arXiv subjects

R. N. Lee

Publications and source records attributed to R. N. Lee.

At least 19 recordsLinked to original sources

arXiv2025

Five W-boson amplitude = near-null decagon

We study a five-leg scattering amplitude on the special Coulomb branch of planar N=4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N=(1,1) super Yang-Mills theory and reducing it down to four space-time dimensions with extra-dimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in 't Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the `square root' of a five-point correlation function of infinitely-heavy half-BPS operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.

hep-th↗

arXiv2023

Two-loop radiative corrections to $e^+ e^-\rightarrow γγ^*$ cross section

The increasing accuracy of current and planned experiments to measure the anomalous magnetic moment of the muon requires more precision and reliability of its theoretical calculation. For this purpose, we calculate the differential cross section for the process of annihilation of an electron-positron pair into two photons, one of which is virtual, accompanied by the emission of soft photons, taking into account radiative corrections of the order $α^2$. The results obtained can be used to improve the accuracy of calculating the contribution of the hadron vacuum polarization to the muon anomalous moment. It is shown that all logarithmically amplified two-loop corrections can be easily found using modern theorems of soft and collinear factorizations and available one-loop results.

hep-ph↗

arXiv2022

Photoproduction of $e^+e^-$ pair in a Coulomb field near the threshold

We consider the electron-positron pair production by a photon in Coulomb field near threshold. We obtain the analytical results for the particle energy spectrum and angular distribution exactly in the parameter $Ze^2/\hbar v$. We show that Furry-Sommerfeld-Maue approximation for the wave functions used by Nishina, Tomonaga and Sakata is not sufficient and leads to wrong results.

hep-ph↗

arXiv2020

Master integrals for bipartite cuts of three-loop photon self energy

We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the $4m$ cut, reduce to Goncharov's polylogarithms. The master integrals for $4m$ cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for $4m$ cut.

hep-ph↗

arXiv2019

$ε$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^+e^-\to 2(Q\bar Q)$

We argue that in many physical calculations where the "eliptic" sectors are involved, one can express the results via iterated integrals with almost all weights being rational. Our method is based on the existence of $ε$-regular basis, which is akin to the $ε$-finite basis defined in Ref. [hep-ph/0601165]. As a demonstration of our technique, we calculate the photon contribution to the total cross section of the production of two $Q\bar Q$ pairs in the electron-positron collisions.

hep-ph↗

arXiv2019

ABJM quantum spectral curve at twist 1: algorithmic perturbative solution

We present an algorithmic perturbative solution of ABJM quantum spectral curve at twist 1 in sl(2) sector for arbitrary spin values, which can be applied to, in principle, arbitrary order of perturbation theory. We determined the class of functions -- products of rational functions in spectral parameter with sums of Baxter polynomials and Hurwitz functions -- closed under elementary operations, such as shifts and partial fractions, as well as differentiation. It turns out, that this class of functions is also sufficient for finding solutions of inhomogeneous Baxter equations involved. For the latter purpose we present recursive construction of the dictionary for the solutions of Baxter equations for given inhomogeneous parts. As an application of the proposed method we present the computation of anomalous dimensions of twist 1 operators at six loop order. There is still a room for improvements of the proposed algorithm related to the simplifications of arising sums. The advanced techniques for their reduction to the basis of generalized harmonic sums will be the subject of subsequent paper. We expect this method to be generalizable to higher twists as well as to other theories, such as N=4 SYM.

hep-th↗

arXiv2018

On analytical perturbative solution of ABJM quantum spectral curve

Recently we showed how non-homogeneous second-order difference equations appearing within ABJM quantum spectral curve description could be solved using Mellin space technique. In particular we provided explicit results for anomalous dimensions of twist 1 operators in sl(2) sector at arbitrary spin values up to four loop order. It was shown that the obtained results may be expressed in terms of harmonic sums decorated by fourth root of unity factors, so that maximum transcendentality principle holds. In this note we show that the same result could be also obtained by direct solution of the mentioned equations in spectral parameter u-space. The solution involves new highly nontrivial identities between hypergeometric functions, which may have various other applications. We expect this method to be more easily generalizable to higher loop orders as well as to other theories, such as N=4 SYM.

hep-th↗

arXiv2018

ABJM quantum spectral curve and Mellin transform

The present techniques for the perturbative solution of quantum spectral curve problems in N=4 SYM and ABJM models are limited to the situation when the states quantum numbers are given explicitly as some integer numbers. These techniques are sufficient to recover full analytical structure of the conserved charges provided that we know a finite basis of functions in terms of which they could be written explicitly. It is known that in the case of N=4 SYM both the contributions of asymptotic Bethe ansatz and wrapping or finite size corrections are expressed in terms of the harmonic sums. However, in the case of ABJM model only the asymptotic contribution can still be written in the harmonic sums basis, while the wrapping corrections part can not. Moreover, the generalization of harmonic sums basis for this problem is not known. In this paper we present a Mellin space technique for the solution of multiloop Baxter equations, which is the main ingredient for the solution of corresponding quantum spectral problems, and provide explicit results for the solution of ABJM quantum spectral curve in the case of twist 1 operators in sl(2) sector for arbitrary spin values up to four loop order with explicit account for wrapping corrections. It is shown that the result for anomalous dimensions could be expressed in terms of harmonic sums decorated by the fourth root of unity factors, so that maximum transcendentality principle holds.

hep-th↗

arXiv2016

Electron-positron pair production in ion collisions at low velocity beyond Born approximation

We derive the spectrum and the total cross section of electromagnetic $e^{+}e^{-}$ pair production in the collisions of two nuclei at low relative velocity $β$. Both free-free and bound-free $e^{+}e^{-}$ pair production is considered. The parameters $η_{A,B}=Z_{A,B}α$ are assumed to be small compared to unity but arbitrary compared to $β$ ($Z_{A,B}$ are the charge numbers of the nuclei and $α$ is the fine structure constant). Due to a suppression of the Born term by high power of $β$, the first Coulomb correction to the amplitude appears to be important at $η_{A,B}\gtrsim β$. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms $\propto M^{-2}$ are not suppressed by the high power of $β$ and may easily dominate at sufficiently small velocities.

physics.atom-ph↗

arXiv2015

Small-angle scattering and quasiclassical approximation beyond leading order

In the present paper we examine the accuracy of the quasiclassical approach on the example of small-angle electron elastic scattering. Using the quasiclassical approach, we derive the differential cross section and the Sherman function for arbitrary localized potential at high energy. These results are exact in the atomic charge number and correspond to the leading and the next-to-leading high-energy small-angle asymptotics for the scattering amplitude. Using the small-angle expansion of the exact amplitude of electron elastic scattering in the Coulomb field, we derive the cross section and the Sherman function with a relative accuracy $θ^2$ and $θ^1$, respectively ($θ$ is the scattering angle). We show that the correction of relative order $θ^2$ to the cross section, as well as that of relative order $θ^1$ to the Sherman function, originates not only from the contribution of large angular momenta $l\gg 1$, but also from that of $l\sim 1$. This means that, in general, it is not possible to go beyond the accuracy of the next-to-leading quasiclassical approximation without taking into account the non-quasiclassical terms.

physics.atom-ph↗

arXiv2015

Double bremsstrahlung from high-energy electron in the atomic field

The differential cross section of double bremsstrahlung from high-energy electron in the electric field of heavy atoms is derived. The results are obtained with the exact account of the atomic field by means of the quasiclassical approximation to the wave functions and the Green's function in the external field. It is shown that the Coulomb corrections to the differential cross section (the difference between the exact result and the result obtained in the leading Born approximation) correspond to small momentum transfers. The Coulomb corrections to the differential cross section of double bremsstrahlung are accumulated in the factor, which coincides with the corresponding factor in the differential cross section of single bremsstrahlung. At small momentum transfer, this factor is very sensitive to the parameters of screening while the Coulomb corrections to the spectrum have the universal form.

hep-ph↗

arXiv2014

High-energy $e^+e^-$ photoproduction in the field of a heavy atom accompanied by bremsstrahlung

Helicity amplitudes and differential cross section of high-energy $e^+e^-$ photoproduction accompanied by bremsstrahlung in the electric field of a heavy atom are derived. The results are exact in the nuclear charge number and obtained in the leading quasiclassical approximation. They correspond to the leading high-energy small-angle asymptotics of the amplitude. It is shown that, in general, the Coulomb corrections essentially modify the differential cross section as compared to the Born result. When the initial photon is circularly polarized the Coulomb corrections lead to the asymmetry in the distribution over the azimuth angles $φ_i$ of produced particles with respect to the replacement $φ_i\to -φ_i$.

hep-ph↗

arXiv2014

Coulomb corrections to electron scattering on the extended source and the proton charge radius

It is shown that the account for the proton charge form factor in the Coulomb corrections to the electron-proton scattering cross section noticeably diminishes the difference between the value of the proton charge radius $r_{\mathrm{E}}$, extracted from the $ep$ scattering data, and that following from the muonic hydrogen data. For the electron energy much higher than the electron mass but much smaller than $r_{\mathrm{E}}^{-1}\approx 230$~MeV, the relative correction has the universal form $δr_{\mathrm{E}}/r_{\mathrm{E}}=-πα/2$, where $α$ is the fine structure constant.

hep-ph↗

arXiv2013

Charge asymmetry in high-energy $μ^+μ^-$ photoproduction in the electric field of a heavy atom

The charge asymmetry in the differential cross section of high-energy $μ^+μ^-$ photoproduction in the electric field of a heavy atom is obtained. This asymmetry arises due to the Coulomb corrections to the amplitude of the process (next-to-leading term with respect to the atomic field). The deviation of the nuclear electric field from the Coulomb field at small distances is crucially important for the charge asymmetry. Though the Coulomb corrections to the total cross section are negligibly small, the charge asymmetry is measurable for selected final states of $μ^+$ and $μ^-$. We further discuss the feasibility for experimental observation of this effect.

nucl-th↗

arXiv2012

Presenting LiteRed: a tool for the Loop InTEgrals REDuction

Mathematica package LiteRed is described. It performs the heuristic search of the symbolic IBP reduction rules for loop integrals. It implements also several convenient tools for the search of the symmetry relations, construction of the differential equations and dimensional recurrence relations.

hep-ph↗

arXiv2012

New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene

A quantum mechanical model of two interacting electrons in graphene is considered. We concentrate on the case of zero total momentum of the pair. We show that the dynamics of the system is very unusual. Both stationary and time-dependent problems are considered. It is shown that the complete set of the wave functions with definite energy includes the new functions, previously overlooked. The time evolution of the wave packet, corresponding to the scattering problem setup, leads to the appearance of the localized state at large time. The asymptotics of this state is found analytically. We obtain the lower bound of the life time of this state, which is connected with the breakdown of the continuous model on the lattice scale. The estimate of this bound gives one a hope to observe the localized states in the experiment.

cond-mat.str-el↗

arXiv2011

Charge asymmetry in the differential cross section of high-energy e+e- photoproduction in the field of a heavy atom

First quasiclassical correction to the differential cross section of high-energy electron-positron photoproduction in the electric field of a heavy atom is obtained with the exact account of the field. This correction is responsible for the charge asymmetry ${\cal A}$ in this process. When the transverse momentum of at least one of the produced particles is much larger than the electron mass $m$, the charge asymmetry can be as large as tens percent. We also estimate the contribution $\tilde{\cal A}$ to the charge asymmetry coming from the Compton-type diagram. For heavy nuclei, this contribution is negligible. For light nuclei, $\tilde{\cal A}$ is noticeable only when the angle between the momenta of electron and positron is of order of $m/ω$ ($ω$ is the photon energy) while the transverse momenta of both particles are much larger than $m$.

hep-ph↗

arXiv2011

Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve

We evaluate a Laurent expansion in dimensional regularization parameter $ε=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.) and extending thereby results by Baikov and Chetyrkin obtained at transcendentality weight seven. We observe only multiple zeta values in our results. Therefore, we conclude that all the four-loop massless propagator integrals, with any integer powers of numerators and propagators, have only multiple zeta values in their epsilon expansions up to transcendentality weight twelve.

hep-th↗