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We discuss how the two existing approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN$^3$LO PDFs with N$^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN$^3$LO PDF sets entering the combination. The combined aN$^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology., Comment: 22 pages, 11 figures, LHAPDF grids available from https://zenodo.org/records/13843626

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., Comment: 12 pages, 11 figures, 1 Table

Parton distribution functions (PDFs) play a central role in calculations for the Large Hadron Collider (LHC). To gain a deeper understanding of the emergence and interplay of constraints on the PDFs in the global QCD analyses, it is important to examine the relative significance and mutual compatibility of the experimental data sets included in the PDF fits. Toward this goal, we discuss the L2 sensitivity, a convenient statistical indicator for exploring the statistical pulls of individual data sets on the best-fit PDFs and identifying tensions between competing data sets. Unlike the Lagrange Multiplier method, the L2 sensitivity can be quickly computed for a range of PDFs and momentum fractions using the published Hessian error sets. We employ the L2 sensitivity as a common metric to study the relative importance of data sets in the recent ATLAS, CTEQ-TEA, MSHT, and reduced PDF4LHC21 PDF analyses at NNLO and approximate N3LO. We illustrate how this method can aid the users of PDFs to identify data sets that are important for a PDF at a given kinematic point, to study quark flavor composition and other detailed features of the PDFs, and to compare the data pulls on the PDFs for various perturbative orders and functional forms. We also address the feasibility of computing the sensitivities using Monte Carlo error PDFs. Together with the article, we present a companion interactive website with a large collection of plotted L2 sensitivities for eight recent PDF releases., Comment: 57 pages, 29 figures; supplementary material (4 pages); journal version with minor changes; online plotter of L2 sensitivities for ATLASpdf21, CT18, MSHT20 PDFs at https://metapdf.hepforge.org/L2/

A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton-hadron and hadron-hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark studies are carried out in order to disentangle the origin of the differences between the three global PDF sets. In particular, dedicated fits based on almost identical theory settings and input datasets are performed by the three groups, highlighting the role played by the respective fitting methodologies. We compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15, demonstrating their good overall consistency and a modest reduction of PDF uncertainties for key LHC processes such as electroweak gauge boson production and Higgs boson production in gluon fusion. We study the phenomenological implications of PDF4LHC21 for a representative selection of inclusive, fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination is made available via the LHAPDF library and provides a robust, user-friendly, and efficient method to estimate the PDF uncertainties associated to theoretical calculations for the upcoming Run III of the LHC and beyond., Comment: 87 pages, 44 figures, 11 tables

The statistical models used to derive the results of experimental analyses are of incredible scientific value and are essential information for analysis preservation and reuse. In this paper, we make the scientific case for systematically publishing the full statistical models and discuss the technical developments that make this practical. By means of a variety of physics cases -- including parton distribution functions, Higgs boson measurements, effective field theory interpretations, direct searches for new physics, heavy flavor physics, direct dark matter detection, world averages, and beyond the Standard Model global fits -- we illustrate how detailed information on the statistical modelling can enhance the short- and long-term impact of experimental results., Comment: 60 pages, 15 figures

I use a very simple deterministic model for the spread of Covid-19 in a large population. Using this to compare the relative decay of the number of deaths per day between different regions in Italy, Spain and England, each applying in principle the same social distancing procedures across the whole country, I obtain an estimate of the total fraction of the population which had already become infected by April 10th. In the most heavily affected regions, Lombardy, Madrid and London, this fraction is higher than expected, i.e. $\approx 0.3$. This result can then be converted to a determination of the infection fatality rate $ifr$, which appears to be $ifr \approx 0.0025-0.005$, and even smaller in London, somewhat lower than usually assumed. Alternatively, the result can also be interpreted as an effectively larger fraction of the population than simple counting would suggest if there is a variation in susceptibility to infection with a variance of up to a value of about 2. The implications are very similar for either interpretation or for a combination of effects., Comment: 19 pages. 6 figures.The updated article considers the possibility of variable susceptibility to infection. The analysis remains unaltered but the interpretation of the results is extended. The overall conclusions are largely unaltered

We describe the inclusion of the photon as an additional component of the proton's Parton Distribution Functions (PDFs) in the MMHT framework. The input for the photon is adopted from the recent LUXqed determination. We describe the similarities and differences above the input scale with other photon PDF determinations and the contributions to the MMHT photon from both leading twist and higher twist contributions, and their uncertainties. We study the impact of QED effects on the quark and gluon PDFs and the fit quality, and outline our development of an equivalent set of neutron PDFs., Comment: 5 pages, 4 figures, conference proceeding

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs., Comment: 80 pages, 15 figures, 28 tables, minor typos corrected, published in Progress in Particle and Nuclear Physics

We provide an updated recommendation for the usage of sets of parton distribution functions (PDFs) and the assessment of PDF and PDF+$\alpha_s$ uncertainties suitable for applications at the LHC Run II. We review developments since the previous PDF4LHC recommendation, and discuss and compare the new generation of PDFs, which include substantial information from experimental data from the Run I of the LHC. We then propose a new prescription for the combination of a suitable subset of the available PDF sets, which is presented in terms of a single combined PDF set. We finally discuss tools which allow for the delivery of this combined set in terms of optimized sets of Hessian eigenvectors or Monte Carlo replicas, and their usage, and provide some examples of their application to LHC phenomenology., Comment: 65 pages, 20 figures, additional benchmark comparison plots available from http://www.hep.ucl.ac.uk/pdf4lhc/mc2h-gallery/website. v2, accepted for publication in Journal of Physics G

The accurate determination of the Parton Distribution Functions (PDFs) of the proton is an essential ingredient of the Large Hadron Collider (LHC) program. PDF uncertainties impact a wide range of processes, from Higgs boson characterisation and precision Standard Model measurements to New Physics searches. A major recent development in modern PDF analyses has been to exploit the wealth of new information contained in precision measurements from the LHC Run I, as well as progress in tools and methods to include these data in PDF fits. In this report we summarise the information that PDF-sensitive measurements at the LHC have provided so far, and review the prospects for further constraining PDFs with data from the recently started Run II. This document aims to provide useful input to the LHC collaborations to prioritise their PDF-sensitive measurements at Run II, as well as a comprehensive reference for the PDF-fitting collaborations., Comment: 55 pages, 13 figures

I present results on continuing updates in PDFs within the framework now called MMHT14 due to both theory improvements and the inclusion of new data sets, including most of the up-to-date LHC data. A new set of PDFs is essentially finalised, with no changes expected to the PDFs presented here., Comment: 6 pages, 5 figures. Proceedings of the 37th International Conference of High-Energy Physics (ICHEP2014), 2-9 July 2014, Valencia, Spain

I consider the effect on partons distribution functions (PDFs) of changes in the theoretical procedure used in a PDF fit. I consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at most $x$ values, the gluon distribution becoming softer at high values of $x$ and larger at small $x$, and the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO. The fit quality also deteriorates.I also consider lowering the kinematic cut on $W^2$ for DIS data and introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$, with changes generally smaller than uncertainties, except for quarks at very high $x$. I show that the fixed flavour scheme and variable flavour scheme structure functions differ significantly for $x \sim 0.01$ at high $Q^2$. I demonstrate that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ in this regime. I conclude that some major differences in PDF sets are largely due to the choice of flavour scheme used., Comment: 6 pages, 11 figures, to appear in proceedings of DIS2013 Workshop

We present a detailed comparison of the most recent sets of NNLO PDFs from the ABM, CT, HERAPDF, MSTW and NNPDF collaborations. We compare parton distributions at low and high scales and parton luminosities relevant for LHC phenomenology. We study the PDF dependence of LHC benchmark inclusive cross sections and differential distributions for electroweak boson and jet production in the cases in which the experimental covariance matrix is available. We quantify the agreement between data and theory by computing the chi2 for each data set with all the various PDFs. PDF comparisons are performed consistently for common values of the strong coupling. We also present a benchmark comparison of jet production at the LHC, comparing the results from various available codes and scale settings. Finally, we discuss the implications of the updated NNLO PDF sets for the combined PDF+alphaS uncertainty in the gluon fusion Higgs production cross section., Comment: 52 pages, 22 figures, accepted for publication in JHEP

We present a new calculation of the cross sections for charged current (CC) and neutral current (NC) $\nu N$ and $\bar{\nu} N$ interactions in the neutrino energy range $10^{4}

This note provides an interim summary of the current recommendations of the PDF4LHC working group for the use of parton distribution functions (PDFs) and of PDF uncertainties at the LHC, for cross section and cross section uncertainty calculations. It also contains a succinct user guide to the computation of PDF uncertainties and correlations using available PDF sets. A companion note (the PDF4LHC Working Group Interim Report) summarizes predictions for benchmark cross sections at the LHC (7 TeV) at NLO using modern PDFs currently available from 6 PDF fitting groups., Comment: 12 pages

This document is intended as a study of benchmark cross sections at the LHC (at 7 TeV) at NLO using modern parton distribution functions currently available from the 6 PDF fitting groups that have participated in this exercise. It also contains a succinct user guide to the computation of PDFs, uncertainties and correlations using available PDF sets. A companion note, also submitted to the archive, provides an interim summary of the current recommendations of the PDF4LHC working group for the use of parton distribution functions and of PDF uncertainties at the LHC, for cross section and cross section uncertainty calculations., Comment: 35 pages

I present a summary of the last in the series of HERA-LHC workshops, CERN, 26-30th May 2008., Comment: To appear in the proceedings of the Ringberg Workshop on New Trends in HERA Physics, October 2008. 12 pages, 14 figures included as .ps or .eps files

We report on new instabilities of the quasi-static equilibrium of water drops pinned by a hydrophobic inclined substrate. The contact line of a statically pinned drop exhibits three transitions of partial depinning: depinning of the advancing and receding parts of the contact line and depinning of the entire contact line leading to the drop's translational motion. We find a region of parameters where the classical Macdougall-Ockrent-Frenkel approach fails to estimate the critical volume of the statically pinned inclined drop.

Vitrification of aqueous cryoprotectant mixtures is essential in cryopreservation of proteins and other biological samples. We report systematic measurements of critical cryoprotective agent (CPA) concentrations required for vitrification during plunge cooling from T=295 K to T=77 K in liquid nitrogen. Measurements on fourteen common CPAs including alcohols (glycerol, methanol, isopropanol), sugars (sucrose, xylitol, dextrose, trehalose), PEGs (ethylene glycol, PEG 200, PEG 2 000, PEG 20 000), glycols (DMSO, MPD), and salt (NaCl) were performed for volumes ranging over four orders of magnitude from ~nL to 20 mkL, and covering the range of interest in protein crystallography. X-ray diffraction measurements on aqueous glycerol mixtures confirm that the polycrystalline-to-vitreous transition occurs within a span of less than 2% w/v in CPA concentration, and that the form of polycrystalline ice (hexagonal or cubic) depends on CPA concentration and cooling rate. For most of the studied cryoprotectants, the critical concentration decreases strongly with volume in the range from ~5 mkL to ~0.1 mkL, typically by a factor of two. By combining measurements of the critical concentration versus volume with cooling time versus volume, we obtain the function of greatest intrinsic physical interest: the critical CPA concentration versus cooling rate during flash cooling. These results provide a basis for more rational design of cryoprotective protocols, and should yield insight into the physics of glass formation in aqueous mixtures., Comment: 8 pages, 6 jpg figure, 2 tables

Motion of protein drops on crystallization media during routine handling is a major factor affecting the reproducibility of crystallization conditions. Drop stability can be enhanced by chemical patterning to more effectively pin the drop's contact line. As an example, a hydrophilic area is patterned on an initially flat hydrophobic glass slide. The drop remains confined to the hydrophilic area, and the maximum drop size that remains stable when the slide is rotated to the vertical position increases. This simple method is readily scalable and has the potential to significantly improve outcomes in hanging and sitting drop crystallization., Comment: text 4 pages, 6 jpg figures