Diffractive Dijet Photoproduction in ep Collisions at HERA

The H1 collaboration Aaron, F.D. ; Alexa, C. ; Andreev, V. ; et al.
Eur.Phys.J.C 70 (2010) 15-37, 2010.
Inspire Record 857109 DOI 10.17182/hepdata.61487

Measurements are presented of single and double-differential dijet cross sections in diffractive photoproduction based on a data sample with an integrated luminosity of 47 pb^-1. The events are of the type ep -> eXY, where the hadronic system X contains at least two jets and is separated by a large rapidity gap from the system Y, which consists of a leading proton or low-mass proton excitation. The dijet cross sections are compared with QCD calculations at next-to-leading order and with a Monte Carlo model based on leading order matrix elements with parton showers. The measured cross sections are smaller than those obtained from the next-to-leading order calculations by a factor of about 0.6. This suppression factor has no significant dependence on the fraction x_gamma of the photon four-momentum entering the hard subprocess. Ratios of the diffractive to the inclusive dijet cross sections are measured for the first time and are compared with Monte Carlo models.

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Diffractive photoproduction of dijetsin $ep$ collisions at HERA

The ZEUS collaboration Chekanov, Sergei ; Derrick, M. ; Magill, S. ; et al.
Eur.Phys.J.C 55 (2008) 177-191, 2008.
Inspire Record 763404 DOI 10.17182/hepdata.63789

Diffractive photoproduction of dijets was measured with the ZEUS detector at the ep collider HERA using an integrated luminosity of 77.2 pb-1. The measurements were made in the kinematic range Q^2 < 1 GeV^2, 0.20 < y < 0.85 and x_pom < 0.025, where Q^2 is the photon virtuality, y is the inelasticity and x_pom is the fraction of the proton momentum taken by the diffractive exchange. The two jets with the highest transverse energy, E_T^jet, were required to satisfy E_T^jet > 7.5 and 6.5 GeV, respectively, and to lie in the pseudorapidity range -1.5 < eta^jet < 1.5. Differential cross sections were compared to perturbative QCD calculations using available parameterisations of diffractive parton distributions of the proton.

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Spin correlation in t anti-t production from p anti-p collisions at S**(1/2) = 1.8-TeV

The D0 collaboration Abbott, B. ; Abolins, M. ; Abramov, V. ; et al.
Phys.Rev.Lett. 85 (2000) 256-261, 2000.
Inspire Record 524260 DOI 10.17182/hepdata.42996

The D0 collaboration has performed a study of spin correlation in tt-bar production for the process tt-bar to bb-bar W^+W^-, where the W bosons decay to e-nu or mu-nu. A sample of six events was collected during an exposure of the D0 detector to an integrated luminosity of approximately 125 pb^-1 of sqrt{s}=1.8 TeV pp-bar collisions. The standard model (SM) predicts that the short lifetime of the top quark ensures the transmission of any spin information at production to the tt-bar decay products. The degree of spin correlation is characterized by a correlation coefficient k. We find that k>-0.25 at the 68% confidence level, in agreement with the SM prediction of k=0.88.

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Pion Pair Production in Photon - Photon Collisions at {SPEAR}

Roussarie, A. ; Burke, D.L. ; Abrams, G.S. ; et al.
Phys.Lett.B 105 (1981) 304-308, 1981.
Inspire Record 166578 DOI 10.17182/hepdata.31056

We report a measurement of the cross section for the process γγ → π + π − at invariant masses 500 MeV/ c 2 < m ππ <2000 MeV/ c 2 . A value for the radiative width of the f(1270) tensor meson Γ f→ γγ = 3.6 ± 0.3 ± 0.5 KeV (helicity λ = 2) has been obtained from a fit to the observed ππ mass spectrum.

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Muon pair production in e p collisions at HERA.

The H1 collaboration Aktas, A. ; Andreev, V. ; Anthonis, T. ; et al.
Phys.Lett.B 583 (2004) 28-40, 2004.
Inspire Record 632638 DOI 10.17182/hepdata.46338

Cross sections for the production of two isolated muons up to high di-muon masses are measured in ep collisions at HERA with the H1 detector in a data sample corresponding to an integrated luminosity of 71 pb^-1 at a centre of mass energy of sqrt{s} = 319 GeV. The results are in good agreement with Standard Model predictions, the dominant process being photon-photon interactions. Additional muons or electrons are searched for in events with two high transverse momentum muons using the full data sample corresponding to 114 pb^-1, where data at sqrt{s} = 301 GeV and sqrt{s} = 319 GeV are combined. Both the di-lepton sample and the tri-lepton sample agree well with the predictions.

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Leading neutron production in e+ p collisions at HERA.

The ZEUS collaboration Chekanov, S. ; Krakauer, D. ; Magill, S. ; et al.
Nucl.Phys.B 637 (2002) 3-56, 2002.
Inspire Record 587158 DOI 10.17182/hepdata.46613

The production of neutrons carrying at least 20% of the proton beam energy ($\xl > 0.2$) in $e^+p$ collisions has been studied with the ZEUS detector at HERA for a wide range of $Q^2$, the photon virtuality, from photoproduction to deep inelastic scattering. The neutron-tagged cross section, $e p\to e' X n$, is measured relative to the inclusive cross section, $e p\to e' X$, thereby reducing the systematic uncertainties. For $\xl >$ 0.3, the rate of neutrons in photoproduction is about half of that measured in hadroproduction, which constitutes a clear breaking of factorisation. There is about a 20% rise in the neutron rate between photoproduction and deep inelastic scattering, which may be attributed to absorptive rescattering in the $\gamma p$ system. For $0.64 < \xl < 0.82$, the rate of neutrons is almost independent of the Bjorken scaling variable $x$ and $Q^2$. However, at lower and higher $\xl$ values, there is a clear but weak dependence on these variables, thus demonstrating the breaking of limiting fragmentation. The neutron-tagged structure function, ${{F}^{\rm\tiny LN(3)}_2}(x,Q^2,\xl)$, rises at low values of $x$ in a way similar to that of the inclusive \ff of the proton. The total $\gamma \pi$ cross section and the structure function of the pion, $F^{\pi}_2(x_\pi,Q^2)$ where $x_\pi = x/(1-\xl)$, have been determined using a one-pion-exchange model, up to uncertainties in the normalisation due to the poorly understood pion flux. At fixed $Q^2$, $F^{\pi}_2$ has approximately the same $x$ dependence as $F_2$ of the proton.

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Inclusive Lambda production in two-photon collisions at LEP.

The L3 collaboration Achard, P. ; Adriani, O. ; Aguilar-Benitez, M. ; et al.
Phys.Lett.B 586 (2004) 140-150, 2004.
Inspire Record 637287 DOI 10.17182/hepdata.48849

The reactions e^+e^- -> e^+e^- Lambda X and e^+e^- -> e^+e^- Lambda X are studied using data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 209 GeV. Inclusive differential cross sections are measured as a function of the lambda transverse momentum, p_t, and pseudo-rapidity, eta, in the ranges 0.4 GeV < p_t < 2.5 GeV and |\eta| < 1.2. The data are compared to Monte Carlo predictions. The differential cross section as a function of p_t is well described by an exponential of the form A exp (- p_t / <p_t>)$.

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Total cross-section in gamma gamma collisions at LEP

The L3 collaboration Acciarri, M. ; Achard, P. ; Adriani, O. ; et al.
Phys.Lett.B 519 (2001) 33-45, 2001.
Inspire Record 552997 DOI 10.17182/hepdata.49853

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 &lt; Wgammagamma &lt; 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.

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Inclusive D*+- production in two photon collisions at LEP

The L3 collaboration Achard, P. ; Adriani, O. ; Aguilar-Benitez, M. ; et al.
Phys.Lett.B 535 (2002) 59-69, 2002.
Inspire Record 585623 DOI 10.17182/hepdata.54885

Inclusive D^{*+-} production in two-photon collisions is studied with the L3 detector at LEP, using 683 pb^{-1} of data collected at centre-of-mass energies from 183 to 208 GeV. Differential cross sections are determined as functions of the transverse momentum and pseudorapidity of the D^{*+-} mesons in the kinematic region 1 GeV &lt; P_T &lt; 12 GeV and |eta| &lt; 1.4. The cross sections sigma(e^+e^- -> e^+e^-D^{*+-}X) in this kinematical region is measured and the sigma(e^+e^- -> e^+e^- cc{bar}X) cross section is derived. The measurements are compared with next-to-leading order perturbative QCD calculations.

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Measurement of eta eta production in two-photon collisions

The Belle collaboration Uehara, S. ; Watanabe, Y. ; Nakazawa, H. ; et al.
Phys.Rev.D 82 (2010) 114031, 2010.
Inspire Record 862260 DOI 10.17182/hepdata.56262

We report the first measurement of the differential cross section for the process gamma gamma --> eta eta in the kinematic range above the eta eta threshold, 1.096 GeV < W < 3.8 GeV over nearly the entire solid angle range, |cos theta*| <= 0.9 or <= 1.0 depending on W, where W and theta* are the energy and eta scattering angle, respectively, in the gamma gamma center-of-mass system. The results are based on a 393 fb^{-1} data sample collected with the Belle detector at the KEKB e^+ e^- collider. In the W range 1.1-2.0 GeV/c^2 we perform an analysis of resonance amplitudes for various partial waves, and at higher energy we compare the energy and the angular dependences of the cross section with predictions of theoretical models and extract contributions of the chi_{cJ} charmonia.

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Inclusive charm production in two-photon collisions at LEP.

The L3 collaboration Acciarri, M. ; Achard, P. ; Adriani, O. ; et al.
Phys.Lett.B 453 (1999) 83-93, 1999.
Inspire Record 481163 DOI 10.17182/hepdata.49252

The cross section of charm production in γγ collisions σ(e + e − →e + e − c c ̄ X) is measured at LEP with the L3 detector at centre-of-mass energies from 91 GeV to 183 GeV. Charmed hadrons are identified by electrons and muons from semileptonic decays. The direct process γγ→c c ̄ is found to be insufficient to describe the data. The measured cross section values and event distributions require contributions from resolved processes, which are sensitive to the gluon density in the photon.

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Inclusive jet production in two-photon collisions at LEP.

The L3 collaboration Achard, P. ; Adriani, O. ; Aguilar-Benitez, M. ; et al.
Phys.Lett.B 602 (2004) 157-166, 2004.
Inspire Record 661114 DOI 10.17182/hepdata.48848

Inclusive jet production, e+e- -> e+e- \ee$ jet X, is studied using 560/pb of data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 209 GeV. The inclusive differential cross section is measured using a k_t jet algorithm as a function of the jet transverse momentum, pt, in the range 3&lt;pt&lt;50 GeV for a pseudorapidity, eta, in the range -1&lt;eta&lt;1. This cross section is well represented by a power law. For high pt, the measured cross section is significantly higher than the NLO QCD predictions, as already observed for inclusive charged and neutral pion production.

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Double tag events in two photon collisions at LEP

The L3 collaboration Achard, P. ; Adriani, O. ; Aguilar-Benitez, M. ; et al.
Phys.Lett.B 531 (2002) 39-51, 2002.
Inspire Record 565440 DOI 10.17182/hepdata.49820

Double-tag events in two-photon collisions are studied using the L3 detector at LEP centre-of-mass energies from root(s)=189 GeV to 209 GeV. The cross sections of the e+e- -> e+e- hadrons and gamma*gamma* -> hadrons processes are measured as a function of the photon virtualities, Q1^2 and Q2^2, of the two-photon mass, W_gammagamma, and of the variable Y=ln(W_gammagamma^2/(Q1 Q2)), for an average photon virtuality &lt;Q2> = 16 GeV2. The results are in agreement with next-to-leading order calculations for the process gamma*gamma* -> q qbar in the interval 2 &lt;= Y &lt;= 5. An excess is observed in the interval 5 &lt; Y &lt;= 7, corresponding to W_gammagamma greater than 40 GeV . This may be interpreted as a sign of resolved photon QCD processes or the onset of BFKL phenomena.

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Di-jet production in gamma-gamma collisions at LEP2

The DELPHI collaboration Abdallah, J. ; Abreu, P. ; Adam, W. ; et al.
Eur.Phys.J.C 58 (2008) 531-541, 2008.
Inspire Record 806241 DOI 10.17182/hepdata.51688

The production of two high-p_T jets in the interactions of quasi-real photons in e+e- collisions at sqrt{s_ee} from 189 GeV to 209 GeV is studied with data corresponding to an integrated e+e- luminosity of 550 pb^{-1}. The jets reconstructed by the k_T cluster algorithm are defined within the pseudo-rapidity range -1 < eta < 1 and with jet transverse momentum, p_T, above 3 GeV/c. The differential di-jet cross-section is measured as a function of the mean transverse momentum ptmean of the jets and is compared to perturbative QCD calculations.

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Measurement of the inclusive differential cross-section for Z bosons as a function of transverse momentum in anti-p p collisions at S**(1/2) = 1.8-TeV

The D0 collaboration Abbott, B. ; Abolins, M. ; Abramov, V. ; et al.
Phys.Rev.D 61 (2000) 032004, 2000.
Inspire Record 503361 DOI 10.17182/hepdata.42104

We present a measurement of the differential cross section as a function of transverse momentum of the Z boson in ppbar collisions at sqrt{s}=1.8 TeV using data collected by the D0 experiment at the Fermilab Tevatron Collider during 1994--1996. We find good agreement between our data and the NNLO resummation prediction and extract values of the non-perturbative parameters for the resummed prediction from a fit to the differential cross section.

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Observation of exclusive electron positron production in hadron hadron collisions.

The CDF collaboration Abulencia, A. ; Adelman, Jahred A. ; Affolder, T. ; et al.
Phys.Rev.Lett. 98 (2007) 112001, 2007.
Inspire Record 732591 DOI 10.17182/hepdata.42744

We present the first observation of exclusive $e^+e^-$ production in hadron-hadron collisions, using $p\bar{p}$ collision data at \mbox{$\sqrt{s}=1.96$ TeV} taken by the Run II Collider Detector at Fermilab, and corresponding to an integrated luminosity of \mbox{532 pb$^{-1}$}. We require the absence of any particle signatures in the detector except for an electron and a positron candidate, each with transverse energy {$E_T>5$ GeV} and pseudorapidity {$|\eta|<2$}. With these criteria, 16 events are observed compared to a background expectation of {$1.9\pm0.3$} events. These events are consistent in cross section and properties with the QED process \mbox{$p\bar{p} \to p + e^+e^- + \bar{p}$} through two-photon exchange. The measured cross section is \mbox{$1.6^{+0.5}_{-0.3}\mathrm{(stat)}\pm0.3\mathrm{(syst)}$ pb}. This agrees with the theoretical prediction of {$1.71 \pm 0.01$ pb}.

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Jets and energy flow in photon - proton collisions at HERA

The H1 collaboration Aid, S. ; Andreev, V. ; Andrieu, B. ; et al.
Z.Phys.C 70 (1996) 17-30, 1996.
Inspire Record 402890 DOI 10.17182/hepdata.44935

Properties of the hadronic final state in photoproduction events with large transverse energy are studied at the electron-proton collider HERA. Distributions of the transverse energy, jets and underlying event energy are compared to $\overline{p}p$ data and QCD calculations. The comparisons show that the $\gamma p$ events can be consistently described by QCD models including -- in addition to the primary hard scattering process -- interactions between the two beam remnants. The differential jet cross sections $d\sigma/dE_T~{jet}$ and $d\sigma/d\eta~{jet}$ are measured.

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Inclusive charged hadron production in two photon collisions at LEP

The L3 collaboration Achard, P. ; Adriani, O. ; Aguilar-Benitez, M. ; et al.
Phys.Lett.B 554 (2003) 105-114, 2003.
Inspire Record 605973 DOI 10.17182/hepdata.48854

Inclusive charged hadron production, e+e- -> e+e- h+- X, is studied using 414 pb-1 of data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 202 GeV. Single particle inclusive differential cross sections are measured as a function of the particle transverse momentum, pt, and pseudo-rapidity, eta. For p_t &lt; 1.5 GeV, the data are well described by an exponential, typical of soft hadronic processes. For higher pt, the onset of perturbative QCD processes is observed. The pi+- production cross section for pt > 5 GeV is much higher than the NLO QCD predictions.

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Measurement of the angular distribution of electrons from W ---> e neutrino decays observed in p anti-p collisions at s**(1/2) = 1.8-TeV

The D0 collaboration Abbott, B. ; Abolins, M. ; Abramov, V. ; et al.
Phys.Rev.D 63 (2001) 072001, 2001.
Inspire Record 533572 DOI 10.17182/hepdata.41717

We present the first measurement of the electron angular distribution parameter alpha_2 in W to e nu events produced in proton-antiproton collisions as a function of the W boson transverse momentum. Our analysis is based on data collected using the D0 detector during the 1994--1995 Fermilab Tevatron run. We compare our results with next-to-leading order perturbative QCD, which predicts an angular distribution of (1 +/- alpha_1 cos theta* + alpha_2 cos^2 theta*), where theta* is the polar angle of the electron in the Collins-Soper frame. In the presence of QCD corrections, the parameters alpha_1 and alpha_2 become functions of p_T^W, the W boson transverse momentum. This measurement provides a test of next-to-leading order QCD corrections which are a non-negligible contribution to the W boson mass measurement.

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Differential cross-section for W boson production as a function of transverse momentum in p anti-p collisions at s**(1/2) = 1.8-TeV

The D0 collaboration Abbott, B. ; Abdesselam, A. ; Abolins, M. ; et al.
Phys.Lett.B 513 (2001) 292-300, 2001.
Inspire Record 535017 DOI 10.17182/hepdata.42950

We report a measurement of the differential cross section for W boson production as a function of its transverse momentum in proton-antiproton collisions at sqrt{s} = 1.8 TeV. The data were collected by the D0 experiment at the Fermilab Tevatron Collider during 1994-1995 and correspond to an integrated luminosity of 85 pb^{-1}. The results are in good agreement with quantum chromodynamics over the entire range of transverse momentum.

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Measurement of inclusive D*+- production in two photon collisions at LEP

The L3 collaboration Acciarri, M. ; Achard, P. ; Adriani, O. ; et al.
Phys.Lett.B 467 (1999) 137-146, 1999.
Inspire Record 505281 DOI 10.17182/hepdata.28070

Inclusive production of $\mathrm{D^{*\pm}}$ mesons in two-photon collisions was measured by the L3 experiment at LEP. The data were collected at a centre-of-mass energy $\sqrt{s} = 189$ GeV with an integrated luminosity of $176.4 \mathrm{pb^{-1}}$. Differential cross sections of the process $\mathrm{e^+e^- \to D^{*\pm} X}$ are determined as functions of the transverse momentum and pseudorapidity of the $\mathrm{D^{*\pm}}$ mesons in the kinematic region 1 GeV $&lt; p_{T}^{\mathrm{D^*}} &lt; 5 $ GeV and $\mathrm{|\eta^{D^*}|} &lt; 1.4$. The cross section integrated over this phase space domain is measured to be $132 \pm 22(stat.) \pm 26(syst.)$ pb. The differential cross sections are compared with next-to-leading order perturbative QCD calculations.

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Angular correlations in three-jet events in ep collisions at HERA

The ZEUS collaboration Chekanov, S. ; Derrick, M. ; Magill, S. ; et al.
Phys.Rev.D 85 (2012) 052008, 2012.
Inspire Record 793931 DOI 10.17182/hepdata.45283

Three-jet production in deep inelastic ep scattering and photoproduction was investigated with the ZEUS detector at HERA using an integrated luminosity of 127 pb-1. Measurements of differential cross sections are presented as functions of angular correlations between the three jets in the final state and the proton-beam direction. These correlations provide a stringent test of perturbative QCD and show sensitivity to the contributions from different colour configurations. Fixed-order perturbative QCD calculations assuming the values of the colour factors C_F, C_A and T_F as derived from a variety of gauge groups were compared to the measurements to study the underlying gauge group symmetry. The measured angular correlations in the deep inelastic ep scattering and photoproduction regimes are consistent with the admixture of colour configurations as predicted by SU(3) and disfavour other symmetry groups, such as SU(N) in the limit of large N.

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Study of D*+- (2010) production in e p collisions at HERA

The ZEUS collaboration Derrick, M. ; Krakauer, D. ; Magill, S. ; et al.
Phys.Lett.B 349 (1995) 225-237, 1995.
Inspire Record 392566 DOI 10.17182/hepdata.45000

We report the first observation of charmed mesons with the ZEUS detector at HERA using the decay channel ${\rm D}~{*+}\rightarrow (\Do \rightarrow {\rm K}~-\pi~+)\pi~+$ (+ c.c.). Clear signals in the mass difference $\Delta M$=$M$(D$~*$)--$M$(D$~0)$ as well as in the $M(K\pi)$ distribution at the D$~0$ mass are found. The $ep$ cross section for inclusive \DSpm\ production with $Q~2<4\GeV~2$ in the $\gamma p$ centre-of-mass energy range $115 < W < 275$ \GeV\ has been determined to be $(32 \pm 7~{+4}_{-7} )$ nb in the kinematic region \mbox{\{$p_T(\DS)\geq $ 1.7 \,\GeV, $|\eta(\DS)| < 1.5 $\}}. Ex\-tra\-po\-la\-ting outside this region, assuming a mass of the charm quark of 1.5 \GeV, we estimate the $ep$ charm cross section to be $\sigma(e p \rightarrow c \bar{c}X ) = (0.45 \pm 0.11~{+0.37}_{-0.22}) \, \mu {\rm b} $ at \mbox{$\sqrt{s} = 296$}\GeV\ and $\langle W \rangle = 198$ \GeV. The average $\gamma p$ charm cross section \mbox{$\sigma(\gamma p \rightarrow c \bar{c}X )$} is found to be \mbox{$(6.3 \pm 2.2~{+6.3}_{-3.0}) \, \mu {\rm b} $} at $\langle W \rangle = 163$ \GeV\ and \mbox{$(16.9 \pm 5.2~{+13.9}_{-8.5}) \, \mu {\rm b} $} at $\langle W \rangle = 243$ \GeV. The increase of the total charm photoproduction cross section by one order of magnitude with respect to low energy data experiments is well described by QCD NLO calculations using singular gluon distributions in the proton.

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A Search for excited fermions in electron - proton collisions at HERA

The ZEUS collaboration Derrick, M. ; Krakauer, D. ; Magill, S. ; et al.
Z.Phys.C 65 (1995) 627-648, 1995.
Inspire Record 378836 DOI 10.17182/hepdata.45049

A search for excited states of the standard model fermions was performed using the ZEUS detector at the HERA electron-proton collider, operating at a centre of mass energy of 296 GeV. In a sample corresponding to an integrated luminosity of 0.55 pb−1, no evidence was found for any resonant state decaying into final states composed of a fermion and a gauge boson. Limits on the coupling strength times branching ratio of excited fermions are presented for masses between 50 GeV and 250 GeV, extending previous search regions significantly.

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Search for single top quark production in ep collisions at HERA

The H1 collaboration Aktas, A. ; Andreev, V. ; Anthonis, T. ; et al.
Eur.Phys.J.C 33 (2004) 9-22, 2004.
Inspire Record 630625 DOI 10.17182/hepdata.46418

A search for single top quark production is performed in e^\pm p collisions at HERA. The search exploits data corresponding to an integrated luminosity of 118.3 pb^-1. A model for the anomalous production of top quarks in a flavour changing neutral current process involving a t-u-gamma coupling is investigated. Decays of top quarks into a b quark and a W boson are considered in the leptonic and the hadronic decay channels of the W. Both a cut-based analysis and a multivariate likelihood analysis are performed to discriminate anomalous top quark production from Standard Model background processes. In the leptonic channel, 5 events are found while 1.31 \pm 0.22 events are expected from the Standard Model background. In the hadronic channel, no excess above the expectation for Standard Model processes is found. These observations lead to a cross section \sigma (ep -> e t X) = 0.29 +0.15 -0.14 pb at \sqrt{s} = 319 GeV. Alternatively, assuming that the observed events are due to a statistical fluctuation, upper limits of 0.55 pb on the anomalous top production cross section and of 0.27 on the t-u-gamma coupling \kappa_{t-u-gamma} are established at the 95% confidence level.

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