We calculate the light quark condensate, the strange quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($χ$PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $χ$PT effective potential and condensates can be mapped onto two-flavor $χ$PT ones by integrating out mesons with strange quark content (kaons and eta), with renormalized couplings. We compare the results for the light quark and pion condensates at finite pseudoscalar source with ($2+1$)-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.
We study the axial-vector form factor of the nucleons at constant and homogenous isospin chemical potential using holographic QCD. Nucleon mass splitting in such isospin medium is taken into account. According to AdS/CFT correspondence, the critical value of the isospin chemical potential μ_I equals to UV- boundary value of the time component of the bulk gauge field. We calculate the axial-vector form factor of the proton and neutron in such background in the framework of the hard-wall model and plot the form factors for the isospin chemical potential critical value μ_I=m_π.
The predictions of an isospin model are compared with the branching ratios of the 5 and 6 pion decays of the tau lepton. In both cases, the isospin model suggests that the tau favours decays in which there is an omega resonance. Recent measurements of such tau decays confirm this hypothesis. If the decay of the tau to 7 pions also proceeds through an intermediate omega, then the isospin model predicts that the branching ratio of the tau to seven charged pions should be small when compared with other 7 pion decays. New limits on this mode appear to support this argument.
The Finslerian curvature is introduced in the three-dimensional isospin space, suggesting that the isospin-pion field transforms according to non-linear Finslerian invariance transformations. The fundamental non-linear realization is associated with the pion field triplet. The Finslerian Lagrangian, as well as the implied pion-field selfinteraction, involves the first but no higher derivatives of the pion field. While the invariance transformations are now nonlinear, the conservation laws are still meaningful and sufficient to get the conservations for the energy-momentum and charges. The Fins…
By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials, taking also into account imaginary quark chemical potential. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that the expectation value becomes zero for the finite current-quark mass, whereas the Banks-Casher relation is obtained…
We investigate the isospin chemical potential effect in the frame of SU(2) Nambu-Jona-Lasinio model. When the isospin chemical potential is less than the vacuum pion mass, the phase structure with two chiral phase transition lines does not happen due to $U_A(1)$ breaking of QCD. When the isospin chemical potential is larger than the vacuum pion mass, the ground state of the system is a Bose-Einstein condensate of charged pions.
We examine the isospin violation in the timelike pion form factor near threshold at next-to-leading order in the chiral expansion using the techniques of Chiral Perturbation Theory. This next-to-leading order contribution contains the first nonvanishing isospin violation. This isospin violation is found to be very small near threshold. In particular, the isospin violation at threshold is found to be of order 10^-4, which should be compared with the few percent level seen in the vector meson resonance region.
We investigate the dispersive contribution by radiative processes such as (pi- proton to neutron gamma) and (pi- proton to Delta gamma) to the pion-nucleon scattering lengths of charged pions in the heavy baryon limit. They give a large isospin violating contribution in the corresponding isoscalar scattering length, but only a small violation in the isovector one. These terms contribute 6.3(3)% to the 1s level shift of pionic hydrogen and give a chiral constant F_pi^2f_1=-25.8(8) MeV.
The final state of the decay D0 --> pi+ pi- pi0 is analyzed in terms of isospin eigenstates. It is shown that the final state is dominated by the isospin-0 component. This suggests that isospin considerations may provide insight into this and perhaps other $\Dz$-meson decay. We also discuss the isospin nature of the nonresonant contribution in the decay, which can be further understood by studying the decay D0 --> pi0 pi0 pi0.
We study the posibility of large isospin fluctuations in high-energy heavy-ion collisions by assuming that pions are produced semiclassically both directly and in pairs through the isovector channel. The leading-particle effect and the factorization property of the scattering amplitude in the impact parameter space are used to define the classical pion field. In terms of the joint probability function $P_{II_{3}}(n_{0},n_{\_})$ for producing $n_{0}$ neutral and $n_{\_}$ negative pions from a definite isospin state $II_{3}$ of the incoming leading-particle system we calculate the two pion corre…
We evaluate the isospin breaking corrections to the scattering amplitude π^- K^+ -> π^- K^+ at threshold in the framework of chiral perturbation theory. This channel is of particular interest for the strong 2S-2P energy level shift in pion-kaon bound states. While a prediction of this level shift is hampered by a large uncertainty in the isoscalar scattering length, we find only a moderate uncertainty of about 3% in the electromagnetic corrections which are relevant for the extraction of the scattering lengths from experiment
We use chiral perturbation theory to evaluate the scattering amplitude for the process Pi^+ K^- to Pi^+ K^- at leading and next-to-leading orders in the chiral counting and in the presence of isospin breaking effects. We also discuss the influence of the latter on the combination of the S-wave Pi K scattering lengths which is relevant for the 2S - 2P energy levels shift of K Pi atoms.
We study possible so far unaccounted isospin breaking effects in the relation between the pion form factor as determined in e^+e^- experiments and the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the tau--decay spectra. In fact the observed 10% discrepancy in the respective pion form factors may be explained by the isospin breaking which is due to the difference between masses and widths of the charged and neutral rho mesons. Since the hadronic contribution to the muon anomalous magnetic moment can be calculated directly in ter…
It is demonstrated that there is a dynamic isospin breaking effect in the near threshold $γ^{*} N\to πN$ reaction due to the mass difference of the up and down quarks, which also causes isospin breaking in the $πN$ system. The photopion reaction is affected through final state $πN$ interactions (formally implemented by unitarity and time reversal invariance). It is also demonstrated that the near threshold $γ\vec{N} \to πN$ reaction is a practical reaction to measure isospin breaking in the $πN$ system, which was first predicted by Weinberg about 20 years ago but has never been experimentally …
A model for the gamma p ----> pion+ pion- p reaction developed earlier is extended to account for all isospin channels. The model includes N, Delta(1232), N^*(1440) and N^*(1520) as intermediate baryonic states and the rho-meson as an intermediate two pion resonance. Although many terms contribute to the cross section, some channels exhibit particular sensitivity to certain mechanisms of resonance excitation or decay and the reactions provide novel information on such mechanisms. In particular the gamma N ----> N^*(1520) ----> Delta(1232) pion process affects all the channels and is a key ingr…
The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional spacetime are investigated in the presence of the isospin $μ_I$ as well as quark number $μ$ chemical potentials both at zero and nonzero temperatures. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with an infinite number of colored quarks. In the plane of parameters $μ_I,μ$ a rather rich phase structure is found, which contains phases with and without pion condensation. Moreover, we have found a great variety of one-quark excitations of these phases, including gapless and gapped quasipa…
The pion superfluidity phase transition at $T-μ_I$ and $μ_q-μ_I$ planes are studied in the framework of Dyson-Schwinger equations. The rainbow truncation and Gaussian effective gluon propagator are employed to calculate pion condensate, $\langleπ\rangle$, as a function of $μ_I$ at finite $T$ and $μ_q$. At $T=(0, 80, 113, 120)$~MeV, the $\langleπ\rangle$ keeps zero when $μ_I$ is less than a critical value $μ_{Ic}(T)$. The $\langleπ\rangle$ at $T=113$~MeV agrees with the lattice QCD result. At the $T-μ_I$ plane, the pion superfluid phase appears at low temperature and high isospin chemical poten…
We analyze the existence of localized finite energy topological excitations on top of the perturbative pion vacuum within the Skyrme model at finite isospin chemical potential and finite pion mass. We show that there is a critical isospin chemical potential $μ_I^c$ above which such solutions cease to exist. We find that $μ_I^c$ is closely related to the value of the pion mass. In particular for vanishing pion mass we obtain $μ_I^c=0$ in contradiction with some results recently reported in the literature. We also find that below $\mui^c$ the skyrmion mass and baryon radius show, at least for th…
The thermal and density corrections, in terms of the isospin chemical potential $\mui $, to the mass of the pions, the decay constant and different condensates are studied in the framework of the SU(2) low energy effective chiral lagrangian at finite temperature in the two phases: The first phase $|\mui|<m$ and the second phase $|\mui|>m$, being $m$ the tree-level pion mass. As a function of temperature for $\mui =0$, the mass remains quite stable, starting to grow for very high values of $T$, confirming previous results. However, there are interesting corrections to the mass when both effects…
The density corrections, in terms of the isospin chemical potential $μ_I$, to the mass of the pions are studied in the framework of the SU(2) low energy effective chiral lagrangian. The pion decay constant $f_π(T, μ_{I})$ is also analized. As a function of temperature for $μ_I =0$, the mass remains quite stable, starting to grow for very high values of $T$, confirming previous results. However, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the $π^{\pm}$ should condensate when $μ_{I} = \mp m_π…
We discuss the electromagnetic corrections to the pion-nucleon scattering lengths generated by minimal e. m. coupling from a knowledge of the low energy expansion of the pion-nucleon elastic scattering amplitude as well as from the nucleon and delta pole terms, all a consequence of purely strong interactions. We assume the heavy baryon limit; the e.m. and axial form factors and the masses are used with their empirical values, such that there is no free parameter. The different terms have a clear physical and intuitive origin. In particular, a large isospin breaking contribution to the isoscala…
We study the thermodynamics and the susceptibilities of quark matter in the framework of two-flavor Nambu-Jona-Lasinio model at finite isospin chemical potential and temperature. Isospin number density, normalized energy density and trace anomaly are shown to be in good agreement with the available lattice data as well as with the results from chiral perturbation theory at zero temperature. We also study how susceptibilities depend on the isospin chemical potential and on temperature. We find a peak for the chiral, pion, and isospin susceptibilities at the critical isospin chemical potential, …
We summarize main points of our recent work where we studied the pion condensation for non-zero isospin chemical potential within a holographic QCD model. We confirmed that the second order phase transition with the mean field exponent occurs when the isospin chemical potential $μ_I$ exceed the pion mass, which is consistent with the result obtained by the chiral effective Lagrangian at $O(p^2)$. We find that a deviation for large $μ_I$ region can be understood as a higher order effects in the chiral effective Lagrangian. Our result shows that the chiral condensate defined by $\tildeσ \equiv \…
In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We co…
The Nambu Jona-Lasinio model with a Polyakov loop is extended to finite isospin chemical potential case, which is characterized by simultaneous coupling of pion condensate, chiral condensate and Polyakov loop. The pion condensate, chiral condensate and the Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting $(T,μ_I)$ phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed and …
The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form factor of the nucleon cannot be accessed through threshold pion electroproduction is unfounded.
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.
We study the pion condensation at finite isospin chemical potential using a holographic QCD model. By solving the equations of motion for the pion fields together with those for the iso-singlet scalar and iso-triplet vector meson fields, we show that the phase transition from the normal phase to the pion condensation phase is second order with the mean field exponent, and that the critical value of the isospin chemical potential $μ_I$ is equal to the pion mass, consistently with the result obtained by the chiral effective Lagrangian at $O(p^2)$. For higher chemical potential, we find a deviati…
Isospin breaking in the $K_{\ell 4}$ form factors induced by the difference between charged and neutral pion masses is discussed within a framework built on suitably subtracted dispersion representations. The $K_{\ell 4}$ form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the $K^\pm\toπ^+π^- e^\pm ν_e$ channel are presented, allowing one to connect the difference of form-factor phase shifts mea…
The correlations between a $B$ meson and a pion produced nearby in phase space should respect isospin reflection symmetry $I_3 \to -I_3$. Thus, one generally expects similar $π^+ B^0$ and $π^- B^+$ correlations (non-exotic channels), and similar $π^- B^0$ and $π^+ B^+$ correlations (exotic channels). Exceptions include (a) fragmentation processes involving exchange of quarks with the producing system, (b) misidentification of charged kaons as charged pions, and (c) effects of decay products of the associated $\overline{B}$. All of these can affect the apparent signal for correlations of charge…
The density corrections, in terms of the isospin chemical potential $μ_I$, to the mass of the pions are investigated in the framework of the SU(2) low energy effective chiral invariant lagrangian. As a function of temperature and $μ_I =0$, the mass remains quite stable, starting to grow for very high values of $T$, confirming previous results. However, the dependence for a non-vanishing chemical potential turns out to be much more dramatic. In particular, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero tem…
We construct the complete effective chiral pion-nucleon Lagrangian in the presence of virtual photons to one loop. As an application, we consider strong and electromagnetic isospin violation for scattering of neutral pions off nucleons. We show that for the scattering lengths these isospin violating terms are of the same size as the purely hadronic ones. We also analyze isospin-violating effects for the $σ$--term. These can be as large as 10% for the absolute value but are negligible for the shift to the Cheng-Dashen point.
Isospin density and thermal corrections for several condensates are discussed, at the one-loop level, in the frame of chiral dynamics with pionic degrees of freedom. The evolution of such objects give an additional insight into the condensed-pion phase transition, that occurs basically when $|\mui|>m_π$, being $|\mui|$ the isospin chemical potential. Calculations are done in both phases, showing a good agreement with lattice results for such condensates.
We perform a calculation of the isospin and hypercharge axialvector current propagators to two loops in SU(3)xSU(3) chiral perturbation theory. A large number of order p^6 divergent counterterms are fixed, and complete two-loop renormalized expressions for the pion and eta masses and decay constants are given. The calculated isospin and hypercharge axialvector polarization functions are used as input in new chiral sum rules, valid to second order in the light quark masses. Some phenomenological implications of these sum rules are considered.
The isospin breaking in the nucleon isovector axial charge, $g_A^3$, are calculated within the external field QCD sum-rule approach. The isospin violations arising from the difference in up and down current quark masses and in up and down quark condensates are included; electromagnetic effects are not considered. We find $δg^3_A/g^3_A \approx (0.5-1.0)\times 10^{-2}$, where $δg^3_A = (g^3_A)_p + (g^3_A)_n$ and $ g^3_A = [(g^3_A)_p - (g^3_A)_n]/2$. Using the Goldberger-Treiman relation, we also obtain an estimate of the isospin breaking in the pion-nucleon coupling constant, $(g_{ppπ_0}-g_{nnπ_…
We revisit the QCD sum-rule treatment of the isospin-breaking axial correlator in light of the recent claim that a previous treatment produced results incompatible with known chiral constraints. The source of the error in the previous analysis is identified, and a corrected version of the sum-rule treatment obtained. It is then shown that, using input from chiral perturbation theory, one may use the resulting sum rule to extract information on the leading chiral behavior of isospin-breaking parameters associated with the coupling of excited pseudoscalar resonances to the axial currents. A rath…
We present an analysis of isospin-breaking effects in threshold pion-nucleon scattering due to the light quark mass difference and the dominant virtual photon effects. We discuss the deviation from various relations, which are exact in the isospin limit. The size of the isospin-violating effects in the relations involving the isovector $πN$ amplitudes is typically of the order of one percent. We also find a new remarkably large effect $(\sim 40%)$ in an isoscalar triangle relation connecting the charged and neutral pion scattering off protons.
We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field. It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors. Within this framework we obtain a general expression for the weak decay $π^- \to l\,\barν_l$ and discuss the corresponding limits of strong and weak external magnetic fields.
We show that a recent claim (H.Haberzettl, Phys. Rev. Lett. 85 (2000) 3576) that one cannot extract the nucleon weak axial form factor G_A (t) from charged pion threshold electroproduction is incorrect. Thus previous calculations remain valid and threshold charged pion electroproduction experiments can indeed be used to determine G_A (t), and they should certainly be pursued.
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory. The so-called triangle relation is found to be violated by about 1.5 %. We encounter a substantial isospin-breaking correction to neutral-pion-nucleon scattering beyond Weinberg's prediction due to a cusp effect. Finally, the application to hadronic atoms is briefly discussed.
Classical considerations suggest that the probability distribution $P(R)$, where $R$ is the ratio of neutral pions to total pions emitted from a disoriented chiral condensate (which has been hypothesized to form in heavy ion reactions) is $R^{-1/2}/2$. Quantum mechanical isospin correlations between the condensate and the remainder of the system can alter this. Moments of the P(R) distribution can be expressed in terms of expectation values of $(I^2/N^2)^m$ where $I$ is the isospin carried by the condensate, $N$ is the number of pions emitted and m is an arbitrary integer. We find that the pro…
I discuss low-energy pion-nucleon scattering in the framework of chiral perturbation theory. I argue that using this theoretical method one is able to handle the in some cases tremendous experimental accuracy (for the low partial waves). I then show how strong and electromagnetic isospin violation can be treated simultaneously. Some first results for neutral pion scattering and the $σ$-term are given.
We discuss a connection between axial anomaly and polarized radiative processes. By comparison with the corresponding unpolarized cases, we consider some physical outputs for the $π^+$ and $Z^0$ polarized radiative decays. We analyse in detail the pattern of mass singularity cancellation.
Equation of state and electric (isospin) charge fluctuations are studied for matter composed of interacting pions. The pion matter is described by self interacting scalar fields via a $ϕ^4-ϕ^6$ type Lagrangian. The mean-field approximation is used, and interaction parameters are fixed by fitting lattice QCD results on the isospin density as a function of the isospin chemical potential at zero temperature. Two scenarios for fixing the model parameters -- with and without the first order phase transition -- are considered, both yielding a satisfactory description of the lattice data. Thermodynam…
We discuss electro-magnetic and weak production of pions on nucleons and show how results of experiments and their interpretation in terms of chiral quark models with explicit meson degrees of freedom combine to reveal the ground-state axial form factors and axial N-Delta transition amplitudes.
Charge and isospin event-by-event fluctuations in high-energy pp-collisions are predicted within the Unitary Eikonal Model, in particular the fluctuation patterns of the ratios of charged-to-charged and neutral-to-charged pions. These fluctuations are found to be sensitive to the presence of unstable resonances, such as $ρ$ and $ω$ mesons. We predict that the charge-fluctuation observable $D_{UEM}$ should be restricted to the interval $8/3\le D_{UEM}\le 4$ depending on the $ρ/π$ production ratio. Also, the isospin fluctuations of the DCC-type of the ratio of neutral-to-charged pions are suppre…
We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler--Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off…
We investigate isospin breaking in low-energy pion-nucleon scattering in the framework of chiral perturbation theory. This work extends the systematic analysis of [1] to the energy range above threshold. Various relations, which identically vanish in the limit of isospin symmetry, are used to quantify isospin breaking effects. We study the energy dependence of the S- and P-wave projections of these ratios and find dramatic effects in the S-waves of those two relations which are given in terms of isoscalar quantities only. This effect drops rather quickly with growing center-of-mass energy.
It is shown that isospin-breaking corrections to the pion-deuteron scattering length can be very large, because of the vanishing of the isospin-symmetric contribution to this scattering length at leading order in chiral perturbation theory. We further demonstrate that these corrections can explain the bulk of the discrepancy between the recent experimental data on pionic hydrogen and pionic deuterium. We also give the first determination of the electromagnetic low-energy constant f1.
We study the two-color QCD matter within two fundamental quark flavors via both chiral perturbation theory and Nambu--Jona-Lasinio model methods. The effective Lagrangian described by low lying meson and baryon, i.e., diquark, is derived, where the excitations locate in the extended $\mathrm{SU}(4)$ flavor symmetry space. We determine the leading order terms on the dependence of the baryon and axial isospin densities. Then, the two-color NJL model is employed to run the numerical simulation and the phase diagram in the plane of $μ-ν_{5}$ is plotted.
Using a self-consistent delta-hole model the pion propagation in isospin asymmetric nuclear matter is studied. In neutron-rich matter, corresponding to heavy nuclei, a significant difference in positive and negative pion light-cone distributions is obtained leading to a nuclear enhancement of up antiquark distribution compared to the down antiquark one. This means that the sea-quark asymmetry in the free nucleon cannot be extracted model independently from an experiment on a neutron-rich nucleus.
The N-Delta axial form factors are determined from neutrino induced pion production ANL & BNL data by using a state of the art theoretical model, which accounts both for background mechanisms and deuteron effects. We find violations of the off diagonal Goldberger-Treiman relation at the level of 2 sigma which might have an impact in background calculations for T2K and MiniBooNE low energy neutrino oscillation precision experiments.
We analyze recent measurements of the nucleon quark sea isospin asymmetry in terms of the chiral quark model. The new measurements indicate that the SU(3) model with modest symmetry breaking and no $η'$ Goldstone boson gives a satisfactory description of data. We also discuss the matching parameter for the axial-vector current. Finally, we analyze the nucleon quark spin polarization measurements directly in the chiral quark model without using any SU(3) symmetry assumption on the hyperon axial-vector form factors. The new data indicate that the chiral quark model gives a remarkably good and co…
We calculate isospin breaking in pion-nucleon scattering in the threshold region in the framework of covariant baryon chiral perturbation theory. All effects due to quark mass differences as well as real and virtual photons are consistently included. As an application, we discuss the energy dependence of the triangle relation that connects elastic scattering on the proton pi+- p --> pi+- p with the charge exchange reaction pi- p --> pi0 n.
The isospin symmetry breakings of q{\bar q} are investigated in the QCD sum rule method. The electromagnetic effects are evaluated following the procedure requiring that the electromagnetic effects for charged meson be gauge invariant. We find that the electromagnetic effects are also dominant in the isospin violations of rho meson, which have been shown to be the case in the mass splittings of pions. The numerical results for the difference of pion decay constants and the masses of rho mesons are presented, which are consistent with the data.
In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $μ_{I5}$ promotes th…
We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study 1) the possibility of inhomogeneous chiral condensates and its competition with a homogeneous pion condensate in the $μ$--$μ_I$ plane at $T=0$ and 2) the phase diagram in the $μ_I$--$T$ plane. In the $μ$--$μ_I$ plane, we find that an inhomogeneous chiral condensate only exists for pion masses lower that 37.1 MeV and does not coexist with a homogeneous pion condensate. In the $μ_I$--$T$ plane, we find that the phase transition to a Bose-condensed phase is of second order for all value…
High energy reactions may produce a state around the collision point that is best described by a classical pion field. Such a field might be an isospin rotated vacuum of the chiral $σ$-model or, as discussed in this work, a solution of the equations of motion resultinng from the coupling of fields of this model to quarks produced in the collision. In such configurations all directions in isospin space are allowed leading to a sizable probability of events with, essentially, only charged particles (Centauros) or all neutral particles (anti-Centauros). (In more common statistical models of multi…
We present an analysis of QCD sum rules for pion form factor in next-to-leading order of perturbation theory for the case of axial-vector pion currents. The theoretical predictions for Q^2-dependence of pion form factor are in good agreement with available experimental data. It is shown, that NLO corrections are large in this case and should be taken into account in rigorous theoretical analysis.
