Nuclear Theory·nucl-th

Thursday·April 1, 2021

8 papers—5 primary·3 cross-listed

01
Neutron stars with a crossover equation of state
J. I. Kapusta🇺🇸 · T. Welle🇺🇸
The question of whether quark matter exists in neutron stars is a long standing one. Generally one finds that a first order phase transition from baryons to quarks softens the equation of state so much that the star would collapse into a black hole. We consider a crossover equation of state, similar to the crossover that is found in lattice QCD studies at finite temperature and zero or small baryon chemical potentials. We find that with reasonable parameters it may be possible to support neutron stars up to about 2.2 solar masses. In that case 1 to 10% of the pressure would be contributed by quark matter in the central core of the highest mass stars.
nucl-thPRC(2021)·45 citations
02
Beta-decay formulas revisited (I): Gamow--Teller and spin-dipole contributions to allowed and first-forbidden transitions
W. Horiuchi🇯🇵 · T. Sato🇯🇵 · Y. Uesaka🇯🇵 · K. Yoshida🇯🇵
We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the low-energy lepton wave functions in a nucleus can be well approximated by a constant and linear to the radius for the $s$ -wave and $p$ -wave wave functions, respectively. We find, however, the deviation from such a simple approximation is evident for heavy nuclei with large $Z$ by numerically solving the Dirac equation. In our proposed formulas, the neutrino wave function is treated exactly as a plane wave, while the electron wave function is obtained by iteratively solving the integral equation, thus we can control the uncertainty of the approximate wave function. The leading-order approximation gives a formula equivalent to the conventional one and overestimates the decay rate. We demonstrate that the next-to-leading-order formula reproduces well the exact result for a schematic transition density as well as a microscopic one obtained by a nuclear energy-density functional method.
nucl-thhep-phPTEP(2021)·8 citations
03
Investigation of multi-step effects for proton inelastic scattering to the $2_{1}^{+}$ state in $^{6}$ He
Shoya Ogawa🇯🇵 · Takuma Matsumoto🇯🇵 · Yoshiko Kanada-En'yo🇯🇵 · Kazuyuki Ogata🇯🇵
Multi-step effects between bound, resonant, and non-resonant states have been investigated by the continuum-discretized coupled-channels method (CDCC). In the CDCC, a resonant state is treated as multiple states fragmented in a resonance energy region, although it is described as a single state in usual coupled-channel calculations. For such the fragmented resonant states, one-step and multi-step contributions to the cross sections should be carefully discussed because the cross sections obtained by the one-step calculation depend on the number of those states, which corresponds to the size of the model space. To clarify the role of the multi-step effects, we propose the one-step calculation without model-space dependence for the fragmented resonant states. Furthermore, we also discuss the multi-step effects between the ground, $2_{1}^{+}$ resonant, and non-resonant states in $^{6}$ He for proton inelastic scattering.
nucl-thPRC(2021)·2 citations
04
From noise to information: The transfer function formalism for uncertainty quantification on nuclear density reconstruction
Giuliani Pablo🇺🇸 · Piekarewicz Jorge🇺🇸
The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments -- such as PREX and CREX -- provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive which is why sound statistical arguments are required to maximize the information gained. For this goal we introduce a new framework, "the transfer function formalism", aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities. The transfer functions (TFs) are built analytically by expressing the linear response of the objective function to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty -- quantified in terms of bias and variance -- of the mean square radius and interior density of $^{48}$ Ca and $^{208}$ Pb. Using relativistic mean field models as a proxy for the weak-charge density -- and assuming that a total of five measurements could be performed on the weak form factor of $^{48}$ Ca and $^{208}$ Pb -- we identify the optimal models and experimental locations that minimize the combined radius and interior uncertainty for both nuclei. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data.
nucl-thPRC(2021)·5 citations
05
Diffuse relaxation approximation in a heated Fermi system
S.V. Lukyanov🇺🇦
An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is considered. The temperature dependence of the obtained expression is established.
nucl-thIJMPE(2021)·4 citations
06
Leading jets and energy loss
Duff Neill🇺🇸 · Felix Ringer🇺🇸 · Nobuo Sato🇺🇸
The formation and evolution of leading jets can be described by jet functions which satisfy non-linear DGLAP-type evolution equations. Different than for inclusive jets, the leading jet functions constitute normalized probability densities for the leading jet to carry a longitudinal momentum fraction relative to the initial fragmenting parton. We present a parton shower algorithm which allows for the calculation of leading-jet cross sections where logarithms of the jet radius and threshold logarithms are resummed to next-to-leading logarithmic (NLL $^{'}$ ) accuracy. By calculating the mean of the leading jet distribution, we are able to quantify the average out-of-jet radiation, the so-called jet energy loss. When an additional reference scale is measured, we are able to determine the energy loss of leading jets at the cross section level which is identical to parton energy loss at leading-logarithmic accuracy. We identify several suitable cross sections for an extraction of the jet energy loss and we present numerical results for leading subjets at the LHC. In addition, we consider hemisphere and event-wide leading jets in electron-positron annihilation similar to measurements performed at LEP. Besides the average energy loss, we also consider its variance and other statistical quantities such as the KL divergence which quantifies the difference between quark and gluon jet energy loss. We expect that our results will be particularly relevant for quantifying the energy loss of quark and gluon jets that propagate through hot or cold nuclear matter.
↳ hep-phhep-exnucl-exnucl-thJHEP(2021)·32 citations
07
Thermodynamic stability, compressibility matrix, and effects of mediated interactions in a strongly-interacting Bose-Fermi mixture
Koki Manabe🇯🇵 · Yoji Ohashi🇯🇵
We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $- U_{BF} < 0$ associated with a hetero-nuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction $U_{BB} \geq 0$ . Including strong hetero-pairing fluctuations associated with the former interaction within the self-consistent $T$ -matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regime with respect $- U_{BF}$ , we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature $T_{clp}$ (leading to density collapse). When $U_{BB} = 0$ , $T_{clp}$ is always higher than the Bose-Einstein condensation (BEC) temperature $T_{c}$ . When $U_{BB} > 0$ , the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the hetero-pairing interaction $- U_{BF}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to inter-particle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.
↳ cond-mat.quant-gasnucl-thPRA(2021)·4 citations
08
Intrinsic Glue and Wilson lines within Dressed Quarks
C. S. R. Costa🇧🇷 · Adam Freese🇺🇸 · Ian C. Cloët🇺🇸 · Bruno El-Bennich🇧🇷 · Gastão Krein🇧🇷 · Peter C. Tandy🇺🇸
We construct a quark target model (QTM) to incorporate intrinsic glue into effective low-energy models of QCD, which often contain only quark degrees of freedom. This method guarantees the gauge invariance of observables order-by-order in the strong coupling. The quark and gluon PDFs for the dressed quarks are obtained in the QTM at leading order. We demonstrate gauge invariance of the results by comparing both covariant and light cone gauges, with the former including an explicit Wilson line contribution. A key finding is that in covariant gauges the Wilson line can carry a significant amount of the light cone momentum. With coupling strength $α_{s} = 0.5$ and dressed quark mass $M_{q} = 0.4$ GeV, we find quark and gluon momentum fractions of $⟨ x ⟩_{q} = 0.81$ and $⟨ x ⟩_{g} = 0.19$ , where the Wilson line contribution to the quark momentum fraction is $- 0.18$ . We use the on-shell renormalization scheme and find that at one-loop this Wilson line contribution does not depend on the covariant gauge but does vanish in light cone gauge as expected. This result demonstrates that it is crucial to account for Wilson line contributions when calculating quantum correlation functions in covariant gauges. We also consider the impact of a gluon mass using the gauge invariant formalism proposed by Cornwall, and combine these QTM results with two quark-level models to obtain quark and gluon PDFs for the pion.
↳ hep-phnucl-thPRC(2021)·5 citations

Affiliations

first authorsco-authorsvia INSPIRE