Related papers: Positivity constraints in QCD
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
We have compared polarized parton densities determined in the NLO QCD fits to polarized structure functions and spin asymmetries. We consider models of such distributions based on MRST 99 and MRST 2001 fits to non-polarized data. Simple…
Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a non-analytic function of a density matrix, existing methods used in the physics literature are insufficient to…
The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new…
Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the…
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy…
We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a…
Approximate relations among transverse momentum dependent quark distribution functions are established in the framework of the QCD parton model. The validity of such results survives QCD evolution effects, owing to the Politzer theorem on…
The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to…
In this paper a solution is given to the nonlinear equation which describes the evolution of the parton cascade in the case of the high parton density. The related physics is discussed as well as some applications to heavy ion-ion…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
I discuss our current understanding of parton distributions. I begin with the underlying theoretical framework, and the way in which different data sets constrain different partons, highlighting recent developments. The methods of examining…
We provide a complete set of supersymmetric constraints for the anomalous dimensions of the conformal twist-two operators to all orders of perturbation theory. Employing them we derive new relations between the exclusive evolution kernels…
The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and…
The usual interpretational rule of quantum mechanics which states that outcomes do not occur when their weights are zero is changed so as to preclude outcomes with weights less than a small but positive value. With this "positive…
I shall present a rather pedagogical discussion of the transversity distributions in the quark-parton model and, in particular, the role of perturbative QCD corrections. Among the topics I shall discuss are: LO and NLO evolution, the Soffer…
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description…
We explore some of the constraints imposed by positivity of the QCD measure (Weingarten's inequalities) on the parameters defining chiral perturbation theory. We find, in particular, that $2 m_q (\mu)\leq B_0(\mu) Z(\mu)$. The use of…