent, including, respectively, the statistical and systematic uncertainties for each of the $D_s^+$ kinematic bins using the $\sqrt{s} =8$ TeV data set. The statistical and systematic uncertainties include the corresponding contributions from the detection asymmetries, and are therefore correlated between the bins. ASYM is defined as ASYM = ((SIG(D/S+)-SIG(D/S-))/(SIG(D/S+)+SIG(D/S+)).

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Creation of quark–gluon plasma droplets with three distinct geometries

The PHENIX collaboration Aidala, C. ; Akiba, Y. ; Alfred, M. ; et al.
Nature Phys. 15 (2019) 214-220, 2019.
Inspire Record 1672133 DOI 10.17182/hepdata.99787

The experimental study of the collisions of heavy nuclei at relativistic energies has established the properties of the quark-gluon plasma (QGP), a state of hot, dense nuclear matter in which quarks and gluons are not bound into hadrons. In this state, matter behaves as a nearly inviscid fluid that efficiently translates initial spatial anisotropies into correlated momentum anisotropies among the produced particles, producing a common velocity field pattern known as collective flow. In recent years, comparable momentum anisotropies have been measured in small-system proton-proton ($p$$+$$p$) and proton-nucleus ($p$$+$$A$) collisions, despite expectations that the volume and lifetime of the medium produced would be too small to form a QGP. Here, we report on the observation of elliptic and triangular flow patterns of charged particles produced in proton-gold ($p$$+$Au), deuteron-gold ($d$$+$Au), and helium-gold ($^3$He$+$Au) collisions at a nucleon-nucleon center-of-mass energy $\sqrt{s_{_{NN}}}$~=~200 GeV. The unique combination of three distinct initial geometries and two flow patterns provides unprecedented model discrimination. Hydrodynamical models, which include the formation of a short-lived QGP droplet, provide a simultaneous description of these measurements.

16 data tables

$v_2$for 0-5% central p+Au collisions

$v_2$for 0-5% central d+Au collisions

$v_2$for 0-5% central $^3$He+Au collisions

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Measurement of $\Upsilon$ production in $pp$ collisions at $\sqrt{s}$= 13 TeV

The LHCb collaboration Aaij, R. ; Adeva, Bernardo ; Adinolfi, Marco ; et al.
JHEP 07 (2018) 134, 2018.
Inspire Record 1670013 DOI 10.17182/hepdata.82210

The production cross-sections of $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ mesons in proton-proton collisions at $\sqrt{s}$= 13 TeV are measured with a data sample corresponding to an integrated luminosity of $277 \pm 11$ $\rm pb^{-1}$ recorded by the LHCb experiment in 2015. The $\Upsilon$ mesons are reconstructed in the decay mode $\Upsilon\to\mu^{+}\mu^{-}$. The differential production cross-sections times the dimuon branching fractions are measured as a function of the $\Upsilon$ transverse momentum, $p_{\rm T}$, and rapidity, $y$, over the range $0 < p_{\rm T}< 30$ GeV/c and $2.0 < y < 4.5$. The ratios of the cross-sections with respect to the LHCb measurement at $\sqrt{s}$= 8 TeV are also determined. The measurements are compared with theoretical predictions based on NRQCD.

14 data tables

Double-differential cross-sections times dimuon branching fraction in different bins of $p_T$ and $y$ for $\Upsilon$(1S) (in pb). The first uncertainty is statistical and the second is systematic.

Double-differential cross-sections times dimuon branching fraction in different bins of $p_T$ and $y$ for $\Upsilon$(2S) (in pb). The first uncertainty is statistical and the second is systematic.

Double-differential cross-sections times dimuon branching fraction in different bins of $p_T$ and $y$ for $\Upsilon$(3S) (in pb). The first uncertainty is statistical and the second is systematic.

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Measurement of the inelastic $pp$ cross-section at a centre-of-mass energy of 13 TeV

The LHCb collaboration Aaij, Roel ; Adeva, Bernardo ; Adinolfi, Marco ; et al.
JHEP 06 (2018) 100, 2018.
Inspire Record 1665223 DOI 10.17182/hepdata.89782

The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13\,TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum $p>2$\,GeV/$c$ in the pseudorapidity range $2<\eta<5$ is determined to be $\sigma_{\rm acc}= 62.2 \pm 0.2 \pm 2.5$\,mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section $\sigma_{\rm inel}= 75.4 \pm 3.0 \pm 4.5$\,mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7\,TeV is also reported.

3 data tables

The cross-section for inelastic $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, yielding one or more prompt long-lived charged particles in the kinematic range $p > 2.0$ GeV/$c$ and $2.0 < \eta < 5.0$ (LHCb acceptance). The quoted uncertainty that is almost completely systematic in nature as the purely statistical uncertainty is found negligible. A particle is long-lived if its proper (mean) lifetime is larger than 30 ps, and it is prompt if it is produced directly in the $pp$ interaction or if none of its ancestors is long-lived.

The total cross-section for inelastic $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, extrapolated from Monte Carlo in similar way to measurement at $\sqrt{s}=7$ TeV.

Update of the total cross-section for inelastic $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 7$ TeV due to improved calibration of the luminosity scale.


Measurement of forward top pair production in the dilepton channel in $pp$ collisions at $\sqrt{s}=13$ TeV

The LHCb collaboration Aaij, Roel ; Adeva, Bernardo ; Adinolfi, Marco ; et al.
JHEP 08 (2018) 174, 2018.
Inspire Record 1662483 DOI 10.17182/hepdata.97367

Forward top quark pair production is studied in $pp$ collisions in the $\mu eb$ final state using a data sample corresponding to an integrated luminosity of 1.93 fb$^{-1}$ collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The cross-section is measured in a fiducial region where both leptons have a transverse momentum greater than 20 GeV and a pseudorapidity between 2.0 and 4.5. The quadrature sum of the azimuthal separation and the difference in pseudorapidities, denoted $\Delta R$, between the two leptons must be larger than 0.1. The $b$-jet axis is required to be separated from both leptons by a $\Delta R$ of 0.5, and to have a transverse momentum in excess of 20 GeV and a pseudorapidity between 2.2 and 4.2. The cross-section is measured to be $$\sigma_{t\bar{t}}= 126\pm19\,(\mathrm{stat})\pm16\,(\mathrm{syst})\pm5\,(\mathrm{lumi})\,\,\mathrm{ fb}$$ where the first uncertainty is statistical, the second is systematic, and the third is due to the luminosity determination. The measurement is compatible with the Standard Model prediction.

1 data table

The measured fiducial cross section. The uncertainty is split into statistical, systematic and uncertainty due to luminosity.


Light isovector resonances in $\pi^- p \to \pi^-\pi^-\pi^+ p$ at 190 GeV/${\it c}$

The COMPASS collaboration Aghasyan, M. ; Alexeev, M.G. ; Alexeev, G.D. ; et al.
Phys.Rev.D 98 (2018) 092003, 2018.
Inspire Record 1655631 DOI 10.17182/hepdata.82958

We have performed the most comprehensive resonance-model fit of $\pi^-\pi^-\pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 &lt; m_{3\pi} &lt; 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 &lt; t' &lt; 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $\pi(1800)$, $a_1(1260)$, $a_2(1320)$, $\pi_2(1670)$, $\pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $\pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $\pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t'$ bins. We extract the relative branching fractions of the $\rho(770) \pi$ and $f_2(1270) \pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t'$ dependence of the intensity of the resonances and of their phases. The $t'$ dependence of the intensities of most resonances differs distinctly from the $t'$ dependence of the nonresonant components. For the first time, we determine the $t'$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.

2 data tables

Real and imaginary parts of the normalized transition amplitudes $\mathcal{T}_a$ of the 14 selected partial waves in the 1100 $(m_{3\pi}, t')$ cells (see Eq. (12) in the paper). The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the transition amplitudes in the column headers. The $m_{3\pi}$ values that are given in the first column correspond to the bin centers. Each of the 100 $m_{3\pi}$ bins is 20 MeV/$c^2$ wide. Since the 11 $t'$ bins are non-equidistant, the lower and upper bounds of each $t'$ bin are given in the column headers. The transition amplitudes define the spin-density matrix elements $\varrho_{ab}$ for waves $a$ and $b$ according to Eq. (18). The spin-density matrix enters the resonance-model fit via Eqs. (33) and (34). The transition amplitudes are normalized via Eqs. (9), (16), and (17) such that the partial-wave intensities $\varrho_{aa} = |\mathcal{T}_a|^2$ are given in units of acceptance-corrected number of events. The relative phase $\Delta\phi_{ab}$ between two waves $a$ and $b$ is given by $\arg(\varrho_{ab}) = \arg(\mathcal{T}_a) - \arg(\mathcal{T}_b)$. Note that only relative phases are well-defined. The phase of the $1^{++}0^+ \rho(770) \pi S$ wave was set to $0^\circ$ so that the corresponding transition amplitudes are real-valued. In the PWA model, some waves are excluded in the region of low $m_{3\pi}$ (see paper and [Phys. Rev. D 95, 032004 (2017)] for a detailed description of the PWA model). For these waves, the transition amplitudes are set to zero. The tables with the covariance matrices of the transition amplitudes for all 1100 $(m_{3\pi}, t')$ cells can be downloaded via the 'Additional Resources' for this table.

Decay phase-space volume $I_{aa}$ for the 14 selected partial waves as a function of $m_{3\pi}$, normalized such that $I_{aa}(m_{3\pi} = 2.5~\text{GeV}/c^2) = 1$. The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the decay phase-space volume in the column headers. The labels are identical to the ones used in the column headers of the table of the transition amplitudes. $I_{aa}$ is calculated using Monte Carlo integration techniques for fixed $m_{3\pi}$ values, which are given in the first column, in the range from 0.5 to 2.5 GeV/$c^2$ in steps of 10 MeV/$c^2$. The statistical uncertainties given for $I_{aa}$ are due to the finite number of Monte Carlo events. $I_{aa}(m_{3\pi})$ is defined in Eq. (6) in the paper and appears in the resonance model in Eqs. (19) and (20).