Transverse-momentum-dependent distributions TMDs are extensions of collinear parton distributions and are important in high-energy physics from both theoretical and phenomenological points of view. We provide a description of the program components and of the different physical frameworks the user can access via the available parameterisations.
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The Quantum Chromodynamics QCD interpretation of high-energy particle reactions requires a simultaneous treatment of processes at different energy scales. Factorisation theorems provide the mathematical framework to properly separate the physical regimes.
For instance, when two protons collide in a Drell—Yan DY event the high-energy partonic cross section is described with a perturbative QCD expansion and the soft physics underlying the structure of the hadrons is treated with parton distribution functions PDFssupplemented by QCD evolution. A PDF describes the likelihood for finding a parton of a particular momentum inside an incoming hadron. In processes with observed hadrons in the final state, fragmentation functions FFs enter to describe the transition from a partonic state to an observed final-state hadron.
For sufficiently inclusive processes, only the component of parton momentum collinear to the momentum of its parent hadron is relevant at leading power leading twist in the hard scale. Factorisation theorems for such processes are traditionally called collinear factorisation theorems. In less inclusive processes, however, sensitivity to the partonic motion transverse to the direction of the parent hadron can become important.
In such cases, the PDFs and FFs must carry information about transverse parton momentum in addition to the collinear momentum.Dear Ghassan, Log equation with different bases
In this context, the functions encoding the hadronic structure are more often referred to as unintegrated parton distribution functions uPDFssee e. In some cases, the differences arise because different formalisms employ similar TMD concepts, but are tailored to specific physical applications.
The former is designed for semi-inclusive processes differential in a particular physical transverse momentum and with a finite and non-zero ratio between the hard scale and the overall energy. The latter high-energy TMD factorisation is designed for the limit of a fixed hard scale and very high energies. Moreover, within each category there are also competing subcategories of approaches.Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be evaluated by lattice QCD simulations.
However, unlike the parton distribution functions, the quasi-parton distribution functions have perturbative ultraviolet power divergences because they are not defined by twist-2 operators. Here in this article, we identify all sources of ultraviolet divergences for the quasi-parton distribution functions in coordinate-space, and demonstrated that power divergences, as well as all logarithmic divergences can be renormalized multiplicatively to all orders in QCD perturbation theory.
Works referenced in this record:. GOV collections:. Title: Renormalizability of quasiparton distribution functions. Abstract Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be evaluated by lattice QCD simulations.
Renormalizability of quasiparton distribution functions. United States: N. Copy to clipboard. United States.
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Physical Review D, Vol. Nuclear Physics B, Vol. Physical Review Letters, Vol. Physics Letters B, Vol. All References journal 35 Search Sort by title. Sort by date. All Cited By text 1 Search Sort by title. Similar Records.In probability and statisticsthe logarithmic distribution also known as the logarithmic series distribution or the log-series distribution is a discrete probability distribution derived from the Maclaurin series expansion.
This leads directly to the probability mass function of a Log p -distributed random variable :. Because of the identity above, the distribution is properly normalized. The cumulative distribution function is. A Poisson compounded with Log p -distributed random variables has a negative binomial distribution. In this way, the negative binomial distribution is seen to be a compound Poisson distribution. Fisher described the logarithmic distribution in a paper that used it to model relative species abundance.Best python pdf library
From Wikipedia, the free encyclopedia. Logarithmic Probability mass function. Journal of Animal Ecology. Archived from the original PDF on Probability distributions List. Benford Bernoulli beta-binomial binomial categorical hypergeometric Poisson binomial Rademacher soliton discrete uniform Zipf Zipf—Mandelbrot.
Cauchy exponential power Fisher's z Gaussian q generalized normal generalized hyperbolic geometric stable Gumbel Holtsmark hyperbolic secant Johnson's S U Landau Laplace asymmetric Laplace logistic noncentral t normal Gaussian normal-inverse Gaussian skew normal slash stable Student's t type-1 Gumbel Tracy—Widom variance-gamma Voigt.
Discrete Ewens multinomial Dirichlet-multinomial negative multinomial Continuous Dirichlet generalized Dirichlet multivariate Laplace multivariate normal multivariate stable multivariate t normal-inverse-gamma normal-gamma Matrix-valued inverse matrix gamma inverse-Wishart matrix normal matrix t matrix gamma normal-inverse-Wishart normal-Wishart Wishart.
Degenerate Dirac delta function Singular Cantor. Circular compound Poisson elliptical exponential natural exponential location—scale maximum entropy mixture Pearson Tweedie wrapped.Recover excel file
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Probability mass function The function is only defined at integer values. The connecting lines are merely guides for the eye. Cumulative distribution function.See what's new with book lending at the Internet Archive.
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EMBED for wordpress. Want more? Advanced embedding details, examples, and help! We identify quark and gluon helicity-flip distributions defined between nucleon states of unequal momenta.
The evolution of these distributions with change of renormalization scale is calculated in the leading-logarithmic approximation. The helicity-flip gluon distributions do not mix with any quark distribution and are thus a unique signature of gluons in the nucleon.
Their contribution to the generalized virtual Compton process is obtained both in the form of a factorization theorem and an operator product expansion. In deeply virtual Compton scattering, they can be probed through distinct angular dependence of the cross section. There are no reviews yet. Be the first one to write a review. Additional Collections.We discuss the resummation of the large logarithmic terms appearing in the heavy-quark effects on parton distribution functions inside the virtual photon.
We incorporate heavy-quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy-quark effects obtained in the previous work.
This method enables us to resum the large logarithmic terms due to heavy-quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and we discuss the property of the resummed heavy-quark effects. This is a preview of subscription content, log in to check access.
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Brodsky, T. Kinoshita, H. Terazawa, Phys. Krawczyk, A. Zembrzuski, M. Staszel, Phys. Klasen, Rev. Schienbein, Ann. Godbole, Nucl. Walsh, P. Zerwas, Phys. B 44 Kingsley, Nucl.
B 6045 Christ, B. Hasslacher, A. Mueller, Phys.Thanks for helping us catch any problems with articles on DeepDyve. We'll do our best to fix them. Check all that apply - Please note that only the first page is available if you have not selected a reading option after clicking "Read Article". Include any more information that will help us locate the issue and fix it faster for you.
An introductory to generalized parton distributions GDPs is given which emphasizes their spectral property and its uses as well as the equivalence of various GDP representations. Furthermore, the status of the theory and phenomenology of hard exclusive processes is shortly reviewed.Dettol mask black
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It is also sometimes known more simply as the logarithmic distribution. Open the Special Distribution Simulator and select the logarithmic series distribution.
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Vary the parameter and note the shape of the probability density function. For selected values of the parameter, run the simulation times and compare the empirical density function to the probability density function. The distribution function and the quantile function do not have simple, closed forms in terms of the standard elementary functions.
Open the special distribution calculator and select the logarithmic series distribution. Vary the parameter and note the shape of the distribution and probability density functions. For selected values of the parameters, compute the median and the first and third quartiles. Recall that a power series can be differentialed term by term within the open interval of convergence.
These results follow easily from the factorial moments. Open the special distribution simulator and select the logarithmic series distribution.
For selected values of the parameter, run the simulation times and compare the empirical mean and standard deviation to the distribution mean and standard deviation. The moment results above actually follow from general results for power series distributions. The compound Poisson distribution based on the logarithmic series distribution gives a negative binomial distribution.
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