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Register a new userThermal behavior, entanglement entropy and parton distributions
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The apparent thermalization of the particles produced in hadronic collisions can be obtained by quantum entanglement of the partons of the initial state once a fast hard collision is produced. The scale of the hard collision is related to the thermal temperature. As the probability distribution of these events is of the form $np(n)$, as a consequence, the von Neumann entropy is larger than in the minimum bias case. The leading contribution to this entropy comes from the logarithm of the number of partons $n$, all with equal probability, making maximal the entropy. In addition there is another contribution related to the width of the parton multiplicity. Asymptotically, the entanglement entropy becomes the logarithm of $sqrt{n}$, indicating that the number of microstates changes with energy from $n$ to $sqrt{n}$.
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We derive one-loop matching relations for the Ioffe-time distributions related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs based on the parton pseudo-distributions approach.
We provide an assessment of the state of the art in various issues related to experimental measurements, phenomenological methods and theoretical results relevant for the determination of parton distribution functions (PDFs) and their uncertainties, with the specific aim of providing benchmarks of different existing approaches and results in view of their application to physics at the LHC. We discuss higher order corrections, we review and compare different approaches to small x resummation, and we assess the possible relevance of parton saturation in the determination of PDFS at HERA and its possible study in LHC processes. We provide various benchmarks of PDF fits, with the specific aim of studying issues of error propagation, non-gaussian uncertainties, choice of functional forms of PDFs, and combination of data from different experiments and different processes. We study the impact of combined HERA (ZEUS-H1) structure function data, their impact on PDF uncertainties, and their implications for the computation of standard candle processes, and we review the recent F_L determination at HERA. Finally, we compare and assess methods for luminosity measurements at the LHC and the impact of PDFs on them.
Through explicit examples we show that twist-4 parton distributions have no parton interpretation in the sense that parton or partons inside a hadron can carry the momentum fraction $x$ of the hadron with $x >1$ or $x<-1$. The studied twist-4 parton distributions of collinear factoization are power-divergent for $vert xvert >1$. The corresponding transverse momentum dependent parton distributions have also no parton interpretation. They are finite. The implications of our results are discussed.
We investigate the relations between transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs) in a light-front quark-diquark model motivated by soft wall AdS/QCD. Many relations are found to have similar structure in different models. It is found that a relation between the Sivers function and the GPD $E_q$ can be obtained in this model in terms of a lensing function. The quark orbital angular momentum is calculated and the results are compared with the results in other similar models. Implications of the results are discussed. Relations among different TMDs in the model are also presented.
Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the RG flow. After introducing a new generalized temperature which satisfies the thermodynamics-like law even in the IR regime, we find that the renormalized entropy and the generalized temperature in the IR limit approach the thermal entropy and thermodynamic temperature of a real thermal system. This result implies that the microscopic quantum entanglement entropy in the IR region leads to the thermodynamic relation up to small quantum corrections caused by the quantum entanglement near the entangling surface. Intriguingly, this IR feature of the entanglement entropy universally happens regardless of the detail of the dual field theory and the shape of the entangling surface. We check this IR universality with a most general geometry called the hyperscaling violation geometry which is dual to a relativistic non-conformal field theory.
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