Charged-hadron and identified-hadron ($K^\mathrm{0}_\mathrm{S}$, $Λ$, $Ξ^\mathrm{-}$) yield measurements in photo-nuclear Pb+Pb and $p$+Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV with ATLAS

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
Phys.Rev.C 111 (2025) 064908, 2025.
Inspire Record 2898746 DOI 10.17182/hepdata.158635

This paper presents the measurement of charged-hadron and identified-hadron ($K^\mathrm{0}_\mathrm{S}$, $Λ$, $Ξ^\mathrm{-}$) yields in photo-nuclear collisions using 1.7 $\mathrm{nb^{-1}}$ of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV Pb+Pb data collected in 2018 with the ATLAS detector at the Large Hadron Collider. Candidate photo-nuclear events are selected using a combination of tracking and calorimeter information, including the zero-degree calorimeter. The yields as a function of transverse momentum and rapidity are measured in these photo-nuclear collisions as a function of charged-particle multiplicity. These photo-nuclear results are compared with 0.1 $\mathrm{nb^{-1}}$ of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV $p$+Pb data collected in 2016 by ATLAS using similar charged-particle multiplicity selections. These photo-nuclear measurements shed light on potential quark-gluon plasma formation in photo-nuclear collisions via observables sensitive to radial flow, enhanced baryon-to-meson ratios, and strangeness enhancement. The results are also compared with the Monte Carlo DPMJET-III generator and hydrodynamic calculations to test whether such photo-nuclear collisions may produce small droplets of quark-gluon plasma that flow collectively.

28 data tables

The multiplicity distribution (#it{N}_{ch}^{rec}) from Pb+Pb photo-nuclear collisions.

The multiplicity distribution (#it{N}_{ch}^{rec}) from p+Pb collisions.

The Charged-hadron yields as a function of pT in different y selections in Pb+Pb photo-nuclear collisions.

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Observation of top-quark pair production in lead-lead collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
Phys.Rev.Lett. 134 (2025) 142301, 2025.
Inspire Record 2849226 DOI 10.17182/hepdata.156982

Top-quark pair production is observed in lead-lead (Pb+Pb) collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV at the Large Hadron Collider with the ATLAS detector. The data sample was recorded in 2015 and 2018, amounting to an integrated luminosity of 1.9 nb$^{-1}$. Events with exactly one electron and one muon and at least two jets are selected. Top-quark pair production is measured with an observed (expected) significance of 5.0 (4.1) standard deviations. The measured top-quark pair production cross-section is $\sigma_{t\bar{t}} = 3.6\;^{+1.0}_{-0.9}\;\mathrm{(stat.)}\;^{+0.8}_{-0.5}\;\mathrm{(syst.)} ~\mathrm{\mu b}$, with a total relative uncertainty of 31%, and is consistent with theoretical predictions using a range of different nuclear parton distribution functions. The observation of this process consolidates the evidence of the existence of all quark flavors in the pre-equilibrium stage of the quark-gluon plasma at very high energy densities, similar to the conditions present in the early universe.

5 data tables

The figure shows the post-fit distribution of events as a function of the dilepton invariant mass ($m_{e\mu}$), in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, with an integrated luminosity of 1.9 nb$^{-1}$. The data correspond to the SR1 (Signal Region 1 (SR\(_1\)):} Events with exactly one muon and one oppositely charged electron, a dilepton invariant mass \( m_{e\mu} \geq 30 \, \mathrm{GeV} \), at least two jets with \( p_T \geq 35 \, \mathrm{GeV} \), and a dilepton transverse momentum \( p_T^{e\mu} > 40 \, \mathrm{GeV} \). This region is expected to be signal-dominated) channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield.

The figure shows the post-fit distribution of events as a function of the dilepton invariant mass ($m_{e\mu}$), in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, with an integrated luminosity of 1.9 nb$^{-1}$. The data correspond to the SR2 (Signal Region 2 (SR\(_2\)):} Events meeting the same criteria as SR\(_1\), but with a dilepton transverse momentum \( p_T^{e\mu} \leq 40 \, \mathrm{GeV} \). This region includes events with a lower \( p_T^{e\mu} \) and has a larger background contribution) channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield.

The impact of systematic uncertainties on the fitted signal-strength parameter $\hat{\mu}$ for the combined fit of all channels. Only the 10 most significant systematic uncertainties are shown and listed in decreasing order of their impact on $\mu$ on the $y$-axis. The empty (filled) blue/cyan boxes correspond to the pre-fit (post-fit) impact on $\mu$, referring to the upper $x$-axis. The impact of each systematic uncertainty, $\Delta \mu$, is calculated by comparing the nominal best-fit value of $\mu$ with the result of the fit when fixing the corresponding nuisance parameter $\theta$ to its best-fit value $\hat{\theta}$ shifted by its pre-fit (post-fit) uncertainties $\hat{\theta} \pm \Delta \theta(\hat{\theta} \pm \Delta \hat{\theta})$. The black points, which refer to the lower $x$-axis, show the pulls of the fitted nuisance parameters, i.e., the deviations of the fitted parameters $\hat{\theta}$ from their nominal values $\theta_0$, normalized to their nominal uncertainties $\Delta \theta$. The black lines show the post-fit uncertainties of the nuisance parameters, relative to their nominal uncertainties, which are indicated by the dashed lines.

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Measurement of photonuclear jet production in ultra-peripheral Pb+Pb collisions at $\sqrt{s_{\text{NN}}} = 5.02$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
Phys.Rev.D 111 (2025) 052006, 2025.
Inspire Record 2829427 DOI 10.17182/hepdata.156979

In ultra-relativistic heavy ion collisions at the LHC, each nucleus acts a sources of high-energy real photons that can scatter off the opposing nucleus in ultra-peripheral photonuclear ($\gamma+A$) collisions. Hard scattering processes initiated by the photons in such collisions provide a novel method for probing nuclear parton distributions in a kinematic region not easily accessible to other measurements. ATLAS has measured production of dijet and multi-jet final states in ultra-peripheral Pb+Pb collisions at $\sqrt{s_{\text{NN}}} = 5.02$ TeV using a data set recorded in 2018 with an integrated luminosity of 1.72 $\text{nb}^{-1}$. Photonuclear final states are selected by requiring a rapidity gap in the photon direction; this selects events where one of the outgoing nuclei remains intact. Jets are reconstructed using the anti-$k_\text{t}$ algorithm with radius parameter, $R = 0.4$. Triple-differential cross-sections, unfolded for detector response, are measured and presented using two sets of kinematic variables. The first set consists of the total transverse momentum ($H_\text{T}$),rapidity, and mass of the jet system. The second set uses $H_\text{T}$ and particle-level nuclear and photon parton momentum fractions, $x_\text{A}$ and $z_{\gamma}$, respectively. The results are compared with leading-order (LO) perturbative QCD calculations of photonuclear jet production cross-sections, where all LO predictions using existing fits fall below the data in the shadowing region. More detailed theoretical comparisons will allow these results to strongly constrain nuclear parton distributions, and these data provide results from the LHC directly comparable to early physics results at the planned Electron-Ion Collider.

3 data tables

The fraction of photonuclear jet events passing the fiducial requirements in which the photon-emitting nucleus does not break up as a function of \zg. The systematic uncertainties are not symmetrized, and correlations in uncertainties are neglected for both the total systematic uncertainty and statistical uncertainty.

Fully unfolded triple-differential cross-sections as a function of $H_\text{T}$, $y_\text{jets}$, and $m_\text{jets}$. Systematic uncertainties are decomposed into symmetrized nuisance parameters, where parameters labelled "Corr" are fully correlated bin-to-bin, while parameters labelled "Uncorr" should be treated as un-correlated bin-to-bin. These cross-sections are not corrected for the effects of additional nuclear break-up. Values for the total fiducial cross-section in each bin are reported with full statistical and systematic uncertainties. Fractions of the total bin volume occupied by the fiducial region, fractions of the total cross-section in that bin satisfying fiducial requirements, and mean bin values for each axis variable are derived from Pythia 8 Monte Carlo and reported as well. For more details on these quantities, see Appendix B.

Fully unfolded triple-differential cross-sections as a function of $H_\text{T}$, $x_\text{A}$, and $z_{\gamma}$. Systematic uncertainties are decomposed into symmetrized nuisance parameters, where parameters labelled "Corr" are fully correlated bin-to-bin, while parameters labelled "Uncorr" should be treated as un-correlated bin-to-bin. These cross-sections are not corrected for the effects of additional nuclear break-up. Values for the total fiducial cross-section in each bin are reported with full statistical and systematic uncertainties. Fractions of the total bin volume occupied by the fiducial region, fractions of the total cross-section in that bin satisfying fiducial requirements, and mean bin values for each axis variable are derived from Pythia 8 Monte Carlo and reported as well. For more details on these quantities, see Appendix B.


Search for magnetic monopole pair production in ultraperipheral Pb+Pb collisions at $\sqrt{s_{_\textrm{NN}}}=5.36$ TeV with the ATLAS detector at the LHC

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
Phys.Rev.Lett. 134 (2025) 061803, 2025.
Inspire Record 2819870 DOI 10.17182/hepdata.153408

This Letter presents a search for highly ionizing magnetic monopoles in 262$~\mu$b$^{-1}$ of ultraperipheral Pb+Pb collision data at $\sqrt{s_{_\textrm{NN}}}=5.36$ TeV collected by the ATLAS detector at the LHC. A new methodology that exploits the properties of clusters of hits reconstructed in the innermost silicon detector layers is introduced to study highly ionizing particles in heavy-ion data. No significant excess above the background, which is estimated using a data-driven technique, is observed. Using a nonperturbative semiclassical model, upper limits at 95% confidence level are set on the cross-section for pair production of monopoles with a single Dirac magnetic charge in the mass range of 20-150 GeV. The search significantly improves on the previous cross-section limits for production of low-mass monopoles in ultraperipheral Pb+Pb collisions.

1 data table

Expected and observed cross-section upper limits computed using the CL$_{s}$ method for $|q_{m}| = 1 g_{\textrm{D}}$ and assuming FPA model


Disentangling sources of momentum fluctuations in Xe+Xe and Pb+Pb collisions with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
Phys.Rev.Lett. 133 (2024) 252301, 2024.
Inspire Record 2806288 DOI 10.17182/hepdata.153671

High-energy nuclear collisions create a quark-gluon plasma, whose initial condition and subsequent expansion vary from event to event, impacting the distribution of the event-wise average transverse momentum ($P([p_{\mathrm{T}}])$). Distinguishing between contributions from fluctuations in the size of the nuclear overlap area (geometrical component) and other sources at fixed size (intrinsic component) presents a challenge. Here, these two components are distinguished by measuring the mean, variance, and skewness of $P([p_{\mathrm{T}}])$ in $^{208}$Pb+$^{208}$Pb and $^{129}$Xe+$^{129}$Xe collisions at $\sqrt{s_{{\mathrm{NN}}}} = 5.02$ and 5.44 TeV, respectively, using the ATLAS detector at the LHC. All observables show distinct changes in behavior in ultra-central collisions, where the geometrical variations are suppressed as the overlap area reaches its maximum. These results demonstrate a new technique to disentangle geometrical and intrinsic fluctuations, enabling constraints on initial condition and properties of the quark-gluon plasma, such as the speed of sound.

42 data tables

Data from Figure 1, panel a, $\left\langle[p_{T}]\right\rangle$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel b, $\left\langle[p_{T}]\right\rangle$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel b, $\left\langle[p_{T}]\right\rangle$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

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Measurements of the suppression and correlations of dijets in Xe+Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV

The ATLAS collaboration Aad, G. ; Abbott, B. ; Abeling, K. ; et al.
Phys.Rev.C 108 (2023) 024906, 2023.
Inspire Record 2630510 DOI 10.17182/hepdata.139684

Measurements of the suppression and correlations of dijets is performed using 3 $\mu$b$^{-1}$ of Xe+Xe data at $\sqrt{s_{\mathrm{NN}}} = 5.44$ TeV collected with the ATLAS detector at the LHC. Dijets with jets reconstructed using the $R=0.4$ anti-$k_t$ algorithm are measured differentially in jet $p_{\text{T}}$ over the range of 32 GeV to 398 GeV and the centrality of the collisions. Significant dijet momentum imbalance is found in the most central Xe+Xe collisions, which decreases in more peripheral collisions. Results from the measurement of per-pair normalized and absolutely normalized dijet $p_{\text{T}}$ balance are compared with previous Pb+Pb measurements at $\sqrt{s_{\mathrm{NN}}} =5.02$ TeV. The differences between the dijet suppression in Xe+Xe and Pb+Pb are further quantified by the ratio of pair nuclear-modification factors. The results are found to be consistent with those measured in Pb+Pb data when compared in classes of the same event activity and when taking into account the difference between the center-of-mass energies of the initial parton scattering process in Xe+Xe and Pb+Pb collisions. These results should provide input for a better understanding of the role of energy density, system size, path length, and fluctuations in the parton energy loss.

62 data tables

The centrality intervals in Xe+Xe collisions and their corresponding TAA with absolute uncertainties.

The centrality intervals in Xe+Xe and Pb+Pb collisions for matching SUM ET FCAL intervals and respective TAA values for Xe+Xe collisions.

The performance of the jet energy scale (JES) for jets with $|y| < 2.1$ evaluated as a function of pT_truth in different centrality bins. Simulated hard scatter events were overlaid onto events from a dedicated sample of minimum-bias Xe+Xe data.

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Dielectron production at midrapidity at low transverse momentum in peripheral and semi-peripheral Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

The ALICE collaboration Acharya, S. ; Adamová, D. ; Adler, A. ; et al.
JHEP 06 (2023) 024, 2023.
Inspire Record 2071861 DOI 10.17182/hepdata.134246

The first measurement of the ${\rm e}^{+}{\rm e}^{-}$ pair production at low lepton pair transverse momentum ($p_{\rm T,ee}$) and low invariant mass ($m_{\rm ee}$) in non-central Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV at the LHC is presented. The dielectron production is studied with the ALICE detector at midrapidity ($|\eta_{\rm e}| < 0.8$) as a function of invariant mass ($0.4 \leq m_{\rm ee} < 2.7$ GeV/$c^2$) in the 50$-$70% and 70$-$90% centrality classes for $p_{\rm T,ee} < 0.1$ GeV/$c$, and as a function of $p_{\rm T,ee}$ in three $m_{\rm ee}$ intervals in the most peripheral Pb$-$Pb collisions. Below a $p_{\rm T,ee}$ of 0.1 GeV/$c$, a clear excess of ${\rm e}^{+}{\rm e}^{-}$ pairs is found compared to the expectations from known hadronic sources and predictions of thermal radiation from the medium. The $m_{\rm ee}$ excess spectra are reproduced, within uncertainties, by different predictions of the photon$-$photon production of dielectrons, where the photons originate from the extremely strong electromagnetic fields generated by the highly Lorentz-contracted Pb nuclei. Lowest-order quantum electrodynamic (QED) calculations, as well as a model that takes into account the impact-parameter dependence of the average transverse momentum of the photons, also provide a good description of the $p_{\rm T,ee}$ spectra. The measured $\sqrt{\langle p_{\rm T,ee}^{2} \rangle}$ of the excess $p_{\rm T,ee}$ spectrum in peripheral Pb$-$Pb collisions is found to be comparable to the values observed previously at RHIC in a similar phase-space region.

10 data tables

Differential $e^+e^-$ yield in 50--70\% Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV as a function of $m_{\rm ee}$ for $p_{\rm T,ee} < 0.1$ GeV/$c$. Electrons are measured within $|\eta_{\rm e}| < 0.8$ and $p_{\rm T,e} > 0.2$ GeV/$c$. The quoted upper limits correspond to a 90% confidence level.

Differential $e^+e^-$ yield in 70--90\% Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV as a function of $m_{\rm ee}$ for $p_{\rm T,ee} < 0.1$ GeV/$c$. Electrons are measured within $|\eta_{\rm e}| < 0.8$ and $p_{\rm T,e} > 0.2$ GeV/$c$.

Differential excess $e^+e^-$ yield in 50--70\% Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV as a function of $m_{\rm ee}$ for $p_{\rm T,ee} < 0.1$ GeV/$c$. Electrons are measured within $|\eta_{\rm e}| < 0.8$ and $p_{\rm T,e} > 0.2$ GeV/$c$. The quoted upper limits correspond to a 90% confidence level.

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First measurement of antideuteron number fluctuations at energies available at the Large Hadron Collider

The ALICE collaboration Acharya, S. ; Adamová, D. ; Adler, A. ; et al.
Phys.Rev.Lett. 131 (2023) 041901, 2023.
Inspire Record 2070391 DOI 10.17182/hepdata.136310

The first measurement of event-by-event antideuteron number fluctuations in high energy heavy-ion collisions is presented. The measurements are carried out at midrapidity ($|\eta| < 0.8$) as a function of collision centrality in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV using the ALICE detector. A significant negative correlation between the produced antiprotons and antideuterons is observed in all collision centralities. The results are compared with coalescence calculations, which fail to describe the measurement, in particular if a correlated production of protons and neutrons is assumed. Thermal-statistical model calculations describe the data within uncertainties only for correlation volumes that are different with respect to those describing proton yields and a similar measurement of net-proton number fluctuations.

5 data tables

Second order to first order cumulant ratio of the $\overline{d}$ multiplicity distribution as a function of collision centrality in Pb-Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV.

Pearson correlation between the measured $\overline{p}$ and $\overline{d}$ as a function of collision centrality in Pb-Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV.

Dependence of $\overline{p}$-$\overline{d}$ correlation on pseudorapidity acceptance of $\overline{p}$ and $\overline{d}$ selection in Pb-Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV. Results are for 0.0--10.0$\%$ collision centrality.

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Underlying-event properties in pp and p$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

The ALICE collaboration Acharya, S. ; Adamová, D. ; Adler, A. ; et al.
JHEP 06 (2023) 023, 2023.
Inspire Record 2071174 DOI 10.17182/hepdata.133032

We report about the properties of the underlying event measured with ALICE at the LHC in pp and p$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. The event activity, quantified by charged-particle number and summed-$p_{\rm T}$ densities, is measured as a function of the leading-particle transverse momentum ($p_{\rm T}^{\rm trig}$). These quantities are studied in three azimuthal-angle regions relative to the leading particle in the event: toward, away, and transverse. Results are presented for three different $p_{\rm T}$ thresholds (0.15, 0.5, and 1 GeV/$c$) at mid-pseudorapidity ($|\eta|<0.8$). The event activity in the transverse region, which is the most sensitive to the underlying event, exhibits similar behaviour in both pp and p$-$Pb collisions, namely, a steep increase with $p_{\rm T}^{\rm trig}$ for low $p_{\rm T}^{\rm trig}$, followed by a saturation at $p_{\rm T}^{\rm trig} \approx 5$ GeV/$c$. The results from pp collisions are compared with existing measurements at other centre-of-mass energies. The quantities in the toward and away regions are also analyzed after the subtraction of the contribution measured in the transverse region. The remaining jet-like particle densities are consistent in pp and p$-$Pb collisions for $p_{\rm T}^{\rm trig}>10$ GeV/$c$, whereas for lower $p_{\rm T}^{\rm trig}$ values the event activity is slightly higher in p$-$Pb than in pp collisions. The measurements are compared with predictions from the PYTHIA 8 and EPOS LHC Monte Carlo event generators.

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Fig. 4: Number density $N_{\rm ch}$ (left) and $\Sigma p_{\rm T}$ (right) distributions as a function of $p_{\rm T}^{\rm trig}$ in Transverse, Away, and Toward regions for $p_{\rm T} >$ 0.5 GeV/$c$. The shaded areas and the error bars around the data points represent the systematic and statistical uncertainties, respectively.

Fig. 5: Number density $N_{\rm ch}$ (left) and $\Sigma p_{\rm T}$ (right) distributions as a function of $p_{\rm T}^{\rm trig}$ in Transverse, Away, and Toward regions for $p_{\rm T} >$ 0.5 GeV/$c$. The shaded areas and the error bars around the data points represent the systematic and statistical uncertainties, respectively.

Fig. 6a: Number density $N_{\rm ch}$ (left) and $\Sigma p_{\rm T}$ (right) distributions as a function of $p_{\rm T}^{\rm trig}$ in Away and Toward regions after the subtraction of Number density $N_{\rm ch}$ and $\Sigma p_{\rm T}$ distributions in the transverse region for pp collisions for $p_{\rm T} >$ 0.5 GeV/$c$. The shaded areas and the error bars around the data points represent the systematic and statistical uncertainties, respectively.

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Measurement of the photon$+b$-jet production differential cross section in $p\bar{p}$ collisions at $\sqrt{s}=1.96~\TeV$

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Acharya, B.S. ; et al.
Phys.Lett.B 714 (2012) 32-39, 2012.
Inspire Record 1095100 DOI 10.17182/hepdata.61739

We present measurements of the differential cross section dsigma/dpT_gamma for the inclusive production of a photon in association with a b-quark jet for photons with rapidities |y_gamma|< 1.0 and 30<pT_gamma <300 GeV, as well as for photons with 1.5<|y_gamma|< 2.5 and 30< pT_gamma <200 GeV, where pT_gamma is the photon transverse momentum. The b-quark jets are required to have pT>15 GeV and rapidity |y_jet| < 1.5. The results are based on data corresponding to an integrated luminosity of 8.7 fb^-1, recorded with the D0 detector at the Fermilab Tevatron $p\bar{p}$ Collider at sqrt(s)=1.96 TeV. The measured cross sections are compared with next-to-leading order perturbative QCD calculations using different sets of parton distribution functions as well as to predictions based on the kT-factorization QCD approach, and those from the Sherpa and Pythia Monte Carlo event generators.

2 data tables

The differential cross section as a function of PT for the production of GAMMA + B-JET in the photon |rapidity/ region < 1.0.

The differential cross section as a function of PT for the production of GAMMA + B-JET in the photon |rapidity| region 1.5-2.5.