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We study two-loop corrections to the scattering amplitude of four massive leptons in quantum electrodynamics. These amplitudes involve previously unknown elliptic Feynman integrals, which we compute analytically using the differential equation method. In doing so, we uncover the details of the elliptic geometry underlying this scattering amplitude and show how to exploit its properties to obtain compact, easy-to-evaluate series expansions that describe the scattering of four massive leptons in QED in the kinematical regions relevant for Bhabha and Møller scattering processes.

We argue that ℓ-loop Yangian-invariant fishnet integrals in two dimensions are connected to a family of Calabi-Yau ℓ folds. The value of the integral can be computed from the periods of the Calabi-Yau, while the Yangian generators provide its Picard-Fuchs differential ideal. Using mirror symmetry, we can identify the value of the integral as the quantum volume of the mirror Calabi-Yau. We find that, similar to what happens in string theory, for ℓ=1 and 2 the value of the integral agrees with the classical volume of the mirror, but starting from ℓ=3, the classical volume gets corrected by instanton contributions. We illustrate these claims on several examples, and we use them to provide for the first time results for 2- and 3-loop Yangian-invariant train track integrals in two dimensions for arbitrary external kinematics.

We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the N^{3}LO rapidity anomalous dimensions to higher order in the dimensional regulator and make use of the soft and rapidity anomalous dimension correspondence in conjunction with the recent determination of the N^{4}LO threshold anomalous dimensions to achieve our result. We show that the results for the quark and gluon rapidity anomalous dimensions at four loops are related by generalized Casimir scaling. Using the N^{4}LO rapidity anomalous dimension, we perform the resummation of the energy-energy correlation in the back-to-back limit at N^{4}LL, achieving for the first time the resummation of an event shape at this logarithmic order. We present numerical results and observe a reduction of perturbative uncertainties on the resummed cross section to below 1%.

We present phenomenological results for the inclusive cross section for the production of a lepton pair via virtual photon exchange at next-to-next-to-next-to-leading order in perturbative QCD. In line with the case of Higgs production, we find that the hadronic cross section receives corrections at the percent level, and the residual dependence on the perturbative scales is reduced. However, unlike in the Higgs case, we observe that the uncertainty band derived from scale variation is no longer contained in the band of the previous order.

We present the inclusive cross section at next-to-next-to-next-to-leading order (N^{3}LO) in perturbative QCD for the production of a Higgs boson via bottom-quark fusion. We employ the five-flavor scheme, treating the bottom quark as a massless parton while retaining a nonvanishing Yukawa coupling to the Higgs boson. We find that the dependence of the hadronic cross section on the renormalization and factorization scales is substantially reduced. For judicious choices of the scales the perturbative expansion of the cross section shows a convergent behavior. We present results for the N^{3}LO cross section at various collider energies. In comparison to the cross section obtained from the Santander matching of the four- and five-flavor schemes, we predict a slightly higher cross section, though the two predictions are consistent within theoretical uncertainties.

We propose an all-loop expression for scattering amplitudes in planar N=4 super Yang-Mills theory in multi-Regge kinematics valid for all multiplicities, all helicity configurations, and arbitrary logarithmic accuracy. Our expression is arrived at from comparing explicit perturbative results with general expectations from the integrable structure of a closely related collinear limit. A crucial ingredient of the analysis is an all-order extension for the central emission vertex that we recently computed at next-to-leading logarithmic accuracy. As an application, we use our all-order formula to prove that all amplitudes in this theory in multi-Regge kinematics are single-valued multiple polylogarithms of uniform transcendental weight.

We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(N_{c}) and with N_{f} massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on N_{c} and N_{f}, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where N_{f}=2N_{c}, we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.

We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g., to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely, contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.

We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multileg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that nondipole corrections appear already for three colored partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally invariant cross ratios for four colored partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the nondipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it depends only on the color charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally, we verify that our result is consistent with expectations from the Regge limit.

We introduce a completely local subtraction method for fully differential predictions at next-to-next-to-leading order (NNLO) accuracy for jet cross sections and use it to compute event shapes in three-jet production in electron-positron collisions. We validate our method on two event shapes, thrust and C parameter, which are already known in the literature at NNLO accuracy and compute for the first time oblateness and the energy-energy correlation at the same accuracy.

We present the cross section for the production of a Higgs boson at hadron colliders at next-to-next-to-next-to-leading order (N^{3}LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N^{3}LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N^{3}LO corrections are of the order of +2.2%. The total scale variation at N^{3}LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.

Direct adsorption of lipoproteins (DALI) is the first lipid apheresis system compatible with whole blood with the advantage of a very simple procedure. A mixture of heparin plus citrate (ACD-A) is used for the anticoagulation regimen (AR). A clinical, prospective, controlled crossover study was performed to test the safety and efficacy of low-dose citrate (LDC) anticoagulation in DALI. Five chronic DALI patients suffering from coronary heart disease and hypercholesterolemia underwent 3 DALI sessions each using the LDC anticoagulation regimen (60 IU heparin/kg body weight as initial bolus; 1:40 ACD-A: blood as perfusion). This was compared to 3 sessions per patient with the standard AR (bolus of 20 IU heparin/kg, 1:20 ACD-A as perfusion). Patient blood volumes (1.6; average of 7,040 ml) were treated with 750 ml adsorber gel per session at a blood flow rate of 60 ml/min. Mean LDL and Lp(a) reductions exceeded 60% with both AR. No clinical side effects were observed. Both AR controlled the coagulation well as evidenced by a sufficient prolongation of the partial prothrombin time (PTT) and activated clotting time as well as low thrombin-antithrombin (TAT) formation. Biocompatibility parameters exhibited favorable results (low activation of complement and cells, and only slight formation of C3a, C5a, beta-thromboglobulin, elastase, and TNF-alpha). The asymptomatic bradykinin generation was comparable in both study arms. LDC optimized the ionized calcium levels and pH in the efferent blood postadsorber. LDC anticoagulation was safe and effective, and may further improve the tolerance of DALI apheresis in hypercholesterolemic patients.

Background and Aim of Study: In routine DALI apheresis--the first technique for direct adsorption of lipoproteins from whole blood--heparin plus citrate (ACD-A) is used as anticoagulation regimen. However, recently several publications have warned of heparin-induced thrombocytopenia as a rare but potentially life-threatening complication of heparin administration (HIT type 2). The aim of the present study was therefore to test the efficacy and biocompatibility of DALI using a heparin-free anticoagulation regimen consisting exclusively of citrate., Methods: Four symptomatic hypercholesterolemic patients on regular DALI apheresis were switched to the heparin-free protocol for two sessions each. Two of the patients were on oral anticoagulation using phenprocoumon. In the weekly sessions, 1.3 patient blood volumes were processed at a blood flow rate of 60 ml/min using ACD-A at a ratio of 1:20 (v/v) during adsorber priming and the session., Results: Clinically, all sessions were essentially uneventful. Uncorrected lipoprotein reductions amounted to 65% for LDL-C, 62% for Lp(a), 53% for VLDL-C, 24% for HDL-C, 17% for triglycerides and 19% for fibrinogen. Cell counts remained virtually constant. No signs of hemolysis or clotting could be detected. Thromboplastin time (Quick) was slightly prolonged and partial thromboplastin time (PTT) moderately elevated in all patients. In contrast, whole blood coagulation time acc. to Lee-White and activated clotting times were increased only in orally anticoagulated patients. Biocompatibility in terms of complement, leukocyte and thrombocyte activation was excellent. Bradykinin activation was moderate peaking at 3038 pg/ml in the efferent line. Systemic thrombin-antithrombin complex (TAT) reflected perfect anticoagulation in orally anticoagulated patients and adequate anticoagulation in the patients without phenprocoumon., Conclusion: In this pilot study, heparin-free DALI apheresis was safe and effective and may thus be performed in LDL-apheresis dependent patients who suffer from heparin intolerance.