Katarzyna Wichmann

HERAFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton and for many different kinds of analyses in Quantum Chromodynamics (QCD). It encodes results from a wide range of experimental measurements in lepton–proton deep inelastic scattering and proton–proton (proton–antiproton) collisions at hadron colliders. These are complemented with a variety of theoretical options for calculating PDF-dependent cross section predictions corresponding to the measurements. The framework covers a large number of the existing methods and schemes used for PDF determination. The data and theoretical predictions are brought together through numerous methodological options for carrying out PDF fits and plotting tools to help to visualise the results. While primarily based on the approach of collinear factorisation, HERAFitter also provides facilities for fits of dipole models and transverse-momentum dependent PDFs. The package can be used to study the impact of new precise measurements from hadron colliders. This paper describes the general structure of HERAFitter and its wide choice of options.

Exclusive rho^0 electroproduction at HERA has been studied with the ZEUS detector using 120 pb^{-1} of integrated luminosity collected during 1996-2000. The analysis was carried out in the kinematic range of photon virtuality 2 < Q^2 < 160 GeV$^2, and gamma^* p centre-of-mass energy 32 < W < 180 GeV. The results include the Q^2 and W dependence of the gamma^* p --> rho^0 p cross section and the distribution of the squared-four-momentum transfer to the proton. The helicity analysis of the decay-matrix elements of the rho^0 was used to study the ratio of the gamma^* p cross section for longitudinal and transverse photon as a function of Q^2 and W. Finally, an effective Pomeron trajectory was extracted. The results are compared to various theoretical predictions.

Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low x and low $$Q^2$$ . A resolution of this tension incorporating $$\ln (1/x)$$ -resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function $$F_L$$ , it also results in a gluon PDF which is steeply rising at low x for low scales, $$Q^2 \simeq 2.5\,\hbox {GeV}^2$$ , contrary to the fixed-order NLO and NNLO gluon PDF.

A study is presented of the impact of updated simulated inclusive electron ion collider deep inelastic scattering data on the determination of the proton and nuclear parton distribution functions (PDFs) at next-to-next-to-leading and next-to-leading order in QCD, respectively. The influence on the proton PDFs is evaluated relative to the HERAPDF2.0 set, which uses inclusive HERA data only, and also relative to the global fitting approach of the MSHT20 PDFs. The impact on nuclear PDFs is assessed relative to the EPPS21 global fit and is presented in terms of nuclear modification ratios. For all cases studied, significant improvements in the PDF uncertainties are observed for several parton species. The most striking impact occurs for the nuclear PDFs in general and for the region of high Bjorken $x$ in the proton PDFs, particularly for the valence quark distributions.

A detailed comparison of HERA data at low Bjorken-$x$ and low four-momentum-transfer squared, ${Q}^{2}$, with predictions based on $\mathrm{ln}{Q}^{2}$ evolution (DGLAP) in perturbative quantum chromodynamics suggests inadequacies of this framework. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, ${F}_{\mathrm{L}}$. This additional term, ${F}_{\mathrm{L}}{A}_{\mathrm{L}}^{\mathrm{HT}}/{Q}^{2}$, improves the description of the reduced cross sections significantly. The resulting predictions for ${F}_{\mathrm{L}}$ suggest that further corrections are required for ${Q}^{2}$ less than about $2\text{ }\text{ }{\mathrm{GeV}}^{2}$.

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.

HERAFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton and for many different kinds of analyses in Quantum Chromodynamics (QCD). It encodes results from a wide range of experimental measurements in lepton-proton deep inelastic scattering and proton-proton (proton-antiproton) collisions at hadron colliders. These are complemented with a variety of theoretical options for calculating PDF-dependent cross section predictions corresponding to the measurements. The framework covers a large number of the existing methods and schemes used for PDF determination. The data and theoretical predictions are brought together through numerous methodological options for carrying out PDF fits and plotting tools to help visualise the results. While primarily based on the approach of collinear factorisation, HERAFitter also provides facilities for fits of dipole models and transverse-momentum dependent PDFs. The package can be used to study the impact of new precise measurements from hadron colliders. This paper describes the general structure of HERAFitter and its wide choice of options.

Combined HERA data on charm production in deep-inelastic scattering have previously been used to determine the charm-quark running mass mc(mc) in the MS‾ renormalisation scheme. Here, the same data are used as a function of the photon virtuality Q2 to evaluate the charm-quark running mass at different scales to one-loop order, in the context of a next-to-leading order QCD analysis. The scale dependence of the mass is found to be consistent with QCD expectations.

Data from high-energy physics (HEP) experiments are collected with significant financial and human effort and are mostly unique. An inter-experimental study group on HEP data preservation and long-term analysis was convened as a panel of the International Committee for Future Accelerators (ICFA). The group was formed by large collider-based experiments and investigated the technical and organisational aspects of HEP data preservation. An intermediate report was released in November 2009 addressing the general issues of data preservation in HEP. This paper includes and extends the intermediate report. It provides an analysis of the research case for data preservation and a detailed description of the various projects at experiment, laboratory and international levels. In addition, the paper provides a concrete proposal for an international organisation in charge of the data management and policies in high-energy physics.

In the present paper, the ATLAS inclusive ${W}^{\ifmmode\pm\else\textpm\fi{}}$ and $Z$ boson production data are analyzed together with the CMS inclusive ${W}^{\ifmmode\pm\else\textpm\fi{}}$ and $Z$ boson production data to investigate any possible tensions between the data sets and to determine the strange sea fraction, within the framework of a parton distribution function fit at next-to next-to-leading order in perturbative QCD.

Abstract Azimuthal correlations in $$\mathrm {Z} +$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>+</mml:mo> </mml:mrow> </mml:math> jet production at large transverse momenta are computed by matching Parton-Branching (PB) TMD parton distributions and showers with NLO calculations via MCatNLO. The predictions are compared with those for dijet production in the same kinematic range. The azimuthal correlations $$\Delta \phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:math> between the Z boson and the leading jet are steeper compared to those in dijet production at transverse momenta $$\mathcal{O}(100)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mn>100</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> GeV , while they become similar for very high transverse momenta $${{\mathcal {O}}}(1000)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1000</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> GeV . The different patterns of $$\mathrm {Z} +$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>+</mml:mo> </mml:mrow> </mml:math> jet and dijet azimuthal correlations can be used to search for potential factorization-breaking effects in the back-to-back region, which depend on the different color and spin structure of the final states and their interferences with the initial states. In order to investigate these effects experimentally, we propose to measure the ratio of the distributions in $$\Delta \phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:math> for $$\mathrm {Z} +$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>+</mml:mo> </mml:mrow> </mml:math> jet- and multijet production at low and at high transverse momenta, and compare the results to predictions obtained assuming factorization. We examine the role of theoretical uncertainties by performing variations of the factorization scale, renormalization scale and matching scale. In particular, we present a comparative study of matching scale uncertainties in the cases of PB-TMD and collinear parton showers.

The combined HERA data for the inclusive deep inelastic scattering (DIS) cross sections for the momentum transfer $Q^2 > 1$ GeV$^2$ are fitted within the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) framework at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy, complemented by a QCD-inspired parameterisation of twist 4 corrections. A modified form of the input parton density functions is also included, motivated by parton saturation mechanism at small Bjorken $x$ and at a low scale. These modifications lead to a significant improvement of the data description in the region of low $Q^2$. For the whole data sample, the new benchmark NNLO DGLAP fit yields $\chi^2$ / d.o.f. $\simeq 1.2$ to be compared to 1.5 resulting from the standard NNLO DGLAP fit. We discuss the results in the context of the parton saturation picture and describe the impact of the higher-twist corrections on the derived parton density functions. The resulting description of the longitudinal proton structure function $F_L$ is consistent with the HERA data. Our estimates of higher-twist contributions to the proton structure functions are comparable to the leading-twist contributions at low $Q^2 \simeq 2$ GeV$^2$ and $x \simeq 10^{-5}$. The $x$-dependence of the twist 4 corrections obtained from the best fit is consistent with the leading twist 4 quasi-partonic operators, corresponding to an exchange of four interacting gluons in the $t$-channel.

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.

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of $$WW$$ di-boson to $$Z$$ boson production cross sections at the LHC.

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.

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.

Abstract Sensitivity to the strong coupling $$\alpha _S(M^2_Z)$$ <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> is investigated using existing Deep Inelastic Scattering data from HERA in combination with projected future measurements from the Electron Ion Collider (EIC) in a next-to-next-to-leading order QCD analysis. A potentially world-leading level of precision is achievable when combining simulated inclusive neutral current EIC data with inclusive charged and neutral current measurements from HERA, with or without the addition of HERA inclusive jet and dijet data. The result can be obtained with substantially less than one year of projected EIC data at the lower end of the EIC centre-of-mass energy range. Some questions remain over the magnitude of uncertainties due to missing higher orders in the theoretical framework.

A phenomenological study of the final combined HERA data on inclusive deep inelastic scattering has been performed. The data are presented and investigated for a kinematic range extending from values of the four-momentum transfer, ${Q}^{2}$, above $1{0}^{4}\text{ }\text{ }{\mathrm{GeV}}^{2}$ down to the lowest values observable at HERA of ${Q}^{2}=0.045\text{ }\text{ }{\mathrm{GeV}}^{2}$ and Bjorken $x$, ${x}_{\text{Bj}}=6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. The data are well described by fits based on perturbative quantum chromodynamics (QCD) using collinear factorisation and evolution of the parton densities encompassed in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi formalism from the highest ${Q}^{2}$ down to ${Q}^{2}$ of a few ${\mathrm{GeV}}^{2}$. The Regge formalism with the soft Pomeron pole can describe the data up to ${Q}^{2}\ensuremath{\approx}0.65\text{ }\text{ }{\mathrm{GeV}}^{2}$. The complete data set can be described by a new fit using the Abramowicz-Levin-Levy-Maor parametrization. The region between the Regge and the perturbative QCD regimes is of particular interest.

A simultaneous Electroweak and QCD fit of electroweak parameters and parton distribution functions to HERA data on deep inelastic scattering is presented. The input data are neutral current and charged current inclusive cross sections measured by the H1 and ZEUS collaborations at the ep collider HERA. The polarisation of the electron beam was taken into account for the ZEUS and H1 data recorded between 2004 and 2007. Results are presented on the vector and axial-vector couplings of the Z boson to u- and d-type quarks. The values are in agreement with Standard Model predictions. The results on a_u and v_u represent the most precise measurements from a single process.

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 project to allow long term access and physics analysis of ZEUS data (ZEUS data preservation) has been established in collaboration with the DESY-IT group. In the ZEUS approach the analysis model is based on the Common Ntuple project, under development since 2006. The real data and all presently available Monte Carlo samples are being preserved in a flat ROOT ntuple format. There is ongoing work to provide the ability to simulate new, additional Monte Carlo samples also in the future. The validation framework of such a scheme using virtualisation techniques is being explored. The goal is to validate the frozen ZEUS software against future changes in hardware and operating system. A cooperation between ZEUS, DESY-IT and the library was established for document digitisation and long-term preservation of collaboration web pages. Part of the ZEUS internal documentation has already been stored within the HEP documentation system INSPIRE. Existing digital documentation, needed to perform physics analysis also in the future, is being centralised and completed.

Sensitivity to the strong coupling $\alpha_S(M^2_Z)$ is investigated using existing Deep Inelastic Scattering data from HERA in combination with projected future measurements from the Electron Ion Collider (EIC) in a next-to-next-to-leading order QCD analysis. A potentially world-leading level of precision is achievable when combining simulated inclusive neutral current EIC data with inclusive charged and neutral current measurements from HERA, with or without the addition of HERA inclusive jet and dijet data. The result can be obtained with substantially less than one year of projected EIC data at the lower end of the EIC centre-of-mass energy range. Some questions remain over the magnitude of uncertainties due to missing higher orders in the theoretical framework.

A study is presented of the impact of simulated inclusive Electron Ion Collider Deep Inelastic Scattering data on the determination of the proton and nuclear parton distribution functions (PDFs) at next-to-next-to-leading and next-to-leading order in QCD, respectively. The influence on the proton PDFs is evaluated relative to the HERAPDF2.0 set, which uses inclusive HERA data only, and also relative to the global fitting approach of the MSHT20 PDFs. The impact on nuclear PDFs is assessed relative to the EPPS21 global fit and is presented in terms of nuclear modification ratios. For all cases studied, significant improvements in the PDF uncertainties are observed for several parton species. The most striking impact occurs for the nuclear PDFs in general and for the region of high Bjorken $x$ in the proton PDFs, particularly for the valence quark distributions.

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.

Recent highlights from the HERA experiments, Hermes, H1 and ZEUS, are reviewed and ideas for future analyses to fully exploit this unique data set are proposed. This document is a summary of a workshop on future physics with HERA data held at DESY, Hamburg at the end of 2014. All areas of HERA physics are covered and contributions from both experimentalists and theorists are included. The document outlines areas where HERA physics can still make a significant contribution, principally in a deeper understanding of QCD, and its relevance to other facilities. Within the framework of the Data Preservation in High Energy Physics, the HERA data have been preserved for analyses to take place over a timescale of 10 years and more. Therefore, although an extensive list of possibilities is presented here, safe storage of the data ensures that it can also be used in the far future should new ideas and analyses be proposed.

Studies of fragmentation and parton density functions are a core component of research in high energy particle and nuclear physics. These quantities are inherently interesting as a probe of the quantum nature of the strong force and are also essential ingredients to additional studies in high energy scattering experiments. These proceedings provide an overview of the state of the art in this area, as presented at the Deep-Inelastic Scattering Conference in the Spring of 2021.

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to leading order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of $WW$ di-boson to $Z$ boson production cross sections at the LHC.

At the ILC machine induced backgrounds, mainly electron-positron pairs from beamstrahlung, will be the most important source of unwanted interactions. Methods of generating, simulating and imposing pair-background on physics events are presented and influence of this background on ILD reconstruction is reviewed. Effects of the background on various ILD detectors are shown for nominal beam parameters and for SB09 reduced beam parameter set and an example of a physics analysis performed with overlayed pair background is given.

Recent results from HERA are presented. The main reviewed subjects are polarized DIS cross sections, parton density determination, diffractive PDFs, multi-jet production and searches for physics beyond the Standard Model.

In the HERAPDF2.0 PDF analysis it was noted that the fit $\chi^2$ worsens significantly at low $Q^2$ for both NLO and NNLO fits. The turn over of the reduced cross section at low-$x$ and low $Q^2$ due to the contribution of the longitudinal cross section $F_L$ is also not very well described. In this paper the prediction for $F_L$ is highlighted and the corresponding extraction of $F_2$ from the data is further investigated, showing discrepancies with description of HERAPDF2.0 at low $x$ and $Q^2$. The effect of adding a simple higher twist term of the form ~$F_L*A/Q^2$ to the description of $F_L$ is investigated. This results in a significantly better description of the reduced cross-sections, $F_2$ and $F_L$ at low $x$, $Q^2$ and a significantly lower $\chi^2$ for the NNLO fit as compared to the NLO fit. This is not the case if the higher twist term is added to $F_2$

The high-precision HERA data can be used as an input to a QCD analysis within the DGLAP formalism to obtain the detailed description of the proton structure in terms of the parton distribution functions (PDFs). However, when searching for Beyond Standard Model (BSM) contributions in the data one should take into account the possibility that the PDF set may already have been biased by partially or totally absorbing previously unrecognised new physics contributions. The ZEUS Collaboration has proposed a new approach to the BSM analysis of the inclusive $ep$ data based on the simultaneous QCD fits of parton distribution functions together with contributions of new physics processes. Unfortunately, limit setting procedure in the frequentist approach is very time consuming in this method, as full QCD analysis has to be repeated for numerous data replicas. We describe a simplified approach, based on the Taylor expansion of the cross section predictions in terms of PDF parameters, which allowed us to reduce the calculation time for the BSM limits by almost two orders of magnitude.

This summary presents personal highlights from the Structure Functions and PDFs Working Group (WG1) at DIS 2016.

Recent highlights from the HERA experiments, Hermes, H1 and ZEUS, are reviewed and ideas for future analyses to fully exploit this unique data set are proposed. This document is a summary of a workshop on future physics with HERA data held at DESY, Hamburg at the end of 2014. All areas of HERA physics are covered and contributions from both experimentalists and theorists are included. The document outlines areas where HERA physics can still make a significant contribution, principally in a deeper understanding of QCD, and its relevance to other facilities. Within the framework of the Data Preservation in High Energy Physics, the HERA data have been preserved for analyses to take place over a timescale of 10 years and more. Therefore, although an extensive list of possibilities is presented here, safe storage of the data ensures that it can also be used in the far future should new ideas and analyses be proposed.

This summary presents personal highlights from the Structure Functions and PDFs Working Group (WG1) at DIS 2016.

In the years 1992-2007, the H1 and ZEUS detectors at the HERA accelerator collected large-luminosity data samples.They provided a high precision and wide kinematic range in the photon virtuality Q 2 and Bjorken x scaling variable for studying Deep Inelastic Scattering (DIS) processes at HERA.The longitudinal lepton-beam polarisation of HERA II gave a unique opportunity to study the helicity structure of the electroweak interaction, proton content, as well as to test the Standard Model.Some of the newest and most precise results from both collaborations are presented here.

A phenomenological study of the final combined HERA data on inclusive deep inelastic scattering (DIS) has been performed. The data are presented and investigated for a kinematic range extending from values of the four-momentum transfer, $Q^2$, above 10$^4$ GeV$^2$ down to the lowest values observable at HERA of $Q^2$ = 0.045 GeV$^2$ and Bjorken $x$, $x_{\rm Bj}$ = 6 $\cdot$ 10$^{-7}$. The data are well described by fits based on perturbative quantum chromodynamics (QCD) using collinear factorisation and evolution of the parton densities encompassed in the DGLAP formalism from the highest $Q^2$ down to $Q^2$ of a few GeV$^2$. The Regge formalism can describe the data up to $Q^2 \approx$ 0.65 GeV$^2$. The complete data set can be described by a new fit using the ALLM parameterisation. The region between the Regge and the perturbative QCD regimes is of particular interest.

Recently, Letters of Intent (LoI) for experiments at the International Linear Collider (ILC) have been submitted. Among the three proposals is the International Large Detector (ILD) concept for which a wide spectrum of studies of SUSY particle properties is presented here. Most of them are benchmark reactions for the ILC and can be used both in physics studies and in work on detector design and optimization, respectively. All studies were performed with a full detector simulation using GEANT4. The importance of this fully detailed simulation is reflected in the results. The presented analyzes have been chosen to be the most challenging for the detector to study its performance and guide the detector development. Additionally the problem of unavoidable beam induced backgrounds at linear colliders is addressed and ways of reducing its impact on physics studies are shown for an example SUSY analysis.

Jet production at hadron colliders provides constraints on the parton distribution functions (PDFs) of the proton, in particular on the gluon distribution. In the present paper, the impact on PDF of CMS inclusive differential jet cross sections at center-of-mass energy of $\sqrt s = 8$ TeV for jets with low momentum $p\mathrm{_T}$ and produced in the forward direction is investigated at next-to leading order in perturbative quantum chromodynamics (QCD). The results of the QCD global analysis are compared with theoretical predictions. The impact of low-$p\mathrm{_T}$ jet measurements on the determination of the gluon distribution is assessed. The inclusion of the discussed measurements adds further constraints on the uncertainty of the gluon distribution at large Bjorken $x > 0.1$, where the low-$p_T$ data have the largest impact.

We discuss our recent results on azimuthal distributions in vector boson + jets and multi-jet production at the LHC, obtained from the matching of next-to-leading order (NLO) perturbative matrix elements with transverse momentum dependent (TMD) parton branching.We present a comparative analysis of boson-jet and jet-jet correlations in the back-to-back region, and a study of the theoretical systematic uncertainties associated with the matching scale in the cases of TMD and collinear parton showers.

Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low $x$ and low $Q^2$. A resolution of this tension incorporating $\ln(1/x)$-resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function $F_L$, it also results in a gluon PDF which is steeply rising at low $x$ for low scales, $Q^2 \simeq 2.5$ GeV$^2$, contrary to the fixed-order NLO and NNLO gluon PDF.

The high-precision HERA data are used to search for Beyond the Standard Model contributions to electron-quark scattering in the framework of $eeqq$ contact interactions (CI). Combined measurements of the inclusive deep inelastic cross sections in neutral and charged current $ep$ scattering are considered, corresponding to a luminosity of around 1 fb$^{-1}$. The analysis of the inclusive $ep$ data is based on the simultaneous fits of parton distribution functions together with contributions of CI couplings to $ep$ scattering. Results are presented for different general CI scenarios and heavy leptoquarks with expected 95% C.L. limits on the CI mass scales in the 10 TeV range.

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.

Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low $x$ and low $Q^2$. A resolution of this tension incorporating $\ln(1/x)$-resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function $F_L$, it also results in a gluon PDF which is steeply rising at low $x$ for low scales, $Q^2 \simeq 2.5$ GeV$^2$, contrary to the fixed-order NLO and NNLO gluon PDF.

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.

Studies of fragmentation and parton density functions are a core component of research in high energy particle and nuclear physics.These quantities are inherently interesting as a probe of the quantum nature of the strong force and are also essential ingredients to additional studies in high energy scattering experiments.These proceedings provide an overview of the state of the art in this area, as presented at the Deep-Inelastic Scattering Conference in the Spring of 2021.

Studies of fragmentation and parton density functions are a core component of researchin high energy particle and nuclear physics. These quantities are inherently interestingas a probe of the quantum nature of the strong force and are also essential ingredients toadditional studies in high energy scattering experiments. These proceedings provide anoverview of the state of the art in this area, as presented at the Deep-Inelastic ScatteringConference in the Spring of 2021.