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Register a new userUnveiling the pole structure of S-matrix using deep learning
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Particle scattering is a powerful tool to unveil the nature of various subatomic phenomena. The key quantity is the scattering amplitude whose analytic structure carries the information of the quantum states. In this work, we demonstrate our first step attempt to extract the pole configuration of inelastic scatterings using the deep learning method. Among various problems, motivated by the recent new hadron phenomena, we develop a curriculum learning method of deep neural network to analyze coupled channel scattering problems. We show how effectively the method works to extract the pole configuration associated with resonances in the $pi N$ scatterings.
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Most of exotic resonances observed in the past decade appear as peak structure near some threshold. These near-threshold phenomena can be interpreted as genuine resonant states or enhanced threshold cusps. Apparently, there is no straightforward way of distinguishing the two structures. In this work, we employ the strength of deep feed-forward neural network in classifying objects with almost similar features. We construct a neural network model with scattering amplitude as input and nature of pole causing the enhancement as output. The training data is generated by an S-matrix satisfying the unitarity and analyticity requirements. Using the separable potential model, we generate a validation data set to measure the networks predictive power. We find that our trained neural network model gives high accuracy when the cut-off parameter of the validation data is within $400$-$800mbox{ MeV}$. As a final test, we use the Nijmegen partial wave and potential models for nucleon-nucleon scattering and show that the network gives the correct nature of pole.
In the standard effective V - A theory of low-energy weak interactions (i.e. in the Standard Model (SM)) we analyze the structure of the correlation coefficients S(E_e) and U(E_e), where E_e is the electron energy. These correlation coefficients were introduced to the electron-energy and angular distribution of the neutron beta decay by Ebel and Feldman ( Nucl. Phys. 4, 213 (1957)) in addition to the set of correlation coefficients proposed by Jackson et al. (Phys. Rev. 106, 517 (1957)). The correlation coefficients $S(E_e)$ and $U(E_e)$ are induced by simultaneous correlations of the neutron and electron spins and electron and antineutrino 3-momenta. These correlation structures do no violate discrete P, C and T symmetries. We analyze the contributions of the radiative corrections of order O(alpha/pi), taken to leading order in the large nucleon mass m_N expansion, and corrections of order O(E_e/m_N), caused by weak magnetism and proton recoil. In addition to the obtained SM corrections we calculate the contributions of interactions beyond the SM (BSM contributions) in terms of the phenomenological coupling constants of BSM interactions by Jackson et al. (Phys. Rev. 106, 517 (1957)) and the second class currents by Weinberg (Phys. Rev. 112, 1375 (1958)).
We study the use of deep learning techniques to reconstruct the kinematics of the deep inelastic scattering (DIS) process in electron-proton collisions. In particular, we use simulated data from the ZEUS experiment at the HERA accelerator facility, and train deep neural networks to reconstruct the kinematic variables $Q^2$ and $x$. Our approach is based on the information used in the classical construction methods, the measurements of the scattered lepton, and the hadronic final state in the detector, but is enhanced through correlations and patterns revealed with the simulated data sets. We show that, with the appropriate selection of a training set, the neural networks sufficiently surpass all classical reconstruction methods on most of the kinematic range considered. Rapid access to large samples of simulated data and the ability of neural networks to effectively extract information from large data sets, both suggest that deep learning techniques to reconstruct DIS kinematics can serve as a rigorous method to combine and outperform the classical reconstruction methods.
Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.
We develop a robust method to extract the pole configuration of a given partial-wave amplitude. In our approach, a deep neural network is constructed where the statistical errors of the experimental data are taken into account. The teaching dataset is constructed using a generic S-matrix parametrization, ensuring that all the poles produced are independent of each other. The inclusion of statistical error results into a noisy classification dataset which we should solve using the curriculum method. As an application, we use the elastic $pi N$ amplitude in the $I(J^P)=1/2(1/2^{-})$ sector where $10^6$ amplitudes are produced by combining points in each error bar of the experimental data. We fed the amplitudes to the trained deep neural network and find that the enhancements in the $pi N$ amplitude are caused by one pole in each nearby unphysical sheet and at most two poles in the distant sheet. Finally, we show that the extracted pole configurations are independent of the way points in each error bar are drawn and combined, demonstrating the statistical robustness of our method.
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