Baryon Loops Research Articles

Diagrammatic representation of scalar QCD and sign problem at nonzero chemical potential

We consider QCD at strong coupling with scalar quarks coupled to a chemical potential. Performing the link integrals we present a diagrammatic representation of the path integral weight. It is based on mesonic and baryonic building blocks, in close analogy to fermionic QCD. Likewise, the baryon loops are subject to a manifest conservation of the baryon number. The sign problem is expected to disappear in this representation and we do confirm this for three flavors, where a scalar baryon can be built and thus a dependence on the chemical potential occurs. For higher flavor number we analyse examples for a potential sign problem in the baryon sector and conjecture that all weights are positive upon exploring the current conservation of each flavor.

Electrical conductivity of hadronic matter from different possible mesonic and baryonic loops

Electromagnetic current-current correlators in pionic and nucleonic medium have been evaluated in the static limit to obtain electrical conductivities for pion and nucleon components respectively, where former decreases and latter one increases with the variation of temperature $T$ and baryon chemical potential $\mu_N$. Therefore, total electrical conductivity of pion and nucleon system exhibits a valley structure in the $T$-$\mu_N$ plane. To get non-divergent and finite values of correlators, finite thermal widths of medium constituents, pion and nucleon have been considered, where these thermal widths have been determined from the in-medium scattering probabilities of pion and nucleon with other mesonic and baryonic resonances, based on effective hadronic model. At $\mu_N=0$, the results of present work are more or less agrees with the results of earlier works and its finite $\mu_N$ extension show a decreasing nature of electrical conductivity for hadronic medium during spanning from freeze out line to quark-hadron transition line in $T$-$\mu_N$ plane.

Shear Viscosity of Pionic and Nucleonic Components from Their Different Possible Mesonic and Baryonic Thermal Fluctuations

Owing to the Kubo relation, the shear viscosities of pionic and nucleonic components have been evaluated from their corresponding retarded correlators of viscous stress tensor in the static limit, which become non-divergent only for the non-zero thermal widths of the constituent particles. In the real-time thermal field theory, the pion and nucleon thermal widths have respectively been obtained from the pion self-energy for different meson, baryon loops and the nucleon self-energy for different pion-baryon loops. We have found a non-monotonic momentum distributions of pion and nucleon thermal widths, which have been integrated out by their respective Bose-enhanced and Pauli-blocked phase space factors during evaluation of their shear viscosities. The viscosity to entropy density ratio for this mixed gas of pion-nucleon system decreases and approaches toward its lower bound as the temperature and baryon chemical potential increase within the relevant domain of hadronic matter.

Leading logarithms for the nucleon mass

Within the heavy baryon chiral perturbation theory approach, we have studied the leading logarithm behavior of the nucleon mass up to four-loop order exactly and we present some results up to six-loop order as well as an all-order conjecture. The same methods allow to calculate the main logarithm multiplying the terms with fractional powers of the quark mass. We calculate thus the coefficients of m2n+1log(n−1)⁡(μ2/m2) and m2n+2logn⁡(μ2/m2), with m the lowest-order pion mass. A side result is the leading divergence for a general heavy baryon loop integral.

Low mass enhanced probability of pion in hadronic matter due to its Landau cut contributions

In the real-time thermal field theory, the pion self-energy at finite temperature and density is evaluated where the different mesonic and baryonic loops are considered. The interactions of pion with the other mesons and baryons in the medium are governed by the effective hadronic Lagrangian densities whose effective strength of coupling constants have been determined from the experimental decay widths of the mesons and baryons. The detail branch cut structures of these different mesonic and baryonic loops are analyzed. The Landau cut contributions of different baryon and meson loops become only relevant around the pion pole and it is completely appeared in presence of medium. The in-medium spectral function of pion has been plotted for different values of temperature, baryon chemical potential as well as three momentum of the pion. A noticeable low mass probability in pion spectral function promise to contribute in the low mass dilepton enhancement via indirect modification of ρ self-energy for loop.

Analysis of ω self-energy at finite temperature and density in the real-time formalism

Using the real time formalism of field theory at finite temperature and density we have evaluated the in-medium ω self-energy from baryon and meson loops. We have analyzed in detail the discontinuities across the branch cuts of the self-energy function and obtained the imaginary part from the non-vanishing contributions in the cut regions. An extensive set of resonances have been considered in the baryon loops. Adding the meson loop contribution we obtain the full modified spectral function of the ω meson in a thermal gas of mesons, baryons and anti-baryons in equilibrium for several values of temperature and baryon chemical potential.

In-medium vector mesons and low mass lepton pairs from heavy ion collisions

The ρ and ω meson self-energy at finite temperature and baryon density have been analysed for an exhaustive set of mesonic and baryonic loops in the real time formulation of thermal field theory. The large enhancement of spectral strength below the nominal ρ mass is seen to cause a substantial enhancement in dilepton pair yield in this mass region. The integrated yield after space-time evolution using relativistic hydrodynamics with quark gluon plasma in the initial state leads to a very good agreement with the experimental data from In-In collisions obtained by the NA60 collaboration.

ρ self-energy at finite temperature and density in the real-time formalism

The ρ meson self-energy in nuclear matter from baryonic loops is analysed in the real-time formulation of field theory at finite temperature and density. The discontinuities across the branch cuts of the self-energy function are evaluated for an exhaustive set of resonances in the loops considering the fully relativistic thermal baryon propagator including anti-baryons. Numerical calculations show a significant broadening of the ρ spectral function coming from the Landau cut. Adding the contribution from mesonic loops, the full spectral function of the ρ in a thermal gas of mesons, baryons and anti-baryons in equilibrium is evaluated at various values of temperature and baryonic chemical potential.

On the role of vector mesons on the η → π0γγ decay width in meson-baryon chiral model

In 1979, it was shown by one of us (M.K.V.) that the contribution to the amplitude of this decay from diagrams with one baryon loop is equal to zero and contributions from diagrams with meson loops appear to be very small. However, pole diagrams with intermediate vector mesons were not considered there. Here, it is shown that the contributions of these pole diagrams dominate. The meson-baryon chiral model used here is compared with known quark chiral models. The obtained results are in satisfactory agreement with recent experimental data.

Anomalous Superfluidity in(2+1)-Dimensional Two-Color Lattice QCD

We study thermodynamics of strongly coupled lattice QCD with two colors of staggered fermions in 2+1 dimensions. The partition function of this model can be written elegantly as a statistical mechanics of dimers and baryon loops. The model is invariant under an SO(3) x U(1) symmetry. At low temperatures, we find evidence for superfluidity in the U(1) symmetry sector while the SO(3) symmetry remains unbroken. The finite temperature phase transition appears to belong to the Kosterlitz-Thouless universality class, but the superfluid density jump rho(s) (T(c)) at the critical temperature T(c) is anomalously higher than the normal value of 2T(c)/pi. We show that, by adding a small SO(3) symmetry breaking term to the model, the superfluid density jump returns to its normal value, implying that the extra symmetry causes anomalous superfluid behavior. Our results may be of interest to researchers studying superfluidity in spin-1 systems.

Modified loop expansion for nuclear matter in a chiral model.

We consider loop expansions for the chirally symmetric linear \ensuremath{\sigma} model. The conventional loop expansion is reviewed, and the tachyon problems due to the large attractive \ensuremath{\sigma}\ensuremath{\pi} and \ensuremath{\sigma}\ensuremath{\sigma} couplings are investigated. We then study a modified loop expansion that sums the repulsive baryon loops to all orders at each order in meson loops. Renormalizability is explicitly demonstrated to modified one-loop order, which corresponds to the relativistic random-phase approximation. We show that tachyons present in the conventional loop expansion are avoided to a large extent, but ghosts arise due to the unphysical behavior of the vacuum loops in this field theory that is not asymptotically free. Implications and possible solutions to this problem are discussed.

Yukawa theories as effective theories of quantum chromodynamics for a large number of colors

An effective theory for low-energy nuclear interactions is proposed, based on results obtained from the 1/${N}_{c}$ expansion of quantum chromodynamics. The Lagrangian is local in the meson sector, but in the baryon sector it is nonlocal both in the meson-baryon Yukawa coupling and in the baryon propagators. It satisfies an important consequence of the 1/${N}_{c}$ expansion, the suppression of baryon loops. Our findings are then shown to support the traditional approaches in nuclear physics and, more especially, the relativistic nuclear many-body theories at baryon-tree level.

On the predictive power of modern chiral lagrangians

The role of renormalization effects by one-meson loop diagrams with respect to quartic derivative couplings of modern chiral lagrangians is discussed for ππ-scattering and η′→η2π decay. Finally, some comments on the duality of quark and baryon loops are given.

The baryon loop tension from continuum QCD

The energy of three static widely separated quarks in a colour singlet state is computed by studying the large area behaviour of different baryon loops in continuum QCD. With the help of a sum rule like approach the corresponding string tensions are obtained in terms of the vacuum condensates. They can be interpreted as due to effective quark-quark forces of half the strength of the quark-antiquark forces, at least.

Baryonic loops and confinement in the three quark channel

The expectation value of three Wilson lines is used for exploring the confinement in the baryonic channel of static quarks. Preliminary results are in good agreement with the q q data.

Baryons and dual unitarization

Processes involving baryons are discussed in the scheme of dual unitarization. In particular, the topological expansion is generalized to any hadronic S-matrix elements involving baryons and/or mesons. Our expansion is based on a model for the baryon propagator, which is a set of three planar Feynman diagrams joined at a junction line. The resulting expansion is a double expansion in 1/ N ( N= the number of quark flavours) and in the number of baryon loops. Based on this, several new observations are made in phenomenological problems, and a unifying point of view is stressed. The scheme is evidently crossing invariant, and unitarity constraints are imposed order by order in 1/ N and in the baryon loop number.

The meson and the baryon in the one-loop dual model of the pomeron

In the lowest order dual loop perturbation theory the crossing and factorisation properties of the pomeron are considered. It is shown that the baryon loop is the necessary complement of the single crossed meson loop in building the low-energy pomeron. Recent experimental indications that in this energy region the pomeron is different in MM, MB and BB processes are naturally explained.

Kaon Partial-Conservation-of-Axial-Vector-Current Anomaly andKL→γγDecay

The low-energy theorem is derived which relates the invariant vertex function of KL→γγ to the corresponding function of 〈2γ|[Q56, Lw]|0〉, where it is assumed that Schwinger and seagull terms, if present, cancel against each other. A chiral Lagrangian model is studied which satisfies PCAC and which has an octet weak Lagrangian with [Q56, Lw]=0. In this model, the effective KL→γγ coupling constant produced by certain baryon loop graphs is found to remain finite as the momentum of the kaon goes to zero. This contradicts the low-energy theorem and indicates the failure of seagull and Schwinger terms to cancel. The effective coupling produced by this anomaly is estimated to give a rate roughly comparable to the experimental one. Implications for mesonic effective-Lagrangian studies of K decays are discussed.

Pion-pion scattering from an SU(3) × SU(3) invariant Lagrangian

Abstract We calculate the low energy pion-pion phase shifts from the SU(3) × SU(3)invariant meson-baryon Lagrangian in the one-loop approximation. The meson loop diagrams are evaluated using superpropagator methods and symmetry arguments. The derivative nature of the meson-baryon coupling leads to one undetermined subtraction constant in the baryon loop amplitudes which is fixed by the requirement that the p-wave exhibits a resonance at the ρ meson mass. Taking the D / F ratio for the meson-baryon coupling from experiment we derive I = 0 and I = 2 s-waves in good agreement with the available data.

Perturbation Theory of Pion Decays

To first order in the pion-baryon couplings, the Feynman diagram for the decay $\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\nu}$ essentially consists of a baryon loop. By requiring it to be finite, one obtains a linear relation between the coupling constants ${g}_{\ensuremath{\pi}N}$, ${g}_{\ensuremath{\pi}\ensuremath{\Sigma}}$, and ${g}_{\ensuremath{\pi}\ensuremath{\Xi}}$. (The coupling to the $\ensuremath{\Lambda}\ensuremath{\Sigma}$ system plays no role here.) A very simple choice of values is conjectured, which produces good agreement with experiment for both the charged and neutral pion decays, when these are calculated to first order in ${g}_{\ensuremath{\pi}N}$.