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The microscopic description of heavy-ion reactions at low beam energies is achieved within hadronic transport approaches. In this article a new approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced and applied to study the production of non-strange particles in heavy-ion reactions at $E_{\rm kin}=0.4-2A$ GeV. First, the model is described including details about the collision criterion, the initial conditions and the resonance formation and decays. To validate the approach, equilibrium properties such as detailed balance are presented and the results are compared to experimental data for elementary cross sections. Finally results for pion and proton production in C+C and Au+Au collisions is confronted with HADES and FOPI data. Predictions for particle production in $\pi+A$ collisions are made., Comment: 30 pages, 30 figures, replaced with published version; only minor changes

Background: Long-baseline experiments such as the planned Deep Underground Neutrino Experiment (DUNE) require theoretical descriptions of the complete event in a neutrino-nucleus reaction. Since nuclear targets are used this requires a good understanding of neutrino-nucleus interactions. Purpose: Develop a consistent theory and code framework for the description of lepton-nucleus interactions that can be used to describe not only inclusive cross sections, but also the complete final state of the reaction. Methods: The Giessen-Boltzmann-Uehling-Uhlenbeck (GiBUU) implementation of quantum-kinetic transport theory is used, with improvements in its treatment of the nuclear ground state and of 2p2h interactions. For the latter an empirical structure function from electron scattering data is used as a basis. Results: Results for electron-induced inclusive cross sections are given as a necessary check for the overall quality of this approach. The calculated neutrino-induced inclusive double-differential cross sections show good agreement with data from neutrino- and antineutrino reactions for different neutrino flavors at MiniBooNE and T2K. Inclusive double-differential cross sections for MicroBooNE, NOvA, MINERvA and LBNF/DUNE are given. Conclusions: Based on the GiBUU model of lepton-nucleus descriptions a good theoretical description of inclusive electron-, neutrino- and antineutrino-nucleus data over a wide range of energies, different neutrino flavors and different experiments is now possible. Since no tuning is involved this theory and code should be reliable also for new energy regimes and target masses. \end{description}, Comment: title changed, version accepted for publication in Phys. Rev. C

The $\Delta(1232) \to \gamma^\ast N$ magnetic dipole form factor ($G_M^\ast$) is described here within a new covariant model that combines the valence quark core together with the pion cloud contributions. The pion cloud term is parameterized by two terms: one connected to the pion electromagnetic form factor, the other to the photon interaction with intermediate baryon states. The model can be used in studies of pp and heavy ion collisions. In the timelike region this new model improves the results obtained with a constant form factor model fixed at its value at zero momentum transfer. At the same time, and in contrast to the Iachello model, this new model predicts a peak for the transition form factor at the expected position, i.e. at the $\rho$ mass pole. We calculate the decay of the $\Delta \to \gamma N$ transition, the Dalitz decay ($\Delta \to e^+ e^- N$), and the $\Delta$ mass distribution function. The impact of the model on dilepton spectra in pp collisions is also discussed., Comment: 11 pages, 10 figures

We calculate dilepton spectra in heavy-ion collisions using a coarse-graining approach to the simulation of the created medium with the UrQMD transport model. This enables the use of dilepton-production rates evaluated in equilibrium quantum-field theory at finite temperatures and chemical potentials., Comment: 4 pages, 2 figures, contribution to the proceedings of "The 15th International Conference on Strangeness in Quark Matter" (SQM 2015), 06-11 July in Dubna, Russia

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. In all the examples emerging from physics, the minimal linear differential operators annihilating these diagonals of rational functions have been shown to actually possess orthogonal or symplectic differential Galois groups. In order to understand the emergence of such orthogonal or symplectic groups, we analyze exhaustively three sets of diagonals of rational functions, corresponding respectively to rational functions of three variables, four variables and six variables. We impose the constraints that the degree of the denominators in each variable is at most one, and the coefficients of the monomials are 0 or $ \pm 1$, so that the analysis can be exhaustive. We find the minimal linear differential operators annihilating the diagonals of these rational functions of three, four, five and six variables. We find that, even for these sets of examples which, at first sight, have no relation with physics, their differential Galois groups are always orthogonal or symplectic groups. We discuss the conditions on the rational functions such that the operators annihilating their diagonals do not correspond to orthogonal or symplectic differential Galois groups, but rather to generic special linear groups., Comment: 28 pages Dedicated to R.J. Baxter, for his 75th birthday

Due to their penetrating nature, electromagnetic probes, i.e., lepton-antilepton pairs (dileptons) and photons are unique tools to gain insight into the nature of the hot and dense medium of strongly-interacting particles created in relativistic heavy-ion collisions, including hints to the nature of the restoration of chiral symmetry of QCD. Of particular interest are the spectral properties of the electromagnetic current-correlation function of these particles within the dense and/or hot medium. The related theoretical investigations of the in-medium properties of the involved particles in both the partonic and hadronic part of the QCD phase diagram underline the importance of a proper understanding of the properties of various hadron resonances in the medium., Comment: 8 pages, 2 figures; Contribution to the proceedings of the Resonance Workshop at Catania 2014

We revisit an order-six linear differential operator having a solution which is a diagonal of a rational function of three variables. Its exterior square has a rational solution, indicating that it has a selected differential Galois group, and is actually homomorphic to its adjoint. We obtain the two corresponding intertwiners giving this homomorphism to the adjoint. We show that these intertwiners are also homomorphic to their adjoint and have a simple decomposition, already underlined in a previous paper, in terms of order-two self-adjoint operators. From these results, we deduce a new form of decomposition of operators for this selected order-six linear differential operator in terms of three order-two self-adjoint operators. We then generalize the previous decomposition to decompositions in terms of an arbitrary number of self-adjoint operators of the same parity order. This yields an infinite family of linear differential operators homomorphic to their adjoint, and, thus, with a selected differential Galois group. We show that the equivalence of such operators is compatible with these canonical decompositions. The rational solutions of the symmetric, or exterior, squares of these selected operators are, noticeably, seen to depend only on the rightmost self-adjoint operator in the decomposition. These results, and tools, are applied on operators of large orders. For instance, it is seen that a large set of (quite massive) operators, associated with reflexive 4-polytopes defining Calabi-Yau 3-folds, obtained recently by P. Lairez, correspond to a particular form of the decomposition detailed in this paper., Comment: 40 pages

In a search for $\omega$ mesic states, the production of $\omega$-mesons in coincidence with forward going protons has been studied in photon induced reactions on $^{12}$C for incident photon energies of 1250 - 3100 MeV. The $\pi^0 \gamma$ pairs from decays of bound or quasi-free $\omega$-mesons have been measured with the CBELSA/TAPS detector system in coincidence with protons registered in the MiniTAPS forward array. Structures in the total energy distribution of the $\pi^0 \gamma$ pairs, which would indicate the population and decay of bound $\omega~^{11}$B states, are not observed. The $\pi^0 \gamma$ cross section of 0.3 nb/MeV/sr observed in the bound state energy regime between -100 and 0 MeV may be accounted for by yield leaking into the bound state regime because of the large in-medium width of the $\omega$-meson. A comparison of the measured total energy distribution with calculations suggests the real part $V_0$ of the $\omega~^{11}$B potential to be small and only weakly attractive with $V_0(\rho=\rho_0) = -15\pm$ 35(stat) $\pm$20(syst) MeV in contrast to some theoretical predictions of attractive potentials with a depth of 100 - 150 MeV., Comment: 13 pages, 8 figures

We present the analysis of the inclusive $K^{0}$ production in p+p and p+Nb collisions measured with the HADES detector at a beam kinetic energy of 3.5 GeV. Data are compared to the GiBUU transport model. The data suggest the presence of a repulsive momentum-dependent kaon potential as predicted by the Chiral Perturbation Theory (ChPT). For the kaon at rest and at normal nuclear density, the ChPT potential amounts to $\approx 35$ MeV. A detailed tuning of the kaon production cross sections implemented in the model has been carried out to reproduce the experimental data measured in p+p collisions. The uncertainties in the parameters of the model were examined with respect to the sensitivity of the experimental results from p+Nb collisions to the in-medium kaon potential., Comment: 13 pages, 14 figures

In this review we first outline the basics of transport theory and its recent generalization to off-shell transport. We then present in some detail the main ingredients of any transport method using in particular the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) implementation of this theory as an example. We discuss the potentials used, the ground state initialization and the collision term, including the in-medium modifications of the latter. The central part of this review covers applications of GiBUU to a wide class of reactions, starting from pion-induced reactions over proton and antiproton reactions on nuclei to heavy-ion collisions (up to about 30 AGeV). A major part concerns also the description of photon-, electron- and neutrino-induced reactions (in the energy range from a few 100 MeV to a few 100 GeV). For this wide class of reactions GiBUU gives an excellent description with the same physics input and the same code being used. We argue that GiBUU is an indispensable tool for any investigation of nuclear reactions in which final-state interactions play a role. Studies of pion-nucleus interactions, nuclear fragmentation, heavy ion reactions, hyper nucleus formation, hadronization, color transparency, electron-nucleus collisions and neutrino-nucleus interactions are all possible applications of GiBUU and are discussed in this article., Comment: 173 pages, review article. v2: Text-rearrangements in sects. 2 and 3 (as accepted for publication in Physics Reports)

The photoproduction of $\omega$ mesons on LH_2, C and Nb has been studied for incident photon energies from 900 to 1300 MeV using the CB/TAPS detector at ELSA. The $\omega$ line shape does not show any significant difference between the LH_2 and the Nb targets. The data are compared with results of transport calculations that predict a sensitivity of the $\omega$ line shape to in-medium modifications near the production threshold on a free nucleon of $E_{\gamma}^{lab}$ = 1109 MeV.}, Comment: 5 pages, 3 figures

We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contribution of the susceptibility of the Ising model for $\, n \le 6$, are operators "associated with elliptic curves". Beyond the simplest factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-four globally nilpotent operator is not reducible to this elliptic curve, modular forms scheme. It is shown to actually correspond to a natural generalization of this elliptic curve, modular forms scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected $_4F_3$ hypergeometric function which can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back, the corresponding Calabi-Yau fourth-order differential operator having a symplectic differential Galois group SP(4,C). The associated mirror maps and higher order Schwarzian ODEs has an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2, Z) symmetry group., Comment: 46 pages

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group., Comment: 36 pages

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $ \chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $ \infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property., Comment: 55 pages

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $ K$ and $ E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $ L_E$ which has $ E$ as solution (or, for off-diagonal correlations to the direct sum of $ L_E$ and $ d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $ L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $ \Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $ L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems., Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 2006

The sigma form of the Painlev{\'e} VI equation contains four arbitrary parameters and generically the solutions can be said to be genuinely ``nonlinear'' because they do not satisfy linear differential equations of finite order. However, when there are certain restrictions on the four parameters there exist one parameter families of solutions which do satisfy (Fuchsian) differential equations of finite order. We here study this phenomena of Fuchsian solutions to the Painlev{\'e} equation with a focus on the particular PVI equation which is satisfied by the diagonal correlation function C(N,N) of the Ising model. We obtain Fuchsian equations of order $N+1$ for C(N,N) and show that the equation for C(N,N) is equivalent to the $N^{th}$ symmetric power of the equation for the elliptic integral $E$. We show that these Fuchsian equations correspond to rational algebraic curves with an additional Riccati structure and we show that the Malmquist Hamiltonian $p,q$ variables are rational functions in complete elliptic integrals. Fuchsian equations for off diagonal correlations $C(N,M)$ are given which extend our considerations to discrete generalizations of Painlev{\'e}., Comment: 18 pages, Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 1905

Relatively low energy and very enhanced alpha-particle groups have been observed in various actinide fractions produced via secondary reactions in a CERN W target which had been irradiated with 24-GeV protons. In particular, 5.14, 5.27 and 5.53 MeV alpha-particle groups with corresponding half-lives of 3.8(+ -)1.0 y, 625(+ -)84 d and 26(+ -)7 d, have been seen in Bk, Es and Lr-No sources, respectively. The measured energies are a few MeV lower than the known g.s. to g.s. alpha-decays in the corresponding neutron-deficient actinide nuclei. The half-lives are 4 to 7 orders of magnitude shorter than expected from the systematics of alpha-particle decay in this region of nuclei. The deduced evaporation residue cross sections are in the mb region, about 4 orders of magnitude higher than expected. A consistent interpretation of the data is given in terms of production of long-lived isomeric states in the second and third wells of the potential-energy surfaces of the parent nuclei, which decay to the corresponding wells in the daughters. The possibility that the isomeric states in the third minimum are actually the true or very near the true ground states of the nuclei, and consequences regarding the production of the long-lived superheavy elements, are discussed., Comment: 27 pages including 8 figures and 4 tables