arXiv subjects
Publications and source records attributed to V. M. Braun.
We develop a new technique and calculate conformal (Gegenbauer) moments of the two-loop coefficient functions in Deeply Virtual Compton Scattering (DVCS). These results are necessary for the extraction of the generalized parton distributions from the experimental data to the NNLO accuracy within the Mellin-Barnes approach.
We use conformal symmetry to calculate the NNLO anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin $N \le 8$ from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the $γγ^\ast\to η$ and $γγ^\ast\to η'$ form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.
We present updated results on the wave function normalization constants and the first moments of the light cone distribution amplitudes for the lowest-lying baryon octet. The analysis is carried out on a large number of $n_f=2+1$ lattice gauge ensembles, including ensembles at physical pion (and kaon) masses. These are spread across five different lattice spacings, enabling a controlled continuum limit. The main differences with respect to our earlier work are the use of two-loop conversion factors to an $\overline{\mathrm{MS}}$-like scheme and of an updated set of low-energy constants in the parametrization of the quark mass dependence. As a byproduct, for the first time, the anomalous dimensions for local three-quark operators with one derivative are obtained.
We calculate $(\sqrt{-t}/Q)^k $ and $(m/Q)^k$ power corrections with $k\le 4$, where $m$ is the target mass and $t$ is the momentum transfer, to several key observables in Deeply Virtual Compton Scattering (DVCS). We find that the power expansion is well convergent up to $|t|/Q^2\lesssim 1/4$ for most of the observables, but is naturally organized in terms of $1/(Q^2+t)$ rather than the nominal hard scale $1/Q^2$. We also argue that target mass corrections remain under control and do not endanger QCD factorization for coherent DVCS on nuclei. These results remove an important source of uncertainties due to the frame dependence and violation of electromagnetic Ward identities in the QCD predictions for the DVCS amplitudes in the leading-twist approximation.
We present explicit expressions for the tree-level "kinematic" twist-three contributions to the nucleon matrix elements of gauge-invariant nonlocal quark-antiquark operators which can be used in lattice calculations of generalized parton distributions (GPDs). These contributions in particular restore the translation invariance of the results up to higher twist four. The calculated twist-three corrections are logarithmically enhanced as compared to the leading twist, and are discontinuous at the kinematic points $x=\pmξ$.
Deeply-virtual Compton scattering gives access to the generalized parton distributions that encode the information on the transverse position of quarks and gluons in the proton in dependence in their longitudinal momentum. In anticipation of the high-precision experimental data in a broad kinematic range from the Electron-Ion Collider, we have calculated the two-loop, next-to-next-to-leading (NNLO) DVCS coefficient functions associated with the dominant Compton form factors $\mathcal H$ and $\mathcal E$ at large energies. The NNLO correction to the imaginary part of $\mathcal H$ appears to be rather large, up to factor two at the input scale $Q^2=4$ GeV$^2$ for simple GPD models, due to a cancellation between quark and gluon contributions.
Using the recent results on the contributions of descendants of the leading twist operators to the operator product expansion of two electromagnetic currents we derive explicit expressions for the kinematic finite-$t$ and target mass corrections to the DVCS helicity amplitudes to the $1/Q^4$ power accuracy. The cancellation of IR divergences for kinematic corrections is demonstrated to all powers in the leading order of perturbation theory. We also argue that target mass corrections in the coherent DVCS from nuclei are small and do not invalidate the factorization theorem.
Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger $4-2ε$ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin $N\le 8$.
Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the $\overline{\rm MS}$ scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the the pion transition form factor $γ^\astγ\to π$ in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large and have to be taken into account. The same coefficient function determines the contribution of the axial-vector generalized parton distributions to deeply-virtual Compton scattering which is investigated at the JLAB 12 GeV accelerator, by COMPASS at CERN, and in the future will be studied at the Electron Ion Collider EIC.
Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the vector flavor-nonsinglet contribution to deeply-virtual Compton scattering (DVCS). The analytic expression for the coefficient function in momentum fraction space is presented in the $\overline{\text{MS}}$ scheme. The corresponding next-to-next-to-leading order correction to the Compton form factor $\mathcal{H}$ for a simple model of the generalized parton distribution appears to be rather large: a factor two smaller than the next-to-leading order correction, approximately $\sim 10$\% of the tree level result in the bulk of the kinematic range, for $Q^2=4$ GeV$^2$.
We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study, we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.
Evolution equations for leading twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at non-integer $d=4-2ε$ space-time dimensions. In this work we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin's scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional ${\overline{\mathrm{MS}}}$-scheme. The results are directly applicable to deeply-virtual Compton scattering and the transition form factor $γ^*γ\toπ$.
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $β$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $γγ^\ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.
We argue that the renormalization factors for nonlocal quark-antiquark and gluon operators at space-like and time-like separations connected by a Wilson line coincide to all orders in perturbation theory. We calculate the anomalous dimensions and renormalization constants of quark-antiquark and gluon operators to three- and two-loop accuracy, respectively, and also compute vacuum expectation values of these operators to three-loop accuracy.
We argue that the evolution kernel for the scale-dependence of the $B$-meson light-cone distribution amplitude (LCDA) can be written, to all orders in perturbation theory, in terms of the generator of special conformal transformations in a modified theory: QCD at critical coupling in non-integer $d\neq 4$ dimensions. Explicit expression for the eigenfunctions of the evolution kernel is derived that is valid, again, to all orders. From a practitioner's point of view the utility of this representation is that it allows to "save one loop" and obtain the evolution kernel to a given order of perturbation theory, up to a constant term, from the calculation of the conformal anomaly at one order less. This construction is verified by explicit calculation at two-loop level.
We present the physics program of the Belle II experiment, located on the intensity frontier SuperKEKB $e^+e^-$ collider. Belle II collected its first collisions in 2018, and is expected to operate for the next decade. It is anticipated to collect 50/ab of collision data over its lifetime. This book is the outcome of a joint effort of Belle II collaborators and theorists through the Belle II theory interface platform (B2TiP), an effort that commenced in 2014. The aim of B2TiP was to elucidate the potential impacts of the Belle II program, which includes a wide scope of physics topics: B physics, charm, tau, quarkonium, electroweak precision measurements and dark sector searches. It is composed of nine working groups (WGs), which are coordinated by teams of theorist and experimentalists conveners: Semileptonic and leptonic B decays, Radiative and Electroweak penguins, phi_1 and phi_2 (time-dependent CP violation) measurements, phi_3 measurements, Charmless hadronic B decay, Charm, Quarkonium(like), tau and low-multiplicity processes, new physics and global fit analyses. This book highlights "golden- and silver-channels", i.e. those that would have the highest potential impact in the field. Theorists scrutinised the role of those measurements and estimated the respective theoretical uncertainties, achievable now as well as prospects for the future. Experimentalists investigated the expected improvements with the large dataset expected from Belle II, taking into account improved performance from the upgraded detector.
We derive the two-loop evolution equation of the B-meson light-cone distribution amplitude which is the last missing element for the next-to-next-to-leading logarithmic resummation of QCD corrections to B decays in QCD factorization. We argue that the evolution kernel to all orders in perturbation theory can be written as a logarithm of the generator of special conformal transformations times the cusp anomalous dimension, up to a scheme-dependent overall constant. Up to this constant term, the evolution kernel to a given order in perturbation theory can be obtained from the calculation of special conformal anomaly at one order less.
QCD in non-integer $d=4-2ε$ space-time dimensions enjoys conformal invariance at the special fine-tuned value of the coupling. Counterterms for composite operators in minimal subtraction schemes do not depend on $ε$ by construction, and therefore the renormalization group equations for composite operators in physical (integer) dimensions inherit conformal symmetry. This observation can be used to restore the complete evolution kernels that take into account mixing with the operators containing total derivatives from their eigenvalues (anomalous dimensions). Using this approach we calculate the two-loop (NLO) evolution kernels for the leading twist flavor-singlet operators in the position space (light-ray operator) representation. As the main result of phenomenological relevance, in this way we are able to confirm the evolution equations of flavor-singlet generalized hadron parton distributions derived earlier by Belitsky and Müller using a different approach.