Monopole Form Factors Research Articles

Zb states as the mixture of the molecular and diquark-anti-diquark components within the effective field theory

In this study, we reconsider the states Zb(10610) and Zb(10650) by investigating the presence of diquark-anti-diquark components as well as the hadronic molecule components in the framework of effective field theory. The different masses of pseudoscalar mesons such as π0, η8, and η0, as well as vector mesons like ρ0 and ω violate the Okubo-Zweig-Iizuka (OZI) rule that is well depicted under the [U(3)L⊗U(3)R]global⊗[U(3)V]local symmetry. To account for the contribution of intermediate bosons of heavy masses within the one-boson-exchange model, we introduce an exponential form factor instead of the commonly used monopole form factor in the past. By solving the coupled-channel Schrödinger equation with the Gaussian expansion method, our numerical results indicate that the Zb(10610) and Zb(10650) states can be explained as hadronic molecules slightly mixing with diquark-anti-diquark states. Published by the American Physical Society 2024

Description of the Proton-Decaying 0_{2}^{+} Resonance of the α Particle.

The recent precise experimental determination of the monopole transition form factor from the ground state of ^{4}He to its 0_{2}^{+} resonance via electron scattering has reinvigorated discussions about the nature of this first excited state of the α particle. The 0_{2}^{+} state has been traditionally interpreted in the literature as the isoscalar monopole resonance (breathing mode) or, alternatively, as a particle-hole shell-model excitation. To better understand the nature of this state, which lies only ∼410 keV above the proton emission threshold, we employ the coupled-channel representation of the no-core Gamow shell model. By considering the [^{3}H+p], [^{3}He+n], and [^{2}H+^{2}H] reaction channels, we explain the excitation energy and monopole form factor of the 0_{2}^{+} state. We argue that the continuum coupling strongly impacts the nature of this state, which carries characteristics of the proton decay threshold.

Deuteron electromagnetic form factors and tensor polarization observables in the framework of the hard-wall AdS/QCD model

We study the electromagnetic form factors and tensor polarization observables of the deuteron in the framework of the hard-wall AdS/QCD model. We find a profile function for the bulk twist vector field, which describes the deuteron on the boundary and fix the infrared boundary cut-off of AdS space in accordance with the ground state mass of the deuteron. We obtain the deuteron charge monopole, quadrupole, and magnetic dipole form factors and tensor polarization observables from the bulk Lagrangians for the deuteron and photon field interactions. We plot the momentum transfer dependence of the form factors and tensor polarization observables and compare our numerical results with those in the soft-wall model and experimental data.

Investigation of the possible DD¯*/BB¯* and DD*/B¯B¯* bound states

In this work, we systematically study the $D{\overline{D}}^{*}/B{\overline{B}}^{*}$ and $D{D}^{*}/\overline{B}{\overline{B}}^{*}$ systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing the direct and crossed one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we find only the isoscalar $D{\overline{D}}^{*}/B{\overline{B}}^{*}$ and $D{D}^{*}/\overline{B}{\overline{B}}^{*}$ systems can exist as bound states. This indicate that the $X(3872)$ and ${T}_{cc}^{+}$ could be accommodated as ${I}^{G}({J}^{PC})={0}^{+}({1}^{++})$ $D{\overline{D}}^{*}$ and $(I){J}^{P}=(0){1}^{+}\text{ }\text{ }D{D}^{*}$ bound states while the bound-state explanations for ${Z}_{b}(10610)$ and ${Z}_{c}(3900)$ are excluded.

Studying the {bar{D}}_1K molecule in the Bethe\u2013Salpeter equation approach

We interpret the X_1(2900) as an S-wave {bar{D}}_1K molecular state in the Bethe–Salpeter equation approach with the ladder and instantaneous approximations for the kernel. By solving the Bethe–Salpeter equation numerically with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the verties, we find the bound state exists. We also study the decay width of the decay X_1(2900) to D^-K^+.

Studying the D1D molecule in the Bethe-Salpeter equation approach

We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not.

Bs1(5778) as a B*K¯ molecule in the Bethe-Salpeter equation approach

We interpret the $B_{s1}(5778)$ as an $S$-wave $B^\ast\bar{K}$ molecular state in the Bethe-Salpeter equation approach. In the ladder and instantaneous approximations, and with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the vertex, we find the bound state exists. We also study the decay widths of the decay $B_{s1}(5778)\rightarrow B_s^\ast\pi$ and the radiative decays $B_{s1}(5778)\rightarrow B_s\gamma$ and $B_{s1}(5778)\rightarrow B_s^{\ast}\gamma$, which will be instructive for the forthcoming experiments.

Studying the Bound State of the BK¯ System in the Bethe-Salpeter Formalism

In this work, we study the BK¯ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector BK¯ systems, and we find that X5568 cannot be a BK¯ molecule.

Nucleon and $${\Delta}$$ Δ Elastic and Transition Form Factors

We compute nucleon and Delta elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a vector-vector contact-interaction. The comparison emphasises that experiment is sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: $G_E^p(Q^2)/G_M^p(Q^2)$ possesses a zero at $Q^2=9.5GeV^2$; any change in the interaction which shifts a zero in the proton ratio to larger $Q^2$ relocates a zero in $G_E^n(Q^2)/G_M^n(Q^2)$ to smaller $Q^2$; and there is likely a value of momentum transfer above which $G_E^n>G_E^p$. Regarding the $\Delta(1232)$-baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the $\Delta(1232)$ Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the N-to-Delta transition, the momentum-dependence of the magnetic transition form factor, $G_M^\ast$, matches that of $G_M^n$ once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations.

Nonmesonic Weak Decay Spectra of Light Hypernuclei

The nonmesonic weak decay spectra of light hypernuclei have been evaluated in a systematic way. As theoretical framework we adopt the independent particle shell model with three different one-meson-exchange transition potentials. Good agreement with data is obtained for proton and neutron kinetic energy spectra of $^4_\Lambda$He, and $^5_\Lambda$He, when the recoil effect is considered. The coincidence spectra of proton-neutron pairs are also accounted for quite reasonably, but it was not possible to reproduce the data for the neutron-neutron pair spectra. It is suggested that the $\pi+K$ meson-exchange model with soft monopole form factors could be a good starting point for describing the dynamics responsible for the decays of these two hypernuclei. The $^4_\Lambda$H~ spectra are also presented.

Bcabsorption cross sections byρmesons

The cross sections of ${B}_{c}$ absorption by $\ensuremath{\rho}$ mesons are calculated using a meson-exchange model based on a hadronic Lagrangian having SU(5) symmetry. Calculated cross sections are found to be in the ranges 0.6--3 and 0.05--0.3 mb for the processes ${B}_{c}^{+}\ensuremath{\rho}\ensuremath{\rightarrow}{D}^{*}B$ and ${B}_{c}^{+}\ensuremath{\rho}\ensuremath{\rightarrow}D{B}^{*}$, respectively, when the monopole form factor is included. The total ${B}_{c}$ absorption cross section by $\ensuremath{\rho}$ mesons is found to be about three times smaller than the calculated total cross section by pions using the same model. These results could be useful in calculating the production rate of ${B}_{c}$ mesons in relativistic heavy-ion collisions.

Exclusive production of lepton, quark and meson pairs in peripheral ultrarelativistic heavy ion collisions

We discuss exclusive production of lepton-antilepton, quark-antiquark, $\pi \pi$ and $\rho^0 \rho^0$ pairs in ultraperipheral, ultrarelativistic heavy-ion collisions. The cross sections for exclusive production of pairs of particles is calculated in Equivalent Photon Approximation (EPA). Realistic (Fourier transform of charge density) charge form factors of nuclei are used and the corresponding results are compared with the cross sections calculated with monopole form factor used in the literature. Absorption effects are discussed and quantified. The cross sections obtained with realistic form factors are significantly smaller than those obtained with the monopole form factors.

Hadronic absorption cross sections ofBc

The cross sections of $B_{c}$\ absorption by $\pi $ mesons are calculated using hadronic Lagrangian based on SU(5) flavor symmetry. Calculated cross sections are found to be in range 2 to 7 mb and 0.2 to 2 mb for the processes $B_{c}^{+}\pi \rightarrow DB$ and $B_{c}^{+}\pi \rightarrow D^{\ast}B^{\ast}$ respectively, when the monopole form factor is included. These results could be useful in calculating production rate of $B_{c}$ meson in relativistic heavy ion collisions.

EXCLUSIVE PRODUCTION OF ρ0ρ0 PAIRS IN ULTRARELATIVISTIC HEAVY ION COLLISIONS

We disuss exclusive electromagnetic production of two neutral ρ0 mesons and show the predictions for the AA → AAρ0ρ0 reactions for gold-gold collisions at the energy of [Formula: see text] and for lead-lead collisions at the energy of [Formula: see text]. The elementary cross section is calculated with the help of the vector-dominance-model (VDM)-Regge approach which usually very well describes the experimental data at large γγ energy. The low-energy γγ → ρ0ρ0 cross section is parametrized. The cross section for nuclear process is calculated by means of the equivalent photon approximation (EPA). We compare the results with realistic charge density with the results for monopole form factor.

Exclusive muon-pair production in ultrarelativistic heavy-ion collisions: Realistic nucleus charge form factor and differential distributions

The cross sections for exclusive muon-pair production in nucleus-nucleus collisions are calculated and several differential distributions are shown. Realistic (Fourier transform of charge density) charge form factors of nuclei are used and the corresponding results are compared with the cross sections calculated with monopole form factor often used in the literature and discussed recently in the context of higher-order QED corrections. Absorption effects are discussed and quantified. The cross sections obtained with realistic form factors are significantly smaller than those obtained with the monopole form factor. The effect is bigger for large muon rapidities and/or large muon transverse momenta. The predictions for the STAR and PHENIX collaboration measurements at RHIC as well as the ALICE and CMS collaborations at LHC are presented.

Parity-violating elastic electron scattering and nuclear structure

We discuss parity-violating elastic electron scattering as a complementary tool in the race for more precise determinations of neutron densities in nuclei. Isovector and isoscalar densities and form factors in N > Z and N = Z stable nuclei are discussed taking 208Pb and 28Si as examples. Distorted wave calculations of parity-violating asymmetries are shown and are compared to the plane wave impulse approximation. The extraction of the ratio between neutron and proton monopole form factors is discussed. The isospin mixing produced by Coulomb interaction in the ground state of N = Z nuclei with Skyrme selfconsistent mean fields is also discussed.

Hadronic absorption cross sections of Bc

The absorption cross sections B c meson by hadronic commoving systems (nucleons) are investigated using a gauged SU 5 hadronic Lagrangian in mesonic exchange model. The energy dependence of dissociation cross sections are calculated from the threshold to higher energies with monopole form factor. Depending on values of the monopole form factor cut off parameter used, the peak cross sections are found significantly large. We present this analysis for the form factor and coupling constants used in calculating the B c dissociation cross sections.

THE ROLE OF LINEAR ALPHA-CLUSTER CONFIGURATION FOR 12C

In the framework of the Alpha Cluster Model extended calculations of form factors of elastic and inelastic [Formula: see text] and [Formula: see text] (7.66 MeV) electron scattering on 12C were performed. Two possible alpha cluster configurations (linear and triangular) were considered for states assigned to different rotational bands and although the configuration mixture was found to be important for explanation of the inelastic monopole form factor, a fully consistent picture, including all available data, was not obtained.

Nucleon momentum distribution in deuteron and other nuclei within the light-front dynamics method

The relativistic light-front dynamics (LFD) method has been shown to give a correct description of the most recent data for the deuteron monopole and quadrupole charge form factors obtained at the Jefferson Laboratory for elastic electron-deuteron scattering for six values of the squared momentum transfer between 0.66 and 1.7 (GeV/c)$^{2}$. The good agreement with the data is in contrast with the results of the existing non-relativistic approaches. In this work we firstly make a complementary test of the LFD applying it to calculate another important characteristic, the nucleon momentum distribution $n(q)$ of the deuteron using six invariant functions $f_{i}$ $(i=1,...,6)$ instead of two ($S$- and $D$-waves) in the nonrelativistic case. The comparison with the $y$-scaling data shows the decisive role of the function $f_{5}$ which at $q\geq$ 500 MeV/c exceeds all other $f$-functions (as well as the $S$- and $D$-waves) for the correct description of $n(q)$ of the deuteron in the high-momentum region. Comparison with other calculations using $S$- and $D$-waves corresponding to various nucleon-nucleon potentials is made. Secondly, using clear indications that the high-momentum components of $n(q)$ in heavier nuclei are related to those in the deuteron, we develop an approach within the natural orbital representation to calculate $n(q)$ in $(A,Z)$-nuclei on the basis of the deuteron momentum distribution. As examples, $n(q)$ in $^{4}$He, $^{12}$C and $^{56}$Fe are calculated and good agreement with the $y$-scaling data is obtained.

The reaction pp→pΛK + near threshold

We analyze the recent total cross section data for $pp \to p\Lambda K^+$ near threshold measured at COSY. Using an effective range approximation for the on-shell $p\Lambda$ S-wave final state interaction we extract from these data the combination ${\cal K} = \sqrt{2|K_s|^2+|K_t|^2} = 0.38$ fm$^4$ of the singlet ($K_s$) and triplet ($K_t$) threshold transition amplitudes. We present an exploratory calculation of various (tree-level) vector and pseudoscalar meson exchange diagrams. Pointlike $\omega$-exchange alone and the combined ($\rho^0,\omega,K^{*+} $)-exchange can explain the experimental value of $\cal K$. The pseudoscalar meson exchanges based on a SU(3) chiral Lagrangian turn out to be too large. However, when adding $\pi^0$-exchange in combination with the resonant $\pi N \to S_{11}(1650)\to K \Lambda$ transition and introducing monopole form factors with a cut-off $\Lambda_c= 1.5$ GeV one is again able to reproduce the experimental value of $\cal K$. More exclusive measurements are necessary to reveal the details of the $pp\to p\Lambda K^+$ production mechanism.