We compute the next-to-next-to-leading order hadronic contribution to muon anomalous magnetic moment originating from photon vacuum polarization. The corresponding three-loop kernel functions are calculated using asymptotic expansion techniques which lead analytic expressions. Our final result, $a_\mu^{\rm had,NNLO} = 1.24 \pm 0.01 \times 10^{-10}$, has same of magnitude as current uncertainty leading and should thus be included in future analyses.

Using new four-loop results for the heavy quark vacuum polarization and data bottom production in electron-positron annihilation, an update on determination of charm- bottom-quark masses through sum rules has been performed. The previous result charm-quark mass, ${m}_{c}(3\text{ }\text{ }\mathrm{GeV})=0.986(13)\text{ }\mathrm{GeV}$, based lowest moment, is supported by from higher moments which lead to consistent values with comparable errors. value quark, ${m}_{b}(10\text{...

We present results for the relation between a heavy quark mass defined in on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method compute integral is briefly described new are used establish relations various short-distance masses MS[over ¯] next-to-next-to-next-to-leading order accuracy. These play an important role accurate determination of masses.

We study the chiral Ising, XY, and Heisenberg models at four-loop order with perturbative renormalization group in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions compute critical exponents for Gross-Neveu-Yukawa fixed points to $\mathcal{O}({\ensuremath{\epsilon}}^{4})$. Further, we provide Pad\'e estimates correlation length exponent, boson fermion anomalous dimension, as well leading correction scaling exponent $2+1$ dimensions. also confirm emergence of supersymmetric field theories...

We present the details of analytic calculation three-loop angle-dependent cusp anomalous dimension in QCD and its supersymmetric extensions, including maximally $$ \mathcal{N}=4 super Yang-Mills theory. The result latter theory is new confirms a conjecture made our previous paper. study various physical limits discuss relation to quark-antiquark potential effects broken conformal symmetry QCD. find that viewed as function angle effective coupling given by light-like reveals remarkable...

In this paper we compute the relation between heavy quark masses defined in modified minimal subtraction and on-shell scheme. Detailed results are presented for all coefficients of SU$(N_c)$ colour factors. The reduction four-loop integrals is performed a general QCD gauge parameter. Some about 380 master computed analytically, others with high numerical precision based on Mellin-Barnes representations, rest numerically help {\tt FIESTA}. We discuss detail precise evaluation integrals....

We present the full analytic result for three loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity terms an effective coupling defined by lightlike dimension. find evidence is universal any gauge theory and use observation predict nonplanar ${n}_{f}$-dependent four

We present the third-order QCD prediction for production of top antitop quark pairs in electron-positron collisions close to threshold dominant S-wave state. observe a significant reduction theoretical uncertainty and discuss sensitivity mass width.

We present analytical five-loop results for the quark mass and field anomalous dimensions, a general gauge group in $$ \overline{\mathrm{MS}} scheme. confirm values known SU(3) from an independent calculation, find full agreement with available large-N f studies.

We compute the static contribution to gravitational interaction potential of two point masses in velocity-independent five-loop (and 5th post-Newtonian) approximation harmonic coordinates effective action a direct calculation. The computation is performed using field methods based on Feynman diagrams momentum-space $d = 3 - 2\varepsilon$ space dimensions. also reproduce previous results including 4th post-Newtonian order.

We focus on a non-abelian gauge field coupled to single (but general) representation of family Nf fermions. By using the same machinery that had allowed us evaluate sub-leading large-Nf term five-loop Beta function earlier, we here report confirmation all-Nf result has in meantime been published by another group. Furthermore, order push forward 5-loop renormalization program regarding parameter dependence, present linear terms complete set anomalous dimensions, an expansion covariant around...

We calculate the motion of binary mass systems in gravity up to sixth post--Newtonian order $G_N^3$ terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes harmonic coordinates. For these contributions we construct a canonical transformation isotropic and EOB coordinates at 5PN agree with results literature \cite{Bern:2019nnu,Damour:2019lcq}. At 6PN compare Hamiltonians either given \cite{Bern:2019nnu} or resulting from scattering...

We calculate the potential contributions of motion binary mass systems in gravity to fifth post--Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates dimensional regularization. Furthermore, singular logarithmic tail are calculated. also consider non--local contributions. Further steps towards complete calculation discussed first comparisons given results literature.

We calculate the unpolarized and polarized three--loop anomalous dimensions splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ NS}^{\rm s}$ in QCD $\overline{\sf MS}$ scheme by using traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For first time we also \pm tr}$ for transversity directly. compare our results to literature.

We calculate the motion of binary mass systems in gravity up to fourth post--Newtonian order. use momentum expansions within an effective field theory approach based on Feynman amplitudes harmonic coordinates by applying dimensional regularization. construct canonical transformations ADM and one body (EOB) compare with other approaches. show that intermediate poles regularization parameter $\varepsilon$ vanish observables classical is not renormalized. The results are illustrated for a...

A bstract We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering structure functions F 2 ( x, Q ) , L xF 3 in $$ \overline{\textrm{MS}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> scheme and polarized of function g 1 Larin up to three-loop order QCD a fully automated way based on method arbitrary high Mellin moments. work case contributing axial-vector couplings or...

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present four-loop correction second third physical moment in low-energy expansions vector, axial-vector scalar Using a Ward identity, obtain fourth pseudo-scalar correlator. briefly discuss impact these results on determination charm mass strong coupling constant using lattice simulations correlators charm- bottom-quark from experimental data...

We combine the known asymptotic behaviour of QCD perturbation series expansion, which relates pole mass a heavy quark to MSbar mass, with exact coefficients up four-loop order determine ultimate uncertainty top-quark due renormalon divergence. perform extensive tests our procedure by varying number colours and flavours, as well scale strong coupling mass. Including an estimate internal bottom charm effect, we conclude that this is around 110 MeV. further additional contribution relation from...

We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing known values SU(3) to a general gauge group. Together with previously published on quark mass -field Beta function, this completes 5-loop renormalization program theories in that gauge.

We present an algorithm which allows to solve analytically linear systems of differential equations factorize first order. The solution is given in terms iterated integrals over alphabet where its structure implied by the coefficient matrix equations. These appear a large variety higher order calculations perturbative Quantum Field Theories. apply this method calculate master three-loop massive form factors for different currents, as illustration, and results vector detail. Here space...

We present analytical results for the $N_f^4$ and $N_f^3$ terms of five-loop Beta function, a general gauge group. While former term agrees with available from large-$N_f$ studies, latter is new extends value known SU(3) an independent calculation.

The abelian Higgs model is the textbook example for superconducting transition and Anderson-Higgs mechanism, has become pivotal in description of deconfined quantum criticality. We study with $n$ complex scalar fields at unprecedented four-loop order $4-\epsilon$ expansion find that annihilation critical bicritical points occurs a number $n_c \approx 182.95\left(1 - 1.752\epsilon + 0.798 \epsilon^2 0.362\epsilon^3\right) \mathcal{O}\left(\epsilon^4\right)\nonumber$. Consequently, below...

We calculate the potential contributions of Hamiltonian in harmonic coordinates up 6PN for binary mass systems to O(GN4) and perform comparisons recent results literature [1] [2].