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# nucl-th updates on arXiv.org

## Nuclear Theory (nucl-th) updates on the arXiv.org e-print archive

Published: 2017-11-21T20:30:00-05:00

Medium-mass hypernuclei and the nucleon-isospin dependence of the three-body hyperon-nucleon-nucleon force. (arXiv:1711.07521v1 [nucl-th])

We report quantum Monte Carlo calculations of single-$\Lambda$ hypernuclei for $A<50$ based on phenomenological two- and three-body hyperon-nucleon forces. We present results for the $\Lambda$ separation energy in different hyperon orbits, showing how the accuracy of theoretical predictions exceeds that of currently available experimental data, especially for medium-mass hypernuclei. We show the results of a sensitivity study that indicate the possibility to investigate the nucleon-isospin dependence of the three-body hyperon-nucleon-nucleon force in the medium-mass region of the hypernuclear chart, where new spectroscopy studies are currently planned. The importance of such a dependence for the description of the physics of hypernuclei, and the consequences for the prediction of neutron star properties are discussed.

Post-prior equivalence for transfer reactions with complex potentials. (arXiv:1711.07540v1 [nucl-th])

In this paper, we address the problem of the post-prior equivalence in the calculation of inclusive breakup and transfer cross sections. For that, we employ the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)], conveniently generalized to include the part of the cross section corresponding the transfer to bound states. We pay particular attention to the case in which the unobserved particle is left in a bound state of the residual nucleus, in which case the theory prescribes the use of a complex potential, responsible for the spreading width of the populated single-particle states. We see that the introduction of this complex potential gives rise to an additional term in the prior cross section formula, not present in the usual case of real binding potentials. The equivalence is numerically tested for reaction induced by deuterons.

The property difference between the neutron star PSR J0348+0432 and its proto neutron star. (arXiv:1711.07669v1 [nucl-th])

The property difference between the neutron star PSR J0348+0432 and its proto neutron star is studied in the framework of the relativistic mean field theory considering neutrino trapping. We see that the central baryon number density of the proto neutron star PSR J0348+0432 is in the range $\rho_{c, PNS}=0.539\sim0.698$ fm$^{-3}$, which is smaller than that of the neutron star PSR J0348+0432 $\rho_{c, NS}=0.634\sim0.859$ fm$^{-3}$. Inside the neutron star PSR J0348+0432, only the neutrons, protons, $\Lambda$ and $\Xi^{-}$ produce, whereas the hyperons $\Sigma^{-}, \Sigma^{0}, \Sigma^{+}$ and $\Xi^{0}$ all do not appear. But in the proto neutron star PSR J0348+0432, hyperons $\Sigma^{-}$, $\Sigma^{0}$, $\Sigma^{+}$ and $\Xi^{0}$ all will produce, though their relative particle number density are still very small, no more than 2\%. This shows that higher temperature will be advantageous to the hyperon production.

Photon Scattering off Nuclei. (arXiv:1711.07718v1 [nucl-th])

The study of nuclear and subnuclear structure by means of photon scattering is outlined. Besides a brief exposition of the formalism a few illustrative examples are discussed.

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions. (arXiv:1711.07773v1 [nucl-th])

The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb+Pb collisions at $\sqrt{s}=2760$GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of $v_2^2$ and $v_4$, of $v_2v_3$ and $v_5$, or of $v_2^3$, $v_3^3$, and $v_6$. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.

Event-by-event fluctuations in p+p and central A+A collisions within relativistic transport models. (arXiv:1711.07789v1 [nucl-th])

Event-by-event multiplicity fluctuations in nucleus-nucleus collisions are studied within the relativistic transport models: EPOS, PHSD, and UrQMD. As measures of particle number fluctuations we consider the scaled variances $\omega[X]$ for positive, negative, and all charged hadrons, and the strongly intensive quantities $\Delta[K^+,\pi^+],$ $\Sigma[K^+,\pi^+]$ for $K^+$ and $\pi^+$ yields. At the SPS energy range the fluctuation measures are calculated for proton-proton, Ar+Sc, and Pb+Pb collisions. Comparison with recent NA61/SHINE and older NA49 measurements of the multiplicity fluctuations is done. The validity of the model of independent sources, and the role of experimental acceptance are studied.

Single particle in a reflection-asymmetric potential. (arXiv:1711.07799v1 [nucl-th])

Single particle moving in a reflection-asymmetric potential is investigated by solving the Schr\"{o}dinger equation of the reflection-asymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic oscillator basis expansion method. In the 3D lattice calculation, the $\textbf{l}^2$ divergence problem is discussed and is avoided by introducing a damping function; the $\langle \textbf{l}^2\rangle_N$ term in non-spherical case is calculated by an equivalent $N$-independent operator form; and the harmonic oscillator potential is motdified to improve the convergence of the iteration. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3D lattice space. The evolution of the single-particle levels in a reflection-asymmetric deformed potential is obtained and discussed by the above two numerical methods, and their consistency is shown in the obtained single-particle energy with difference smaller than 10$^{-4}~[\hbar\omega_0]$.

Dispersive analysis tools for $\pi\pi$ and $\pi K$ scattering. (arXiv:1711.07861v1 [hep-ph])

In this talk we discuss the relevance of dispersive methods and their different applications to obtain simple but rigorous parameterizations of pion-pion and kaon-pion scattering. We show as an example our latest dispersive analysis of $\pi K$ scattering, where we provide simple parameterizations of data satisfying Forward Dispersion Relations up to 1.6 GeV.

Isospin Breaking in Heavy-Meson Decay Constants. (arXiv:1711.07899v1 [hep-ph])

Evaluation of Borelized QCD sum rules in the so-called local-duality limit of infinitely large Borel mass parameter provides an alternate route for extraction of the dependence of the decay constants of heavy-light mesons on the mass $m_q$ of the involved light quark $q$: For appropriate choices of the two-point correlation functions of currents interpolating the hadrons under study, the local-duality limit forces all nonperturbative contributions parametrized by vacuum condensates to such kind of correlator to vanish. As a consequence, the sought $m_q$ dependence of the heavy-light meson decay constants proves to be controlled primarily by the correlator contributions from perturbative QCD. Our knowledge of the analytic behaviour of the latter as functions of $m_q$ enables us to derive the $m_q$ dependence of the decay constants of both pseudoscalar and vector heavy-light mesons, for which we estimate strong isospin breaking to be of the order of 1 MeV for both charm and beauty sectors.

Finite-size effects on the Phase Structure of the Walecka Model. (arXiv:1711.07934v1 [nucl-th])

In this work we investigate the finite-size effects on the phase structure of Walecka model within the framework of generalized Zeta-function, focusing on the influence of temperature as well as the number and length of compactified spatial dimensions. Here we concentrate on the situation of larger values of the coupling between the scalar and fermion fields, in which a phase transition of first order takes place. The phase transitions are analyzed and compared with the system in the situations of one, two and three compactified spatial dimensions. Our findings suggest that the thermodynamic behavior of the system depends on the length and number of spatial dimensions, with the symmetric phase being favored as the size of the system diminishes.

Three-fluid Hydrodynamics-based Event Simulator Extended by UrQMD final State interactions (THESEUS) for FAIR-NICA-SPS-BES/RHIC energies. (arXiv:1711.07959v1 [nucl-th])

We present a new event generator based on the three-fluid hydrodynamics (3FH) approach, followed by a particlization at the hydrodynamic decoupling surface and a subsequent UrQMD afterburner stage based on the microscopic UrQMD transport model that accounts for hadronic final state interactions. First results for Au+Au collisions are presented. The following topics are addressed: the directed flow, transverse-mass spectra, as well as rapidity distributions of protons, pions and kaons for two model equations of state, one with a first-order phase transition, the other with a crossover transition. Preliminary results on the femtoscopy are also discussed. We analyze the accuracy of reproduction of the 3FH results by the new event generator and the effect of the subsequent UrQMD afterburner stage.

$K\pi$ $I=1/2$ $S$-wave from $\eta_c$ decay data at BaBar and classic Meson-Meson scattering from LASS. (arXiv:1701.04881v2 [hep-ph] UPDATED)

A recent analysis of data on the two photon production of the $\eta_c$ and its decay to $K(K\pi)$ has determined the $K\pi$ $S$-wave amplitude in a "model-independent" way assuming primarily that the additional kaon is a spectator in this decay. The purpose of this paper is to fit these results, together with classic $K\pi$ production data from LASS, within a formalism that implements unitarity for the di-meson interaction. This fixes the $I=1/2$ $K\pi\to K\pi$ $S$-wave amplitude up to 2.4 GeV. This resolves the Barrelet ambiguity in the original LASS analysis, and constrains the amount of inelasticity in $K\pi$ scattering, highlighting that this becomes significant beyond 1.8 GeV. This result needs to be checked by experimental information on the many inelastic channels, in particular $K\eta^\prime$ and $K\pi\pi\pi$. Our analysis provides a single representation for the $K\pi$ $S$-wave from threshold, controlled by Chiral Perturbation Theory, through the broad $\kappa$, $K_0^*(1430)$ and $K_0^*(1950)$ resonances. There is no arbitrary sum of Breit-Wigner forms and random backgrounds for real $K\pi$ masses. Rather the form provides a representation that can be translated to other processes with $K\pi$ interactions with their own coupling functions, while automatically maintaining consistency with the chiral dynamics near threshold, with the LASS data and the new results on $\eta_c$ decay.

Coherent J/$\psi$ photoproduction in hadronic heavy-ion collisions. (arXiv:1705.01460v2 [nucl-th] UPDATED)

A significant excess of J/$\psi$ yield at very low transverse momentum ($p_T < 0.3$ GeV/c) was observed by the ALICE and STAR collaborations in peripheral A+A collisions, which points to evidence of coherent photoproduction of J/$\psi$ in violent hadronic interactions. Theoretically, the photoproduction of J$/\psi$ in hadronic collisions raises questions about how spectator and non-spectator nucleons participate in the coherent reaction. For the first time, we argue that the strong interactions in the overlapping region of incoming nuclei may disturb the coherent production, leaving room for different coupling assumptions. Furthermore, first considerations of the destructive interference between photoproduction on ions moving in opposite directions in hadronic heavy-ion collisions are included.

This letter presents calculations of J$/\psi$ production from coherent photon-nucleus ($\gamma + A \rightarrow \text{J}/\psi + A$) interactions in hadronic A+A collisions at RHIC and LHC energies with both nucleus and spectator coupling hypotheses. The coherent J/$\psi$ yield as a function of centrality and differential distributions as a function of transverse momentum, azimuthal angle and rapidity in different centrality bins are shown and found to be significantly different for different coupling scenarios, calling for future experimental measurements.

Sea Quarks Contribution to the Nucleon Magnetic Moment and Charge Radius at the Physical Point. (arXiv:1705.05849v2 [hep-lat] UPDATED)

We report a comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon magnetic moment, charge radius, and the electric and magnetic form factors. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We adopt a model-independent extrapolation of the nucleon magnetic moment and the charge radius. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light and strange disconnected-sea quarks contribution to the nucleon magnetic moment is $\mu_M\,(\text{DI})=-0.022(11)(09)\,\mu_N$ and to the nucleon mean square charge radius is $\langle r^2\rangle_E\,\text{(DI)}=-0.019(05)(05)$ fm$^2$ which is about $1/3$ of the difference between the $\langle r_p^2\rangle_E$ of electron-proton scattering and that of muonic atom and so cannot be ignored in obtaining the proton charge radius in the lattice QCD calculation. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about $1\%$, a negative $2.5(9)\%$ contribution to the proton mean square charge radius and a relatively larger positive $16.3(6.1)\%$ contribution to the neutron mean square charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light and strange disconnected-sea quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of $0\leq Q^2\leq 0.5$ GeV$^2$.

The tightly bound nuclei in the liquid drop model. (arXiv:1709.01386v2 [nucl-th] UPDATED)

In this paper, we shall use the liquid drop model of the atomic nuclei to analytically prove that the mean binding energy per nucleon curve has local extrema at A = 58.6960, Z = 26.3908 and at A = 62.0178, Z = 27.7506. The Lagrange method of multipliers is used to arrive at these results and we have let the values of A and Z take continuous fractional values. The shell model that shows why 62Ni is the most tightly bound nucleus is outlined. A brief account on stellar nucleosynthesis is presented to show why 56Fe is more abundant than 62Ni and 58Fe. We believe that the analytical proof presented in this paper can be a useful tool to the instructors to introduce the nucleus with the highest mean binding energy per nucleon.

Asymptotically Free Theory with Scale Invariant Thermodynamics. (arXiv:1709.03457v2 [hep-ph] UPDATED)

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasi-particle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

Relativistic particle in a box: Klein-Gordon vs Dirac Equations. (arXiv:1711.06313v1 [quant-ph] CROSS LISTED)

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.