arXiv subjects

Norbert Kaiser

Publications and source records attributed to Norbert Kaiser.

At least 19 recordsLinked to original sources

arXiv2026

Two-pion exchange nucleon-nucleon potentials with Roper resonance excitation

Motivated by the recent paper arXiv:2602.11815 [nucl-th], we calculate in these notes the spectral functions (i.e. imaginary parts) of the NN-potentials as they arise from $2\pi$-exchange with single and double Roper resonance excitation. In contrast to the full one-loop calculation, the spectral functions of the isoscalar and isovector central and tensor potentials can be given in simple analytical form. The pertinent momentum-space potentials $V_C(q), W_C(q), V_T(q), W_T(q)$ are obtained via subtracted dispersion relations. This representation allows also to include a regulator function, that tames high-momentum components of the chiral $2\pi$-exchange. The calculation is extended to $2\pi$-exchange with combined $\Delta(1232)$-isobar and Roper resonance excitation.

nucl-th↗

arXiv2026

Liquid-gas phase transition of nuclear matter

A survey is presented summarizing the empirical evidence for and interpretations of a first-order liquid-gas phase transition in nuclear matter. Earlier developments and the present state of knowledge about the extraction of the critical point for such a transition, primarily from the systematics of multifragmention data, are outlined. By analogy with a Van der Waals equation of state, the empirically deduced critical temperature and pressure permit to draw a schematic picture of the underlying nuclear potential. More detailed approaches to the liquid-gas transition using self-consistent nuclear Hartree-Fock and variational calculations are described. Critical exponents are reported. Then chiral effective field theory, as the low-energy realization of QCD, is discussed in the context of nuclear thermodynamics. Its implications for the liquid-gas transition in symmetric nuclear matter as well as in neutron-rich matter are reviewed.

nucl-th↗

arXiv2024

Sizes of the Nucleon

Evidences are updated and strengthened for the two-scales picture of low-energy nucleon structure as a compact `hard' valence quark core surrounded by a `soft' cloud of quark-antiquark pairs (the meson cloud). These considerations are quantified by a spectral analysis of the mean-squared radii associated with the isoscalar and isovector electric form factors of the nucleon. Further supporting arguments come from corresponding studies of the axial and mass form factors and their inferred radii. Separating low-mass (mesonic) and high-mass (short-range) contributions in the spectral representations of each of these form factors, we conclude that a central core with an r.m.s. radius of about 1/2 fm results consistently as the common feature in all cases. Implications are discussed for baryonic matter at densities beyond that of equilibrium nuclear matter.

nucl-th↗

arXiv2023

Solving the matrix exponential function for special orthogonal groups SO(n) and the exceptional G$_2$

In this work the matrix exponential function is solved analytically for the special orthogonal groups $SO(n)$ up to $n=9$. The number of occurring $k$-th matrix powers gets limited to $0\leq k \leq n-1$ by exploiting the Cayley-Hamilton relation. The corresponding expansion coefficients can be expressed as cosine and sine functions of a vector-norm $V$ and the roots of a polynomial equation that depends on a few specific invariants. Besides the well known case of $SO(3)$, a quadratic equation needs to be solved for $n=4,5$, a cubic equation for $n=6,7$, and a quartic equation for $n=8,9$. As an interesting subgroup of $SO(7)$, the exceptional Lie group $G_2$ of dimension $14$ is constructed via the matrix exponential function through a remarkably simple constraint on an invariant, $\xi=1$. The calculation of the trace of the $SO(n)$-matrices arising from the exponential function, results in a sum of cosines of several angles, which specify the associated conjugation class as a point on a maximal torus.

math-ph↗

arXiv2023

Evidence against a strong first-order phase transition in neutron star cores: impact of new data

With the aim of exploring the evidence for or against phase transitions in cold and dense baryonic matter, the inference of the sound speed and equation-of-state for dense matter in neutron stars is extended in view of recent new observational data. The impact of the heavy (2.35 $M_\odot$) black widow pulsar PSR J0952-0607 and of the unusually light supernova remnant HESS J1731-347 is inspected. In addition a detailed re-analysis is performed of the low-density constraint based on chiral effective field theory and of the perturbative QCD constraint at asymptotically high densities, in order to clarify the influence of these constraints on the inference procedure. The trace anomaly measure, $\Delta = 1/3 - P/\varepsilon$, is also computed and discussed. A systematic Bayes factor assessment quantifies the evidence (or non-evidence) of low averaged sound speeds $(c_s^2 \leq 0.1)$, a prerequisite for a phase transition, within the range of densities realized in the core of neutron stars. One of the consequences of including PSR J0952-0607 in the data base is a further stiffening of the equation-of-state, resulting for a 2.1 solar-mass neutron star in a reduced central density of less than five times the equilibrium density of normal nuclear matter at the 68\% level. The evidence against small sound speeds in neutron star cores is further strengthened. Within the inferred 68\% posterior credible bands, only a weak first-order phase transition with a coexistence density interval $\Delta n/n \lesssim 0.2$ would be compatible with the observed data.

nucl-th↗

arXiv2023

The mass of charged pions in neutron star matter

We examine the behavior of charged pions in neutron-rich matter using heavy-baryon chiral perturbation theory. This study is motivated by the prospect that pions, or pion-like excitations, may be relevant in neutron-rich matter encountered in core-collapse supernovae and neutron star mergers. We find, as previously expected, that the $\pi^-$ mass increases with density and precludes s-wave condensation at $n_B\lesssim n_{\text{sat}}$, where $n_{\text{sat}} \simeq 0.16 \text{fm}^{-3}$ is the nuclear saturation density, and the mass of the $\pi^+$ mode decreases with density. The uncertainty in these predictions increases rapidly for $n_B \gtrsim n_{\text{sat}} $ because low energy constants associated with the two-pion-two-nucleon operators in chiral perturbation theory are poorly constrained. We find that these uncertainties are especially large in symmetric nuclear matter and should be included in the analysis of pion-nucleus interactions at low energy and pionic atoms. In neutron-rich matter, accounting for the self-energy difference between neutrons and protons related to the nuclear symmetry energy has several effects. It alters the power counting of certain higher-order contributions to the pion self-energy. Previously unimportant but attractive diagrams are enhanced and result in a modest reduction of the pion masses. Furthermore, in the low-wavelength limit, a collective mode with the quantum numbers of the $\pi^+$ appears.

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arXiv2022

Inference of the sound speed and related properties of neutron stars

Information on the phase structure of strongly interacting matter at high baryon densities can be gained from observations of neutron stars and their detailed analysis. In the present work Bayesian inference methods are used to set constraints on the speed of sound in the interior of neutron stars, based on recent multi-messenger data in combination with limiting conditions from nuclear physics at low densities. Two general parametric representations are introduced for the sound speed $c_s$ in order to examine the independence with respect to choices for the parametrisation of Priors. Credible regions for neutron star properties are analysed, in particular with reference to the quest for possible phase transitions in cold dense matter. The evaluation of Bayes factors implies extreme evidence for a violation of the conformal bound, $c_s^2 \leq 1/3$, inside neutron stars. Given the presently existing data base, it can be concluded that the occurrence of a first-order phase transition in the core of even a two-solar-mass neutron star is unlikely, while a continuous crossover cannot be ruled out. At the same time it is pointed out that the discovery of a superheavy neutron star with a mass $ M \sim 2.3 - 2.4\, M_\odot$ would strengthen evidence for a phase change in the deep interior of the star.

nucl-th↗

arXiv2022

Solving the matrix exponential function for the groups SU(3), SU(4) and Sp(2)

The well known analytical formula for $SU(2)$ matrices $U = \exp(i \vec \tau \!\cdot\! \vec \varphi\,) = \cos|\vec \varphi\,| + i\vec \tau \!\cdot\! \hat\varphi \, \sin|\vec \varphi\,|$\\ is extended to the $SU(3)$ group with eight real parameters. The resulting analytical formula involves the sum over three real roots of a cubic equation, corresponding to the so-called irreducible case, where one has to employ the trisection of an angle. When going to the special unitary group $SU(4)$ with 15 real prameters, the analytical formula involves the sum over four real roots of a quartic equation. The associated cubic resolvent equation with three positive roots belongs again to the irreducible case. Furthermore, by imposing the pertinent condition on $SU(4)$ matrices one can also treat the symplectic group $Sp(2)$ with ten real parameters. Since there the roots occur as two pairs of opposite sign, this simplifies the analytical formula for $Sp(2)$ matrices considerably. An outlook to the situation with analytical formulas for $SU(5)$, $SU(6)$ and $Sp(3)$ is also given.

nucl-th↗

arXiv2022

Radiative corrections to elastic muon-proton scattering at low momentum transfers

We systematically calculate the radiative corrections of order $\alpha/\pi$ to elastic muon-proton scattering at low momentum transfers. These include vacuum polarization, photon-loop form factors of the muon and the proton, two-photon exchange corrections and soft photon radiation. In particular, we discuss these corrections for the kinematics of the upcomimg AMBER experiment with a $100\,$GeV muon beam energy. It is found that for the ratio to the Born cross section, only the minor terms from the photon-loop form factors of the proton and two-photon exchange depend on the proton structure predetermined by the strong interactions. Since a prominent role among the radiative corrections is played by soft photon radiation, the calculation of the bremsstrahlung process $\mu p \to\mu p \gamma$ should be extended beyond the soft photon approximation and tailored to the specific experimental conditions.

hep-ph↗

arXiv2021

Effects of order $\alpha^3$ on the determination of the Pauli form factor $F_2$ of the $\tau$-lepton

We introduce optimal observables to measure the Pauli form factor $F_2$ of the $\tau$-lepton in the pair-production process $e^-e^+ \to \tau^- \tau^+$ from the intensity distribution of the decay products. The spin-density matrix for the production process is calculated in QED up to order $\alpha^3$ including virtual photon-loops and soft bremsstrahlung, as well the $\gamma Z^0$ interference. We find that the decay channel $(\rho^- \nu_\tau)\times(\rho^+ \bar\nu_\tau)$ yields the best resolution for Re$F_2(s)$ and Im$F_2(s)$ due to its high branching fraction. We also study the bias that is introduced in the determination of $F_2$ , if the production spin-density matrix is taken in tree-level (one-photon exchange) approximation.

hep-ph↗

arXiv2021

Fluctuations and phases in baryonic matter

The phase structure of baryonic matter is investigated with focus on the role of fluctuations beyond the mean-field approximation. The prototype test case studied is the chiral nucleon-meson model, with added comments on the chiral quark-meson model. Applications to the liquid-gas phase transition in nuclear matter and extensions to dense matter are performed. The role of vacuum fluctuations and thermal excitations is systematically explored. It is pointed out that such fluctuations tend to stabilise the hadronic phase characterised by spontaneously broken chiral symmetry, shifting the chiral restoration transition to very high densities. This stabilisation effect is shown to be further enhanced by additional dynamical fluctuations treated with functional renormalisation group methods.

nucl-th↗

arXiv2020

Nucleon-Nucleon Scattering with Coupled Nucleon-Delta Channels in Chiral Effective Field Theory

In this work the elastic scattering of two nucleons is calculated in chiral effective field theory at next-to-leading order taking into account the coupled N$\Delta$-, $\Delta$N- and $\Delta\Delta$-channels. To solve the coupled channel scattering equation one needs as input the potentials for all combinations of these initial and final states. Up to next-to leading order these (transition) potentials arise from one-pion exchange, two-pion exchange and contact interactions. For the two-pion exchange we give analytic expressions for the spectral functions derived from all contributing one-loop diagrams. The forms of the contact potentials at leading and next-to-leading order are determined. We perform a fit of the low energy constants, that belong to the $NN \rightarrow NN$ contact potential and contribute up to next-to-leading order to $S$- and $P$-waves of NN scattering only. The influence of the $\Delta$-isobar dynamics entering through the coupled channels is studied in detail.

nucl-th↗

arXiv2020

Hyperon-nuclear interactions from SU(3) chiral effective field theory

The interaction between hyperons and nucleons has a wide range of applications in strangeness nuclear physics and is a topic of continuing great interest. These interactions are not only important for hyperon-nucleon scattering but also essential as basic input to studies of hyperon-nuclear few- and many-body systems including hypernuclei and neutron star matter. We review the systematic derivation and construction of such baryonic forces from the symmetries of quantum chromodynamics within non-relativistic SU(3) chiral effective field theory. Several applications of the resulting potentials are presented for topics of current interest in strangeness nuclear physics.

nucl-th↗

arXiv2020

Hyperon-nucleon three-body forces and strangeness in neutron stars

Three-body forces acting on a $\Lambda$ hyperon in a nuclear medium are investigated, with special focus on the so-called hyperon puzzle in neutron stars. The hyperon-nucleon two-body interaction deduced from SU(3) chiral effective field theory is employed at next-to-leading order. Hyperon-nucleon three-body forces are approximated using saturation by decuplet baryons and are transcribed to density-dependent effective two-body interactions. These together are taken as input in a Brueckner-Bethe-Goldstone equation with explicit treatment of the $\Lambda N\leftrightarrow\Sigma N$ and $\Lambda NN\leftrightarrow\Sigma NN$ coupled channels. Single-particle potentials of a $\Lambda$ hyperon in symmetric nuclear matter and neutron matter are calculated. With parameters of the $\Lambda NN$ three-body force constrained by hypernuclear phenomenology, extrapolations to high baryon density are performed. By comparison of the $\Lambda$ and neutron chemical potentials at densities characteristic of the core of neutron stars it is found that the combined repulsive effects of two- and three-body correlations makes the appearance of $\Lambda$ hyperons in neutron stars energetically unfavourable, thus offering a possible solution to a longstanding question.

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arXiv2019

Implementing chiral three-body forces in terms of medium-dependent two-body forces

Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many-body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a simpler approach is given by employing instead a medium-dependent NN interaction V_med that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of V_med from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range $2\pi$-exchange term, a mid-range $1\pi$-exchange component and a short-range contact term. Several applications of V_med to the equation of state of cold nuclear and neutron matter, the nucleon single-particle potential in nuclear matter, and the nuclear quasiparticle interaction are discussed. We also explore differences in using local vs. nonlocal regulating functions on 3N forces and make direct comparisons to exact results at low order in perturbation theory expansions for the equation of state and single-particle potential. We end with a discussion and numerical calculation of the in-medium NN potential V_med from the next-to-next-to-next-to-leading order (N3LO) chiral 3N force, which consists of a series of long-range and short-range terms.

nucl-th↗

arXiv2017

Meson-baryon scattering to one-loop order in heavy baryon chiral perturbation theory

We calculate the T-matrices of pseudoscalar meson octet-baryon scattering to one-loop order in SU(3) heavy baryon chiral perturbation theory. The pertinent combinations of low-energy constants are determined by fitting to phase shifts of $\pi N$ and $K N$ scattering and the corresponding data. By using these low-energy constants, we obtain the strong phase shift difference of $\pi \Lambda$ scattering at the $\Xi$ mass, $\delta_P-\delta_S=(8.8 \pm 0.2)$ degrees, in agreement with experimental results. We find that the phase shifts in the $S_{01}$($\pi \Sigma$), $S_{01}$($K \Xi$), $S_{01}$($\overline{K} N$), and $S_{11}$($\overline{K} \Sigma$) waves are so strong that resonances may be generated dynamically in all these channels. We also predict the scattering lengths and make comparisons with the results obtained from the threshold T-matrices in heavy baryon chiral perturbation theory and the method of covariant infrared regularization. The issue of convergence is also discussed in detail.

nucl-th↗

arXiv2016

Density-dependent effective baryon-baryon interaction from chiral three-baryon forces

A density-dependent effective potential for the baryon-baryon interaction in the presence of the (hyper)nuclear medium is constructed, based on the leading (irreducible) three-baryon forces derived within SU(3) chiral effective field theory. We evaluate the contributions from three classes: contact terms, one-pion exchange and two-pion exchange. In the strangeness-zero sector we recover the known result for the in-medium nucleon-nucleon interaction. Explicit expressions for the Lambda-nucleon in-medium potential in (asymmetric) nuclear matter are presented. Our results are suitable for implementation into calculations of (hyper)nuclear matter. In order to estimate the low-energy constants of the leading three-baryon forces we introduce the decuplet baryons as explicit degrees of freedom and construct the relevant terms in the minimal non-relativistic Lagrangian. With these, the constants are estimated through decuplet saturation. Utilizing this approximation we provide numerical results for the effect of the three-body force in symmetric nuclear matter and pure neutron matter on the Lambda-nucleon interaction. A moderate repulsion that increases with density is found in comparison to the free Lambda-nucleon interaction.

nucl-th↗

arXiv2016

Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory

The isospin-asymmetry dependence of the nuclear matter equation of state obtained from microscopic chiral two- and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospin-asymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in the low-temperature and high-density regime where the radius of convergence of the expansion is generically zero, the inclusion of higher-order terms beyond the leading quadratic approximation leads overall to a significantly poorer description of the isospin-asymmetry dependence. In contrast, at high temperatures and densities well below nuclear saturation density, the interaction contributions to the higher-order coefficients are negligible and the deviations from the quadratic approximation are predominantly from the noninteracting term in the many-body perturbation series. Furthermore, we extract the leading logarithmic term in the isospin-asymmetry expansion of the equation of state at zero temperature from the analysis of linear combinations of finite differences. It is shown that the logarithmic term leads to a considerably improved description of the isospin-asymmetry dependence at zero temperature.

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