arXiv subjects

Vladimir M. Braun

Publications and source records attributed to Vladimir M. Braun.

17 recordsLinked to original sources

arXiv2026

Finite-$t$ and target mass corrections for the short-distance expansion of quasi(pseudo) GPDs

We calculate the ``kinematic'' corrections $t/P_z^2$ and $m_N^2/P_z^2$ to the short distance expansion of gauge-invariant nonlocal quark-antiquark operators sandwiched between nucleon states with different momenta. Here $t$ is the momentum transfer, $m_N$ is the nucleon mass and $P_z$ is the momentum component in the direction of the quark-antiquark separation, which is assumed to be large. These matrix elements can be calculated in lattice QCD and, at leading twist, expressed in terms of moments of the generalized parton distrubutions (GPDs). Our results allow one to control one of principal uncertainties in such calculations and extend their region of applicability to larger momentum transfers, which is important in the quest to access the three-dimension image of the proton. The calculated corrections turn out to be significant for a realistic lattice QCD setup.

hep-ph↗

arXiv2024

The two-loop coefficient functions for double deeply virtual Compton scattering

Making use of conformal symmetry of large-$n_f$ QCD in $d=4-2ε$ dimensions at the Wilson-Fischer fixed point, we calculate the two-loop coefficient functions in the operator product expansion of two electromagnetic currents in general kinematics with two different photon virtualities. This result is necessary for the description of the double deeply virtual Compton scattering to the next-to-next-to-leading order accuracy, but is also interesting for a range of other two-photon processes. We present analytic expression for the coefficient function in momentum fraction space in the $\overline{\text{MS}}$ scheme and study its numerical impact on the Compton form factors for a simple model of the generalized parton distributions. The calculated corrections turn out to be large and are significant for the kinematics of proposed experiments.

hep-ph↗

arXiv2022

Higher Twists

Higher twist corrections refer to a certain class of contributions to hard processes in strong interactions that are suppressed by a power of the hard scale. This is a very broad field of research which is becoming more and more important as the accuracy of the available experimental data increases. I give an overview of some basic relevant theory concepts and technical developments, and briefly discuss a few phenomenological applications.

hep-ph↗

arXiv2021

QCD factorization for twist-three axial-vector parton quasidistributions

The transverse component of the axial-vector correlation function of quark fields is a natural starting object for lattice calculations of twist-3 nucleon parton distribution functions. In this work we derive the corresponding factorization expression in terms of twist-2 and twist-3 collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for the axial-vector quasi- and pseudodistributions.

hep-ph↗

arXiv2021

QCD factorization for chiral-odd parton quasi- and pseudo-distributions

We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions $h_L(x)$ and $e(x)$, and also the twist-two transversity distribution $δq(x)$. The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the $h_L$ quasi(pseudo)-distribution can be separated from the twist-three part by virtue of an exact Jaffe-Ji-like relation.

hep-ph↗

arXiv2020

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors. The calculation is carried out on 35 different CLS ensembles with $N_f=2+1$ flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to $a=0.039\,$fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane. The present arXiv version (v3) includes an Addendum where we update the results using the recently calculated three-loop matching factors for the conversion from the RI'/SMOM to the $\overline{\text{MS}}$ scheme. We find $a_2^π=0.116^{+19}_{-20}$ for the pion, $a_1^K=0.0525^{+31}_{-33}$ and $a_2^K=0.106^{+15}_{-16}$ for the kaon. We also include the previous values, which were obtained with two-loop matching.

hep-lat↗

arXiv2019

Light-cone distribution amplitudes of octet baryons from lattice QCD

We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039\,\mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit.

hep-lat↗

arXiv2018

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter $δ^π_2$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.

hep-lat↗

arXiv2018

Pion and Kaon Distribution Amplitudes from lattice QCD: towards the continuum limit

We present the current status of a non-perturbative lattice calculation of the moments of the pion and kaon distribution amplitudes by the RQCD collaboration. Our investigation is carried out using $N_f=2+1$ dynamical, non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5 different lattice spacings and pion masses down to the physical pion mass. A combined continuum and chiral extrapolation to the physical point is performed along two independent quark mass trajectories simultaneously. We employ momentum smearing in order to decrease the contamination by excited states and increase statistical precision.

hep-lat↗

arXiv2018

Integrability in heavy quark effective theory

It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry $C(u)$ of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.

hep-th↗

arXiv2018

Pion distribution amplitude from Euclidean correlation functions

Following the proposal in [1], we study the feasibility to calculate the pion distribution amplitude (DA) from suitably chosen Euclidean correlation functions at large momentum. In our lattice study we employ the novel momentum smearing technique [2,3]. This approach is complementary to the calculations of the lowest moments of the DA using the Wilson operator product expansion and avoids mixing with lower dimensional local operators on the lattice. The theoretical status of this method is similar to that of quasi-distributions [4], which has recently been applied to the same problem in [5]. The similarities and differences between these two techniques are highlighted.

hep-lat↗

arXiv2017

The $ρ$-meson light-cone distribution amplitudes from lattice QCD

We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized $ρ$ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between $0.060\,\text{fm}$ and $0.081\,\text{fm}$, different lattice volumes up to $m_πL = 6.7$ and pion masses down to $m_π=150\,\text{MeV}$. Bare lattice results are renormalized non-perturbatively using a variant of the RI'-MOM scheme and converted to the $\overline{\text{MS}}$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants $f_ρ^T/f_ρ^{\vphantom{T}} = 0.629(8)$ and the values of the second Gegenbauer moments $a_2^\parallel = 0.132(27)$ and $a_2^\perp = 0.101(22)$ at the scale $μ= 2\,\text{GeV}$ for the longitudinally and transversely polarized $ρ$ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of $ρ\toππ$ decay at the smaller pion masses is not taken into account.

hep-lat↗

arXiv2016

Light-cone distribution amplitudes of the baryon octet

We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using $N_f=2+1$ flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.

hep-lat↗

arXiv2014

Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite-$t$ and target mass corrections

We carry out the first complete calculation of kinematic power corrections $\sim t/Q^2$ and $\sim m^2/Q^2$ to several key observables in Deeply Virtual Compton Scattering. The issue of convention dependence of the leading twist approximation is discussed in detail. In addition we work out representations for the higher twist corrections in terms of double distributions, Mellin-Barnes integrals and also within a dissipative framework. This study removes an important source of uncertainties in the QCD predictions for intermediate photon virtualities $Q^2\sim 1$-$5\,{\rm GeV}^2$ that are accessible in the existing and planned experiments. In particular the finite-$t$ corrections are significant and must be taken into account in the data analysis.

hep-ph↗

arXiv2008

Wave functions of the nucleon and its parity partner from lattice QCD

We compute moments of distribution amplitudes using gauge configurations with two flavors of clover fermions from QCDSF/DIK and operators which are optimized with respect to their behavior under the lattice symmetries. The knowledge of these quantities helps in understanding the internal structure of hadrons and in the analysis of (semi-)exclusive processes. We present results for the nucleon distribution amplitude which suggest that the asymmetries (the deviations from the asymptotic form) are smaller than indicated by sum rule calculations. Using the same approach we were also able to calculate the same quantities for the $N^\star(1535)$, the parity partner of the nucleon. These results show a stronger deviation from the asymptotic form.

hep-lat↗

arXiv2008

Distribution Amplitudes of the Lambda_b Baryon in QCD

The QCD description of exclusive decays of the $Λ_b$ baryon involves hadronic matrix elements of non-local light ray operators, the light-cone distribution amplitudes. We introduce the complete set of three--quark distribution amplitudes and calculate the renormalization scale dependence for the leading twist. At leading order in the strong coupling the evolution is driven by pairwise two--quark interactions: heavy--light involving Sudakov logarithms as in the B-meson case, and light--light as in light mesons. We solve the evolution equation and show that its main effect is to generate a radiative tail extending to high energies. Finally, we present simple models for the distribution amplitudes based on QCD sum rules, and study the effect of the evolution on these models.

hep-ph↗

arXiv2004

Renormalon approach to higher-twist distribution amplitudes and the convergence of the conformal expansion

Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach which does not rely on conformal symmetry but is based instead on renormalon analysis. This way we obtain an upper bound for the contributions of higher conformal spin operators, which translates into a bound on the end--point behavior of DA. The existence of such a bound is important for proving factorization theorems. For the two-particle twist-four DA we find in the renormalon model that the conformal expansion converges but it does not converge uniformly near the end points. This means that power corrections to observables which are particularly sensitive to the region where one valence quark is soft, may be underestimated when using the first few terms in the conformal expansion. The renormalon models of twist-four DA of the pion and the rho meson are constructed and can be used as a viable alternative to existing models.

hep-ph↗