Ground State Vector Research Articles

Charge distributions of pseudoscalar and vector mesons from Dyson-Schwinger equations

We combine the Dyson-Schwinger/Bethe-Salpeter equations framework with modern numerical reconstruction methods to derive the three-dimensional and transverse two-dimensional charge distribution of an array of ground-state pseudoscalar and vector mesons from their elastic electromagnetic form factor in the low-momentum region. The charge radii obtained by averaging over the reconstructed charge distributions have been checked to be consistent with those calculated from the slope of the elastic electromagnetic form factor at zero transferred momentum. The capability of the reconstruction procedure for capturing a reliable low-distance charge distribution is discussed and argued to work down to distances of around 0.1 fm, such that it might be potentially applied to extract, e.g., mass densities from gravitational form factors. Published by the American Physical Society 2024

Predictions of the missing excited vector heavy–light mesons: the mass difference method

A prediction study for the not yet discovered cs¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c\\overline{s}$$\\end{document} and bs¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b\\overline{s}$$\\end{document} meson states of the 13D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1^{3}D_1$$\\end{document} quantum numbers is conducted, denoted as Ds\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_s$$\\end{document} and Bs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_s$$\\end{document}, respectively. By employing our method, both states of ground and excited vector mesons are considered, which predominantly correspond to the ground state vector mesons with quantum numbers n2S+1LJ=13S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n~ ^{2S+1}L_{J} = 1 ~ ^{3}S_1$$\\end{document} and to the orbitally excited vector mesons with quantum numbers n2S+1LJ=13D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n~ ^{2\\,S+1}L_{J} = 1~ ^{3}D_1$$\\end{document}. The considered method depends on the difference in the masses for the relevant states from orbitally and ground state vector mesons. Theoretical calculations are in good agreements with newly published data.

Reduced basis emulation of pairing in finite systems

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing highly accurate results. This work is meant to show that the RBM is an efficient and accurate emulator for the strong correlations induced by the pairing interaction in a variety of finite systems like ultrasmall superconducting grains, interacting topological superfluids and mesoscopic hybrid superconductor-semiconductor devices, all of which require an expensive, beyond-mean-field, particle-number conserving description. These systems are modelled by the number-conserving Richardson pairing Hamiltonian and its appropriate generalizations. Their ground state is solved for exactly using the Density Matrix Renormalization Group. The reduced basis is assembled iteratively from a small number of exact ground state vectors, well-chosen from across the relevant parameter space using a fast estimate of the emulation error and a greedy local optimization algorithm. The reduced basis emulation is found to accurately describe the weak-to-strong pairing cross-over in small grains, the third-order topological phase transition of the interacting Richardson-Kitaev chain, and the complex charge stability diagram of a hybrid quantum dot - superconductor device. RBMs are thus confirmed to be cheap and accurate emulators for the widely encountered superconducting phenomena. Capable of providing orders of magnitude computational speed-up with respect to approaches based only on traditional many-body solvers, they open new possibilities in building and solving models of interacting many-body systems and in better interfacing them with experimental design and data analysis.

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

The open XXZ spin chain with the anisotropy \Delta=-\frac12Δ=−12 and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain’s ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state’s logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

Precision calculation of isospin-symmetry-breaking corrections to T=1/2 mirror decays using configuration-interaction framework built upon multireference charge-dependent density functional theory

We present systematic study of isospin impurities ($\alpha_{\rm ISB}$) to the wave functions of $T=1/2$, $11\leq A \leq 47$ mirror nuclei and the isospin-symmetry-breaking (ISB) corrections ($\delta_{\rm ISB}^{\rm V}$) to their ground state vector $\beta$-decays using, for the first time, multi-reference charge-dependent density functional theory (MR-DFT) that includes strong-force-rooted class-III interaction adjusted to correct for the Nolen-Schiffer anomaly in nuclear masses. We demonstrate that, unexpectedly, the strong-force-rooted isovector force gives rise to a large systematic increase of $\alpha_{\rm ISB}$ and $\delta_{\rm ISB}^{\rm V}$ as compared to the results obtained within MR-DFT that uses Coulomb interaction as the only source of ISB. This, in turn, increases a central value of the $V_{\rm ud}$ element of the CKM matrix extracted from the $T=1/2$ mirrors bringing it closer to the value obtained form the purely vector superallowed $0^+ \to 0^+$ transitions. In order to compute the value of $V_{\rm ud}$, we performed precision calculation of the Fermi matrix elements in $A=19, 21, 35$, and 37 mirror nuclei using DFT-rooted configuration-interaction model that includes all relevant axially-deformed particle-hole configurations built upon Nilsson orbitals originating from the spherical $sd$ shell. Our calculations yield $|V_{\rm ud}|=0.9736(16)$.

Variational approaches to constructing the many-body nuclear ground state for quantum computing

We explore the preparation of specific nuclear states on gate-based quantum hardware using variational algorithms. Large-scale classical diagonalizations of the nuclear shell model have reached sizes of ${10}^{9}--{10}^{10}$ basis states but are still severely limited by computational resources. Quantum computing can, in principle, solve such systems exactly with exponentially fewer resources than classical computing. Exact solutions for large systems require many qubits and large gate depth, but variational approaches can effectively limit the required gate depth. We use the unitary coupled cluster approach to construct approximations of the ground-state vectors, later to be used in dynamics calculations. The testing ground is the phenomenological shell model space, which allows us to mimic the complexity of the internucleon interactions. We find that often one needs to minimize over a large number of parameters, using a large number of entanglements that makes the application on existing hardware challenging. Prospects for rapid improvements with more capable hardware are, however, very encouraging.

Existence and stability of vector solitary waves for nonlinear Schrödinger systems of Hartree-type with Bessel potential

In this paper, we study a class of two-dimensional nonlinear Schrödinger systems of Hartree-type with Bessel potential kernel, which models the propagation and interaction of two-color light beams in nematic liquid crystals. The global well-posedness is proved by using fixed point argument, Gagliardo-Nirenberg inequality and conservation laws. In addition, we also obtain the existence and orbital stability of ground state vector solitary waves applying variational methods and Concentration-compactness Lemma.

Self-gravitating vector dark matter

We derive the non-relativistic limit of a massive vector field. We show that the Cartesian spatial components of the vector behave as three identical, non-interacting scalar fields. We find classes of spherical, cylindrical, and planar self-gravitating vector solitons in the Newtonian limit. The gravitational properties of the lowest-energy vector solitons$\mathrm{-}$the gravitational potential and density field$\mathrm{-}$depend only on the net mass of the soliton and the vector particle mass. In particular, these self-gravitating, ground-state vector solitons are independent of the distribution of energy across the vector field components, and are indistinguishable from their scalar-field counterparts. Fuzzy Vector Dark Matter models can therefore give rise to halo cores with identical observational properties to the ones in scalar Fuzzy Dark Matter models. We also provide novel hedgehog vector soliton solutions, which cannot be observed in scalar-field theories. The gravitational binding of the lowest-energy hedgehog halo is about three times weaker than the ground-state vector soliton. Finally, we show that no spherically symmetric solitons exist with a divergence-free vector field.

Identifying phase transition point of <i>J</i><sub>1</sub>-<i>J</i><sub>2</sub> antiferromagnetic Heisenberg spin chain by machine learning

Studying quantum phase transitions through order parameters is a traditional method, but studying phase transitions by machine learning is a brand new field. The ability of machine learning to classify, identify, or interpret massive data sets may provide physicists with similar analyses of the exponentially large data sets embodied in the Hilbert space of quantum many-body system. In this work, we propose a method of using unsupervised learning algorithm of the Gaussian mixture model to classify the state vectors of the <i>J</i><sub>1</sub>-<i>J</i><sub>2</sub> antiferromagnetic Heisenberg spin chain system, then the supervised learning algorithm of the convolutional neural network is used to identify the classification point given by the unsupervised learning algorithm, and the cross-validation method is adopted to verify the learning effect. Using this method, we study the <i>J</i><sub>1</sub>-<i>J</i><sub>2</sub> Heisenberg spin chain system with chain length <i>N</i> = 8, 10, 12, 16 and obtain the same conclusion. The first order phase transition point of <i>J</i><sub>1</sub>-<i>J</i><sub>2</sub> antiferromagnetic Heisenberg spin chain system can be accurately found from the ground state vector, but the infinite order phase transition point cannot be found from the ground state vector. The first order and the infinite order phase transition point can be found from the first excited state vector, which indirectly shows that the first excited state may contain more information than the ground state of <i>J</i><sub>1</sub>-<i>J</i><sub>2</sub> antiferromagnetic Heisenberg spin chain system. The visualization of the state vector shows the reliability of the machine learning algorithm, which can extract the feature information from the state vector. The result reveals that the machine learning techniques can directly find some possible phase transition points from a large set of state vectorwithout prior knowledge of the energy or locality conditions of the Hamiltonian, which may assists us in studying unknown systems. Supervised learning can verify the phase transition points given by unsupervised learning, thereby indicating that we can discover some useful information about unknown systems only through machine learning techniques. Machine learning techniques can be a basic research tool in strong quantum-correlated systems, and it can be adapted to more complex systems, which can help us dig up hidden information.

Decay properties of P-wave bottom baryons within light-cone sum rules

We use the method of light-cone sum rules to study decay properties of P-wave bottom baryons belonging to the SU(3) flavor mathbf {6}_F representation. In Cui et al. (Phys Rev D 99:094021, 2019) we have studied their mass spectrum and pionic decays, and found that the varSigma _{b}(6097) and varXi _{b}(6227) can be well interpreted as P-wave bottom baryons of J^P = 3/2^-. In this paper we further study their decays into ground-state bottom baryons and vector mesons. We propose to search for a new state varXi _b({5/2}^-), that is the J^P = 5/2^- partner state of the varXi _{b}(6227), in the varXi _b({5/2}^-) rightarrow varXi _b^{*}rho rightarrow varXi _b^{*}pi pi decay process. Its mass is 12 pm 5 MeV larger than that of the varXi _{b}(6227).

The Ground-State Vector of the XY Heisenberg Chain and the Gauss Decomposition

The XY Heisenberg spin 1/2 chain is considered in the fermion representation. The construction of the ground state-vector is based on the group-theoretical approach. The exact expression for the ground state-vector will allow to study the combinatorics of the correlation functions of the model.

A pattern for the flavor dependent quark-antiquark interaction

A flavor dependent kernel is constructed based on the rainbow-ladder truncation of the Dyson-Schwinger and Bethe-Salpeter equations in quantum chromodynamics. The quark-antiquark interaction is composed of a flavor dependent infrared part and a flavor independent ultraviolet part. Our model gives a successful and unified description of the light, heavy and heavy-light ground state pseudoscalar and vector mesons. Our model shows, for the first time, that the infrared enhanced quark-antiquark interaction is stronger and wider for lighter quarks.

Masses of ground-state mesons and baryons, including those with heavy quarks

Using a confining, symmetry-preserving regularisation of a vector$\times$vector contact interaction, we compute the spectra of ground-state pseudoscalar and vector $(f\bar g)$ mesons, scalar and axial-vector $(fg)$ diquarks, and $J^P=1/2^+, 3/2^+$ $(fgh)$ baryons, where $f,g,h \in \{u,d,s,c,b\}$. The diquark correlations are essentially dynamical and play a key role in formulating and solving the three-valence-quark baryon problems. The baryon spectrum obtained from this largely-algebraic approach reproduces the 22 known experimental masses with an accuracy of $2.9(2.4)$%. It also possesses the richness of states typical of constituent-quark models, predicting many heavy-quark baryons not yet observed. This study indicates that diquark correlations are an important component of all baryons; and owing to the dynamical character of the diquarks, it is typically the lightest allowed diquark correlation which defines the most important component of a baryon's Faddeev amplitude.

Twist-2 pseudoscalar and vector meson distribution amplitudes in light-front quark model with exponential-type confining potential

We study the twist-2 distribution amplitudes (DAs) and the decay constants of pseudoscalar light ($\pi$, $K$) and heavy ($D$, $D_s$, $B$, $B_s$) mesons as well as the longitudinally and transversely polarized vector light ($\rho$, $K^*$) and heavy ($D^*$, $D_s^*$, $B^*$, $B_s^*$) mesons in the light-front quark model with the Coulomb plus exponential-type confining potential $V_{\rm {exp}} = a + b e^{\alpha r}$ in addition to the hyperfine interaction. We first compute the mass spectra of ground state pseudoscalar and vector light and heavy mesons and fix the model parameters necessary for the analysis, applying the variational principle with the trial wave function up to the first three lowest order harmonic oscillator (HO) wave functions $\Phi(x, \textbf{k}_\bot) = \sum_{n=1}^{3} c_n \phi_{nS}$. We then obtain the numerical results for the corresponding decay constants of light and heavy mesons. We estimate the DAs, analyze their variation as a function of momentum fraction and compute the first six $\xi$-moments of the $B$ and $D$ mesons as well. We compare our results with the available experimental data as well as with the other theoretical model predictions.

On the orthogonality of states with approximate wavefunctions.

A variational solution to the eigenvalue problem for the Hamiltonian H, with orthogonality restrictions on eigenvectors of H to the vector H ∣ Φ0〉, where ∣Φ0〉 is an approximate ground-state vector, is proposed as a means to calculate excited states. The asymptotic projection (AP) method proposed previously is further developed and applied to solve this problem in a simple way. We demonstrate that the AP methodology does not require an evaluation of the matrix elements of operator H2, whereas conventional approaches-such as the elimination of off-diagonal Lagrange multipliers method, projection operator techniques, and other methods-do. It is shown, based on the results obtained for the single-electron molecular ions H2+, HeH2+, and H32+, that applying the new method to determine excited-state wavefunctions yields the upper bounds for excited-state energies. We demonstrate that regardless of whether the orthogonality constraint for states (〈Φ| Φ0〉 = 0) is applied, the zero-coupling constraint(〈Φ| H| Φ0〉 = 0) is imposed, or both of these restrictions are enforced simultaneously, practically the same excited-state energy is obtained if the basis set is almost complete. For the systems considered here, all schemes are capable of giving a sub-μhartree level of accuracy for the ground and excited states computed with different basis sets.

Hamiltonian renormalisation I: derivation from Osterwalder–Schrader reconstruction

A possible avenue towards a non-perturbative quantum field theory (QFT) on Minkowski space is the constructive approach which employs the Euclidian path integral formulation, in the presence of both ultraviolet (UV) and infrared (IR) regulators, as starting point. The UV regulator is to be taken away by renormalisation group techniques which in case of success leads to a measure on the space of generalised Euclidian fields in finite volume. The removal of the IR regulator corresponds to the thermodynamic limit of the system in the statistical physics sense. If the resulting measure obeys the Osterwalder–Schrader axioms, the actual QFT on Minkowski space is then obtained by Osterwalder–Schrader reconstruction.In this work we study the question whether it is possible to reformulate the renormalisation group non-perturbatively directly at the operator (Hamiltonian) level. Hamiltonian renormalisation would be the natural route to follow if one had easier access to an interacting Hamiltonian operator rather than to a path integral, at least in the presence of UV and/or IR cut-off, which is generically the case in complicated gauge theories such as general relativity.Our guiding principle for the definition of the direct Hamiltonian renormalisation group is that it results in the same continuum theory as the covariant (path integral) renormalisation group. This makes the present work different from other approaches to Hamiltonian renormalisation. In order to achieve this, we invert the Osterwalder–Schrader reconstruction, which may be called Osterwalder–Schrader construction of a Wiener measure from the underlying Hamiltonian theory. The resulting correspondence between reflection positive measures and Osterwalder–Schrader data consisting of a Hilbert space, a Hamiltonian and a ground state vector allows us to monitor the effect of the renormalisation flow of measures in terms of their Osterwalder–Schrader data which motivates a natural direct Hamiltonian renormalisation scheme.

On Radiative Decay of Heavy Vector Mesons <i>V</i> → <i>Pγ</i> in the Scalar Strong Interaction Hadron Theory

Radiative decay of heavy ground state vector meson V → Pγ is treated semi-classically in the scalar strong interaction hadron theory. The treatment successfully employs the new wave function of the vector meson updated here. The ratio of the available J/ψ and decay rates agrees with prediction. The values of the predicted rates are also in order of magnitude agreement with measurements. These agreements are the only ones directly computed from a first principles’ theory.

Excited vector mesons: phenomenology and predictions for a yet unknown vector ss state with a mass of about 1.93 GeV

The firm understanding of standard quark-antiquark states (including excited states) is necessary to search for non-conventional mesons with the same quantum numbers. In this work, we study the phenomenology of two nonets of excited vector mesons, which predominantly correspond to radially excited vector mesons with quantum numbers n2S+1LJ = 23S1 and to orbitally excited vector mesons with quantum numbers n2S+1LJ = 13D1. We evaluate the decays of these mesons into two pseudoscalar mesons and into a pseudoscalar and a ground-state vector meson by making use of a relativistic quantum field theoretical model based on flavor symmetry. Moreover, we also study the radiative decays into a photon and a pseudoscalar meson by using vector meson dominance. We compare our results to the PDG and comment on open issues concerning the corresponding measured resonances. Within our approach, we are also able to make predictions for a not-yet discovered ss state in the n2S+1LJ = 13D1 nonet, which has a mass of about 1.93 GeV. This resonance can be searched in the upcoming GlueX and CLAS12 experiments which take place at the Jefferson Lab.

A new approach to continuous multi-scale analysis in nonrelativistic QED: ground states and photon number bounds for the spin-boson model with critical infrared singularity

We introduce a new method for the study of spectral problems in nonrelativistic quantum electrodynamics, NR QED. The method is based on the so-called Pizzo’s Method (Ann Henri Poincare 4(3):439–486, 2003) or multi-scale analysis. We use it to prove existence and uniqueness of ground-state eigenvalues for the spin-boson model with critical infrared behavior. Denoting by H the corresponding Hamiltonian, we construct its ground-state eigenvalue using a continuous family of infrared cutoff Hamiltonians \((H_t)_{t \ge 0}\) such that as the parameter t tends to infinity, the cutoff is removed. The continuous method we introduce in this paper enjoys many advantages (and it has no disadvantages) with respect to the discrete version (where the parameter t takes its values in a discrete set). The reason is that it is a natural extension of the discrete iteration method, and therefore, it incorporates at the same time both: tools from the discrete approach and techniques from the area of differential equations. Actually, in our proof the analysis of the cutoff Hamiltonians \((H_t)_{t \in [0, \infty )}\) is carried out with the help of our calculations and proofs in Bach et al. (J Math Anal Appl 453:773–797, 2017). However, our main argument borrows ideas from differential equations, more specifically Gronwall’s inequality. Furthermore, we prove that the expectation value of the photon number operator (\({\mathcal {N}}_\mathrm{ph}\)) on the ground state is bounded and, moreover, that the ground-state vector belongs to the domain of \({\mathcal {N}}^{1 -\epsilon }_\mathrm{ph}\), where \(\epsilon >0\) is as small as we want, depending on the coupling constant.

Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field.

In this work we analyze the ground-state properties of the s=1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field B_{x} and the strength of the next-nearest-neighbor interaction J_{2}, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and 〈2,2〉 phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the 〈2,2〉 phases is possibly of first order.