Positive Parity Research Articles

Symplectic symmetry approach to clustering in atomic nuclei: the case of 24Mg

Abstract Symplectic symmetry approach to clustering (SSAC) in atomic nuclei, recently proposed, is modified and further developed in more detail. It is firstly applied to the light two-cluster 20Ne + α system of 24Mg, the latter exhibiting well developed low-energy K π = 0 1 + , K π = 2 1 + and K π = 0 1 − rotational bands in its spectrum. A simple algebraic Hamiltonian, consisting of dynamical symmetry, residual and vertical mixing parts is used to describe these three lowest rotational bands of positive and negative parity in 24Mg. A good description of the excitation energies is obtained by considering only the SU(3) cluster states restricted to the stretched many-particle Hilbert subspace, built on the leading Pauli allowed SU(3) multiplet for the positive- and negative-parity states, respectively. The coupling to the higher cluster-model configurations allows us to describe the known low-lying experimentally observed B(E2) transition probabilities within and between the cluster states of the three bands under consideration without the use of an effective charge.

Core excitation in 92Mo up to high-spin

Abstract An in-beam gamma-ray spectroscopy study of the even-even nucleus 92Mo
has been carried out using the 30Si + 65Cu, 18O + 80Se reactions at beam energies of
120 and 99 MeV, respectively. Angular distribution from oriented state ratio (RADO)
and linear polarization (Δasym) measurements have fixed most of the tentatively
assigned spin-parity of the high energy levels. A large-scale shell-model calculation
using the GWBXG interaction has been carried out to understand the configuration
and structure of both positive and negative parity states up to the highest observed
spin. The high-spin states primarily originate from the coupling of excited proton and
neutron-core structures in an almost stretched manner. The systematics of energy
required for forming a neutron particle-hole pair excitation, νg9/2→νd5/2, is discussed.
Lifetime of few high-spin states have been measured using DSAM. Additionally, a
qualitative argument is proposed to explain the comparatively strong E1 transition
feeding the 7310.9-keV level.

Production mechanism of the hidden charm pentaquark states Pcc¯

We investigate hidden charm pentaquark states using an off-shell coupled-channel formalism involving heavy meson and singly heavy baryon scattering. Our approach utilizes an effective Lagrangian to construct the kernel amplitudes, which respect both heavy quark symmetry and hidden local symmetry. After solving the coupled integral equations, we obtain the transition amplitudes for J/ψN scattering and various heavy meson and singly heavy baryon scattering processes. We identify seven distinct peaks related to molecular states of heavy mesons D¯ (D¯*) and singly heavy baryons Σc (Σc*). Four of these peaks can be associated with the known Pcc¯ states: Pcc¯(4312), Pcc¯(4380), Pcc¯(4440), and Pcc¯(4457). We predict two additional resonances with masses around 4.5 GeV, which we interpret as D¯*Σc* molecular states, and identify one cusp structure. Additionally, we predict two P-wave pentaquark states with positive parity, which may be candidates for genuine pentaquark configurations. Notably, these pentaquark states undergo significant modifications in the J/ψN elastic channel, with some even disappearing due to interference from the positive parity channel. The present investigation may provide insight into the absence of pentaquark states in J/ψ photoproduction observed by the GlueX Collaboration. Published by the American Physical Society 2024

First radial excitations of baryons in a contact interaction: Mass spectrum

We compute masses of twenty positive parity first radial excitations of spin-1/2 and spin-3/2 baryons composed of u, d, s, c, and b quarks in a quark-diquark picture within a contact interaction model. These excitations comprise of two elements; one characterized by a zero in the Faddeev amplitude, representing a radial excitation of the quark-diquark system and the other marked by a zero in the diquark’s Bethe-Salpeter amplitude, corresponding to an intrinsic excitation of the diquark correlation. Wherever possible, we compare our results with other models and/or experiment. We verify that the masses obtained through our model conform to the spacing rules for all the baryons studied, whether light or heavy and whether of spin-1/2 or spin-3/2. The computed masses do not just offer a guide to the future experimental searches but also compare well with the existing candidates for the possible radial excitations of some heavy baryons. Published by the American Physical Society 2024

Investigation on the Ω(2012) from QCD sum rules

We study the recently observed Ω(2012) baryon in quantum chromodynamics (QCD) sum rules. We construct the P-wave Ω baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin 1/2 and 3/2. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of JP=1/2− and 3/2− states to be M1/2−=2.07−0.07+0.07 GeV and M3/2−=2.05−0.10+0.09 GeV. Both results are in good agreement with the experimental result. Therefore, it is likely that the Ω(2012) is a negative parity state, which is interpreted as a P-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties. Published by the American Physical Society 2024

Intruder band mixing in an ab initio description of 12Be

The spectrum of ▪ exhibits exotic features, e.g., an intruder ground state and shape coexistence, normally associated with the breakdown of a shell closure. While previous phenomenological treatments indicated the ground state has substantial contributions from intruder configurations, it is only with advances in computational abilities and improved interactions that this intruder mixing is observed in ab initio no-core shell model (NCSM) predictions. In this work, we extract electromagnetic observables and symmetry decompositions from the NCSM wave functions to demonstrate that the low-lying positive parity spectrum can be explained in terms of mixing of rotational bands with very different intrinsic structure coexisting within the low-lying spectrum. These observed bands exhibit an approximate SU(3) symmetry and are qualitatively consistent with Elliott model predictions.

QCD sum rules for positive and negative parity heavy baryons at next-to-leading order in αs -expansion

QCD sum rules for positive and negative parity heavy baryons in the heavy quark limit are formulated. We apply the method to Λ and Σ channels. We include the next-to-leading order corrections in αs-expansion to dimension 0 and 3 terms in the operator product expansion. The corrections lead to the considerable reduction of the predicted masses and significantly improves the stability with respect to the Borel parameter, especially for negative parity states. It is also found that, in the heavy quark limit, chiral odd condensates do not contribute to the negative parity states. Published by the American Physical Society 2024

Properties of Fairness Measures in the Context of Varying Class Imbalance and Protected Group Ratios

Society is increasingly relying on predictive models in fields like criminal justice, credit risk management, and hiring. To prevent such automated systems from discriminating against people belonging to certain groups, fairness measures have become a crucial component in socially relevant applications of machine learning. However, existing fairness measures have been designed to assess the bias between predictions for protected groups without considering the imbalance in the classes of the target variable. Current research on the potential effect of class imbalance on fairness focuses on practical applications rather than dataset-independent measure properties. In this article, we study the general properties of fairness measures for changing class and protected group proportions. For this purpose, we analyze the probability mass functions of six of the most popular group fairness measures. We also measure how the probability of achieving perfect fairness changes for varying class imbalance ratios. Moreover, we relate the dataset-independent properties of fairness measures described in this work to classifier fairness in real-life tasks. Our results show that measures such as Equal Opportunity and Positive Predictive Parity are more sensitive to changes in class imbalance than Accuracy Equality. These findings can help guide researchers and practitioners in choosing the most appropriate fairness measures for their classification problems.

Classical simulation of non-Gaussian fermionic circuits

We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.

Doubly charmed pentaquark states in QCD sum rules

We have studied the mass spectra of doubly charmed pentaquark states in the Λc(*)D(*) and Σc(*)D(*) channels with JP=1/2±, 3/2±, and 5/2± within the framework of quantum chromodynamics sum rules. We use the parity projected sum rules to separate the contributions of negative and positive parities from the two-point correlations induced by the pentaquark interpolating currents. Our results show that the bound states of Pcc pentaquarks may exist in the ΛcD(12−), ΣcD(12−), ΣcD*(32−), Λc*D(32−), Λc*D*(52−) channels with negative-parity and ΣcD(12+), ΣcD*(32+), Σc*D(32+) channels with positive-parity, since their masses are predicted to be lower than the corresponding meson-baryon thresholds. However, they are still allowed to decay into the Ξcc(*)π final states via strong interaction. The triply charged Pcc+++(ccuud¯) and neutral Pcc0(ccddu¯) in the isospin quartet would definitely be pentaquark states due to their exotic charges. We suggest searching for these characteristic doubly charmed pentaquark signals in the Pcc+++→Ξcc(*)++π+/ρ+, Σc(*)++D(*)+ and Pcc0→Ξcc(*)+π−/ρ−, Σc(*)0D(*)0 decays in the near future. Published by the American Physical Society 2024

Study of Octupole Transitions in Xe, Ba, Ce and Nd Nuclei within Interacting Boson Model

For nuclei with 54≤Z≤60 and 86≤N≤94, the results regarding the excitation spectra at low energies, both in positive and negative parity, as well as the transition probabilities for electric dipole (B(E1)), quadrupole (B(E2)), and octupole transitions (B(E(3)), indicate the emergence of significant octupole behavior. These observations have been made using the Interacting Boson Model-1 (IBM-1). The study examines the onset of octupole deformation and its impact on the spectroscopic characteristics in even-even neutron-rich lanthanide isotopes, specifically in the Ba and Nd nuclei. The investigation compares the results obtained from the Interacting Boson Model-1 (IBM-1) with the existing experimental data. The focus is on understanding how the addition of neutrons influences the development of octupole deformation and its manifestation in the observed spectroscopic features. The onset of strong octupolarity for Z≈ 56 and N ≈ 88 nuclei is indicated by the results obtained for the electric dipole, quadrupole, and octupole transition probabilities, as well as the low-energy positive and negative-parity excitation spectra. Conversely, discrepancies between the spectroscopic data and the IBM results suggest that the mapping quality needs to be evaluated in order to determine if the mapped boson Hamiltonian or the fermionic calculations are the source of the issues.

Investigations of Λ states with spin-parity 32±

The present study provides spectroscopic investigations of spin-32 Λ baryons with both positive and negative parities. The analysis mainly focuses on three states, namely 1P, 2P, and 2S, and corresponding masses are calculated using the QCD sum rule method. To implement the method, we apply two types of interpolating currents with octet and singlet quantum numbers and compare the corresponding results with the reported masses of experimentally observed states. From the comparisons, it is extracted that the results of interpolating current with octet quantum numbers are in good agreement with the experimentally measured masses. The masses obtained with this interpolating current are m=1513.64±8.76 MeV for 1P state with JP=32−, m′=1687.91±0.31 MeV for 2P state with JP=32− and m˜=1882.37±11.95 MeV for 2S state with JP=32+ and they are consistent with the experimental masses of Λ(1520), Λ(1690), and Λ(1890), respectively, which confirm their spin-parity quantum numbers. Besides, we calculate the corresponding current coupling constants, which are utilized as inputs in the calculations of different form factors defining the widths of the states under study. Published by the American Physical Society 2024

An Application of Interacting Boson Fermion-Fermion Model (IBFFM) for <sup>134</sup>Cs Nucleus

This work concerns the calculations of interacting boson fermion-fermion model (IBFFM) for the odd-odd nucleus <sup>134</sup>Cs. The energy levels (positive and negative parity states), electric transition probability B(E2), magnetic transition probability B(M1), quadrupole and magnetic dipole moments have been studied in this work. The IBFFM results are compared with the available experimental data. In the present work, the IBFFM pattern of total and parametric dependent level densities for the odd-odd nucleus <sup>134</sup>Cs is investigated and compared to the pattern found in previous investigations in the framework of combinatorial and spectral distribution approaches. When comparing the theoretical values with the available experimental values, it was found that there is a good match between them. This is due to the values of the Hamiltonian parameters that were found accurately, so this IBFFM model is considered one of the effective models in studying the nuclear structure of odd-odd nuclei. The level density of the odd-odd nucleus <sup>196</sup>Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes. The IBFFM spin-dependent level densities show high-spin reduction with respect to Bethe formula. This can be well accounted for by a modified spin-dependent level density formula.

Resonance contributions to nucleon spin structure in holographic QCD

We study polarized inelastic electron-nucleon scattering at low momentum transfer in the Witten-Sakai-Sugimoto model of holographic QCD, focusing on resonance production contributions to the nucleon spin structure functions. Our analysis includes both spin 3/2 and spin 1/2 low-lying nucleon resonances with positive and negative parity. We determine, in turn, the helicity amplitudes for nucleon-resonance transitions and the resonance contributions to the neutron and proton generalized spin polarizabilities. Extrapolating the model parameters to realistic QCD data, our analysis, triggered by recent experimental results from Jefferson Lab, agrees with the observation that the ∆(1232) resonance gives the dominant contribution to the forward spin polarizabilities at low momentum transfer. The contribution is negative and tends to zero as the momentum transfer increases. As expected, the contribution of the ∆(1232) to the longitudinal-transverse polarizabilities is instead negligible. The latter, for both nucleons, turn out to be negative functions with zero asymptote. The holographic results, at least for the proton where enough data are available, are in qualitative agreement with the resonance contributions to the spin polarizabilities extracted from experimental data on the helicity amplitudes.

Non-zero temperature study of spin 1/2 charmed baryons using lattice gauge theory

We study the behaviour of spin 1/2 charmed baryons as the temperature increases. We make use of anisotropic lattice QCD simulations with Nf=2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_f = 2 + 1$$\\end{document} dynamical flavours. After determining the positive and negative parity ground state masses at the lowest temperature, we investigate the effect of rising temperature using ratios of thermal lattice correlators with both so-called reconstructed correlators and with simple model correlators. This avoids difficulties associated with non-zero temperature fitting or spectral reconstruction. We find that temperature effects are prominent throughout the hadronic phase for all negative parity channels considered and for some positive parity channels. Subsequently and where possible, we determine the masses of the ground states as a function of temperature. Finally we consider the effect of chiral symmetry restoration and extract an estimate of the pseudocritical temperature from singly charmed baryonic correlators.

Coexistence of low-K oblate and high-K prolate g9/2 proton-hole bands in 115Sb

A positive parity sequence of ΔI=2γ transitions has been identified above Iπ=9/2+ state (Ex=2019 keV) in 115Sb through in-beam γ ray spectroscopic technique. Rotational features of this sequence are found similar to a low-K decoupled band. Observation of this newly identified low-K decoupled band, along with the earlier reported strongly coupled high-K band in this nucleus, provides the first experimental evidence for prolate-oblate shape coexistence associated with g9/2 proton-hole configuration around Z=50 shell closure. Experimental results are reproduced reasonably well in the frameworks of the projected shell model and the total Routhian surface calculations.

Fluctuations and correlations of baryonic chiral partners

The exploration of critical phenomena in phase transitions of strongly interacting matter governed by quantum chromodynamics (QCD) is one of the goals of present ultrarelativistic heavy-ion collision experiments at BNL and CERN. The key research direction is to locate the putative critical point on the phase diagram of QCD linked to the chiral symmetry restoration at finite temperature and/or density. One of the main theoretical tools used for this purpose is the fluctuations of conserved charges, such as the net-baryon number. However, due to experimental limitations, analyses of heavy-ion collision data suffer from a very doubtful basing of the net-proton number being a proxy for the total net-baryon number fluctuations. In this work, we use the parity doublet model to investigate the fluctuations of the net-baryon number density in hot and dense hadronic matter. The model accounts for chiral criticality within the mean-field approximation. We focus on the qualitative properties and systematics of the first- and second-order susceptibility of the net-baryon number density, and their ratios for nucleons of positive and negative parity, as well as their correlator. We show that the fluctuations of the positive-parity nucleon do not necessarily reflect the fluctuations of the total net-baryon number density at the phase boundary of the chiral phase transition. We also investigate the nontrivial structure of the correlator. Furthermore, we discuss and quantify the differences between the fluctuations of the net-baryon number density in the vicinity of the chiral and liquid-gas phase transition in nuclear matter. We indicate a possible relevance of our results with the interpretation of the experimental data on net-proton number fluctuations in heavy-ion collisions. Published by the American Physical Society 2024

Interplay of baryonic chiral partners in fluctuations of netbaryon number density

In this contribution, we use the parity doublet model to investigate the fluctuations of the net-baryon number density. We discuss the systematics of the susceptibilities and their ratios for nucleons of positive and negative parity, as well as their correlator. We demonstrate that the fluctuations of positiveparity nucleon do not reflect the fluctuations of the total net-baryon number at the chiral phase transition.

Formalizing Fairness: Statistical Measures of Parity for Recidivism Prediction Instruments

Recidivism prediction instruments (RPI) are increasingly employed as an algorithmic arm of the criminal justice system to assist in bond, sentencing, and probation determinations. Due process and ethics guidelines require that RPIs, such as the Correctional Offender Management Profiling for Alternative Sanctions (COMPAS), apply a fair assessment in making recidivism predictions. To establish fair RPIs, we must first define standards of fairness and methods to measure bias in RPI outputs. However, defining algorithmic fairness can be cryptic and context-dependent. Scholars have proposed different criteria for what defines a fair RPI. Unfortunately, these criteria are conflicting and mutually exclusive; it is mathematically impossible for a system to satisfy all of them simultaneously. Thus, to ensure fairness in RPIs, we need to separate the wheat from the chaff and identify the most suitable fairness criterion based on philosophical, normative, and practical considerations. In this article, I propose that false positive parity is the best statistical measure of parity for use in assessing the fairness of RPIs. I reach this conclusion by examining the three-pronged debate over the appropriate measure for assessing bias in COMPAS and evaluating the validity and justifications of the arguments. I attempt to answer the following two important questions. (1) What are the most essential factors for substantiating fairness in the criminal justice system and are thus necessary conditions in any algorithmic bias measurement? (2) Which statistical measure of parity best meets these necessary conditions in assessing fairness in RPIs? Furthermore, I aim to present these statistical concepts and their practical meaning in a manner which is easily digestible without a statistics background.

Investigating Fully Strange Tetraquark System with Positive Parity in a Chiral Quark Model

Motivated by the intriguing discovery of X(6900) by the LHCb collaboration, we undertake a comprehensive study of the ss¯ss¯ tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark (ss-s¯s¯) structure and meson–meson (ss¯-ss¯) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with JP=0+, namely, R(0,2150) and R(0,2915), as well as a resonant state with JP=1+, denoted as R(1,2950), and a resonant state with JP=2+, denoted as R(2,2850), utilizing the real-scaling method. By comparing their energies and widths, we suggest that R(0,2915) and R(1,2950) may share characteristics with X(6900), while R(0,2150) could be a promising candidate for the experimental state f0(2100). We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.