Pion Modes Research Articles

Kinetics of hydrodynamic pions in chiral perturbation theory

We determine the kinetic coefficients of ultrasoft pions using chiral perturbation theory at finite temperature close to the chiral limit. This is used to compute the axial charge diffusion and damping coefficients in the hydrodynamic effective theory for these pion waves. We show that to provide a leading order answer for these coefficients one needs to explore the dynamics of hard, soft, and ultrasoft pion modes, which are represented microscopically by the appropriate kinetic and hydrodynamic descriptions..

On pion mass and decay constant from theory

We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and lead to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine structure coupling at pionic energies. The pion decay constant 92 MeV results from comparing the fourth-order self-coupling in an effective pion field theory with the corresponding fourth-order term in the Higgs potential. We suggest analogies with the Goldberger-Treiman relation.

Pion family in AdS/QCD: The next generation from configurational entropy

The two flavour AdS/QCD, with chiral and gluon condensates, sets in the description of the pion family and its mass spectra. Using gravity-dilaton-gluon backgrounds, entropic Regge-like trajectories for the pion family are then derived. They relate the $\pi$ mesons underlying configurational entropy to both the pions excitation wave mode number and the pions experimental mass spectra, yielding a reliable prediction for the mass spectra of higher excitation pion modes, to be experimentally detected.

Search for sterile neutrinos decaying into pions at the LHC

We study the possibility to observe sterile neutrinos with masses in the range between 5 GeV and 20 GeV at the LHC, using the exclusive semileptonic modes involving pions, namely W to lepton + N to n pions + lepton+lepton (n = 1, 2, 3). The two pion and three pion modes require extrapolations of form factors to large time-like $q^2$, which we do using vector dominance models as well as light front holographic QCD, with remarkable agreement. This mass region is difficult to explore with inclusive dilepton+dijet modes or trilepton modes and impossible to explore in rare meson decays. While particle identification is a real challenge in these modes, vertex displacement due to the long living neutrino in the above mass range can greatly help reduce backgrounds. Assuming a sample of $10^9$ W bosons at the end of the LHC Run 2, these modes could discover a sterile neutrino in the above mass range or improve the current bounds on the heavy-to-light lepton mixings by an order of magnitude, $U_{l N}^2 \sim 2 \times 10^{-6}$. Moreover, by studying the equal sign and opposite sign dileptons, the Majorana or Dirac character of the sterile neutrino may be revealed.

Quantum and stringy corrections to the equation of state of holographic QCD matter and the nature of the chiral transition

We consider the finite temperature phase diagram of holographic QCD in the Veneziano limit (Nc large, Nf large with xf=Nf/Nc fixed) and calculate one string-loop corrections to the free energy in certain approximations. Such corrections, especially due to the pion modes are unsuppressed in the Veneziano limit. We find that under some extra assumptions the first order transition following from classical gravity solutions can become second order. If stringy asymptotics are of a special form and there are residual interactions it may even become of third order. Operationally these computations imply modelling the low temperature chiral symmetry breaking phase with a hadron gas containing Nf^2 massless Goldstone bosons and an exponential spectrum of massive hadrons. A third order transition is possible only if repulsive hadron interactions via the excluded volume effect are included.

Viscosity of neutron star matter andr-modes in rotating pulsars

We study viscosity of the neutron star matter and $r$-mode instability in rotating neutron stars. Contributions to the shear and bulk viscosities from various processes are calculated with account of in-medium modifications of the nucleon-nucleon interaction. A softening of the pion mode and a possibility of the pion condensation are included. The nucleon pairing is incorporated. In the shear viscosity we include the lepton contribution calculated with account of the Landau damping in the photon exchange, the nucleon contribution described by the medium-modified one pion exchange, and other terms, such as the novel phonon contribution in the 1S$_0$ superfluid neutron phase, and the neutrino term in the neutrino opacity region. The nucleon shear viscosity depends on the density rather moderately and proves to be much less than the lepton term. Among the terms contributing to the bulk viscosity, the term from the medium modified Urca reactions possesses strongest density dependence because of the pion softening. Contributions to the bulk viscosity arising from other reactions induced by charged weak currents are included. The radiative bulk viscosity induced by charged and neutral weak currents in the region of the neutrino transparency of the star is also calculated with account for in-medium effects. The computed frequency boundary of the $r$-mode stability for the stars with the mass $\ge 1.8 M_{\odot}$ proves to be above the frequencies of all rotating young pulsars. To explain the stability of rapid rotation of old pulsars in X-ray binaries we propose a novel efficient mechanism associated with appearance of condensates of low-lying modes of bosonic excitations with finite momentum and/or with an enhancement of the inhomogeneous pion/kaon condensates in some parts of the star, if the angular velocity exceeds a critical value.

Computation of the electromagnetic pion form factor from lattice QCD in theεregime

We calculate the electromagnetic pion form factor in lattice QCD with 2+1 flavors of the dynamical overlap quarks. Up and down quark masses are set below their physical values so that the system is in the so-called epsilon regime with the small size of our lattice ~ 1.8 fm. The finite volume corrections are generally expected to be ~ 100% in the epsilon regime. We, however, find a way to automatically cancel the dominant part of them. Inserting non-zero momenta and taking appropriate ratios of the two and three point functions, we can eliminate the contribution from the zero-momentum pion mode. Then the remaining finite volume effect is a small perturbation from the non-zero modes. Our lattice data agree with this theoretical prediction and the extracted pion charge radius is consistent with the experiment.

Study of exclusiveB→Xuℓνdecays and extraction of|Vub|using full reconstruction tagging at the Belle experiment

We report the results of a study of the exclusive semileptonic decays B->pi0lnu, B->pi+lnu, B->rho0lnu, B->rho+lnu and B->omegalnu, where l represents an electron or a muon. The events are tagged by fully reconstructing a second B meson in the event in a hadronic decay mode. The measured branching fractions are Br(B->pi0lnu) = (0.80 +- 0.08 +- 0.04)x10^-4, Br(B->pi+lnu) = (1.49 +- 0.09 +- 0.07)x10^-4, Br(B->rho0lnu) = (1.83 +- 0.10 +- 0.10)x10^-4, Br(B->rho+lnu) = (3.22 +- 0.27 +- 0.24)x10^-4, and Br(B->omegalnu) =(1.07 +- 0.16 +- 0.07)x10^-4, where the first error is statistical and the second one is systematic. The obtained branching fractions are inclusive of soft photon emission. We also determine the branching fractions as a function of the 4-momentum transfer squared to the leptonic system q^2=(p_l+p_nu)^2, where p_l and p_nu are the lepton and neutrino 4-momenta, respectively. Using the pion modes, a recent LCSR calculation, lattice QCD results and a model-independent description of the hadronic form factor, a value of the CKM matrix element |V_{ub}| = (3.52 +- 0.29)x10^-3 is extracted. For the first time, a charmless state with invariant mass greater than 1 GeV/c^2, which might be dominated by the decay B->f2lnu, is observed. These results are obtained from a 711 1/fb data sample that contains 772 millions BB pairs, collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^+ e^- collider.

Photon-to-pion transition form factor and pion distribution amplitude from holographic QCD

We try to understand the recently observed anomalous behavior of the photon-to-pion transition form factor in the holographic QCD approach. First the holographic description of the anomalous \gamma^*\gamma^*\pi^0 form factor is reviewed and applied to various models. It is illustrated that in describing the anomalous form factor, the holographic approach is asymptotically dual to the perturbative QCD (pQCD) framework, with the pion mode \pi(z)\sim z corresponding to the asymptotic pion distribution amplitude. This indicates some inconsistency in light-front holography, since \pi(z)\sim z would be dual to \varphi(x)\sim \sqrt{x(1-x)} there. After clarifying these subtleties, we employ the relation between the holographic and the perturbative expressions to study possible asymptotic violation of the transition form factor. It is found that if one require that the asymptotic form factor possess a pQCD-like expression, the pion mode can only be ultraviolet-enhanced by logarithmic factors. The minimally deformed pion mode will then be of the form \pi(z)\sim z\ln (z\Lambda)^{-1}. We suppose that this deformation may be due to the coupling of the pion with a nontrivial open string tachyon field, and then the parameter $\Lambda$ will be related to the quark condensate. Interestingly, this pion mode leads immediately to Radyushkin's logarithmic model, which fitted very well the experimental data in the large-Q^2 region. On the other side, the pQCD interpretation with a flat-like pion distribution amplitude, proposed by Radyushkin and Polyakov, fails to possess a holographic expression.

Neutrino Processes in Neutron Stars

The aim of these lectures is to introduce basic processes responsible for cooling of neutron stars and to show how to calculate the neutrino production rate in dense strongly interacting nuclear medium. The formalism is presented that treats on equal footing one-nucleon and multiple-nucleon processes and reactions with virtual bosonic modes and condensates. We demonstrate that neutrino emission from dense hadronic component in neutron stars is subject of strong modifications due to collective effects in the nuclear matter. With the most important in-medium processes incorporated in the cooling code an overall agreement with available soft X ray data can be easily achieved. With these findings the so-called “standard” and “non-standard” cooling scenarios are replaced by one general “nuclear medium cooling scenario” which relates slow and rapid neutron star coolings to the star masses (interior densities).The lectures are split in four parts. Part I : After short introduction to the neutron star cooling problem we show how to calculate neutrino reaction rates of the most efficient one-nucleon and two-nucleon processes. No medium effects are taken into account in this instance. The effects of a possible nucleon pairing are discussed. We demonstrate that the data on neutron star cooling cannot be described without inclusion of medium effects. It motivates an assumption that masses of the neutron stars are different and that neutrino reaction rates should be strongly density dependent. Part II : We introduce the Green’s function diagram technique for systems in and out of equilibrium and the optical theorem formalism. The latter allows to perform calculations of production rates with full Green’s functions including all off-mass-shell effects. We demonstrate how this formalism works within the quasiparticle approximation.Part III : The basic concepts of the nuclear Fermi liquid approach are introduced. We show how strong interaction effects can be included within the Green’s function formalism. Softening of the pion mode with an baryon density increase is explicitly incorporated. We show examples of inconsistencies in calculations without inclusion of medium effects. Then we demonstrate calculations of different reaction rates in non-superfluid nuclear matter with taking into account medium effects. Many new reaction channels are open up in the medium and should be analyzed. Part IV : We discuss the neutrino production reactions in superfluid nuclear systems. The reaction rates of processes associated with the pair breaking and formation are calculated. Special attention is focused on the gauge invariance and the exact fulfillment of the Ward identities for the vector current. Finally we present comparison of calculations of neutron star cooling performed within nuclear medium cooling scenario with the available data.

Electrical neutrality and pion modes in the two flavor Polyakov–Nambu–Jona-Lasinio model

We study the phase diagram and the pion modes in the electrically neutral two flavor Polyakov\char21{}Nambu\char21{}Jona-Lasinio model. One of the main results of this paper is that in the model with massive quarks, when electrical neutrality is required, pions do not condense in the ground state of the model: the isospin chemical potential ${\ensuremath{\mu}}_{I}=\ensuremath{-}{\ensuremath{\mu}}_{e}/2$ is always smaller than the value required for pion condensation to occur. Moreover we investigate on the pions and $\ensuremath{\sigma}$ mass spectra. We find that the qualitative behavior of the masses resembles that obtained in the Nambu\char21{}Jona-Lasinio model. We close this paper by studying the intriguing possibility that bound states with the quantum numbers of the pions can be formed above the chiral phase transition.

Restless pions: Orbifold boundary conditions and noise suppression in lattice QCD

The study of one or more baryons in lattice QCD is severely hindered by the exponential decay in time of the signal-to-noise ratio. The rate at which the signal-to-noise decreases is a function of the pion mass. More precisely, it depends on the minimum allowed pion energy in the box, which, for periodic boundary conditions, is equal to its mass. We propose a set of boundary conditions, given by a “parity orbifold” construction, which eliminates the zero momentum pion modes, raising the minimum pion energy and thereby improving the signal-to-noise ratio of (multi)-baryon correlation functions at long Euclidean times. We discuss variations of these “restless pions” boundary conditions and focus on their impact on the study of nuclear forces.

Phase Diagram and Pion Modes of the Neutral Nambu-Jona Lasinio Model with the Polyakov Loop

I discuss recent results obtained by our group within the Nambu-Jona Lasinio model with the Polyakov loop. I focus on the two flavor version of the model, discussing the phase diagram in the $\mu-T$ plane in the case in which electrical neutrality is required. One of the results is that pion condensation is not observed in our model when a physical mass for the light quarks is considered.

Study of dipion transitions amongΥ(3S),Υ(2S), andΥ(1S)states

We present measurements of decay matrix elements for hadronic transitions of the form Upsilon(nS) -> pi pi Upsilon(mS) where (n, m) = (3, 1), (2, 1), and (3, 2). We reconstruct charged and neutral pion modes with the final state Upsilon decaying to either mu+mu- or e+e-. Dalitz plot distributions for the twelve decay modes are fit individually as well as jointly assuming isospin symmetry, thereby measuring the matrix elements of the decay amplitude. We observe and account for the anomaly previously noted in the di-pion invariant mass distribution for the Upsilon(3S) -> pi pi Upsilon(1S) transition and obtain good descriptions of the dynamics of the decay using the most general decay amplitude allowed by partial conservation of the axial-vector current (PCAC) considerations. The fits further indicate that the Upsilon(2S) -> pi pi Upsilon(1S) and Upsilon(3S) -> pi pi Upsilon(2S) transitions also show the presence of terms in the decay amplitude that were previously ignored, although at a relatively suppressed level.

Pion superfluidity and meson properties at finite isospin density

We investigate pion superfluidity and its effect on meson properties and equation of state at finite temperature and isospin and baryon densities in the frame of a standard flavor SU(2) NJL model. In mean field approximation to quarks and random phase approximation to mesons, the critical isospin chemical potential for pion superfluidity is exactly the pion mass in the vacuum, and corresponding to the isospin symmetry spontaneous breaking, there is in the pion superfluidity phase a Goldstone mode which is the linear combination of the normal sigma and charged pion modes. We calculate numerically the gap equations for the chiral and pion condensates, the phase diagrams, the meson spectra, and the equation of state, and compare them with that obtained in other effective models. The competitions between pion superfluidity and color superconductivity at finite baryon density and between pion and kaon superfluidity at finite strangeness density in flavor SU(3) NJL model are briefly discussed.

Amplification of Quantum Meson Modes in the Late Time of the Chiral Phase Transition

It is shown that there exists a possibility of amplification of amplitudes of quantum pion modes with low momenta in the late time of chiral phase transition by using the Gaussian wave functional approximation in the O(4) linear sigma model. It is also shown that the amplification occurs in the mechanism of the resonance by forced oscillation as well as the parametric resonance induced by the small oscillation of the chiral condensate. These mechanisms are investigated in both the case of spatially homogeneous system and the spatially expanded system described by the Bjorken coordinate.

From QFT to a disoriented chiral condensate

A quantum field theoretical model for the dynamics of the disoriented chiral condensate is presented. A unified approach to relate the quantum field theory directly to the formation, decay and signals of the DCC and its evolution is taken. We use a background field analysis of the O(4) sigma model keeping one-loop quantum corrections (quadratic order in the fluctuations). An evolution of the quantum fluctuations in an external, expanding metric which simulates the expansion of the plasma, is carried out. We examine, in detail, the amplification of the low momentum pion modes with two competing effects, the expansion rate of the plasma and the transition rate of the vacuum configuration from a metastable state into a stable state.We show the effect of DCC formation on the multiplicity distributions and the Bose-Einstein correlations.

Self consistent and covariant propagation of pions, nucleon and isobar resonances in cold nuclear matter

We evaluate the in-medium spectral functions for pions, nucleon and isobar resonances in a self consistent and covariant manner. The calculations are based on a recently developed formulation which leads to predictions in terms of the pion–nucleon scattering phase shifts and a set of Migdal parameters describing important short range correlation effects. We do not observe significant softening of pion modes if we insist on reasonable isobar resonance properties but predict a considerable broadening of the N ( 1440 ) and N ( 1520 ) resonances in nuclear matter. Contrasted results are obtained for the s-wave N ( 1535 ) and N ( 1650 ) resonances which are affected by a nuclear environment very little. The properties of slowly moving isobar's in nuclear matter are found to depend very sensitively on a soft form factor in the π N N vertex, which is not controlled by the πN scattering data.

Time-evolution of collective meson fields and amplification of quantum meson modes in chiral phase transition

The time evolution of quantum meson fields in te O(4) linear sigma model is investigated in a context of the dynamical chiral phase transition. It is shown that amplitudes of quantum pion modes are amplified due to both mechanisms of a parametric resonance and a resonance by the forced oscillation according to the small oscillation of the chiral condensate in the late time of chiral phase transition.

Parametric Resonance versus Forced Oscillation in Time-Evolution of Quantum Meson Fields

The time evolution of quantum meson fields in the O(4)-linear sigma model is treated approximately. It is shown that the amplification of the amplitudes of pion modes with low momenta occurs through both parametric resonance and forced oscillation.