Bound State Mass Research Articles

Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks

Two newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is M=m1+m2+C′+βxx+c0x\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M=m_1+m_2+C'+\\beta _x\\sqrt{x+c_{0x}}$$\\end{document}, (x=l,nr)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(x=l,\\,n_r)$$\\end{document}. Another reads M=m1+C′+βx2(x+c0x)+43πβxm23/2(x+c0x)1/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M=m_1+C'+\\sqrt{\\beta _x^2(x+c_{0x})+\\frac{4}{3}\\sqrt{{\\pi }{\\beta _x}}m^{3/2}_2(x+c_{0x})^{1/4}}$$\\end{document}. M is the bound state mass. m1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_1$$\\end{document} and m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_2$$\\end{document} are the masses of the heavy constituent and the light constituent, respectively. l is the orbital angular momentum and nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_r$$\\end{document} is the radial quantum number. βx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _x$$\\end{document} and c0x\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{0x}$$\\end{document} are fitted. m1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_1$$\\end{document}, m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_2$$\\end{document} and C′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C'$$\\end{document} are input parameters. These two formulas consider both of the masses of heavy constituent and light constituent. We find that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks satisfy these two formulas. When applying the first formula, the heavy-light systems satisfy the universal description irrespective of both of the masses of the light constituents and the heavy constituent. When using the second relation, the heavy-light systems satisfy the universal description irrespective of the mass of the heavy constituent. The fitted slopes differ distinctively for the heavy-light mesons, baryons and tetraquarks, respectively. When employing the first relation, the average values of cfnr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{fn_r}$$\\end{document} (cfl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{fl}$$\\end{document}) are 1.026, 0.794 and 0.553 (1.026, 0.749 and 0.579) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Upon application of the second relation, the mean values of cfnr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{fn_r}$$\\end{document} (cfl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{fl}$$\\end{document}) are 1.108, 0.896 and 0.647 (1.114, 0.855 and 0.676) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Moreover, the fitted results show that the Regge trajectories for the heavy-light systems are concave downwards in the (M2,nr)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(M^2,\\,n_r)$$\\end{document} and (M2,l)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(M^2,\\,l)$$\\end{document} planes.

Evolution of pion mass with temperature

We study the evolution of light quarks with isospin symmetry and the pion masses in the presence of a thermal bath and study their temperature dependence. In addition, we analyze the inclusion of a coupling with temperature dependence. We attempt to study the dissolution of bound-states at temperatures higher than the critical temperature, but we found that the model shows that the bound-state's mass increases. We base our study on a momentum-independent symmetry-preserving truncation scheme contact interaction in the Schwinger-Dyson equations framework.

Mass Spectra of Mesonic Molecules at Finite Temperature

At a finite temperature, exotic hadronic systems, mass spectrum was studied using the quark structure and the radial Schrödinger equation with the Cornell interaction potential representing the hadronic interaction. The projective unitary representation has been used in the study of hadronic ground states in physics. A relativistic bound state's mass spectrum with temperature dependence is shown to have a unique feature. The resulting values are compared to experimental and theoretical values, and the study showed a high level of conformity with additional values wherever feasible.

Three-boson stability for boosted interactions towards the zero-range limit

We study the three-boson bound-state mass and wave functions for ground and excited states within the three-body relativistic framework with Kamada and Glöcke boosted potentials in the limit of a zero-range interaction. We adopt a nonrelativistic short-range separable potential, with Yamaguchi and Gaussian form factors, and drive them towards the zero-range limit by letting the form factors' momentum scales go to large values while keeping the two-body binding fixed. We show that the three-boson relativistic masses and wave functions are model-independent towards the zero-range limit, and the Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov effect. Furthermore, the stability in the zero-range limit is a result of the reduction of boosted potential with the increase of the virtual pair center of mass momentum within the three-boson system. Finally, we compare the present results with Light-Front and Euclidean calculations.

Gauge/Gravity Dynamics for Composite Higgs Models and the Top Mass.

We provide gauge/gravity dual descriptions of explicit realizations of the strong coupling sector of composite Higgs models using insights from nonconformal examples of the AdS/CFT correspondence. We calculate particle masses and pion decay constants for proposed Sp(4) and SU(4) gauge theories, where there is the best lattice data for comparison. Our results compare favorably to lattice studies and go beyond those due to a greater flexibility in choosing the fermion content. That content changes the running dynamics and its choice can lead to sizable changes in the bound state masses. We describe top partners by a dual fermionic field in the bulk. Including suitable higher dimension operators can ensure a top mass consistent with the standard model.

Quarks and light (pseudo-)scalar mesons at finite chemical potential

We investigate the properties of light scalar and pseudoscalar mesons at finite (light) quark chemical potential. To this end we solve a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators in Landau-gauge QCD and extend earlier results for $ N_{\mathrm{f}} = 2+1$ dynamical quark flavors to finite chemical potential at zero temperature. We then determine the meson bound state masses, wave functions, and decay constants for chemical potentials below the first-order phase transition from their homogeneous Bethe-Salpeter equation. We study the changes in the quark dressing functions and Bethe-Salpeter wave functions with chemical potential. In particular, we trace charge-conjugation parity breaking. Furthermore, we confirm the validity of the Silver-Blaze property: all dependencies of colored quantities on chemical potential cancel out in observables and we observe constant masses and decay constants up to and into the coexistence region of the first-order chiral phase transition.

Nonperturbative Functional Renormalization-Group Approach to the Sine-Gordon Model and the Lukyanov-Zamolodchikov Conjecture.

We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value ⟨e^{(i/2)nβφ}⟩ of the exponential fields in the massive phase (n is integer and 2π/β denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01.

Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions

The quantum Ising chain with the interaction decaying as a power law $1/r^{1+\sigma}$ of the distance between spins $r$ was investigated numerically. A particular attention was paid to the low-energy spectrum, namely, the single-magnon and two-magnon-bound-state masses, $m_{1,2}$, respectively, in the ordered phase. It is anticipated that for each $\sigma$, the scaled bound-state mass $m_2/m_1$ should take a universal constant (critical amplitude ratio) in the vicinity of the critical point. In this paper, we calculated the amplitude ratio $m_2/m_1$ with the exact diagonalization method, which yields the spectral information such as $m_{1,2}$ directly. As a result, we found that the scaled mass $m_2/m_1$ exhibits a non-monotonic dependence on $\sigma$; that is, the bound state is stabilized by an intermediate value of $\sigma$. Such a feature is accordant with a recent observation based on the non-perturbative-renormalization-group method.

Goldstonic pseudoscalar mesons in Bethe–Salpeter-inspired setting

For a two-particle bound-state equation closer to its Bethe–Salpeter origins than Salpeter’s equation, with effective interaction kernel deliberately forged such as to ensure, in the limit of zero mass of the bound-state constituents, the vanishing of the arising bound-state mass, we scrutinize the emerging features of the lightest pseudoscalar mesons for their agreement with the behavior predicted by a generalization of the Gell-Mann–Oakes–Renner relation.

Analytic properties of the quark propagator from an effective infrared interaction model

In this paper, I investigate the analytic properties of the quark propagator Dyson-Schwinger equation (DSE) in the Landau gauge. In the quark self-energy, the combined gluon propagator and quark-gluon vertex is modeled by an effective interaction (the so-called Maris-Tandy interaction), where the ultraviolet term is neglected. This renders the loop integrand of the quark self-energy analytic on the cut plane $\ensuremath{-}\ensuremath{\pi}<arg(x)<\ensuremath{\pi}$ of the square of the external momentum. Exploiting the simplicity of the truncation, I study solutions of the quark propagator in the domain $x\ensuremath{\in}[\ensuremath{-}5.1,0]\phantom{\rule{0.16em}{0ex}}{\text{GeV}}^{2}\ifmmode\times\else\texttimes\fi{}i[0,10.2]\phantom{\rule{0.16em}{0ex}}{\text{GeV}}^{2}$. Because of a complex conjugation symmetry, this region fully covers the parabolic integration domain for Bethe-Salpeter equations (BSEs) for bound state masses of up to 4.5 GeV. Employing a novel numerical technique that is based on highly parallel computation on graphics processing units (GPUs), I extract more than 6500 poles in this region, which arise as the bare quark mass is varied over a wide range of closely spaced values. The poles are grouped in 23 individual trajectories that capture the movement of the poles in the complex region as the bare mass is varied. The raw data of the pole locations and residues is provided as Supplemental Material, which can be used to parametrize solutions of the complex quark propagator for a wide range of bare mass values and for large bound-state masses. This study is a first step towards an extension of previous work on the analytic continuation of perturbative one-loop integrals, with the long-term goal of establishing a framework that allows for the numerical extraction of the analytic properties of the quark propagator with a truncation that extends beyond the rainbow by making adequate adjustments in the contour of the radial integration of the quark self-energy.

F(750), we miss you as bound state of 6 top and 6 antitop

We collect and estimate support for our long speculated “multiple point principle”[Formula: see text] saying that there should be several vacua all having (compared to the scales of high energy physics) very low energy densities. In pure Standard Model, we suggest there being three “multiple point principle” low energy density vacua, “present,” “condensate” and “high field” vacuum. We fit the mass in our picture of a long speculated bound state[Formula: see text] of 6 top and 6 antitop quarks in three quite independent ways and get remarkably within our crude accuracy the same mass in all three fits! The new point of the present paper is to estimate the bound state mass in what we could call a bag-model estimation. The two other fits, which we review, obtain the mass of the bound state by fitting to the multiple point principle prediction of degenerate vacua. Our remarkable agreement of our three mass-fits can be interpreted to mean that we have calculated at the end the energy densities of the two extra speculated vacua and found that they are indeed very small. Unfortunately, the recently much discussed statistical fluctuation peak F(750)[Formula: see text] that has now been revealed to be just a fluctuation, very accidentally matches our fitted mass of the bound state remarkably well with the mass of this fluctuation 750 GeV.

Diphoton decay of the Higgs boson and new bound states of top and antitop quarks

We consider the constraints, provided by the LHC results on Higgs boson decay into 2 photons and its production via gluon fusion, on the previously proposed Standard Model (SM) strongly bound state S of six top quarks and six antitop quarks. A correlation is predicted between the ratios [Formula: see text] and [Formula: see text] of the Higgs diphoton decay and gluon production amplitudes, respectively to their SM values. We estimate the contribution to these amplitudes from one-loop diagrams involving the 12 quark bound state S and related excited states using an atomic physics based model. We find two regions of parameter space consistent with the ATLAS and CMS data on [Formula: see text] at the three sigma level: a region close to the SM values [Formula: see text] with the mass of the bound state [Formula: see text][Formula: see text]GeV and a region with [Formula: see text] corresponding to a bound state mass of [Formula: see text][Formula: see text]GeV.

Massive holographic QCD in the Veneziano limit

QCD at finite, flavor independent quark mass is analyzed by using bottom-up holography in the Veneziano limit, where the backreaction of quarks to the gluon dynamics is fully included. The dependence on the quark mass of observables such as the bound state masses, the chiral condensate, the S-parameter, and the critical temperatures is studied. Many of the results are argued to be universal, i.e., independent of the details of the holographic model, and compared to explicit computations in the V-QCD models. The effect of adding four-fermion operators in QCD is also discussed.

Electromagnetic and gravitational form factors in simulated QED and Yukawa model

The light-cone Fock state representation of composite systems has a number of remarkable properties and for systems such as hadrons they have exact representation for angular momentum, energy–momentum tensor. We investigate the electromagnetic and gravitational form factors with zero momentum transfer in Quantum Electrodynamics (QED) and Yukawa theory. To improve the convergence near the end points of x qualitatively as well as to check the consistency of the model, we differentiate the wave function w.r.t. bound state mass. We test the behavior of the anomalous gravitomagnetic moment, which follows directly from the Lorentz boost properties of the light-cone Fock representation, for the simulated model as well as the Yukawa model. We also discuss the Pauli form factor obtained from the spin-flip matrix element.

Integral representations combining ladders and crossed-ladders

We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the "half-ladder" with N rungs in x - space (iii) the four-point ladder with N rungs in x - space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.

Present Status of the Bethe–Salpeter Approach in Minkowski Space

Recently developed methods allowing to find the solutions of the Bethe–Salpeter equations in Minkowski space, both for the bound and scattering states, are reviewed. For the bound states, one obtains the bound state mass and the corresponding BS amplitude. For the scattering states, the phase shifts (complex above the meson creation threshold) and the half-off-shell BS amplitude are found. Using these solutions, the elastic and transition electromagnetic form factors are calculated.

Dynamic AdS/QCD and the spectrum of walking gauge theories

We present a simple AdS/QCD model in which the formation of the chiral condensate is dynamically determined. The gauge dynamics is input through the running of the quark bilinear's anomalous dimension, gamma. The condensate provides a dynamically generated infra-red wall in the computation of mesonic bound state masses and decay constants. As an example, we use the model, with perturbative computations of the running of gamma, to study SU(3) gauge theory with a continuous number of quark flavours, Nf. We follow the behaviour of the spectrum as we approach the conformal window through a walking gauge theory regime. We show such walking theories display a BKT phase transition, with Miransky scaling, as one approaches the edge of the conformal window at the critical value of Nf. We show that these walking theories possess an enhanced quark condensate, a light Higgs like excitation and argue that the non-perturbative contribution to S falls to zero. We also study the deformation of the BKT transition when the quarks have a current mass which may be of use for understanding lattice simulations of walking theories.

Towards a Born term for hadrons

We study bound states of Abelian gauge theory in $D=1+1$ dimensions using an equal-time, Poincar\'e-covariant framework. The normalization of the linear confining potential is determined by a boundary condition in the solution of Gauss' law for the instantaneous ${A}^{0}$ field. As in the case of the Dirac equation, the norm of the relativistic fermion-antifermion ($f\overline{f}$) wave functions gives inclusive particle densities. However, while the Dirac spectrum is known to be continuous we find that regular $f\overline{f}$ solutions exist only for discrete bound-state masses. The $f\overline{f}$ wave functions are consistent with the parton picture when the kinetic energy of the fermions is large compared to the binding potential. We verify that the electromagnetic form factors of the bound states are gauge invariant and calculate the parton distributions from the transition form factors in the Bjorken limit. For relativistic states we find a large sea contribution at low ${x}_{Bj}$. Since the potential is independent of the gauge coupling the bound states may serve as ``Born terms'' in a perturbative expansion, in analogy to the usual plane wave in and out states.

Strong binding and shrinkage of single and double <span style="text-decoration: overline;"><i>K</i></span> nuclear systems (<i>K</i><sup>−</sup><i>pp</i>, <i>K</i><sup>−</sup><i>ppn</i>, <i>K</i><sup>−</sup><i>K</i><sup>−</sup><i>p</i> and <i>K</i><sup>−</sup><i>K</i><sup>−</sup><i>pp</i>) predicted by Faddeev-Yakubovsky calculations

Non-relativistic Faddeev and Faddeev-Yakubovsky calculations were made for K−pp, K−ppn, K−K−p and K−K−pp kaonic nuclear clusters, where the quasi bound states were treated as bound states by employing real separable potential models for the K−-K− and the K−-nucleon interactions as well as for the nucleon-nucleon interaction. The binding energies and spatial shrinkages of these states, obtained for various values of the interaction, were found to increase rapidly with the interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the interaction in the dense nuclear medium are given. Using the Λ(1405) ansatz with a PDG mass of 1405 MeV/c2 for K−p, the following ground-state binding energies together with the wave functions were obtained: 51.5 MeV (K−pp), 69 MeV (K−ppn), 30.4 MeV (K−K−p) and 93 MeV (K−K−pp), which are in good agreement with previous results of variational calculation based on the Akaishi-Yamazaki coupled-channel potential. The K−K−pp state has a significantly increased density where the two nucleons are located very close to each other, in spite of the inner NN repulsion. Relativistic corrections on the calculated non-relativistic results indicate substantial lowering of the bound-state masses, especially of K−K−pp, toward the kaon condensation regime. The fact that the recently observed binding energy of K−pp is much larger (by a factor of 2) than the originally predicted one may infer an enhancement of the interaction in dense nuclei by about 25% possibly due to chiral symmetry restoration. In this respect some qualitative accounts are given based on “clearing QCD vacuum” model of Brown, Kubodera and Rho.

LHC would-beγγexcess as a nonperturbative effect of the electroweak interaction

The recently reported would-be excess at 125 GeV in invariant mass distribution of $\ensuremath{\gamma}\ensuremath{\gamma}$ and of ${l}^{+}{l}^{+}{l}^{\ensuremath{-}}{l}^{\ensuremath{-}}$ obtained in the course of the Higgs boson search at LHC is tentatively interpreted as a scalar bound state of two $W$. Nonperturbative effects of electroweak interactions obtained by the application of the Bogoliubov compensation approach lead to such bound states due to the existence of anomalous three-boson gauge-invariant effective interactions. The application of this scheme gives satisfactory agreement with existing data without any adjusting parameter except for the bound state mass 125 GeV, while $\ensuremath{\sigma}\mathrm{BR}$ for $\ensuremath{\gamma}\ensuremath{\gamma}$ resonance is predicted to be twice as much as the value for the standard model Higgs. The decay channel $\ensuremath{\gamma}{l}^{+}{l}^{\ensuremath{-}}$ and an effect in $3\ensuremath{\gamma}$ production may serve as decisive checks of the interpretation.