Krzysztof Graczyk Homepage
-
In preparation
-
-
Cezary Juszczak and Krzysztof M. Graczyk
in preparation: C++ library for shallow neural networks in Bayesian framework,
arxiv:2412.xxxxx.
<<<<<
Abstract:
-
tba
-
Krzysztof M. Graczyk, Dawid Strzelczyk, Maciej Matyka
in preparation: working title: Diffusion revisited,
arxiv:2410.xxxxx.
<<<<<
Abstract:
-
tba
-
Remigiusz Durka, Krzysztof M. Graczyk,
in preparation: working title: Supersymmetry for SuperGravity,
arxiv:2410.xxxxx.
<<<<<
Abstract:
-
tba
-
Hemant Prasad, Jan T. Sobczyk, Artur M. Ankowski, Rwik Dharmapal Banerjee, , Krzysztof M. Graczyk, Beata Kowal,
tba,
arxiv:2410.xxxxx.
<<<<<
Abstract:
-
tba
-
Beata Kowal, Krzysztof M. Graczyk, Artur M. Ankowski, Rwik Dharmapal Banerjee, Hemant Prasad, Jan T. Sobczyk,
tba,
arxiv:2407.xxxxx.
<<<<<
Abstract:
-
tba
-
Peer reviewed articles
-
-
B. E. Kowal, K. M. Graczyk, A. M. Ankowski, R. Dharmapal Banerjee, H. Prasad, J. T. Sobczyk,
Empirical fits to inclusive electron-carbon scattering data obtained by deep-learning methods,
arxiv:2312.17298.
<<<<<
Abstract:
-
Employing the neural network framework, we obtain empirical fits to the electron-scattering cross section for carbon over
a broad kinematic region, extending from the quasielastic peak, through resonance excitation, to the onset of deep-inelastic scattering.
We consider two different methods of obtaining such model-independent parametrizations and the corresponding uncertainties:
based on the NNPDF approach [J. High Energy Phys. 2002, 062], and on the Monte Carlo dropout.
In our analysis, the $\chi^2$ function defines the loss function, including point-to-point uncertainties and considering the systematic normalization uncertainties for each independent set of measurements. Our statistical approaches lead to fits of comparable quality and similar uncertainties of the order of $7$\% and $12$\% for the first and the second approaches, respectively. To test these models, we compare their predictions to a~test dataset, excluded from the training process, a~dataset lying beyond the covered kinematic region, and theoretical predictions obtained within the spectral function approach. The predictions of both models agree with experimental measurements and the theoretical predictions. However,
the first statistical approach shows better interpolation and extrapolation abilities than the one based on the dropout algorithm.
-
Krzysztof M. Graczyk, and Kornel Witkowski
Bayesian Reasoning for Physics Informed Neural Networks,
arxiv:2308.13222.
<<<<<
Abstract:
-
Physics informed neural network (PINN) approach in Bayesian formulation is presented.
We adopt the Bayesian neural network framework formulated by MacKay (Neural Computation 4 (3) (1992) 448).
The posterior densities are obtained from Laplace approximation.
For each model (fit), the so-called evidence is computed. It is a measure that classifies the hypothesis.
The most optimal solution has the maximal value of the evidence.
The Bayesian framework allows us to control the impact of the boundary contribution to the total loss.
Indeed, the relative weights of loss components are fine-tuned by the Bayesian algorithm.
We solve heat, wave, and Burger's equations. The obtained results are in good agreement with the exact solutions.
All solutions are provided with the uncertainties computed within the Bayesian framework.
-
R. Dharmapal Banerjee, A. M. Ankowski, K. M. Graczyk, B. E. Kowal, H. Prasad, J. T. Sobczyk,
JLab spectral functions of argon in NuWro and their implications for MicroBooNE,
Phys. Rev. Dxxx, xxxxxx (2024), arxiv:2312.13369.
,
<<<<<
Abstract:
-
The Short-Baseline Neutrino program in Fermilab aims to resolve the nature of the low-energy excess events observed
in LSND and MiniBooNE, and analyze with unprecedented precision neutrino interactions with argon.
These studies require reliable estimate of neutrino cross sections, in particular for charged current quasielastic scattering (CCQE).
Here, we report updates of the NuWro Monte Carlo generator that, most notably,
bring the state-of-the-art spectral functions to model the ground state properties of the argon nucleus,
and improve the accuracy of the cross sections at low energies by accounting for the effects of the nuclear Coulomb potential.
We discuss these developments in the context of electron and neutrino interactions,
by comparing updated NuWro predictions to experimental data from Jefferson Laboratory Hall A and MicroBooNE.
The MicroBooNE CCQE data are described with the chi2 per degree of freedom of 0.7, compared with 1.0 in the local Fermi gas model.
The largest improvement is observed for the angular distributions of the produced protons, where the ?2 reduces nearly by half.
Being obtained using the axial form factor parametrization from MINERvA,
our results indicate a~consistency between the CCQE measurements in MINERvA and MicroBooNE.
-
Krzysztof M. Graczyk, and Beata Kowal
Neutral current neutrino and antineutrino scattering off the polarized nucleon,
Phys. Rev. D108, 093002 (2023).
<<<<<
Abstract:
-
The elastic and inelastic neutral current neutrino (antineutrino) scattering off the polarized nucleon is discussed.
The inelastic scattering concerns the single-pion production process.
We show that the spin asymmetries' measurement can help to distinguish between neutrino and antineutrino
neutral current scattering processes. The spin asymmetries also encode information about a type of target.
Eventually, detailed studies of the inelastic spin asymmetries can improve understanding of the resonant-nonresonant pion production mechanism.
-
Krzysztof M. Graczyk, Dawid Strzelczyk, Maciej Matyka,
Deep learning for diffusion in porous media,
Sci Rep 13, 9769 (2023).
<<<<<
Abstract:
-
We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning. We distinguish two tasks. In the first, networks based on the analysis of the system's geometry predict porosity and effective diffusion coefficient. In the second, networks reconstruct the concentration map. In the first task, we propose two types of CNN models: the C-Net and the encoder part of the U-Net. Both networks are modified by adding a self-normalization module [Graczyk \textit{et al.}, Sci Rep 12, 10583 (2022)]. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sand packings-like samples overshoots or undershoots for biological-like samples. In the second task, we propose the usage of the U-Net architecture. It accurately reconstructs the concentration fields. In contrast to the first task, the network trained on one data type works well for the other. For instance, the model trained on sand packings-like samples works perfectly on biological-like samples. Eventually, for both types of the data, we fit exponents in the Archie's law to find tortuosity that is used to describe the dependence of the effective diffusion on porosity.
-
Remigiusz Durka, Krzysztof M. Graczyk,
N=2 resonant superalgebra for supergravity,
Phys. Lett. B 833, 137366 (2022)
<<<<<
Abstract:
-
We present new superalgebra for $\mathcal{N}=2$ $D=3,4$ supergravity theory endowed with the $U(1)$ generator. The superalgebra is rooted in the so-called Soroka-Soroka algebra and spanned by the Lorentz $J_{ab}$ and Lorentz-like $Z_{ab}$, translation $P_a$ and $T$ generators, as well as two supercharges $Q^I_\alpha$. It is the only possible realization for a given generator content. We construct a corresponding 3D Chern-Simons supergravity realization of the superalgebra and discuss its relevance.
-
Krzysztof M. Graczyk, Jarosław Pawlowski, Sylwia Majchrowska, Tomasz Golan,
Self-Normalized Density Map (SNDM) for Counting Microbiological Obejcts,
Sci Rep 12, 10583 (2022)
<<<<<
Abstract:
-
The statistical properties of the density map (DM) approach to counting microbiological objects on
images are studied in detail. The DM is given by U 2-Net. Two statistical methods for deep neural
networks are utilized: the bootstrap and the Monte Carlo (MC) dropout. The detailed analysis of the
uncertainties for the DM predictions leads to a deeper understanding of the DM model’s deficiencies.
Based on our investigation, we propose a self-normalization module in the network. The improved
network model, called Self-Normalized Density Map (SNDM), can correct its output density map
by itself to accurately predict the total number of objects in the image. The SNDM architecture
outperforms the original model. Moreover, both statistical frameworks—bootstrap and MC dropout—
have consistent statistical results for SNDM, which were not observed in the original model. The
SNDM efficiency is comparable with the detector-base models, such as Faster and Cascade R-CNN
detectors.
-
Remigiusz Durka, Krzysztof M. Graczyk,
Resonant superalgebras for supergravity,
Eur. Phys. J. C 82, 254 (2022).
<<<<<
Abstract:
-
Using a newly developed highly efficient computational method of generating 'resonating' algebraic structures, we achieve the supersymmetric extensions of algebras going beyond the Poincaré and Anti-de Sitter ones. Considered class of algebras include additional bosonic generators Zab (Lorentz-like) and Ua (translational-like) added to the standard Lorentz generator Jab and translation generator Pa. Our analysis includes cases up to two fermionic charges, Q? and Y?. We reevaluated previously published results and obtained completely new algebras up to two of Lorentz-like, translation-like, and supercharge-like generators (JP+Q)+(ZU+Y)=JPZU+QY. In the last case, among 667 founded superalgebras 264 are suitable for supergravity construction.
-
Krzysztof M. Graczyk, Beata E. Kowal
Model dependence of the polarization asymmetries in weak pion production off the nucleon,
Phys. Rev. D104, 033005 (2021).
<<<<<
Abstract:
-
The work presents the study of the polarization observables in the single pion production (SPP) induced by the interaction of the muon neutrino (antineutrino) with nucleons. The SPP cross sections and spin asymmetries are computed within two phenomenological models. One is based on the nonlinear sigma model [E. Hernandez, J. Nieves, and M. Valverde, Phys. Rev. D 76, 033005 (2007)] and the other has origin in the linear sigma model [G. L. Fogli and G. Nardulli, Nucl. Phys. B160, 116 (1979)]. First, we show that the final nucleon polarization and target spin asymmetries are good observables to obtain information about the
C5A axial form factor. Second, we demonstrate that the nucleon polarization and the target spin asymmetries are sensitive to the relative phase between resonance and nonresonance amplitudes. We conclude that the polarization of the final nucleon and the target spin asymmetry are promising observables for testing SPP models, including studies of the axial content of
?(1232) resonance and unitarization procedures.
-
Krzysztof M. Graczyk, M. Matyka
Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning,
Sci Rep 10, 21488 (2020)
<<<<<
Abstract:
-
Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity (?), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with ??(0.37,0.99) which covers five orders of magnitude a span for permeability k?(0.78,2.1×105) and tortuosity T?(1.03,2.74). It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and ? has been obtained and compared with the empirical estimate.
-
Krzysztof M. Graczyk, Beata E. Kowal
Spin asymmetries in quasielastic charged current neutrino-nucleon scattering,
Phys. Rev. D101, 073002 (2020).
<<<<<
Abstract:
-
The work concerns the quasielastic charged current neutrino-neutron and antineutrino-proton interactions. Single, double, and triple spin asymmetries are computed and analyzed. The spin asymmetries are sensitive to the axial form factor of the nucleon.
In particular, the target-recoil double spin asymmetry and the lepton-target-recoil triple spin asymmetry depend strongly on the axial form factor of the nucleon. Indeed, the sign and shape of these components depend on the axial mass parameter. All the asymmetries, except the lepton polarization, are observables well suited to study the nonstandard interactions described by the second class current contribution.
-
Krzysztof M. Graczyk, Beata E. Kowal
Spin asymmetry in single pion production induced by weak interactions of neutrinos with polarized nucleons,
Phys. Rev. D99, 053002 (2019).
<<<<<
Abstract:
-
The single pion production (SPP) in the charged-current neutrino (antineutrino) scattering off the polarized nucleon is discussed. The spin asymmetry is predicted within two approaches. The longitudinal and perpendicular, to the neutrino momentum, spin polarizations of the target nucleon are considered. It is shown, in several examples, that the spin asymmetry contains complementary to spin averaged cross section measurements information about the SPP dynamics. Indeed, the spin asymmetry is sensitive to the nonresonance background description of the SPP model. For the normal polarization of the target the spin asymmetry is given by the interference between the resonance and the nonresonance contributions.
-
Luis Alvarez-Ruso, Krzysztof M. Graczyk, Eduardo Saul-Sala,
Nucleon axial form factor from a Bayesian neural-network analysis of neutrino-scattering data,
Phys. Rev. C99, 025204 (2019).
<<<<<
Abstract:
-
The Bayesian approach for feedforward neural networks has been applied to the extraction of the nucleon
axial form factor from the neutrino-deuteron-scattering data measured by the Argonne National Laboratory
bubble-chamber experiment. This framework allows to perform a model-independent determination of the axial
form factor from data. When the low 0.05 < Q2 < 0.10-GeV2 data are included in the analysis, the resulting
axial radius disagrees with available determinations. Furthermore, a large sensitivity to the corrections from
the deuteron structure is obtained. In turn, when the low-Q2 region is not taken into account with or without
deuteron corrections, no significant deviations from previous determinations have been observed. A more
accurate determination of the nucleon axial form factor requires new precise measurements of neutrino-induced
quasielastic scattering on hydrogen and deuterium.
-
Krzysztof M. Graczyk and B. E. Kowal,
Polarization transfer in weak pion production off the nucleon,
Phys. Rev. D97, 013001 (2018).
<<<<<
Abstract:
-
Polarization transfer (PT) observables in the single pion production induced by the charged current
interaction of the neutrino with the nucleon are examined. The polarization components of the final
nucleon and the charged lepton are calculated within two models for the pion production.
The predictions are made for neutrino energy of the order of 1 GeV as well as for the T2K energy distribution.
It is demonstrated that the PT observables, the degree of polarization and the polarization components of outgoing fermions,
are sensitive to assumptions about the nonresonant background model.
In particular it is shown that the normal components of the polarization of the outgoing nucleon and the lepton
are determined by the interference between the resonant (RES) and nonresonant (NB) amplitudes.
Moreover, the sign of the normal component of the polarization of the charged lepton is fixed
by the relative sign between the RES and the NB amplitudes.
-
K. M. Graczyk and C. Juszczak,
Zemach moments of proton from Bayesian inference,
Phys. Rev. C91, 045205 (2015).
<<<<<
Abstract:
-
The first and the third Zemach moments are obtained, $\langle r \rangle_{(2)}= 1.1108\pm 0.0021 $ fm and $\langle r^3\rangle_{(2)}=2.889 \pm 0.008$ fm$^3$,
from the Bayesian analysis of the elastic $ep$ scattering data.
The quantitative discussion of the dependence of the results
on the parametrization choice is presented and the corresponding systematic uncertainties are estimated -- about 0.6\% and 1.6\% for the first and the third Zemach moments respectively.
-
K. M. Graczyk and C. Juszczak,
Applications of Neural Networks in Hadron Physics,
J.Phys. G: Nucl. Phys. 42 034019 (2015).
invited contribution to special issue entaitled "Enhancing the interaction between nuclear experiment and theory through information and statistics" (ISNET).
<<<<<
Abstract:
-
The Bayesian approach for the feed-forward neural networks is reviewed.
Its potential for usage in hadron physics is discussed.
As an example of the application the study of the the two-photon exchange effect is presented. We focus on the model comparison,
the estimation of the systematic uncertainties due to the choice of the model, and the over-fitting.
As an illustration the predictions of the cross sections ratio $d \sigma(e^+ p\to e^+ p)/d \sigma(e^- p\to e^- p)$
are given together with the estimate of the uncertainty due to the parametrization choice.
-
Krzysztof M. Graczyk and Cezary Juszczak,
Proton Radius from Bayesian Inference,
Phys. Rev. C90, 054334 (2014).
<<<<<
Abstract:
-
The methods of Bayesian statistics are used to extract the value of the proton radius
from the elastic $ep$ scattering data in a model independent way.
To achieve that goal a large number of parametrizations
(equivalent to neural network schemes) are considered and ranked by
their conditional probability $P(\mathrm{parametrization}\,|\,\mathrm{data})$ instead of using the minimal error criterion.
As a result the most probable proton radii values ($r_E^p=0.899\pm 0.003$ fm, $r_M^p=0.879\pm 0.007$ fm) are obtained and systematic error due to freedom in the choice of parametrization is estimated.
Correcting the data for the two photon exchange effect leads to smaller difference between the extracted values of $r_E^p$ and $r_M^p$.
The results disagree with recent muonic atom measurements.
-
Krzysztof M. Graczyk, Jakub Zmuda, Jan T. Sobczyk,
Electroweak Form Factors of the Delta(1232) Resonance,
Phys. Rev. D90, 093001 (2014).
<<<<<
Abstract:
-
Nucleon $\to \Delta(1232)$ transition electroweak form factors are discussed in a single pion production model
with nonresonant background terms originating from a chiral perturbation theory.
Fits to electron-proton scattering F2 as well as neutrino scattering bubble chamber experimental
data are performed. Both \nu-proton and \nu-neutron channel data are discussed in a unified statistical model.
A new parametrization of the $N\to\Delta(1232)$ vector form factors is proposed.
In the case of model with deuteron nuclear effects fit to neutrino scattering data gives the axial mass M_{A\Delta}=0.85+0.09-0.08 (GeV) and
C5A(0) = 1.10+0.15-0.14 in accordance with Goldberger-Treiman relation. However, the consistency is spoiled when the deuteron effects are omitted
i.e. in this case the fit gives the axial mass M_{A\Delta}=0.81+0.09-0.09 GeV and C5A(0)=0.93+0.13-0.13.
-
Krzysztof M. Graczyk,
Relevance of Two-Boson Exchange Effect in Quasi-elastic Charged Current Neutrino-Nucleon Interaction,
Phys. Lett. B732, 315 (2014).
<<<<<
Abstract:
-
Two-boson exchange (TBE) correction in $\nu n \to l^- p$ and $\nu p\to l^+ n$ reactions is estimated. The TBE contribution is
given by $W\gamma$ box diagrams. The calculations are performed for 1 GeV neutrinos and for the MiniBooNE and the
T2K energy spectra. The TBE correction to the total cross section is of the order of $2\div 4\%$ (with respect to the Born
contribution) in the case of $\nu_e$ and $\overline{\nu}_e$ and $1 \div 2\%$ in the case of $\nu_\mu$ and $\overline{\nu}_\mu$.
-
Krzysztof M. Graczyk,
Comparison of Neural Network and Hadronic Model Predictions of Two-Photon Exchange Effect,
Phys. Rev. C 88, 065205 (2013).
<<<<<
Abstract:
-
Predictions for the two-photon exchange (TPE) correction to unpolarized $ep$ elastic cross section,
obtained within two different approaches, are confronted and discussed in details. In the first one the TPE correction is extracted from experimental data by applying the Bayesian neural network (BNN) statistical framework. In the other the TPE is given by box diagrams, with the nucleon and the $P_{33}$ resonance as the hadronic intermediate states. Two different form factor parametrizations for both the proton and the $P_{33}$ resonance are taken into consideration. Proton form factors are obtained from the global fit of the full model (with the TPE correction) to the unpolarized cross section data. Predictions of both methods agree well in the intermediate $Q^2$ range, $(1,3)$ GeV$^2$. Above $Q^2=3$ GeV$^2$ the agreement is on $2\sigma$ level. Below $Q^2=1$ GeV$^2$ the consistency between both approaches is broken. The values of the proton radius extracted within both models are given.
In both cases predictions for VEPP-3 experiment have been obtained and confronted with the preliminary experimental results.
-
T. Golan, K. M. Graczyk, C. Juszczak, and J. T. Sobczyk,
Extraction of axial mass and strangeness values from the MiniBooNE neutral current elastic cross section measurement,
Phys. Rev. C 88, 024612 (2013).
<<<<<
Abstract:
-
Results of the analysis of the MiniBooNE experiment data for the neutral current elastic neutrino scattering off the CH2
target with the NuWro Monte Carlo generator are presented. The inclusion in the analysis of the two-body current contribution leads to
the axial mass value MA=1.10-0.15+0.13 GeV, consistent with the older evaluations based on the neutrino-deuteron scattering data.
The strange quark contribution to the nucleon spin is estimated with the value gAs=-0.4-0.3+0.5.
-
Krzysztof M. Graczyk,
Two-Photon Exchange Effect Studied with Neural Networks,
Phys. Rev. C 84, 034314 (2011).
<<<<<
Abstract:
-
An approach to the extraction of the two-photon exchange (TPE) correction from elastic ep scattering data is presented.
The cross-section, polarization transfer (PT), and charge asymmetry data are considered. It is assumed that the TPE correction to the PT data is negligible. The form factors and TPE correcting term are given by one multidimensional function approximated by the feedforward neural network (NN). To find a model-independent approximation, the Bayesian framework for the NNs is adapted. A large number of different parametrizations is considered. The most optimal model is indicated by the Bayesian algorithm. The obtained fit of the TPE correction behaves linearly in ? but it has a nontrivial Q2 dependence.
A strong dependence of the TPE fit on the choice of parametrization is observed.
-
Krzysztof M. Graczyk, Piotr Plonski, Robert Sulej,
Neural Network Parameterizations of Electromagnetic Nucleon Form Factors,
JHEP09(2010) 053.
<<<<<
Abstract:
-
The electromagnetic nucleon form-factors data are studied with artificial feed forward neural networks.
As a result the unbiased model-independent form-factor parametrizations are evaluated together with uncertainties.
The Bayesian approach for the neural networks is adapted for chi2 error-like function and applied to the data analysis.
The sequence of the feed forward neural networks with one hidden layer of units is considered.
The given neural network represents a particular form-factor parametrization. The so-called evidence
(the measure of how much the data favor given statistical model) is computed with the Bayesian framework and it is used
to determine the best form factor parametrization.
-
Krzysztof M. Graczyk, Danuta Kiełczewska, Paweł Przewłocki, Jan T. Sobczyk,
C5A axial form factor from bubble chamber experiments,
Phys. Rev. D80, 093001 (2009).
<<<<<
Abstract:
-
A careful reanalysis of both Argonne National Laboratory and Brookhaven National Laboratory data for weak single pion production is done. We consider deuteron nuclear effects and normalization (flux) uncertainties in both experiments. We demonstrate that these two sets of data are in good agreement. For the dipole parametrization of $C_5^A(Q^2)$, we obtain $C_5^A(0)=1.19\pm 0.08$, $M_A=0.94\pm 0.03$~GeV.
As an application we present the discussion of the uncertainty of the neutral current 1$\pi^0$ production cross section, important for the T2K neutrino oscillation experiment.
-
W. M. Alberico, S. M. Bilenky, C. Giunti, K. M. Graczyk,
The ratio of e+- p scattering cross sections predicted from the global fit of elastic ep data,
J. Phys. G. Nucl. Part. Phys. 36, 115009 (2009).
<<<<<
Abstract:
-
We present predictions for the value of the cross section ratio $\sigma(e^+p \to e^+p)/\sigma(e^-p \to e^-p)$, determined from our fit of the elastic $ep$ cross section and polarization data. In this fit we took into account the phenomenological two-photon exchange dispersive correction.
The cross section ratios which are expected to be measured by the VEPP-3 experiment are computed. The kinematical region which will be covered by the E04-116 JLab experiment is also considered. It is shown that for both experiments the predicted cross section ratios deviate from unity within more than $3\sigma$.
-
W. M. Alberico, S. M. Bilenky, C. Giunti, K. M. Graczyk,
Electromagnetic form factors of the nucleon: New fit and analysis of uncertainties,
Phys. Rev. C 79, 065204 (2009).
<<<<<
Abstract:
-
Electromagnetic form factors of proton and neutron, obtained from a new fit of data, are presented. The proton form factors are obtained from a simultaneous fit to the ratio $\mu_p G_{Ep}/G_{Mp}$ determined from polarization transfer measurements and to $ep$ elastic cross section data. Phenomenological two-photon exchange corrections are taken into account. The present fit for proton was performed in the kinematical region $Q^2\in (0,6)$ GeV$^2$. Both for protons and neutrons we use the latest available data. For all form factors the uncertainties and correlations of form factor parameters are investigated with the $\chi^2$ method.
-
K. M. Graczyk, J. T. Sobczyk,
Lepton mass effects in weak CC single pion production,
Phys. Rev. D77, 053003 (2008).
<<<<<
Abstract:
-
Different approaches to take into account nonzero lepton mass in the Rein-Sehgal model are compared. Modification of the axial current due to pion pole term are included and it is shown that they lead to large reduction of antineutrino cross section and a change of the shape of $d\sigma/dQ^2$.
-
K. M. Graczyk, J. T. Sobczyk,
Form Factors in the Quark Resonance Model,
Phys. Rev. D77, 053001 (2008).
<<<<<
Erratum: Phys. Rev. D 79, 079903(E) (2009).
<<<<<
Abstract:
-
Vector and axial form factors in the quark resonance model are analyzed with a combination of theoretical and phenomenological arguments. The new form of form factors is deduced from $\Delta$(1232) excitation models and available data. The vector part is shown to agree with the resonant contribution to electron-proton inclusive $F_2$ data. The axial part is obtained by finding a simultaneous fit to ANL and BNL $\frac{d \sigma}{d Q^2}$ neutrino scattering data. The best fit corresponds to $C_5^A(0)=0.88$ in the Rarita Schwinger formalism.
-
K. M. Graczyk, C. Juszczak, J. T. Sobczyk,
Quark-Hadron Duality in the Rein-Sehgal Model,
Nucl. Phys. A781, 227 (2007).
<<<<<
Abstract:
-
The quark-hadron duality in CC and NC neutrino interactions is discussed under assumptions that single pion production is described accurately by
the Rein-Sehgal model and that it allows reconstruction of the inclusive cross section in the resonance region.
The duality is measured by means of integrals of structure functions in the Nachtmann variable for $Q^2<3$ GeV$^2$.
The results depend on the precision with which contributions from single pion production channels in the overall cross sections are known.
Several approaches to evaluate them are compared.
The duality is predicted to be seen for proton target reactions and to be absent for neutron and isoscalar targets. Two-component duality between resonant and valence quark contributions to structure functions is also investigated.
-
A. Ankowski et al.,
Energy reconstruction of electromagnetic showers from pi0 decays with the ICARUS T600 Liquid Argon TPC,
Acta Phys.Polon.B41, 103 (2010).
<<<<<
-
A. Ankowski et al.,
Characterization of ETL 9357FLA Photomultiplier Tubes for
Cryogenic Temperature Applications,
Nucl. Instrum. Meth. A556, 146(2006).
<<<<<
-
A. Ankowski et al.,
Measurement of through-going particle momentum by means of multiple scattering with the ICARUS T600 TPC
Eur.Phys.J. C48 (2006) 667.
<<<<<
-
Krzysztof M. Graczyk,
Tau polarization in quasielastic charged-current neutrino (antineutrino)-nucleus scattering,
Nucl. Phys. A748, 313 (2005).
<<<<<
Abstract:
-
The quasielastic charged-current (CC) tau neutrino (antineutrino)-nucleus scattering is considered.
The dependence of tau polarization on nuclear-structure effects is discussed in detail.
The description of the nucleus is based on the Mean-Field Theory (MFT). The ground state of nucleus
is described using the Relativistic Fermi Gas model (FG). The effective mass is introduced as well
as the ring Random Phase Approximation (RPA) effects are taken into account in the framework of relativistic meson-nucleon model. The Local Density Approximation (LDA) is used for the argon nucleus, having in mind possible application to the ICARUS experiment.
The discussion concentrates on the threshold region where the $\tau^-$
can be unpolarized and the nuclear effects play an important role.
-
K. M. Graczyk, J. T. Sobczyk,
Algebraic solution of RPA equations for CC quasi-elastic neutrino-nucleus scattering,
Eur. Phys. J. C31, 177 (2003).
<<<<<
Abstract:
-
The algebraic solution of RPA equations nucleon re-interactions in the case of quasi elastic charged current neutrino - nucleus scattering is presented. Abelian algebra of matrices allows to extract four independent corrections to cross section separatly.Results of numerical computations are shown.
-
M. Amoruso, et al.,
Design, construction and tests of the ICARUS T600 detector,
Nucl. Instrum. Meth. A527, 329 (2004).
<<<<<
- M. Amoruso, et al.,
Study of electron recombination in liquid Argon with the ICARUS TP,
Nucl. Instrum. Meth. A523, 275 (2004).
<<<<<
- M. Antonello, et al.,
Detection of cherenkov light emission in liquid Argon,
Nucl. Instrum. Meth. A516, 348 (2004).
<<<<<
-
M. Amoruso, et al.,
Analysis of the liquid argon purity in the ICARUS T600 TPC,
Nucl. Instrum. Meth. A516, 68 (2004).
<<<<<
-
S. Amoruso, et al.,
Measurement of Mu decay spectrum with the ICARUS liquid argon TPC,
Eur. Phys. J. C33, 233 (2004).
<<<<<
-
F. Arneodo, et al.,
Observation of long ionizing tracks with the ICARUS T600 first half-modul.
Nucl. Instrum. Meth. A508, 287 (2003).
<<<<<
-
Conference proceedings
-
-
Remigiusz Durka, Krzysztof M. Graczyk,
Resonant enlargements of the Poincar'e/AdS (super)algebras from pattern-based analysis,
R. Durka, K. M. Garczyk, Acta Phys. Pol. B Proc. Suppl. 16, 6-A11 (2023)
<<<<<
Abstract:
-
Applying an efficient pattern-based computational method of generating the so-called 'resonating' algebraic structures results in a broad class of the new Lie (super)algebras. Those structures are enlargements of the Poincar\' {e} or Anti-de-Sitter (super)algebras, and they inherit the AdS base (anti)commutation pattern. Obtained superalgebras are rooted in the semigroup expansion method and Maxwell and Soroka-Soroka algebras, spanned by the Lorentz generator $J_{ab}$, translations $P_{a}$ and additional Lorentz-like generator $Z_{ab}$. Considered configurations include cases up to two fermionic supercharges $Q_{\alpha}$ and offer interesting modi?cations to the gauge (super)gravity theories.
-
Krzysztof M. Graczyk and Beata E. Kowal,
Polarization effects in neutrino-nucleon interactions,
Acta Phys. Polon. B50 (2019) 1771
<<<<<
Abstract:
-
Our recent investigations of the spin asymmetry observables in the charged current inelastic and quasielastic
neutrino (antineutrino)-nucleon scattering are reviewed. The spin asymmetry observables contain
full information about the structure of the electroweak neutrino-nucleon vertex.
Hence they can be used to constrain the cross-section models for the single pion production in $\nu$-nucleon scattering as well as allows to study the axial content of the nucleon and the second class current contribution to the quasielastic scattering amplitudes.
-
Luis Alvarez-Ruso, Krzysztof M. Graczyk and Eduardo Saul-Sala,
Neural network study of the nucleon axial form-factor,
PoS 341 (2018) 101
<<<<<
Abstract:
-
We have performed the first Bayesian neural-network analysis of neutrino-deuteron scattering
data [1]. The nucleon axial form factor has been extracted from quasielastic scattering data collected
by the Argonne National Laboratory (ANL) bubble chamber experiment using a modelindependent
parametrization. The results are in agreement with previous determinations only
when the low 0.05 < Q2 < 0.10 GeV2 region is excluded from the analysis. This suggests that
corrections from the deuteron structure may play a crucial role at low Q2, although experimental
errors in this kinematic region could have also been underestimated. With new and more precise
measurements of neutrino-induced quasielastic scattering on hydrogen and deuterium, the present
framework would be readily applicable to unravel the axial structure of the nucleon.
-
Krzysztof M. Graczyk and Beata E. Kowal
Nonresonant background signal in the polarization transfer in the weak pion production off the nucleon,
Neutrino 2018 conference proceedings, (2018) Zenodo, 10.5281/zenodo.1301014
<<<<<
Abstract:
-
Polarization transfer (PT) observables in the single pion production induced by the charged current neutrino-nucleon interaction are examined within two models. The predictions are made for neutrino energy of the order of 1 GeV as well as for the T2K energy flux. It is demonstrated that the PT observables: the degree of polarization and the polarization components of outgoing fermions are sensitive to the details of the nonresonant background model. It is shown that the normal component of the polarization of the outgoing nucleon and the charged lepton are determined by the interference between the resonant (RES) and nonresonant (NB) amplitudes. Moreover, the sign of the normal component of the polarization of the charged lepton is related to the relative sign between the RES and the NB amplitudes. The presentation is based on: Phys.Rev. D97 (2018) no.1, 013001, and Acta Phys.Polon. B48, 2219 (2017).
-
Beata E. Kowal and Krzysztof M. Graczyk,
Single pion production in neutrino-nucleon scattering studied with FORM package,
Proceedings of student poster session of the VII International Pontecorvo Neutrino Physics School (Prague, Czech Republic, August 20 - September 1, 2017), edited by F. Simkovic, - Dubna: JINR, ISBN 978-5-9530-0484-8
<<<<<
Abstract:
-
Two models for the single pion production induced by interactions of the neutrinos
with the nucleons are studied. The nonresonant background contribution is a subject of analysis.
It is shown that the normal component of the polarization of the charged lepton is sensitive on
the nonresonant background contribution. It is also demonstrated that the FORM language can be
utilized to evaluate all necessary transition matrix elements and the single pion production cross
sections.
-
Krzysztof M. Graczyk and Beata E. Kowal,
Single Pion Production Induced by Neutrino-Nucleon Interactions,
Acta Phys. Polon. B48 (2017) 2219
<<<<<
Abstract:
-
This talk presents short review of the single pion production (SPP) in
the neutrino-nucleon scattering. The attention is focused on the discus-
sion of the main difficulties in modeling the SPP processes. New physical
observables, which may constrain the theoretical models, are proposed.
-
J. Zmuda, K. M. Graczyk, C. Juszczak, J. T. Sobczyk,
NuWro Monte Carlo generator of neutrino interactions -
first electron scattering results,
Acta Phys. Polon. B46 (2015) 11, 2329
<<<<<
Abstract:
-
NuWro Monte Carlo generator of events is presented. It is a numerical
environment containing all necessary ingredients to simulate interactions
of neutrinos with nucleons and nuclei in realistic experimental situation in
wide neutrino energy range. It can be used both for data analysis as well
as studies of nuclear effects in neutrino interactions. The first results and
functionalities of eWro - module of NuWro dedicated to electron nucleus
scattering - are also presented.
-
J. Żmuda, K. M. Graczyk,
Electroweak Single Pion Production and Form Factors of the Delta(1232) Resonance,
AIP. Conf. Proc. 1680 (2015) 020013
<<<<<
Abstract:
-
We extend and review our analysis of the nucleon to Delta(1232) transition electroweak form factors from Ref. [1]. New fit of the Delta(1232) vector form factors to electron-proton scattering
F2 structure function is introduced as well, leading to results different from the popular parametrization of Ref. [2]. A clear model dependence of the extracted parameters emerges.
Fit to neutrino scattering data is performed in all available isospin channels. The resulting axial mass is M_{A\Delta}=0.85^{+0.09}_{-0.08} (GeV) and $C_5^A(0) = 1.10^{+0.15}_{-0.14}.
The latter value is in accordance with Goldberger-Treiman relation as long as the deuteron effects are included.
-
Krzysztof M. Graczyk,
N-Delta weak transition,
AIP Conf. Proc. 1405, (2011) 134
<<<<<
Abstract:
-
A short review of the Rein-Sehgal and isobar models is presented. The attention is focused on the nucleon-$\Delta$(1232) weak transition form-factors.
The results of the recent re-analyses of the ANL and BNL bubble chamber neutrino-deuteron scattering data are discussed.
-
P. Przewłocki, K. M. Graczyk, D. Kiełczewska, J.T. Sobczyk,
Pion production uncertainty in context of Tokai2Kamioka (T2K) experiment,
Contributed to European Strategy for Future Neutrino Physics, CERN, Geneva, Switzerland, 1-3 Oct 2009, pp. 250-252
<<<<<
Abstract:
-
We evaluate uncertainty of the neutral current pi0 production coming from limited
knowledge of axial form-factor. The uncertainties of the form-factor parameters
are obtained from a self-consistent fit to the results of ANL and BNL
experiments measuring pion production free of significant nuclear effects. The
evaluated uncertainities are important for T2K background estimates.
-
Krzysztof M. Graczyk,
Quark-hadron duality in lepton scattering off nucleons,
AIP Conf.Proc.1222:238 (2010)
<<<<<
Abstract:
-
The quark-hadron (QH) duality in lepton scattering off nucleons is studied with the resonance quark model. It is shown that in the case of neutrino scattering off isoscalar target the duality is simultaneously observed for charged and neutral currents $xF_1^{\nu N}$, $F_2^{\nu N}$, and $xF_3^{\nu N}$ weak structure functions.
We demonstrate that the QH duality can be useful property for modeling structure functions in the so-called resonance region. As an example it is shown that combining the relativistic quark model predictions with the duality arguments allows to construct the inclusive resonance $F_2^{ep}$ structure function.
-
Krzysztof M. Graczyk,
Single pion production induced by neutrino-nucleon interactions,
PoS (EPS-HEP 2009) 286.
<<<<<
Abstract:
-
This talk presents some of the results of the re-analysis \cite{Graczyk:2009qm} of the bubble chamber
data for single pion production induced by neutrino scattering off deuteron.
It is shown that ANL and BNL data are statistically consistent.
The validity of the Adler relations (between $P_{33}(1232)$ resonance axial form factors) is also investigated.
-
Krzysztof M. Graczyk, D. Kiełczewska, Jan T. Sobczyk,
C5A form factor from ANL experiment,
Acta. Phys. Polon. B40, (2009) 2565.
<<<<<
Abstract:
-
$C_5^A(Q^2)$ axial form factor is extracted from the ANL neutrino-deuteron
scattering data with deuteron structure effects taken into consideration.
The best fit of the $C_5^A(Q^2)$ axial form factor is obtained assuming dipole
parametrization with $C_5^A(0)=1.13\pm0.15$ and $M_A=0.94\pm 0.08$ GeV.
-
K. M. Graczyk,
Resonance contribution to single pion production in neutrino-nucleon scattering,
Proceedings of 27th International Workshop on Nuclear Theory, BM Trade Ltd., pp. 95-105 (2008) ISSN: 1313-2822, arXiv:0810.1247
<<<<<
Abstract:
-
Single pion production in neutrino-nucleon scattering is discussed. The neutrino energies characteristic for T2K project are considered. Two new parameterizations of $C_5^A$ axial form factor are proposed. Both of them are obtained in simultaneous fit to ANL and BNL data.
One of them (which fits better to BNL data) leads to $d\sigma/dQ^2$ differential cross section which is significantly reduced at low $Q^2$.
-
Krzysztof M. Graczyk, J. T. Sobczyk,
On description of D(1232) region in the Rein-Sehgal model,
AIP Conf.Proc.967, 205 (2007).
<<<<<
Abstract:
-
New vector and axial form factors in the Rein-Sehgal model are proposed.
The vector part is constructed after experimental
fits of the helicity amplitudes for electroproduction of Delta(1232) resonance.
The axial part is calculated after Q2 distribution of events in the ANL.
-
Krzysztof M. Graczyk,
Analysis of the Rein-Sehgal model in the context of the quark-hadron duality,
Acta. Phys. Polon. B37, 2321 (2006).
<<<<<
Abstract:
-
An analysis of the Rein--Sehgal model in the context of the quark--hadron duality hypothesis is presented.
The resonance region structure functions reconstructed from the
Rein--Sehgal model at different values of Q2RES are compared with the
DIS structure functions calculated at higher Q2DIS.
The ratios of corresponding integrals in the Nachtman variable
are also calculated and presented as functions of Q2RES.
The obtained functions are approximately flat for
Q2RES > 0.5 GeV2 but the quark--hadron duality is not observed.
-
K. M. Graczyk, C. Juszczak, J. T. Sobczyk,
Appearance of quark-hadron duality in the Rein-Sehgal model,
Nucl. Phys. B (Proc. Suppl.) 159, 241 (2006).
<<<<<
Abstract:
-
Quark-hadron duality in neutrino-nucleon reactions is investigated under the assumption that cross sections
in the resonance region are given by the Rein-Sehgal model. The quantitative analysis of the duality is done by
means of appropriate integrals of the structure functions in the Nachtmann variable.
We conclude that with the definition of the resonance region $W\in (M+m_{\pi}, 2$ GeV) the duality holds for neutrino-proton reaction $F_2$ structure function
for $Q^2\in (0.5, 3)$ GeV$^2$ and it is absent for neutrino-neutron reaction.
-
K.M. Graczyk,
Tau polarization in charged current neutrino-nucleon Deep Inelastic Scattering,
Nucl. Phys. (Proc. Suppl.) 139, 150 (2005).
<<<<<
Abstract:
-
Numerical results for the degree of polarization of \tau^- produced in (CC) neutrino - nucleon Deep Inelastic Scattering (DIS) are presented.
Calculations are done in the threshold region, where the \tau^- scattered by the small angles and can be partially polarized.
The cross sections and polarization are calculated by using the GRV98 parton distributions functions (PDF's) and the GRV98 with modifications of
A. Bodek at.al.
-
J.T. Sobczyk, J.A. Nowak, K.M. Graczyk,
WRONG - Wrocław neutrino generator of events for single pion production,
Nucl. Phys. B (Proc. Suppl.) 139, 266 (2005).
<<<<<
Abstract:
-
We constructed a new Monte Carlo generator of events for neutrino CC single pion production on free nucleon targets.
The code uses dynamical models of the DIS with the PDFs modified according to the recent JLab data and of the Delta excitation.
A comparison with experimental data was done in three channels for the total cross sections and for the distributions of events in invariant hadronic mass.
-
Preprints
-
-
K.M. Graczyk,
Local Density Approximations in charged-current quasielastic neutrino on Oxygen, Argon and Iron scattering,
nucl-th/0401053.
<<<<<
-
Talks
-
-
Analysis of the Rein-Sehgal model in the context of the quark-hadron duality.
XX Max Born Symposium
Nuclear effects in neutrino interactions,
Wrocław, Poland, December 7-10, 2005.
-
On Description of the Resonance Region in the FKR Model.
Fifth International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region:
NuInt07 Conference,
Fermilab (Batavia), Illinois, USA 30 May – 3 June, 2007.
-
Single pion production in neutrino-nucleon scattering,
Meeting of the INFN Theory Collaboration PI31,
ECT* Trento, Italy, 27-28 March, 2008.
-
Resonance contribution to single pion production in neutrino-nucleon scattering
,
27th International Workshop on Nuclear Theory,
Rila Mountains, Bulgaria, 22-28 June, 2008.
-
C5A axial form factor determined from the bubble chamber experiments,
Neutrino interactions: from theory to
Monte Carlo simulations, 45th Karpacz Winter School of Theoretical Physics,
Lądek Zdrój, Poland, February 2-11, 2009.
-
Single pion production induced by neutrino-nucleon interactions.
The 2009 Europhysics Conference on High Energy Physics, APS HEP 2009,
Cracow, Poland, 16-22 July, 2009.
-
Quark-Hadron Duality in lepton scattering off nuclei.
N u F a c t 0 9 - 11th International Workshop on
Neutrino Factories, Superbeams and Beta Beams,
Chicago, USA, 20-25 July, 2009. Invited talk
-
N-Delta Weak Transition.
Seventh International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region:
NuInt11 conference,
7-11 March, 2011, Dehradun, India. Invited talk
-
Radiative Corrections in Charged Current Quasielastic νN scattering.
International Workshop on Neutrino Factories Super Beams and Beta Beams, NUFACT13,
19-24 August, 2013, IHEP, Beijing, China.
Invited talk
-
Two-boson exchange in (quasi)elastic lepton scattering off nucleons.
Theory Meeting Experiment 2014 (TMEX), Neutrinos and Cosmos,
Warsaw, 3-5 September 2014.
-
Neutrino-nucleon/nucleus interactions,
Astroparticle physics in Poland,
Warsaw, May 11-13, 2015.
-
Modeling nucleon form factors with methods of Bayesian neural networks
Information and statistics in nuclear experiment and theory: ISNET-3 Workshop,
16-20 November, 2015, ECT* Trento, Italy. Invited talk
-
Pion production induced by neutrino-nucleon interactions,
Matter To The Deepest
Recent Developments In Physics Of Fundamental Interactions
XLI International Conference of Theoretical Physics
,
3-8 September 2017, Podlesice, Poland. Invited talk
-
Nucleon axial form factor from a Bayesian neural-network analysis of neutrino-scattering data,
Uncertainty Quantification (UQ) at the Extremes (ISNET-6)
,
8-12 October 2018, Darmstadt, Germany. Invited talk
-
Modeling Vector and Axial Nucleon Form Factors with Bayesian Neural Networks,
Nu-Physics and Machine Learning Lightning Talks,
17-19 June 2020, Chicago, USA. On-line participation
-
Tortuosity using CNN's,
CFD in Wroclaw #9,
10th of June 2022, Wrocław, Poland.
-
Predicting porous medium properties by deep neural network,
Big data analytical methods for complex systems,
6-7 October, 2022, Faculty of Mathematics and Computer Science, University of Wroclaw, Wrocław, Poland.
-
Poster presentations
-
-
Tau polarization in charged current neutrino-nucleon Deep Inelastic Scattering
Third International Workshop on Neutrino-Nucleus Interactions in few GeV region: NuInt04 conference,
LNGS, Gran Sasso, Italy, 17-21 March 2004.
-
Appearance of quark-hadron duality in the Rein-Sehgal model.
Fourth International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region,
Okayama, 26-29 Septemebr, 2005.
-
The degree of the polarization of the Tau lepton produced in the Neutrino-Nucleus Scattering.
VII School on Non-Accelerator Astroparticle Physics,
ICTP, Trieste, Italy, 26 July – 6 August, 2004.
-
Electron Interactions in NuWro,
presented by Cezary Juszczak,
Theory Meeting Experiment 2014 (TMEX), Neutrinos and Cosmos,
Warsaw, 3-5 September 2014.
-
Single pion production in neutrino-nucleon scattering studied with FORM package,
presented by Beata E. Kowal,
VII International Pontecorvo Neutrino Physics School,
Prague, Czech Republic, August 20 - September 1, 2017
-
Nonresonant background signal in the polarization transfer in the weak pion production off the nucleon,
Neutrino 2018,
Heidelberg, Germany, 4-9 June, 2018
-
Polarization effects in neutrino-nucleon interactions, main author B. Kowal,
Neutrino 2020,
Fermilab, USA, June 22 to July 2, 2020
-
Tortuosity and permeability of random porous medium using deep learning,Maciej Matyka and Krzysztof M. Graczyk,
InterPore2021,
online from 31 May – 4 June, 2021
-
Seminars
-
-
Sieci neuronowe a fizyka
Seminar for high school students,
Wydział Fizyki i Astronomii UWr., Wrocław, Poland, 16-12-2023.
-
Głębokie sieci neuronowe - rewolucja w rozwoju technolgicznym i badaniach naukowych
Seminar for high school students,
Interdyscyplinarnego Seminarium Studium Generale Universitatis Wratislaviensis im. Profesora Jana Mozrzymasa, Wrocław, Poland, 16-12-2023.
-
Neutrina Najdziwniejsze cząstki materii,
Seminar for high school students,
Wydział Fizyki i Astronomii UWr., Wrocław, Poland, 12-11-2005.
-
Analysis of the Rein-Sehgal model in the context of quark-hadron duality,
,
JINR Dubna, Russia, 12-05-2006.
-
Modelowanie oddziaływania neutrin z materią w konfrontacji z eksperymentem,
Warszawa, 23-03-2007.
-
Badanie oscylacji neutrin w eksperymencie T2K
,
Meeting of Astroparticle and Neutrino polish communities: Perspektywy astrofizyki cząstek,
Kraków, Poland, (14-18)-10-2007
-
Single pion production in neutrino-nucleon scattering
,
INFN and University of Torino, 20-02-2008.
-
Produkcja pojedynczych pionów w oddziaływaniu neutrino-deuteron - re-analiza
danych z eksperymentów ANL i BNL
,
Warszawa, Seminarium Warszawskiej Grupy Neutrinowej, IPJ, 20-03-2009.
-
Neutrina - boski posłaniec tajemnic natury,
Koło naukowe „Migacz”, Wydział Fizyki i Astronomii, Uniwersytet Wrocławski, 12-10-2011
-
Neutrino Physics Division scientific activity,
Winter Kindergarden, Lądek Zdrój, 10-02-2013.
-
Neural Network and Theoretical Predictions of TPE Effect in Elastic ep Scattering,
Katowice, seminarium Zakładu Teorii Pola i Cząstek Elementarnych, Uniwersytet Śląski, Instytut Fizyki, 14-05-2013.
-
Two-Photon Exchange Effect in Elastic ep Scattering,
Warszawa, Seminarium Teorii Oddziaływań Elementarnych, Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, 13-01-2014.
-
Bayesian Inference in Investigation of Lepton-Nucleon Interactions,
Wrocław, Seminarium Instytutowe, Instytut Fizyki Teoretycznej, Uniwersytet Wrocławski, 14-10-2016.