Search results for "Matrix"
showing 10 items of 3205 documents
Hessian PDF reweighting meets the Bayesian methods
2014
We discuss the Hessian PDF reweighting - a technique intended to estimate the effects that new measurements have on a set of PDFs. The method stems straightforwardly from considering new data in a usual $\chi^2$-fit and it naturally incorporates also non-zero values for the tolerance, $\Delta\chi^2>1$. In comparison to the contemporary Bayesian reweighting techniques, there is no need to generate large ensembles of PDF Monte-Carlo replicas, and the observables need to be evaluated only with the central and the error sets of the original PDFs. In spite of the apparently rather different methodologies, we find that the Hessian and the Bayesian techniques are actually equivalent if the $\Delta…
Impact of dijet and D-meson data from 5.02 TeV p+Pb collisions on nuclear PDFs
2020
We discuss the new constraints on gluon parton distribution function (PDF) in lead nucleus, derivable with the Hessian PDF reweighting method from the 5.02 TeV p+Pb measurements of dijet (CMS) and $D^0$-meson (LHCb) nuclear modification ratios. The impact is found to be significant, placing stringent constraints in the mid- and previously unconstrained small-$x$ regions. The CMS dijet data confirm the existence of gluon anti-shadowing and the onset of small-$x$ shadowing, as well as reduce the gluon PDF uncertainties in the larger-$x$ region. The gluon constraints from the LHCb $D^0$ data, reaching down to $x \sim 10^{-5}$ and derived in a NLO perturbative QCD approach, provide a remarkable…
Can we fit nuclear PDFs with the high-x CLAS data?
2020
AbstractNuclear parton distribution functions (nuclear PDFs) are non-perturbative objects that encode the partonic behaviour of bound nucleons. To avoid potential higher-twist contributions, the data probing the high-x end of nuclear PDFs are sometimes left out from the global extractions despite their potential to constrain the fit parameters. In the present work we focus on the kinematic corner covered by the new high-x data measured by the CLAS/JLab collaboration. By using the Hessian re-weighting technique, we are able to quantitatively test the compatibility of these data with globally analyzed nuclear PDFs and explore the expected impact on the valence-quark distributions at high x. W…
Bayesian PDF reweighting meets the Hessian methods
2016
Volume: 273 New data coming from the LHC experiments have a potential to extend the current knowledge of parton distribution functions (PDFs). As a short cut to the cumbersome and time consuming task of performing a new PDF fit, re weighting methods have been proposed. In this talk, we introduce the so-called Hessian re-weighting, valid for PDF fits that carried out a Hessian error analysis, and compare it with the better-known Bayesian methods. We determine the existence of an agreement between the two approaches, and illustrate this using the inclusive jet production at the LHC. Peer reviewed
PDF reweighting in the Hessian matrix approach
2014
We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an existing set of PDFs. By construction, the method discussed here applies to the PDF fits that carried out a Hessian error analysis using a non-zero tolerance $\Delta\chi^2$. The principle is validated by considering a simple, transparent example. We are also able to establish an agreement with the Bayesian technique provided that the tolerance criterion is appropriately accounted for and that a purely exponential Bayesian likelihood is assumed. As a practi…
Impact of CMS dijets in 5.02 TeV pPb and pp collisions on EPPS16 nuclear PDFs
2018
The CMS measurement of dijet pseudorapidity distributions in pPb versus pp collisions at 5.02 TeV provides a direct probe on nuclear gluon PDFs. We show that while the predicted pPb pseudorapidity distributions suffer from sizable free-proton PDF uncertainties, the ratios of the pPb and pp distributions are practically insensitive to scale and free-proton PDF choices. We find the CMS data on pPb to pp ratios to be in good agreement with the EPPS16 nuclear modifications. Using a non-quadratic extension of the Hessian PDF reweighting method, we study the impact of these data on the EPPS16 nuclear PDFs. Relative to EPPS16, we find stronger evidence for mid-x gluon antishadowing as well as indi…
A note on Sobolev isometric immersions below W2,2 regularity
2017
Abstract This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W 2 , 2 setting. We show that the Hessian of each coordinate function of a W 2 , p , p 2 , isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W 2 , p , p 2 , isometric immersion from a bounded domain of R 2 into R 3 that has multiple singularities.
Nuclear parton distribution functions with uncertainties in a general mass variable flavor number scheme
2020
In this article we obtain a new set of nuclear parton distribution functions (nuclear PDFs) at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. The common nuclear deep-inelastic scattering (DIS) data analyzed in our study are complemented by the available charged-current neutrino DIS data with nuclear targets and data from Drell-Yan cross-section measurements for several nuclear targets. In addition, the most recent DIS data from the Jefferson Lab CLAS and Hall C experiments are also added to our data sample. For these specific datasets, we consider the impact of target mass corrections and higher twist effects which are expected to be important in the r…
A program for the simultaneous potentiometric determination of protonation constants and electrode calibration parameters
2005
A program for the potentiometric determination of the protonation constants of mononuclear polyprotic substances is described. A maximum of twelve parameters can be determined simultaneously, including up to six protonation constants, four electrode calibration parameters, the protolysis constant of the solvent and the titrant concentration. Optimization is carried out by using the non-simplified Newton-Raphson method, which is potentiated by the Marquardt algorithm and a distance speeding-up coefficient. A direct search method is also used to improve the initial set of values. Variances are calculated very accurately, since the real Hessian function is used. Statistical weights and ionic s…
Stroboscopic detection of nuclear resonance in an arbitrary scattering channel
2015
The theory of heterodyne/stroboscopic detection of nuclear resonance scattering is developed, starting from the total scattering matrix as a product of the matrix of the reference sample and the sample under study. This general approach holds for any dynamical scattering channel. The forward channel, which is discussed in detail in the literature, reveals the speciality that electronic scattering causes only an energy independent diminution of the intensity. For all other channels, complex resonance line shapes in the heterodyne/stroboscopic spectra - as a result of interference of electronic and nuclear scattering - is encountered. The grazing incidence case is evaluated and described in d…