Nur Zulaiha Jomhari

Laminar and turbulent mixed convection heat transfer of water/Cu nanofluids in a rectangular shallow cavity was studied utilizing a two-phase mixture model. The upper movable lid of the cavity was at a lower temperature compared to the bottom wall. Simulations were performed for Grashof numbers of 105 (laminar flow) and 1010 (turbulent flow) for Richardson numbers from 0.03 to 30, and nanoparticle volume fractions of 0.00–0.04. The two-dimensional governing equations were discretized using a finite volume method. The effects of nanoparticle concentration, shear and buoyancy forces, and turbulence on flow and thermal behavior of nanofluid flow were studied. The model predictions for very low solid volume fraction (φ ≈ 0) were found to be in good agreement with earlier numerical studies for a base fluid. It is shown that for specific Grashof (Gr) and Richardson (Ri) numbers, increasing the volume fraction of nanoparticles enhances the convective heat transfer coefficient and consequently the Nusselt number (Nu) while having a negligible effect on the wall shear stress and the corresponding skin friction factor.

The effect of radiation on laminar and turbulent mixed convection heat transfer of a semitransparent medium in a square enclosure was studied numerically using the Finite Volume Method. A structured mesh and the SIMPLE algorithm were utilized to model the governing equations. Turbulence and radiation were modeled with the RNG<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>k</mml:mi><mml:mtext>-</mml:mtext><mml:mi>ε</mml:mi></mml:math>model and Discrete Ordinates (DO) model, respectively. For Richardson numbers ranging from 0.1 to 10, simulations were performed for Rayleigh numbers in laminar flow (10 4 ) and turbulent flow (10 8 ). The model predictions were validated against previous numerical studies and good agreement was observed. The simulated results indicate that for laminar and turbulent motion states, computing the radiation heat transfer significantly enhanced the Nusselt number (Nu) as well as the heat transfer coefficient. Higher Richardson numbers did not noticeably affect the average Nusselt number and corresponding heat transfer rate. Besides, as expected, the heat transfer rate for the turbulent flow regime surpassed that in the laminar regime. The simulations additionally demonstrated that for a constant Richardson number, computing the radiation heat transfer majorly affected the heat transfer structure in the enclosure; however, its impact on the fluid flow structure was negligible.

Measurements of open charm and beauty production cross sections in deep inelastic ep scattering at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross sections are obtained in the kinematic range of negative four-momentum transfer squared of the photon $$2.5~\hbox {GeV}^2\le Q^2 \le 2000\, \hbox {GeV}^2$$ and Bjorken scaling variable $$3 \cdot 10^{-5} \le x_\mathrm{Bj} \le 5 \cdot 10^{-2}$$ . The combination method accounts for the correlations of the statistical and systematic uncertainties among the different datasets. Perturbative QCD calculations are compared to the combined data. A next-to-leading order QCD analysis is performed using these data together with the combined inclusive deep inelastic scattering cross sections from HERA. The running charm- and beauty-quark masses are determined as $$m_c(m_c) = 1.290^{+0.046}_{-0.041} \mathrm{(exp/fit)}$$ $${}^{+0.062}_{-0.014} \mathrm{(model)}$$ $${}^{+0.003}_{-0.031} \mathrm{(parameterisation)}$$ GeV and $$m_b(m_b) = 4.049^{+0.104}_{-0.109} \mathrm{(exp/fit)}$$ $${}^{+0.090}_{-0.032} \mathrm{(model)}$$ $${}^{+0.001}_{-0.031} \mathrm{(parameterisation)}~\mathrm{GeV}$$ .

Two-particle azimuthal correlations have been measured in neutral current deep inelastic ep scattering with virtuality Q2> 5 GeV2 at a centre-of-mass energy $$ \sqrt{s} $$ = 318 GeV recorded with the ZEUS detector at HERA. The correlations of charged particles have been measured in the range of laboratory pseudorapidity −1.5 < η < 2.0 and transverse momentum 0.1 < pT< 5.0 GeV and event multiplicities Nch up to six times larger than the average 〈Nch〉 ≈ 5. The two-particle correlations have been measured in terms of the angular observables cn{2} = 〈〈cosnΔφ〉〉, where n is between 1 and 4 and ∆φ is the relative azimuthal angle between the two particles. Comparisons with available models of deep inelastic scattering, which are tuned to reproduce inclusive particle production, suggest that the measured two-particle correlations are dominated by contributions from multijet production. The correlations observed here do not indicate the kind of collective behaviour recently observed at the highest RHIC and LHC energies in high-multiplicity hadronic collisions.

Abstract The HERAPDF2.0 ensemble of parton distribution functions (PDFs) was introduced in 2015. The final stage is presented, a next-to-next-to-leading-order (NNLO) analysis of the HERA data on inclusive deep inelastic ep scattering together with jet data as published by the H1 and ZEUS collaborations. A perturbative QCD fit, simultaneously of $$\alpha _s(M_Z^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and the PDFs, was performed with the result $$\alpha _s(M_Z^2)= 0.1156 \pm 0.0011~\mathrm{(exp)}~ ^{+0.0001}_{-0.0002}~ \mathrm{(model}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.1156</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0011</mml:mn> <mml:mspace /> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>exp</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msubsup> <mml:mspace /> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.0002</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0001</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace /> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>model</mml:mi> </mml:mrow> </mml:mrow> </mml:math> $$\mathrm{+ parameterisation)}~ \pm 0.0029~\mathrm{(scale)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mi>parameterisation</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mspace /> <mml:mo>±</mml:mo> <mml:mn>0.0029</mml:mn> <mml:mspace /> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>scale</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . The PDF sets of HERAPDF2.0Jets NNLO were determined with separate fits using two fixed values of $$\alpha _s(M_Z^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\alpha _s(M_Z^2)=0.1155$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.1155</mml:mn> </mml:mrow> </mml:math> and 0.118, since the latter value was already chosen for the published HERAPDF2.0 NNLO analysis based on HERA inclusive DIS data only. The different sets of PDFs are presented, evaluated and compared. The consistency of the PDFs determined with and without the jet data demonstrates the consistency of HERA inclusive and jet-production cross-section data. The inclusion of the jet data reduced the uncertainty on the gluon PDF. Predictions based on the PDFs of HERAPDF2.0Jets NNLO give an excellent description of the jet-production data used as input.

Production of exclusive dijets in diffractive deep inelastic $$e^\pm p$$ scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 372 pb $$^{-1}$$ . The measurement was performed for $$\gamma ^{*}$$ –p centre-of-mass energies in the range $$90< W < {250}\,{\mathrm{GeV}}$$ and for photon virtualities $$Q^2 > {25}\,{\mathrm{GeV}^{2}}$$ . Energy flows around the jet axis are presented. The cross section is presented as a function of $$\beta $$ and $$\phi $$ , where $$\beta =x/x_\mathrm{I\!P}$$ , x is the Bjorken variable and $$x_\mathrm{I\!P}$$ is the proton fractional longitudinal momentum loss. The angle $$\phi $$ is defined by the $$\gamma ^{*}$$ –dijet plane and the $$\gamma ^{*}$$ – $$e^\pm $$ plane in the rest frame of the diffractive final state. The $$\phi $$ cross section is measured in bins of $$\beta $$ . The results are compared to predictions from models based on different assumptions about the nature of the diffractive exchange.

A simultaneous fit of parton distribution functions (PDFs) and electroweak parameters to HERA data on deep inelastic scattering is presented. The input data are the neutral current and charged current inclusive cross sections which were previously used in the QCD analysis leading to the HERAPDF2.0 PDFs. In addition, the polarization of the electron beam was taken into account for the ZEUS data recorded between 2004 and 2007. Results on the vector and axial-vector couplings of the $Z$ boson to $u$- and $d$-type quarks, on the value of the electroweak mixing angle and the mass of the $W$ boson are presented. The values obtained for the electroweak parameters are in agreement with Standard Model predictions.

A bstract A search for new top quark interactions is performed within the framework of an effective field theory using the associated production of either one or two top quarks with a Z boson in multilepton final states. The data sample corresponds to an integrated luminosity of 138 fb − 1 of proton-proton collisions at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 13 TeV collected by the CMS experiment at the LHC. Five dimension-six operators modifying the electroweak interactions of the top quark are considered. Novel machine-learning techniques are used to enhance the sensitivity to effects arising from these operators. Distributions used for the signal extraction are parameterized in terms of Wilson coefficients describing the interaction strengths of the operators. All five Wilson coefficients are simultaneously fit to data and 95% confidence level intervals are computed. All results are consistent with the SM expectations.

The exclusive deep inelastic electroproduction of ψ(2S) and J/ψ(1S) at an ep centre-of-mass energy of 317 GeV has been studied with the ZEUS detector at HERA in the kinematic range 2<Q2<80 GeV2, 30<W<210 GeV and |t|<1 GeV2, where Q2 is the photon virtuality, W is the photon–proton centre-of-mass energy and t is the squared four-momentum transfer at the proton vertex. The data for 2<Q2<5 GeV2 were taken in the HERA I running period and correspond to an integrated luminosity of 114 pb−1. The data for 5<Q2<80 GeV2 are from both HERA I and HERA II periods and correspond to an integrated luminosity of 468 pb−1. The decay modes analysed were μ+μ− and J/ψ(1S)π+π− for the ψ(2S) and μ+μ− for the J/ψ(1S). The cross-section ratio σψ(2S)/σJ/ψ(1S) has been measured as a function of Q2,W and t. The results are compared to predictions of QCD-inspired models of exclusive vector-meson production.

The high-precision HERA data allows searches up to TeV scales for beyond the Standard Model contributions to electron–quark scattering. Combined measurements of the inclusive deep inelastic cross sections in neutral and charged current ep scattering corresponding to a luminosity of around 1 fb−1 have been used in this analysis. A new approach to the beyond the Standard Model analysis of the inclusive ep data is presented; simultaneous fits of parton distribution functions together with contributions of “new physics” processes were performed. Results are presented considering a finite radius of quarks within the quark form-factor model. The resulting 95% C.L. upper limit on the effective quark radius is 0.43⋅10−16cm.

At large values of $x$, the parton distribution functions (PDFs) of the proton are poorly constrained and there are considerable variations between different global fits. Data at such high $x$ have already been published by the ZEUS Collaboration, but not yet used in PDF extractions. A technique for comparing predictions based on different PDF sets to the observed number of events in the ZEUS data is presented. It is applied to compare predictions from the most commonly used PDFs to published ZEUS data at high Bjorken $x$. A wide variation is found in the ability of the PDFs to predict the observed results. A scheme for including the ZEUS high-$x$ data in future PDF extractions is discussed.

High-precision HERA data corresponding to a luminosity of around $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ have been used in the framework of $eeqq$ contact interactions (CI) to set limits on possible high-energy contributions beyond the Standard Model to electron-quark scattering. Measurements of the inclusive deep inelastic cross sections in neutral and charged current $ep$ scattering were considered. The analysis of the $ep$ data has been based on simultaneous fits of parton distribution functions including contributions of CI couplings to $ep$ scattering. Several general CI models and scenarios with heavy leptoquarks were considered. Improvements in the description of the inclusive HERA data were obtained for a few models. Since a statistically significant deviation from the Standard Model cannot be established, limits in the TeV range were set on all models considered.

Lorentz and $CPT$ symmetry in the quark sector of the Standard Model are studied in the context of an effective field theory using ZEUS ${e}^{\ifmmode\pm\else\textpm\fi{}}p$ data. Symmetry-violating effects can lead to time-dependent oscillations of otherwise time-independent observables, including scattering cross sections. An analysis using five years of inclusive neutral-current deep inelastic scattering events corresponding to an integrated HERA luminosity of $372\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ at $\sqrt{s}=318\text{ }\text{ }\mathrm{GeV}$ has been performed. No evidence for oscillations in sidereal time has been observed within statistical and systematic uncertainties. Constraints, most for the first time, are placed on 42 coefficients parametrizing dominant $CPT$-even dimension-four and $CPT$-odd dimension-five spin-independent modifications to the propagation and interaction of light quarks.

A bstract Charm production in charged current deep inelastic scattering has been measured for the first time in e ± p collisions, using data collected with the ZEUS detector at HERA, corresponding to an integrated luminosity of 358 pb −1 . Results are presented separately for e + p and e − p scattering at a centre-of-mass energy of $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 318 GeV within a kinematic phase-space region of 200 GeV 2 &lt; Q 2 &lt; 60000 GeV 2 and y &lt; 0.9, where Q 2 is the squared four-momentum transfer and y is the inelasticity. The measured cross sections of electroweak charm production are consistent with expectations from the Standard Model within the large statistical uncertainties.

A search for a narrow baryonic state in the $pK^0_S$ and $\bar{p}K^0_S$ system has been performed in $ep$ collisions at HERA with the ZEUS detector using an integrated luminosity of 358 pb$^{-1}$ taken in 2003-2007. The search was performed with deep inelastic scattering events at an $ep$ centre-of-mass energy of 318 GeV for exchanged photon virtuality, $Q^2$, between 20 and 100 $\rm{} GeV^{2}$. Contrary to evidence presented for such a state around 1.52 GeV in a previous ZEUS analysis using a sample of 121 pb$^{-1}$ taken in 1996-2000, no resonance peak was found in the $p(\bar{p})K^0_S$ invariant-mass distribution in the range 1.45-1.7 GeV. Upper limits on the production cross section are set.

The photoproduction of isolated photons has been measured in diffractive events recorded by the ZEUS detector at HERA.Cross sections are evaluated in the photon transverse-energy and pseudorapidity ranges 5 < E γ T < 15 GeV and -0.7 < η γ < 0.9, inclusively, and also with a jet with transverse energy and pseudorapidity in the ranges 4 < E jet T < 35 GeV and -1.5 < η jet < 1.8, using a total integrated electronproton luminosity of 456 pb -1 .A number of kinematic variables were studied and compared to predictions from the RAPGAP Monte Carlo model.An excess of data is observed above the RAPGAP predictions for z meas P > 0.9, where z meas P is the fraction of the longitudinal momentum of the colorless "Pomeron" exchange that is transferred to the photon-jet final state, giving evidence for direct Pomeron interactions.

The high-precision HERA data allows searches up to TeV scales for Beyond the Standard Model contributions to electron-quark scattering. Combined measurements of the inclusive deep inelastic cross sections in neutral and charged current $ep$ scattering corresponding to a luminosity of around 1 fb$^{-1}$ have been used in this analysis. A approach to the beyond the Standard Model analysis of the inclusive $ep$ data is presented; simultaneous fits of parton distribution functions together with contributions of new physics processes were performed. Results are presented considering a finite radius of quarks within the quark form-factor model. The resulting 95% C.L. upper limit on the effective quark radius is $0.43\cdot 10^{-16}$ cm.

A simultaneous fit of parton distribution functions (PDFs) and electroweak parameters to HERA data on deep inelastic scattering is presented. The input data are the neutral current and charged current inclusive cross sections which were previously used in the QCD analysis leading to the HERAPDF2.0 PDFs. In addition, the polarisation of the electron beam was taken into account for the ZEUS data recorded between 2004 and 2007. Results on the vector and axial-vector couplings of the Z boson to u- and d-type quarks, on the value of the electroweak mixing angle and the mass of the W boson are presented. The values obtained for the electroweak parameters are in agreement with Standard Model predictions.

Abstract A new measurement of inclusive-jet cross sections in the Breit frame in neutral current deep inelastic scattering using the ZEUS detector at the HERA collider is presented. The data were taken in the years 2004–2007 at a centre-of-mass energy of $$318\,\,\textrm{GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>318</mml:mn> <mml:mspace /> <mml:mspace /> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> and correspond to an integrated luminosity of $$347\,\,\textrm{pb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>347</mml:mn> <mml:mspace /> <mml:mspace /> <mml:msup> <mml:mtext>pb</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The jets were reconstructed using the $$k_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> -algorithm in the Breit reference frame. They have been measured as a function of the squared momentum transfer, $$Q^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , and the transverse momentum of the jets in the Breit frame, $$p_{\perp ,\text {Breit}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mo>⊥</mml:mo> <mml:mo>,</mml:mo> <mml:mtext>Breit</mml:mtext> </mml:mrow> </mml:msub> </mml:math> . The measured jet cross sections are compared to previous measurements and to perturbative QCD predictions. The measurement has been used in a next-to-next-to-leading-order QCD analysis to perform a simultaneous determination of parton distribution functions of the proton and the strong coupling, resulting in a value of $$\alpha _s(M_Z^2) = 0.1142 \pm 0.0017 \text {~(experimental/fit)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.1142</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0017</mml:mn> <mml:mspace /> <mml:mtext>(experimental/fit)</mml:mtext> </mml:mrow> </mml:math> $${}_{-0.0007}^{+0.0006} \text {~(model/parameterisation)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow /> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.0007</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0006</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace /> <mml:mtext>(model/parameterisation)</mml:mtext> </mml:mrow> </mml:math> $${}_{-0.0004}^{+0.0006} \text {~(scale)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow /> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.0004</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0006</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace /> <mml:mtext>(scale)</mml:mtext> </mml:mrow> </mml:math> , whose accuracy is improved compared to similar measurements. In addition, the running of the strong coupling is demonstrated using data obtained at different scales.

Isolated photons with high transverse energy have been studied in deep inelastic ep scattering with the ZEUS detector at HERA, using an integrated luminosity of 326 pb−1 in the range of exchanged-photon virtuality 10-350 GeV2. Outgoing isolated photons with transverse energy 4 < E < 15 GeV and pseudorapidity − 0.7 < η γ < 0.9 were measured with accompanying jets having transverse energy and pseudorapidity 2.5 < E jet < 35 GeV and −1.5 < ηjet < 1.8, respectively. Differential cross sections are presented for the following variables: the fraction of the incoming photon energy and momentum that is transferred to the outgoing photon and the leading jet; the fraction of the incoming proton energy transferred to the photon and leading jet; the differences in azimuthal angle and pseudorapidity between the outgoing photon and the leading jet and between the outgoing photon and the scattered electron. Comparisons are made with theoretical predictions: a leading-logarithm Monte Carlo simulation, a next-to-leading-order QCD prediction, and a prediction using the k T -factorisation approach.

Production of exclusive dijets in diffractive deep inelastic $e^\pm p$ scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 372 pb$^{-1}$. The measurement was performed for $γ^*-p$ centre-of-mass energies in the range $90 &lt; W &lt; 250$ GeV and for photon virtualities $Q^2 &gt; 25$ GeV$^2$. Energy and transverse-energy flows around the jet axis are presented. The cross section is presented as a function of $β$ and $ϕ$, where $β=x/x_{\rm I\!P}$, $x$ is the Bjorken variable and $x_{\rm I\!P}$ is the proton fractional longitudinal momentum loss. The angle $ϕ$ is defined by the $γ^*-$dijet plane and the $γ^*-e^\pm$ plane in the rest frame of the diffractive final state. The $ϕ$ cross section is measured in bins of $β$. The results are compared to predictions from models based on different assumptions about the nature of the diffractive exchange.

Isolated photons with high transverse energy have been studied in deep inelastic $ep$ scattering with the ZEUS detector at HERA, using an integrated luminosity of $326\,$ pb$^{-1}$ in the range of exchanged-photon virtuality $10 - 350$ GeV$^2$. Outgoing isolated photons with transverse energy $4<E_T^\gamma< 15$ GeV and pseudorapidity $-0.7 <\eta^\gamma< 0.9$ were measured with accompanying jets having transverse energy and pseudorapidity $2.5 <E_T^{jet}<35$ GeV and $-1.5<\eta^{jet}< 1.8$, respectively. Differential cross sections are presented for the following variables: the fraction of the incoming photon energy and momentum that is transferred to the outgoing photon and the leading jet; the fraction of the incoming proton energy transferred to the photon and leading jet; the differences in azimuthal angle and pseudorapidity between the outgoing photon and the leading jet and between the outgoing photon and the scattered electron. Comparisons are made with theoretical predictions: a leading-logarithm Monte Carlo simulation, a next-to-leading-order QCD prediction, and a prediction using the $k_T$-factorisation approach.

Charm production in charged current deep inelastic scattering has been measured for the first time in $e^{\pm}p$ collisions, using data collected with the ZEUS detector at HERA, corresponding to an integrated luminosity of $358 pb^{-1}$. Results are presented separately for $e^{+}p$ and $e^{-}p$ scattering at a centre-of-mass energy of $\sqrt{s} = 318 GeV$ within a kinematic phase-space region of $200 GeV^{2}<Q^{2}<60000 GeV^{2}$ and $y<0.9$, where $Q^{2}$ is the squared four-momentum transfer and $y$ is the inelasticity. The measured cross sections of electroweak charm production are consistent with expectations from the Standard Model within the large statistical uncertainties.

Collective behaviour of final-state hadrons, and multiparton interactions are studied in high-multiplicity $ep$ scattering at a centre-of-mass energy $\sqrt{s}=318$ GeV with the ZEUS detector at HERA. Two- and four-particle azimuthal correlations, as well as multiplicity, transverse momentum, and pseudorapidity distributions for charged-particle multiplicities $N_{\textrm{ch}} \geq 20$ are measured. The dependence of two-particle correlations on the virtuality of the exchanged photon shows a clear transition from photoproduction to neutral current deep inelastic scattering. For the multiplicities studied, neither the measurements in photoproduction processes nor those in neutral current deep inelastic scattering indicate significant collective behaviour of the kind observed in high-multiplicity hadronic collisions at RHIC and the LHC. Comparisons of PYTHIA predictions with the measurements in photoproduction strongly indicate the presence of multiparton interactions from hadronic fluctuations of the exchanged photon.

The HERAPDF2.0 ensemble of parton distribution functions (PDFs) was introduced in 2015. The final stage is presented, a next-to-next-to-leading-order (NNLO) analysis of the HERA data on inclusive deep inelastic $ep$ scattering together with jet data as published by the H1 and ZEUS collaborations. A perturbative QCD fit, simultaneously of $\alpha_s(M_Z^2)$ and and the PDFs, was performed with the result $\alpha_s(M_Z^2) = 0.1156 \pm 0.0011~{\rm (exp)}~ ^{+0.0001}_{-0.0002}~ {\rm (model}$ ${\rm +~parameterisation)}~ \pm 0.0029~{\rm (scale)}$. The PDF sets of HERAPDF2.0Jets NNLO were determined with separate fits using two fixed values of $\alpha_s(M_Z^2)$, $\alpha_s(M_Z^2)=0.1155$ and $0.118$, since the latter value was already chosen for the published HERAPDF2.0 NNLO analysis based on HERA inclusive DIS data only. The different sets of PDFs are presented, evaluated and compared. The consistency of the PDFs determined with and without the jet data demonstrates the consistency of HERA inclusive and jet-production cross-section data. The inclusion of the jet data reduced the uncertainty on the gluon PDF. Predictions based on the PDFs of HERAPDF2.0Jets NNLO give an excellent description of the jet-production data used as input.