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We review the current status of the theory predictions for elastic [Formula omitted]-e scattering, describing the recent activities and future plans of the theory initiative related to the proposed MUonE experiment.

We review the current status of the theory predictions for elastic μ - e scattering, describing the recent activities and future plans of the theory initiative related to the proposed MUonE experiment.

We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in D = 4-2*epsilon dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order epsilon, to be combined with the 1/epsilon divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for 1S, 2S, and 2P states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the Zalpha-expansion. We compare the results obtained to the existing literature.

Objectives This study analyzed the relationship children have with technological devices and took into account the physical, psychological and behavioral effects of the excessive use of new technology in comparison with the short amount of time spent in practicing sports. Methods Altogether 585 students completed a questionnaire on the use of video display terminals (VDT), television (TV) sets and playstations, and on their health, following the use of such devices. A subsample completed a questionnaire on sports activities. Results The main result was that the total average time spent in front of a playstation, VDT, and TV was very high, and a large percentage of children complain of eyestrain or musculoskeletal disorders after the use of VDT or playstations. In addition, most of the young people surveyed tended to practice very little sport. Conclusions The authors concluded that it is very important to pay more attention to the quality of children's leisure-time activities in order to stimulate active and healthy lifestyles.

In this paper we continue the work begun in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the 3-loop self-mass integral with three equal masses and on-shell external momentum. We collect and analyze a number of results on double and triple elliptic integrals. By using very high-precision numerical fits, for the first time we are able to identify a very compact analytical expression for the 4-loop on-shell self-mass integral with 4 equal masses, that is one of the master integrals of the 4-loop electron g-2. Moreover, we fit the analytical expressions of some integrals which appear in lattice perturbation theory, and in particular the 4-dimensional generalized Watson integral.

We review the current status of the theory predictions for elastic \\(\\mu\\)-\\(e\\) scattering, describing the recent activities and future plans of the theory initiative related to the proposed MUonE experiment.

In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.

Nous prouvons dans cet article que presque tout entier s'écrit comme la somme d'un cube, d'un bicarré, ..., et d'une puissance dixième. We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.

In this paper we calculate at high-precision the Laurent expansions in e=(4-D)/2 of the 17 master integrals which appeared in the analytical calculation of 3-loop QED contribution to the electron g-2, using difference and differential equations. The coefficients of the expansions so obtained are in perfect agreement with all the analytical expressions already known. The values of coefficients not previously known will be used in the high-precision calculation of the 4-loop QED contribution to the electron g-2.