Isospin Conservation Research Articles

Electroweak evolution equations and isospin conservation

In processes taking place at energies much higher than the weak scale, electroweak corrections can be taken into account by using electroweak evolution equations, that are analogous to the DGLAP equations in QCD. We show that weak isospin conservation in these equations imposes to modify the expressions of the splitting functions commonly used in the literature. These modifications have a profound impact on the parton distribution functions.

Strong decays of Pcs(4338) and its high isospin cousin via QCD sum rules

In the present work, the strong decays of the newly observed Pcs(4338) as well as its high isospin cousin Pcs(4460) are studied via the QCD sum rules. According to conservation of isospin, spin, and parity, the hadronic coupling constants in four decay channels are obtained; then, the partial decay widths are obtained. The total width of the Pcs(4338) coincides with the experimental data nicely, while the predictions for the Pcs(4460) can be testified in the future experiment and shed light on the nature of the Pcs(4338). Published by the American Physical Society 2024

On the Relations between Fermion Masses and Isospin Couplings in the Microscopic Model

AbstractQuark and lepton masses and mixings are considered in the framework of the microscopic model. The most general ansatz for the interactions among tetrons leads to a Hamiltonian involving Dzyaloshinskii‐Moriya (DM), Heisenberg and torsional isospin forces. Diagonalization of the Hamiltonian provides for 24 eigenvalues which are identified as the quark and lepton masses. While the masses of the third and second family arise from DM and Heisenberg type of isospin interactions, light family masses are related to torsional interactions among tetrons. Neutrino masses turn out to be special in that they are given in terms of tiny isospin non‐conserving DM, Heisenberg and torsional couplings. The approach not only leads to masses, but also allows to calculate the quark and lepton eigenstates, an issue, which is important for the determination of the CKM and PMNS mixing matrices. Compact expressions for the eigenfunctions of are given. The almost exact isospin conservation of the system dictates the form of the lepton states and makes them independent of all the couplings in . As a consequence, a parameter‐free analytic expression for the PMNS matrix is derived which fits numerically all the measured matrix components. The formula includes a prediction of the leptonic Jarlskog invariant . An outlook is given on the treatment of the CKM matrix.

Strong decays of the P c(4312) and its isospin cousin via the QCD sum rules* *Supported by the National Natural Science Foundation (12175068) and the Fundamental Research Funds for the Central Universities of China

In this study, considering the conservation of isospin in the strong decays, we investigate the strong decays of the pentaquark molecule candidate and its possible higher isospin cousin in the framework of the QCD sum rules. Further, the pole residue of the Δ baryon with isospin eigenstate is obtained. If the possible pentaquark molecule candidate could be determined, it would shed light on the interpretations of the states in future experiments.

The joint conservation assumption of CPT and weak isospin and color charge

The conservation of CPT is considered applicable to all physical laws, but more and more research has discovered the possibility of CPT violation. This paper attempts to find a more complex and essential conservation than CPT conservation. This paper uses the method of theoretical structural analysis to discover the relationship between C, P, T symmetry, phase rotation symmetry, space rotation symmetry, and time translation symmetry, and prove the relationship between CPT symmetry, charge conservation, angular momentum conservation and energy conservation by studying the transformation modes of phase space, space, and time. Then the composition rules of uncertainty relationships and the fact that charge, weak isospin, and color charge are all related to the internal symmetry of matter are used to provide evidence for the inherent connection between charge, weak isospin rotation, and color charge demonstrating the similarity among these three. Finally, the joint conservation of CPT, weak isospin, and color charge are proposed.

Towards a Nonperturbative Formulation of the Jet Charge.

The jet charge is an old observable that has proven uniquely useful for discrimination of jets initiated by different flavors of light quarks, for example. In this Letter, we propose an approach to understanding the jet charge by establishing simple, robust assumptions that hold to good approximation nonperturbatively, such as isospin conservation and large particle multiplicity in the jets, forgoing any attempt at a perturbative analysis. From these assumptions, the jet charge distribution with fixed particle multiplicity takes the form of a Gaussian by the central limit theorem and whose mean and variance are related to fractional-power moments of single particle energy distributions. These results make several concrete predictions for the scaling of the jet charge with the multiplicity, explaining many of the results already in the literature, and new results we validate in MonteCarlo simulation.

Measurement of relative isotopic yield distribution of even-even fission fragments from U235 ( nth,f ) following γ -ray spectroscopy

A detailed investigation on the relative isotopic distributions has been carried out for the first time in case of even-even correlated fission fragments for the $^{235}\mathrm{U}({n}_{\text{th}},f$) fission reaction. High-statistics data were obtained in a prompt $\ensuremath{\gamma}$-ray spectroscopy measurement during the EXILL campaign at ILL, Grenoble, France. The extensive off-line analysis of the coincidence data have been carried out using four different coincidence methods. Combining the results from two-dimensional $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ and three-dimensional $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence analysis, a comprehensive picture of the relative isotopic yield distributions of the even-even neutron-rich fission fragments has emerged. The experimentally observed results have been substantiated by the theoretical calculations based on a novel approach of isospin conservation, and a reasonable agreement has been obtained. The calculations following the semiempirical GEF model have also been carried out. The results from the GEF model calculations are found to be in fair agreement with the experimental results.

Isospin conservation in compound nuclear fusion–fission reactions – empirical evidence

Isospin symmetry has gained importance in nuclear phenomena involving heavy nuclei in recent years. We present empirical evidence of isospin dependence in the compound nuclear fission cross-sections and fission widths, which suggests the idea that the compound nucleus (CN) possibly retains the memory of the isospin when it is formed and affects the CN fission. This idea was first proposed by E.L. Yadrovsky [E.L. Yadrovsky, Phys. Lett. 55B, 157 (1975)]. An observable difference between the fission branching ratios in two different isospin states suggests that the CN seems to remember its isospin at the point of formation. Further, the data also suggest a possible new signature of weakening of the CN process and gradual transition to non-compound processes as the energy rises. This is a very interesting and useful observation which needs to be confirmed by further and more precise experiments.

The cross section of e^+e^-rightarrow Lambda overline{Sigma }{}^0+text {c.c.} as a litmus test of isospin violation in the decays of vector charmonia into Lambda overline{Sigma }{}^0+text {c.c.}

Under the aegis of isospin conservation, the amplitudes in Born approximation, i.e., considering the only one-photon-exchange mechanism, of the decay psi rightarrow Lambda overline{Sigma }{}^0+text {c.c.}, where psi is a vector charmonium, and of the reaction e^+e^-rightarrow Lambda overline{Sigma }{}^0+text {c.c.} at the psi mass, are parametrized by the same electromagnetic coupling. It follows that, the modulus of such a coupling can be extracted from the data on the two observables: the decay branching fraction and the annihilation cross section. By considering the first two vector charmonia, J/psi and psi (2S), it is found that, especially in the case of psi (2S), there is a substantial discrepancy between the values of the modulus of the same electromagnetic coupling extracted from the branching ratio and the cross section. We propose, as a possible explanation for such a disagreement, the presence in the decay amplitude of isospin-violating contributions driven by two different mechanisms, that, however, appear to be more favored in the psi (2S) than in the J/psi decays.

Observation of T=3/2 isobaric analog states in Be9 using p+Li8 resonance scattering

Background: Resonance scattering has been extensively used to study the structure of exotic, neutron-deficient nuclei. Extension of the resonance scattering technique to neutron-rich nuclei was suggested more than 20 years ago. This development is based on the isospin conservation law. In spite of broad field of the application, it has never gained a wide-spread acceptance. Purpose: To benchmark the experimental approach to study the structure of exotic neutron-rich nuclei through resonance scattering on a proton target. Method: The excitation function for p+8Li resonance scattering is measured using a thick target by recording coincidence between light and heavy recoils, populating T=3/2 isobaric analog states (IAS) in 9Be. Results: A good fit of the 8Li(p,p)8Li resonance elastic scattering excitation function was obtained using previously tentatively known 5/2- T=3/2 state at 18.65 MeV in 9Be and a new broad T=3/2 s-wave state - the 5/2+ at 18.5 MeV. These results fit the expected iso-mirror properties for the T=3/2 A=9 iso-quartet. Conclusions: Our analysis confirmed isospin as a good quantum number for the investigated highly excited T=3/2 states and demonstrated that studying the structure of neutron-rich exotic nuclei through IAS is a promising approach.

Study on possible molecular states composed of ΛcD¯ ( ΛbB ) and ΣcD¯ ( ΣbB ) within the Bethe-Salpeter framework

$P_c(4312)$ observed by the LHCb collaboration is confirmed as a pentaquark and its structure, production, and decay behaviors attract great attention from theorists and experimentalists. Since its mass is very close to sum of $\Sigma_c$ and $\bar D$ masses, it is naturally tempted to be considered as a molecular state composed of $\Sigma_c$ and $\bar D$. Moreover, $P_c(4312)$ is observed in the channel with $J/\psi p$ final state, requiring that isospin conservation $P_c(4312)$ is an isospin-1/2 eigenstate. In literature, several groups used various models to estimate its spectrum. We systematically study the pentaquarks within the framework of the Bethe-Salpeter equation; thus $P_c(4312)$ is an excellent target because of the available data. We calculate the spectrum of $P_c(4312)$ in terms of the Bethe-Salpter equations and further study its decay modes. Some predictions on other possible pentaquark states that can be tested in future experiments are made.

Valley isospin of interface states in a graphene pn junction in the quantum Hall regime

In the presence of crossed electric and magnetic fields, a graphene ribbon has chiral states running along sample edges and along boundaries between $p$-doped and $n$-doped regions. We here consider the scattering of edge states into interface states, which takes place whereever the $pn$ interface crosses the sample boundary, as well as the reverse process. For a graphene ribbon with armchair boundaries, the evolution of edge states into interface states and {\em vice versa} is governed by the conservation of valley isospin. Although valley isospin is not conserved in simplified models of a ribbon with zigzag boundaries, we find that arguments based on isospin conservation can be applied to a more realistic modeling of the graphene ribbon, which takes account of the lifting of electron-hole degeneracy. The valley isospin of interface states is an important factor determining the conductance of a graphene $pn$ junction in a quantizing magnetic field.

Phenomenological view on baryon-baryon potentials from lattice QCD simulations

A qualitative discussion on the range of the potentials as they result from the phenomenological meson-exchange picture and from lattice simulations by the HAL QCD Collaboration is presented. For the former pion- and/or $\eta$-meson exchange are considered together with the scalar-isoscalar component of correlated $\pi\pi /K \bar K$ exchange. It is observed that the intuitive expectation for the behavior of the baryon-baryon potentials for large separations, associated with the exchange of one and/or two pions, does not always match with the potentials extracted from the lattice simulations. Only in cases where pion exchange provides the longest ranged contribution, like in the $\Xi N$ system, a reasonable qualitative agreement between the phenomenological and the lattice QCD potentials is found for baryon-baryon separations of $r \gtrsim 1$ fm. For the $\Omega N$ and $\Omega\Omega$ interactions where isospin conservation rules out one-pion exchange a large mismatch is observed, with the potentials by the HAL QCD Collaboration being much longer ranged and much stronger at large distances as compared to the phenomenological expectation. This casts some doubts on the applicability of using these potentials in few- or many-body systems.

Searching for the odderon in ultraperipheral proton-ion collisions at the LHC

We explore the possibility of observing Odderon exchange in proton--ion collisions at the LHC, via the ultraperipheral photoproduction of C-even mesons. As well as the signal, we consider in detail the principle backgrounds, due to QCD--initiated production (i.e. double Pomeron exchange) and $\gamma\gamma$ fusion. We find that while the photon--initiated background is dominant at very small momentum transfer, this can be effectively removed by placing a reasonable cut on the transverse momentum of the produced meson. In the case of QCD--initiated production, we show this is in general strongly suppressed by the small probability of no additional particle production in the central detector, namely the survival factor. In some scenarios, this suppression is sufficient to permit the observation of Odderon exchange in Pb$-p$ collisions in a clean environment, or else to place bounds on this. We in addition identify the cases of $\pi^0$ and $\eta(548)$ production as particularly promising channels. Here, the QCD--initiated background is absent for $\pi^0$ due to isospin conservation and very small for $\eta(548)$ due to its dominantly flavour octet nature and odd parity.

Test of isospin conservation in thermal neutron-induced fission of $$^{245}\mathrm{Cm}$$ 245 Cm

We have recently shown that the general trends of partition-wise fission fragment mass distribution in heavy-ion-induced compound nuclear (CN) fission of heavy nuclei can be reproduced reasonably well by using the concept of isospin conservation, hence providing a direct evidence of isospin conservation in neutron-rich systems [Jain et al, Nucl Data Sheets 120, 123 (2014); Garg and Jain, Phys. Scr. 92, 094001 (2017); Jain and Garg, EPJ Web of Conference 178, 05007 (2018); Garg et al, Phys. Scr. 93, 124008 (2018)]. In this paper, we test the concept of isospin conservation to reproduce the fission fragment mass distribution emerging from thermal neutron-induced CN fission reaction, $$^{245}\mathrm{Cm}(n_{\mathrm{th}}, \hbox {f})$$ . As earlier, we use Kelson’s conjectures [I Kelson, Proceedings of the Conference on Nuclear Isospin (Academic Press, New York, 1969)] to assign isospin to neutron-rich fragments emitted in fission, which suggest the formation of fission fragments in isobaric analogue states. We calculate the relative yields of neutron-rich fragments using the concept of isospin conservation and basic isospin algebra. The calculated results reproduce the experimentally known partition-wise mass distributions quite well. This highlights the usefulness of isospin as an approximately good quantum number in neutron-rich nuclei. This also allows us to predict the fragment distribution of the most symmetric Cd–Cd partition and the heavier mass fragment distributions, both not measured so far.

Investigation of Isospin Conservation Effects on Pre-Equilibrium Nuclear Reactions for Some Nuclei

The pre-equilibrium emission spectra have been studied and calculated using the exciton model. The calculations took different reactions (nucleon – nucleon, nucleon – cluster, cluster – nucleon) at low and high incident energies to investigate and study the influence of adding the isospin conservation effects into the nuclear level density on the energy spectra. The isospin conservation effect added to the state density showed no significance variation for mixed and conserved isospin calculations for all reactions at different incident energies. The results were obtained by depending on the PRECO-2006 code of C. Kalbach.

Role of isospin and its conservation in neutron-rich fission fragments

Following on from our earlier paper Garg and Jain (2017 Phys. Scr. 92 094001) containing some initial results, we present a detailed discussion and complete results in this paper, which provide the first direct evidence for the validity of isospin as a nearly good quantum number in neutron-rich systems. The evidence comes from the reproduction of the general features of the partition-wise relative yields of neutron-rich fission fragments produced in two heavy-ion induced fusion fission reactions, namely 208Pb (18O, f) and 238U (18O, f), by using the concept of isospin conservation. To fix the isospin values and use the isospin algebra, we invoke what we term Kelson’s conjectures. We present a consistent scheme for isospin assignments based on these considerations. Our calculated results confirm that isospin behaves as an approximately good quantum number in neutron-rich systems, in this case, the fission fragments.

Isospin Conservation in Neutron Rich Systems of Heavy Nuclei

It is generally believed that isospin would diminish in its importance as we go towards heavy mass region due to isospin mixing caused by the growing Coulomb forces. However, it was realized quite early that isospin could become an important and useful quantum number for all nuclei including heavy nuclei due to neutron richness of the systems [1]. Lane and Soper [2] also showed in a theoretical calculation that isospin indeed remains quite good in heavy mass neutron rich systems. In this paper, we present isospin based calculations [3, 4] for the fission fragment distributions obtained from heavy-ion fusion fission reactions. We discuss in detail the procedure adopted to assign the isospin values and the role of neutron multiplicity data in obtaining the total fission fragment distributions. We show that the observed fragment distributions can be reproduced rather reasonably well by the calculations based on the idea of conservation of isospin. This is a direct experimental evidence of the validity of isospin in heavy nuclei, which arises largely due to the neutron-rich nature of heavy nuclei and their fragments. This result may eventually become useful for the theories of nuclear fission and also in other practical applications.

Goodness of isospin in neutron rich systems from the fission fragment distribution

We present the results of our calculations for the relative yields of neutron-rich fission fragments emitted in 208Pb (18O, fission) reaction by using the concept of the conservation of isospin and compare with the experimental data. We take into account a range of isospin values allowed by the isospin algebra and assume that the fission fragments are formed in isobaric analog states. We also take into account the neutron multiplicity data for various neutron-emission channels in each partition, and use them to obtain the weight factors in calculating the yields. We then calculate the relative yields of the fission fragments. Our calculated results are able to reproduce the experimental trends reasonably well. This is the first direct evidence of the isospin conservation in neutron-rich systems and may prove a very useful tool in their studies.

New G -parity violating amplitude in the J/ψ decay?

The $J/\psi$ meson has negative $G$-parity so that, in the limit of isospin conservation, its decay into $\pi^+\pi^-$ should be purely electromagnetic. However, the measured branching fraction $\mathcal{B}(J/\psi\to\pi^+\pi^-)$ exceeds by more than 3.9 standard deviations the expectation computed according to BaBar data on the $e^+e^-\to\pi^+\pi^-$ cross section. The possibility that the two-gluon plus one-photon decay mechanism is not suppressed by $G$-parity conservation is discussed, even by considering other multi-pion decay channels. As also obtained by phenomenological computation, such a decay mechanism could be responsible for the observed discrepancy. Finally, we notice that the BESIII experiment, having the potential to perform an accurate measurement of the $e^+e^-\to\pi^+\pi^-$ cross section in the 3 GeV energy region, can definitely prove or disprove this strong $G$-parity-violating mechanism by confirming or confuting the BaBar data.