Continuation of Direct Products of Distributions

If, in some problems, one has to deal with the ``product'' of distributions $\rm f_i$ (also called generalized functions) $\rm\bar T = \Pi^m_{i=1} f_i$, this product has a priori no definite meaning as a functional $(\rm \bar T, \phi)$ for $\rm\phi \in S$. But if $\rm x^{\kappa +1} \Pi^m_{i=1} f_i$ exists, whatever the associativity is between some powers $\rm r_i$ of $\rm x$ ($\rm r_i \in \Bbb N, \sum_i r_i\leq \kappa +1, r_i \geq 0$) and the various $\rm f_i$, then a continuation of the linear functional $\rm \bar T$ from $\rm M$ onto $\rm S^{(N)}$ for some $\rm N$ is shown to exist in such a way that $\rm x^{\kappa +1} \bar T$ is defined unambiguously, and $\rm (\bar T, \phi), \phi \in S$, significant, though not unique.Comment: 3 pages, late

On the Four-Color-Map Theorem

Coloring planar Feynman diagrams in spinor quantum electrodynamics, is a non trivial model soluble without computer. Four colors are necessary and sufficient.Comment: 8 page

A search for exact superstring vacua

We investigate $2d$ sigma-models with a $2+N$ dimensional Minkowski signature target space metric and Killing symmetry, specifically supersymmetrized, and see under which conditions they might lead to corresponding exact string vacua. It appears that the issue relies heavily on the properties of the vector $M_{\mu}$, a reparametrization term, which needs to possess a definite form for the Weyl invariance to be satisfied. We give, in the $n = 1$ supersymmetric case, two non-renormalization theorems from which we can relate the $u$ component of $M_{\mu}$ to the $\beta^G_{uu}$ function. We work out this $(u,u)$ component of the $\beta^G$ function and find a non-vanishing contribution at four loops. Therefore, it turns out that at order $\alpha^{\prime 4}$, there are in general non-vanishing contributions to $M_u$ that prevent us from deducing superstring vacua in closed form.Comment: 9 pages, latex, CERN-TH.6946/9

Explicit supertring vacua in a background of gravitational waves and dilaton

We present an explicit solution of superstring effective equations, represented by gravitational waves and dilaton backgrounds. Particular solutions will be examined in a forthcoming note.Comment: 10 pages, latex, CERN-TH.7373/9

Precise mass-dependent QED contributions to leptonic g-2 at order alpha^2 and alpha^3

Improved values for the two- and three-loop mass-dependent QED contributions to the anomalous magnetic moments of the electron, muon, and tau lepton are presented. The Standard Model prediction for the electron (g-2) is compared with its most precise recent measurement, providing a value of the fine-structure constant in agreement with a recently published determination. For the tau lepton, differences with previously published results are found and discussed. An updated value of the fine-structure constant is presented in "Note added after publication."Comment: 6 pages, 1 figure. v2: New determination of alpha presented (based on the recent electron g-2 measurement). v3: New formulae added in Sec.IIB. v4: Updated value of alpha presente

Analytical eighth-order light-by-light QED contributions from leptons with heavier masses to the anomalous magnetic moment of electron

The important consequences of the recent results of the numerical evaluations of eighth and tenth order QED contributions to the anomalous magnetic moment of electron are commented. The correctness of the results of the numerical evaluation of new eighth order QED corrections to the electron anomaly are supported by the demonstration of their consistency with the new analytical expressions for the QED contributions to $a_e$ from the diagrams with fourth-order light-by-light scattering muon and tau-lepton loops. The consistency of the similar results are demonstrated in the case of eighth order massive dependent contribution to the muon anomalous magnetic moment.Comment: 6 pages, LaTeX, The preliminary version of the longer work with the same title was registered as CERN Preprint during the visit to Theory Division of CERN in January of 201

Revised value of the eighth-order electron g-2

The contribution to the eighth-order anomalous magnetic moment (g-2) of the electron from a set of diagrams without closed lepton loops is recalculated using a new FORTRAN code generated by an automatic code generator. Comparing the contributions of individual diagrams of old and new calculations, we found an inconsistency in the old treatment of infrared subtraction terms in two diagrams. Correcting this error leads to the revised value -1.9144 (35) (alpha/pi)^4 for the eighth-order term. This theoretical change induces the shift of the inverse of the fine structure constant by -6.41180(73)x10^{-7}.Comment: 4 pages, 1 figure, typo is correcte

Chk1 requirement for high global rates of replication fork progression during normal vertebrate S phase

Chk1 protein kinase maintains replication fork stability in metazoan cells in response to DNA damage and DNA replication inhibitors. Here, we have employed DNA fiber labeling to quantify, for the first time, the extent to which Chk1 maintains global replication fork rates during normal vertebrate S phase. We report that replication fork rates in Chk1¿/¿ chicken DT40 cells are on average half of those observed with wild-type cells. Similar results were observed if Chk1 was inhibited or depleted in wild-type DT40 cells or HeLa cells by incubation with Chk1 inhibitor or small interfering RNA. In addition, reduced rates of fork extension were observed with permeabilized Chk1¿/¿ cells in vitro. The requirement for Chk1 for high fork rates during normal S phase was not to suppress promiscuous homologous recombination at replication forks, because inhibition of Chk1 similarly slowed fork progression in XRCC3¿/¿ DT40 cells. Rather, we observed an increased number of replication fibers in Chk1¿/¿ cells in which the nascent strand is single-stranded, supporting the idea that slow global fork rates in unperturbed Chk1¿/¿ cells are associated with the accumulation of aberrant replication fork structure