arXiv subjects
Publications and source records attributed to R. N. Lee.
We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $ε=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.
Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Zα/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these Green's functions are considered in detail.
We apply the DRA method to the calculation of the four-loop `QED-type' tadpoles. For arbitrary space-time dimensionality D the results have the form of multiple convergent sums. We use these results to obtain the epsilon-expansion of the integrals around D=3 and D=4.
We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g-2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm.
We review the method of the calculation of multiloop integrals recently suggested in Ref.[Lee2010]. A simple method of derivation of the dimensional recurrence relation suitable for automatization is given. Some new analytic results are given.
We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.
We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop integrals. The representations derived have a form of exponentially converging sums. Several examples of the developed technique are given.
The Coulomb corrections to the cross section of $e^+e^-$ pair production in ultrarelativistic nuclear collisions are calculated in the next-to-leading approximation with respect to the parameter $L=\ln γ_Aγ_B$ ($γ_{A,B}$ are the Lorentz factors of colliding nuclei). We found considerable reduction of the Coulomb corrections even for large $γ_Aγ_B$ due to the suppression of the production of $e^+e^-$ pair with the total energy of the order of a few electron masses in the rest frame of one of the nuclei. Our result explains why the deviation from the Born result were not observed in the experiment at SPS.
The quasiclassical correction to the Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Moliere's formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Moliere's formula.
The excessiveness of integration-by-part (IBP) identities is discussed. The Lie-algebraic structure of the IBP identities is used to reduce the number of the IBP equations to be considered. It is shown that Lorentz-invariance (LI) identities do not bring any information additional to that contained in the IBP identities, and therefore, can be discarded.
We derive the low-energy expansion of $(Zα) ^{2}$ and $(Zα) ^{4}$ terms of the polarization operator in the Coulomb field. Physical applications such as the low-energy Delbrück scattering and "magnetic loop" contribution to the $g$ factor of the bound electron are considered.
The correction to the wave function of the ground state in a hydrogen-like atom due to an external homogenous magnetic field is found exactly in the parameter $Zα$. The $j=1/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the external homogeneous magnetic field is found for arbitrary $n$. The $j=3/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the nuclear magnetic moment is also found for arbitrary $n$. Using these results, we have calculated the shielding of the nuclear magnetic moment by the $ns_{1/2}$ electron.
Using the quasiclassical Green's function in the Coulomb field, we analyze the probabilities of single and multiple $e^+e^-$-pair production at fixed impact parameter $b$ between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter $Z_Bα$, and exactly in $Z_Aα$, $Z_{A}$ and $Z_{B}$ are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for $Z_Aα, Z_Bα\lesssim 1$.
New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an application of this method, we calculate the two--loop master integral for "crossed--triangle" topology which was previously known only up to $O(\ep)$ order. The case when a topology contains several master integrals is also considered. We present an algorithm of the term-by-term calculation of the asymptotical expansion in this case and analyze in detail the "crossed--box" topology with three master integrals.
Formulas for the corrections to the energy levels and wave functions of a spin-zero particle bound in a strong field are derived. General case of the sum of a Lorentz-scalar potential and zero component of a Lorentz-vector potential is considered. The forms of the corrections differ essentially from those for spin-1/2 particles. As an example of application of our results, we evaluated the electric polarizability of a ground state of a spin-zero particle bound in a strong Coulomb field.
We consider the $g$ factor of a spin-1/2 particle (electron or muon) bound by an arbitrary central field. We present an approach which allows one to express the relativistic $g$ factor in terms of the binding energy. We derive the general expression for the correction to the $g$ factor caused by a deviation of the central potential from the Coulomb one. As the application of this method, we consider the corrections to the $g$ factor due to the finite nuclear size, including vacuum polarization radiative correction. The effect of the anomalous magnetic moment is also taken into account.
The contribution of the light-by-light diagram to the g factor of electron and muon bound in Coulomb field is obtained. For electron in a ground state, our results are in good agreement with the results of other authors obtained numerically for large Z. For relatively small Z our results have essentially higher accuracy as compared to the previous ones. For muonic atoms, the contribution is obtained for the first time with the high accuracy in whole region of Z.
First correction to the high-energy asymptotics of the total $e^+e^-$ photoproduction cross section in the electric field of a heavy atom is obtained with the exact account of this field. The consideration is based on the use of the quasiclassical electron Green function in an external electric field. The influence of screening on the Coulomb corrections is examined in the leading approximation. It turns out that the high-energy asymptotics of the corresponding correction is independent of the photon energy. The detailed comparison of our results with experimental data is performed. This comparison has justified the analytical result and allowed us to elaborate a simple ansatz for the next-to-leading correction. Using this ansatz, good agreement with the experimental data is obtained for photon energies above a few $MeV$. In the region where both produced particles are relativistic, the corrections to the high-energy asymptotics of the electron (positron) spectrum are obtained. In addition, analogous corrections to the bremsstrahlung spectrum are derived starting from the corresponding results for pair production.