The exclusive electroproduction of J/psi mesons, ep->epJ/psi, has been studied with the ZEUS detector at HERA for virtualities of the exchanged photon in the ranges 0.15<Q^2<0.8 GeV^2 and 2<Q^2<100 GeV^2 using integrated luminosities of 69 pb^-1 and 83 pb^-1, respectively.The photon-proton centre-of-mass energy was in the range 30<W<220 GeV and the squared four-momentum transfer at the proton vertex |t|<1.The cross sections and decay angular distributions are presented as functions of Q^2, W and t. The effective parameters of the Pomeron trajectory are in agreement with those found in J/psi photoproduction. The spin-density matrix elements, calculated from the decay angular distributions, are consistent with the hypothesis of s-channel helicity conservation. The ratio of the longitudinal to transverse cross sections, sigma_L/sigma_T, grows with Q^2, whilst no dependence on W or t is observed. The results are in agreement with perturbative QCD calculations and exhibit a strong sensitivity to the gluon distribution in the proton.
Cross sections for exclusive J/PSI production as a function of W in the Q**2 region 0.15 to 0.18 GeV**2.
Cross sections for exclusive J/PSI production as a function of W in the Q**2 region 2 to 5 GeV**2.
Cross sections for exclusive J/PSI production as a function of W in the Q**2 region 5 to 10 GeV**2.
A study of the inclusive charged hadron production in two-photon collisions is described. The data were collected with the DELPHI detector at LEP II. Results on the inclusive single-particle p_T distribution and the differential charged hadrons dsigma/dp_T cross-section are presented and compared to the predictions of perturbative NLO QCD calculations and to published results.
Differential inclusive DSIG/DPT distribution of charged particles produced in GAMMA* GAMMA* interaction with two pseudorapidity cut offs.
Inclusive non-diffractive photoproduction of rho(770)^0, K^*(892)^0 and phi(1020) mesons is investigated with the H1 detector in ep collisions at HERA. The corresponding average \gamma p centre-of-mass energy is 210 GeV. The mesons are measured in the transverse momentum range 0.5<p_T<7 GeV and the rapidity range |y_{lab}|<1. Differential cross sections are presented as a function of transverse momentum and rapidity, and are compared to the predictions of hadroproduction models.
Inclusive non-diffractive photoproduction cross sections in the specified kinematic region.
Ratios of cross sections.
Inclusive non-diffractive photoproduction invariant differential cross sections as a function of PT in the specified kinematic range.
Cross-sections for the photoproduction of events containing four high-$E_{\rm T}$ jets have been measured with the ZEUS detector using an integrated luminosity of 38.7 pb$^{-1}$. At low invariant mass of the four-jet system, $m_{\rm 4J}$, the observed event distributions are sensitive to the underlying event model. The inclusion of multi-parton interactions in Monte Carlo simulations lead to a significantly better description of the data. For $m_{\rm 4J} > 50 $ GeV the data is adequately described by models with no simulation of an underlying event, suggesting that this is a kinematic region suitable for comparison with perturbative QCD calculations.
The measured normalised costheta3 distributions.
The measured normalised psi3 distributions.
The measured normalised X3 distributions.
The production of energetic neutrons in $ep$ collisions has been studied with the ZEUS detector at HERA. The neutron energy and $p_T^2$ distributions were measured with a forward neutron calorimeter and tracker in a $40 \pb^{-1}$ sample of inclusive deep inelastic scattering (DIS) data and a $6 \pb^{-1}$ sample of photoproduction data. The neutron yield in photoproduction is suppressed relative to DIS for the lower neutron energies and the neutrons have a steeper $p_T^2$ distribution, consistent with the expectation from absorption models. The distributions are compared to HERA measurements of leading protons. The neutron energy and transverse-momentum distributions in DIS are compared to Monte Carlo simulations and to the predictions of particle exchange models. Models of pion exchange incorporating absorption and additional secondary meson exchanges give a good description of the data.
Ratio of leading neutron to inclusive cross sections integrated to the full PT range.
Normalized double differential cross sections for leading neutron production for the full DIS sample. Statistical errors only are given.
Normalized double differential cross sections for leading neutron production for the full DIS sample. Statistical errors only are given.
Differential cross sections for jet photoproduction in the reaction ep --> e jet X have been measured with the ZEUS detector at HERA using 82.2 pb^-1 of integrated luminosity. Inclusive jet cross sections are presented as a function of the jet transverse energy, E_T^jet, for jets with E_T^jet > 17 GeV and pseudorapidity -1 < eta^jet < 2.5, in the gamma-p centre-of-mass-energy range 142 < W_gamma-p < 293 GeV. Scaled jet invariant cross sections are presented as a function of the dimensionless variable x_T = 2 E_T^jet/W_gamma-p for <W_gamma-p> = 180 and 255 GeV. Next-to-leading-order QCD calculations give a good description of the measured differential cross sections in both magnitude and shape. The ratio of scaled jet invariant cross sections at the two <W_gamma-p> values shows clear non-scaling behaviour. A value for the strong coupling constant of alpha_s(M_Z) = 0.1224 +- 0.0001 (stat.) + 0.0022 - 0.0019 (exp.) + 0.0054 - 0.0042 (th.) has been extracted from a QCD analysis of the measured dsigma/dE_T^jet. The variation of alpha_s with E_T^jet is in good agreement with the running of alpha_s as predicted by QCD.
Measured inclusive jet cross section.
Measured scaled jet invariant cross section in two W intervals.
Ratio of the measured scaled jet invariant cross section in the two W intervals.
The dependence of the photon structure on the photon virtuality, Q^2, is studied by measuring the reaction e^+p\to e^+ + {\rm jet} + {\rm jet} + {\rm X} at photon-proton centre-of-mass energies 134 < W < 223 GeV. Events have been selected in the Q^2 ranges \approx 0 GeV^2, 0.1-0.55 GeV^2, and 1.5-4.5 GeV^2, having two jets with transverse energy E_T^{jet} > 5.5 GeV in the final state. The dijet cross section has been measured as a function of the fractional momentum of the photon participating in the hard process, x_gamma. The ratio of the dijet cross section with x_gamma < 0.75 to that with x_gamma > 0.75 decreases as Q^2 increases. The data are compared with the predictions of NLO pQCD and leading-order Monte Carlo programs using various parton distribution functions of the photon. The measurements can be interpreted in terms of a resolved photon component that falls with Q^2 but remains present at values of Q^2 up to 4.5 GeV^2. However, none of the models considered gives a good description of the data.
Dijet cross section for the low ET set of cuts.
Dijet cross section for the high ET set of cuts.
Ratio of Dijet cross sections as a function of Q**2 for XOBS(C=GAMMA) less than to greater than 0.75 for the lower ET cuts.
Cross sections for elastic production of J/Psi mesons in photoproduction and electroproduction are measured in electron proton collisions at HERA using an integrated luminosity of 55 pb^{-1}. Results are presented for photon virtualities Q^2 up to 80 GeV^2. The dependence on the photon-proton centre of mass energy W_{gamma p} is analysed in the range 40 < \Wgp < 305 GeV in photoproduction and 40 < \Wgp < 160 GeV in electroproduction. The \Wgp dependences of the cross sections do not change significantly with Q^2 and can be described by models based on perturbative QCD. Within such models, the data show a high sensitivity to the gluon density of the proton in the domain of low Bjorken x and low Q^2. Differential cross sections d\sigma/dt, where t is the squared four-momentum transfer at the proton vertex, are measured in the range |t|<1.2 GeV^2 as functions of \Wgp and Q^2. Effective Pomeron trajectories are determined for photoproduction and electroproduction. The J/Psi production and decay angular distributions are consistent with s-channel helicity conservation. The ratio of the cross sections for longitudinally and transversely polarised photons is measured as a function of Q^2 and is found to be described by perturbative QCD based models.
Cross section for elastic J/PSI photoproduction in Q**2 bins for W = 90 GeV and ABS(T) < 1.2 GeV**2.
Cross section for elastic J/PSI photoproduction in W bins for ABS(T) < 1.2 GeV**2 and Q**2 < 1 GeV**2.. There are two cross sections for the 205 to 235 GeV bin due to overlapping data sets. The mean is 151 +- 8 (DSYS=20) nb.
Cross section for elastic J/PSI photoproduction as a function of W in Q**2 bins for ABS(T) < 1.2 GeV**2.
Exclusive rho^0 rho^0 production in two-photon collisions between a quasi-real and a mid-virtuality photon is studied with data collected at LEP at centre-of-mass energies 183GeV < sqrt{s} < 209GeV with a total integrated luminosity of 684.8/pb. The cross section of the process gamma gamma* -> rho^0 rho^0 is determined as a function of the photon virtuality, q^2, and the two-photon centre-of-mass energy, Wgg, in the kinematic region: 0.2GeV^2 < q^2 < 0.85GeV^2 and 1.1GeV < Wgg < 3GeV.
Production cross section as a function of Q**2. Differential cross sectionsare corrected to the centre of each bin.
Production cross section for two-photon data as a function of Q**2.
Production cross section as a function of W.
Exclusive rho+rho- production in two-photon collisions between a quasi-real photon, gamma, and a mid-virtuality photon, gamma*, is studied with data collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* -> rho+ rho- process is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2 < 30 GeV^2.
Production cross section as a function of Q**2. Differential cross sectionsare corrected to the centre of each bin.
Production cross section for two-photon data as a function of Q**2.
Production cross section as a function of W.
Deep inelastic scattering and its diffractive component, ep -> e'gamma*p ->e'XN, have been studied at HERA with the ZEUS detector using an integrated luminosity of 4.2 pb-1. The measurement covers a wide range in the gamma*p c.m. energy W (37 - 245 GeV), photon virtuality Q2 (2.2 - 80 GeV2) and mass Mx. The diffractive cross section for Mx > 2 GeV rises strongly with W: the rise is steeper with increasing Q2. The latter observation excludes the description of diffractive deep inelastic scattering in terms of the exchange of a single Pomeron. The ratio of diffractive to total cross section is constant as a function of W, in contradiction to the expectation of Regge phenomenology combined with a naive extension of the optical theorem to gamma*p scattering. Above Mx of 8 GeV, the ratio is flat with Q2, indicating a leading-twist behaviour of the diffractive cross section. The data are also presented in terms of the diffractive structure function, F2D(3)(beta,xpom,Q2), of the proton. For fixed beta, the Q2 dependence of xpom F2D(3) changes with xpom in violation of Regge factorisation. For fixed xpom, xpom F2D(3) rises as beta -> 0, the rise accelerating with increasing Q2. These positive scaling violations suggest substantial contributions of perturbative effects in the diffractive DIS cross section.
Measurement of the proton structure function F2 at Q**2 = 2.7 GeV**2.
Measurement of the proton structure function F2 at Q**2 = 4.0 GeV**2.
Measurement of the proton structure function F2 at Q**2 = 6.0 GeV**2.
The QED processes e^+ e^- -> e^+ e^- \mu^+ \mu^- and e^+ e^- -> e^+ e^- \tau^+ \tau^- are studied with the L3 detector at LEP using an untagged data sample collected at centre-of-mass energies 161 GeV < sqrt{s} < 209 GeV. The tau-pairs are observed through the associated decay of one tau into e\nu\nu and the other into \pi\pi\nu . The cross sections are measured as a function of sqrt{s}. For muon pairs, the cross section of the \gamma\gamma -> \mu^+\mu^- process is also measured as a function of the two-photon centre-of-mass energy for 3 GeV < W_{\gamma\gamma} < 40 GeV. Good agreement is found between these measurements and the O(\alpha^4) QED expectations. In addition, limits on the anomalous magnetic and electric dipole moments of the tau lepton are extracted.
Cross sections for muon-pair production as a function of centre of mass energy.
Cross sections for tau-pair production as a function of centre of mass energy.
Cross sections for the process GAMMA GAMMA --> MU+ MU- as a function of W.
The diffractive photoproduction of J/psi mesons is measured with the H1 detector at the ep collider HERA using an integrated luminosity of 78 pb^-1. The differential cross section d sigma(gamma p -> J/psi Y) / d t is studied in the range 2 < |t| < 30 GeV^2, where t is the square of the four-momentum transferred at the proton vertex. The cross section is also presented as a function of the photon-proton centre-of-mass energy W in three t intervals, spanning the range 50 < W < 200 GeV. A fast rise of the cross section with W is observed for each t range and the slope for the effective linear Pomeron trajectory is measured to be alpha^\prime= -0.0135 \pm 0.0074 (stat.) \pm 0.0051 (syst.) GeV^-2. The measurements are compared with perturbative QCD models based on BFKL and DGLAP evolution. The data are found to be compatible with s-channel helicity conservation.
The differential photoproduction cross section DSIG/DT for diffractive J/PSI production.
The J/PSI photoproduction cross section as a function of W for the ABS(T) range 2 to 5 GeV**2.
The J/PSI photoproduction cross section as a function of W for the ABS(T) range 5 to 10 GeV**2.
The reaction e^+e^- -> e^+e^- proton antiproton is studied with the L3 detector at LEP. The analysis is based on data collected at e^+e^- center-of-mass energies from 183 GeV to 209 GeV, corresponding to an integrated luminosity of 667 pb^-1. The gamma gamma -> proton antiproton differential cross section is measured in the range of the two-photon center-of-mass energy from 2.1 GeV to 4.5 GeV. The results are compared to the predictions of the three-quark and quark-diquark models.
Total cross section for P PBAR production at a mean centre-of-mass energy of 197 GeV.
The cross section as a function of W for ABS(COS(THETA)) < 0.6.
The differential cross section as a function of COS(THETA*) for three W ranges.
Exclusive rho rho production in two-photon collisions involving a single highly virtual photon is studied with data collected at LEP at centre-of-mass energies 89GeV < \sqrt{s} < 209GeV with a total integrated luminosity of 854.7pb^-1 The cross section of the process gamma gamma^* -> rho rho is determined as a function of the photon virtuality, Q^2 and the two-photon centre-of-mass energy, Wgg, in the kinematic region: 1.2GeV^2 < Q^2 < 30GeV^2 and 1.1GeV < Wgg < 3GeV.
Production cross sections as a function of Q**2. The differential cross sections are corrected to the centre of each bin.
Production cross section for the two photon data as a function of Q**2.
Differential cross section for non-resonance and RHO0 RHO0 data corrected to the centre of each bin.
Dijet angular distributions of photoproduction events in which a $D^{*\pm}$ meson is produced in association with one of two energetic jets have been measured with the ZEUS detector at HERA, using an integrated luminosity of 120 pb$^{-1}$. Differential cross sections as a function of the angle between the charm-jet and the proton-beam direction in the dijet rest frame have been measured for samples enriched in direct or resolved photon events. The results are compared with predictions from leading-order parton-shower Monte Carlo models and with next-to-leading-order QCD calculations. The angular distributions show clear evidence for the existence of charm originating from the photon.
The differential cross section DSIG/DXOBS(C=GAMMA) as a function of XOBS(C=GAMMA).
The differential cross section DSIG/DXOBS(C=PROTON) as a function of XOBS(C=PROTON).
The dijet angular distributions as a function of the absolute value of the dijet scattering angle for two XOBS(C=GAMMA) regions separating resolved and direct photon processes.
Inclusive jet cross sections are measured in photoproduction at HERA using the H1 detector. The data sample of e+ p -> e+ + jet + X events in the kinematic range of photon virtualities Q^2 < 1 GeV^2 and photon-proton centre-of-mass energies 95 < W_gammap < 285 GeV represents an integrated luminosity of 24.1 pb^-1. Jets are defined using the inclusive k_T algorithm. Single- and multi-differential cross sections are measured as functions of jet transverse energy E_T^jet and pseudorapidity \eta^jet in the domain 5 < E_T^jet < 75 GeV and -1 < \eta^jet < 2.5. The cross sections are found to be in good agreement with next-to-leading order perturbative QCD calculations corrected for fragmentation and underlying event effects. The cross section differential in E_T^jet, which varies by six orders of magnitude over the measured range, is compared with similar distributions from p pbar colliders at equal and higher energies.
Measured differential E+ P cross section DSIG/DET for inclusive jet photoproduction (Q**2 < 1 GeV**2) integrated over the jet pseudorapidity range -1 to 2.5 in the W(C=GAMMA P) range 95 to 285 GeV.
Measured differential E+ P cross section DSIG/DET for inclusive jet photoproduction (Q**2 < 1 GeV**2) integrated over the jet pseudorapidity range -1 to 2.5 in the W(C=GAMMA P) ranges 95 to 212, and 212 to 285 GeV.
Measured differential E+ P cross section DSIG/DET for inclusive jet photoproduction for the two Q**2 ranges integrated over the jet pseudorapidity range -1to 2.5 in the W(C=GAMMA P) range 164 to 242 GeV.
Diffractive dissociation of virtual photons, gamma* p-->Xp, has been studied in ep interactions with the ZEUS detector at HERA using an integrated luminosity of approx. 10 pb^-1. The data cover photon virtualities 0.17 < Q^2< 0.70 GeV^2 and 3 < Q^2< 80 GeV^2 with 3<M_X<38 GeV, where M_X is the mass of the hadronic final state.
The double differential cross section d2sig/dmx/dt measured with the LPS method for the Q**2 range 0.17 to 0.70 GeV**2.
The double differential cross section d2sig/dmx/dt measured with the LPS method for the Q**2 range 3 to 9 GeV**2.
The double differential cross section d2sig/dmx/dt measured with the LPS method for the Q**2 range 9 to 80 GeV**2.
The leptoproduction of J/psi mesons is studied in inelastic reactions for four momentum transfers 2<Q^2<100GeV^2. The data were taken with the H1 detector at the electron proton collider HERA and correspond to an integrated luminosity of 77 pb-1. Single differential and double differential cross sections are measured with increased precision compared with previous analyses. New leading order calculations within the non-relativistic QCD factorisation approach including colour octet and colour singlet contributions are compared with the data and are found to give a reasonable description of most distributions. An exception is the shape of the distribution in the J/psi fractional energy, z, which deviates significantly from that of the data. Comparisons with photoproduction are made and the polarisation of the produced J/psi meson is analysed.
J/PSI leptoproduction differential cross section as a function of Q**2.
J/PSI leptoproduction differential cross section as a function of Z.
J/PSI leptoproduction differential cross section as a function of W.
An analysis of inelastic photoproduction of J/Psi mesons is presented using data collected at the ep collider HERA corresponding to an integrated luminosity of above 80pb-1. Differential and double differential cross sections are measured in a wide kinematic region: 60<W_gammap<260 GeV, 1<p_t^2< 60 GeV^2 and 0.05<z<0.9, where z is the fraction of the energy of the exchanged photon transferred to the J/Psi meson in the rest frame of the target proton. Cross sections at z<0.3 are presented for the first time. Theoretical calculations within the Colour Singlet Model at NLO for direct photon processes are shown to give a good description of the data in the medium z region (0.3<z<0.9) up to the highest p_t^2 values. A calculation using a k_t factorisation approach in LO in the Colour Singlet Model is also able to describe these data. The data in the full z range are also compared to LO calculations within a non-relativistic QCD framework including color octet and colour singlet contributions for direct and resolved photons. It seems possible to reconcile data and theory with modest contributions from colour octet processes. The polarisation of the J/Psi meson is measured as a function of z and p_t,psi and is reasonably described by the theoretical predictions.
The inelastic J/PSI production cross section as a function of W.
The inelastic J/PSI production cross section as a function of Z.
The double differential cross section for J/PSI production as a function of Z and PT**2.
Strange baryon pair production in two-photon collisions is studied with the L3 detector at LEP. The analysis is based on data collected at e+e- centre-of-mass energies from 91 GeV to 208 GeV, corresponding to an integrated luminosity of 844 pb-1. The processes gamma gamma -> Lambda Anti-lambda and gamma gamma -> Sigma0 Anti-sigma0 are identified. Their cross sections as a function of the gamma gamma centre-of-mass energy are measured and results are compared to predictions of the quark-diquark model.
Cross sections for LAMBDA and SIGMA0 pair production in the mass region 2.23 to 3.5 GeV.
Cross sections for LAMBDA pair production as a function of the 2 photon invariant mass W. The average W of each bin is assumes a W**(-8) distribution.
Cross sections for SIGMA0 pair production as a function of the 2 photon invariant mass W. The average W of each bin is assumes a W**(-8) distribution.
The exclusive photoproduction of J/psi mesons, gamma p->J/psi p, has been studied in ep collisions with the ZEUS detector at HERA, in the kinematic range 20<W<290 GeV, where W is the photon-proton centre-of-mass energy. The J/psi mesons were reconstructed in the muon and the electron decay channels using integrated luminosities of 38 pb^-1 and 55 pb^-1, respectively. The helicity structure of J/psi production shows that the hypothesis of s-channel helicity conservation is satisfied at the two standard-deviation level. The total cross section and the differential cross-section dsigma/dt, where t is the squared four-momentum transfer at the proton vertex, are presented as a function of W, for |t|<1.8 GeV^2. The t distribution exhibits an exponential shape with a slope parameter increasing logarithmically with W with a value b=4.15 \pm 0.05 (stat.)^{+0.30}_{-0.18} (syst.) GeV^-2 at W=90 GeV. The effective parameters of the Pomeron trajectory are alphapom(0) = 1.200 \pm 0.009(stat.)^{+0.004}_{-0.010}(syst.) and alphappom= 0.115 \pm 0.018(stat.)^{+0.008}_{-0.015}(syst.) GeV^-2.
The total exclusive J/PSI photoproduction cross section, the differential cross section extrapolated to t=0 and the slope parameter of the exponential t dependence as afunction of W, the photon-proton c.m. energy, for data from J/PSI muon decay.
The total exclusive J/PSI photoproduction cross section as a function of W,the photon-proton c.m. energy, for data from J/PSI electron decays.
The differential cross section extrapolated to t=0 and the slope parameter of the exponential t dependence for exclusive J/PSI photoproduction as a function of W, the photon-proton c.m. energy for data from J/PSI electron decays.
The reaction e+e- -> e+e- gamma* gamma* -> e+e- hadrons for quasi-real photons is studied using data from root(s) = 183 GeV up to 202 GeV. Results on the total cross sections sigma(e+e- -> e+e- hadrons) and sigma(+e- gamma* gamma* -> e+e- hadrons) are given for the two-photon centre-of-mass energies 5 GeV < Wgammagamma < 185 GeV. The total cross section of two real photons is described by a Regge parametrisation. We observe a steeper rise with the two-photon centre-of-mass energy as compared to the hadron-hadron and the photon-proton cross sections. The data are also compared to the expectations of different theoretical models.
The measured total cross section for E+ E- --> E+ E- HADRONS. The first DSYS error is the total experimental systematic uncertainty and the second DSYS error is the uncertainty introduced by unfolding the data with PYTHIA and PHOJET corrections seperately.
The total cross section for two photon production of hadrons. The final column gives the data averaged over all energies together with the experimental systematic error (first DSYS) and the difference between the average and the data unfolded with PHOJET (lower sign) and PYTHIA (upper sign) seperately (second DSYS).
The total hadronic cross-section sigma_gg(W) for the interaction of real photons, gg->hadrons, is measured for gg centre-of-mass energies 10<W<110 GeV. The cross-section is extracted from a measurement of the process e+e- -> e+e-g*g* -> e+e- hardrons, using a luminosity function for the photon flux together with form factors for extrapolating to real photons (Q^2=0 GeV^2). The data were taken with the OPAL detector at LEP at e+e- centre-of-mass energies 161, 172 and 183 GeV. The cross-section sigma_gg(W) is compared with Regge factorisation and with the energy dependence observed in gp and pp interactions. The data are also compared to models which predict a faster rise of sigma_gg(W) compared to gp and pp interactions due to additional hard gg interactions not present in hadronic collisions.
No description provided.
No description provided.
Measurements of the two-photon interaction e + e − → e + e − + hadrons at s ≃ 91 GeV and s ≃ 183 GeV are presented. The double-tag events, collected with the L3 detector, correspond to interated luminosities of 140 pb −1 at 91 GeV and 52 pb −1 at 183 GeV. The cross-section of γ ∗ γ ∗ collisions has been measured at 〈 Q 2 〉 = 3.5 GeV 2 and 〈 Q 2 〉 = 14 GeV 2 . The data agree well with predictions based on perturbative QCD, while the Quark Parton Model alone is insufficient to describe the data.
No description provided.
No description provided.
No description provided.
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