There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

http://repositorium.sdum.uminho.pt/bitstream/1822/48763/1/1-s2.0-S037026931200857X-main.pdf

Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC

https://digital.csic.es/bitstream/10261/108964/1/experiment%20at%20the%20LHC.pdf

Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC

We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling all these computations — parton-level fixed order, shower-matched, merged — in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV e + e − collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.

/pdf/the-automated-computation-of-tree-level-and-next-to-leading-4etm0g6w46.pdf

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

We present updated leading-order, next-to-leading order and next-to-next-to-leading order parton distribution functions (“MSTW 2008”) determined from global analysis of hard-scattering data within the standard framework of leading-twist fixed-order collinear factorisation in the $\overline{\mathrm{MS}}$
 
scheme. These parton distributions supersede the previously available “MRST” sets and should be used for the first LHC data taking and for the associated theoretical calculations. New data sets fitted include CCFR/NuTeV dimuon cross sections, which constrain the strange-quark and -antiquark distributions, and Tevatron Run II data on inclusive jet production, the lepton charge asymmetry from W decays and the Z rapidity distribution. Uncertainties are propagated from the experimental errors on the fitted data points using a new dynamic procedure for each eigenvector of the covariance matrix. We discuss the major changes compared to previous MRST fits, briefly compare to parton distributions obtained by other fitting groups, and give predictions for the W and Z total cross sections at the Tevatron and LHC.

/pdf/parton-distributions-for-the-lhc-4lvvi85r8i.pdf

Parton distributions for the LHC

We present an investigation of the theoretical uncertainties in parton distribution functions (PDFs) due to missing higher-order corrections in the perturbative predictions used in the fit, and their relationship to the uncertainties in subsequent predictions made using the PDFs. We consider in particular the standard approach of factorization and renormalization scale variation, and derive general results for the consistent application of these at the PDF fit stage. To do this, we use the fact that a PDF fit may be recast in a physical basis, where the PDFs themselves are bypassed entirely, and one instead relates measured observables to predicted ones. In the case of factorization scale variation we find that in various situations there is a high degree of effective correlation between the variation in the fit and in predicted observables. In particular, including such a variation in both cases can lead to an exaggerated theoretical uncertainty. More generally, a careful treatment of this correlation appears mandatory, at least within the standard scale variation paradigm. For the renormalization scale, the situation is less straightforward, but again we highlight the potential for correlations between related processes in the fit and predictions to enter at the same level as between processes in the fit or prediction alone.

/pdf/on-the-consistent-use-of-scale-variations-in-pdf-fits-and-1x2jy8xdsd.pdf

On the Consistent Use of Scale Variations in PDF Fits and Predictions

We investigate the Monte Carlo approach to propagation of experimental uncertainties within the context of the established "MSTW 2008" global analysis of parton distribution functions (PDFs) of the proton at next-to-leading order in the strong coupling. We show that the Monte Carlo approach using replicas of the original data gives PDF uncertainties in good agreement with the usual Hessian approach using the standard Delta(chi^2) = 1 criterion, then we explore potential parameterisation bias by increasing the number of free parameters, concluding that any parameterisation bias is likely to be small, with the exception of the valence-quark distributions at low momentum fractions x. We motivate the need for a larger tolerance, Delta(chi^2) > 1, by making fits to restricted data sets and idealised consistent or inconsistent pseudodata. Instead of using data replicas, we alternatively produce PDF sets randomly distributed according to the covariance matrix of fit parameters including appropriate tolerance values, then we demonstrate a simpler method to produce an arbitrary number of random predictions on-the-fly from the existing eigenvector PDF sets. Finally, as a simple example application, we use Bayesian reweighting to study the effect of recent LHC data on the lepton charge asymmetry from W boson decays.

/pdf/study-of-monte-carlo-approach-to-experimental-uncertainty-4zeyrbi7sv.pdf

Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs

We present the latest results of studies within the MMHT PDF framework.
We discuss the impact of the most recent ATLAS 7 TeV jet data,
demonstrating that while a good fit can be achieved for individual jet rapidity
bins, it is not possible to achieve a good description of the data
when all bins are fitted. We examine the role that the experimental correlated
systematic uncertainties play in this, and demonstrate that by simply
decorrelating no more than two sources of error between rapidity bins, a
remarkably improved description of the data can be achieved. We then
study the impact of NNLO corrections, showing that a mild decrease in
the fit quality is produced. We also present the results of including new
LHC W, Z, W + c and tt¯ data on the MMHT14 PDF set, showing that a
marked decrease in the s + ¯s uncertainty is in particular achieved. Finally,
some discussion of the latest work towards the inclusion of the photon PDF
within the MMHT framework is presented.

/pdf/mmht-pdfs-updates-and-outlook-2o7wvh641l.pdf

MMHT PDFs: Updates and Outlook

We investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $\alpha_S(M_Z^2)$ and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $\alpha_S(M_Z^2)$ to be a free parameter in the MSHT20 global analyses of deep-inelastic and related hard scattering data, at both NLO and NNLO in QCD perturbation theory. We also study the constraints on $\alpha_S(M_Z^2)$ which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $\alpha_S(M_Z^2)$, spanning the range $\alpha_S(M_Z^2)=0.108$ to $0.130$ in units of $0.001$. We make all resulting PDFs sets available. We find that the best fit values are $\alpha_S(M_Z^2)=0.1203\pm 0.0015$ and $0.1174\pm 0.0013$ at NLO and NNLO respectively. We investigate the relationship between the variations in $\alpha_S(M_Z^2)$ and the uncertainties on the PDFs, and illustrate this by calculating the cross sections for key processes at the LHC. We also perform fits where we allow the heavy quark masses $m_c$ and $m_b$ to vary away from their default values and make PDF sets available in steps of $\Delta m_c =0.05~{\rm GeV}$ and $\Delta m_b =0.25~{\rm GeV}$, using the pole mass definition of the quark masses. As for varying $\alpha_S(M_Z^2)$ values, we present the variation in the PDFs and in the predictions. We examine the comparison to data, particularly the HERA data on charm and bottom cross sections and note that our default values are very largely compatible with best fits to data. We provide PDF sets with 3 and 4 active quark flavours, as well as the standard value of 5 flavours.

/pdf/an-investigation-of-the-alpha-s-and-heavy-quark-mass-1w0lm4ct91.pdf

An investigation of the $\alpha_S$ and heavy quark mass dependence in the MSHT20 global PDF analysis.

We investigate the variation in the MMHT2014 PDFs when we allow the heavy quark masses $m_c$ and $m_b$ to vary away from their default values. We make PDF sets available in steps of $\Delta m_c =0.05~{\rm GeV}$ and $\Delta m_b =0.25~{\rm GeV}$, and present the variation in the PDFs and in the predictions. We examine the comparison to the HERA data on charm and beauty structure functions and note that in each case the heavy quark data, and the inclusive data, have a slight preference for lower masses than our default values. We provide PDF sets with 3 and 4 active quark flavours, as well as the standard value of 5 flavours. We use the pole mass definition of the quark masses, as in the default MMHT2014 analysis, but briefly comment on the $\overline{\rm MS}$ definition.

/pdf/charm-and-beauty-quark-masses-in-the-mmht2014-global-pdf-1loigrja2d.pdf

Robert S. Thorne

Papers

On the Consistent Use of Scale Variations in PDF Fits and Predictions

Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs

MMHT PDFs: Updates and Outlook

An investigation of the $\alpha_S$ and heavy quark mass dependence in the MSHT20 global PDF analysis.

Charm and beauty quark masses in the MMHT2014 global PDF analysis