Chiral Symmetry Constraints Research Articles

Chiral symmetry constraints on resonant amplitudes

We discuss the impact of chiral symmetry constraints on the quark-mass dependence of meson resonance pole positions, which are encoded in non-perturbative parametrizations of meson scattering amplitudes. Model-independent conditions on such parametrizations are derived, which are shown to guarantee the correct functional form of the leading quark-mass corrections to the resonance pole positions. Some model amplitudes for ππ scattering, widely used for the determination of ρ and σ resonance properties from results of lattice simulations, are tested explicitly with respect to these conditions.

Spin of the proton in chiral effective field theory

Proton spin is investigated in chiral effective field theory through an examination of the singlet axial charge, $a_0$, and the two non-singlet axial charges, $a_3$ and $a_8$. Finite-range regularization is considered as it provides an effective model for estimating the role of disconnected sea-quark loop contributions to baryon observables. Baryon octet and decuplet intermediate states are included to enrich the spin and flavour structure of the nucleon, redistributing spin under the constraints of chiral symmetry. In this context, the proton spin puzzle is well understood with the calculation describing all three of the axial charges reasonably well. The strange quark contribution to the proton spin is negative with magnitude 0.01. With appropriate $Q^2$ evolution, we find the singlet axial charge at the experimental scale to be ${\hat a}_0 = 0.31^{+0.04}_{-0.05}$, consistent with the range of current experimental values.

Dalitz plot studies ofD0→KS0π+π−decays in a factorization approach

The presently available high-statistics data of the D0 --> K0S pi+ pi- processes measured by the Belle and BABAR Collaborations are analyzed within a quasi two-body QCD factorization framework. Starting from the weak effective Hamiltonian, tree and annihilation amplitudes build up the D0 --> K0S pi+ pi- decay amplitude. Two of the three final-state mesons are assumed to form a single scalar, vector or tensor state originating from a quark-antiquark pair so that the factorization hypothesis can be applied. The meson-meson final state interactions are described by K pi and pi pi scalar and vector form factors for the S and P waves and by relativistic Breit-Wigner formulae for the D waves. A combined chi^2 fit to a Belle Dalitz plot density distribution, to the total experimental branching fraction and to the tau^- --> K0S pi- nu_tau decay data is carried out to fix the 33 free parameters. These are mainly related to the strengths of the scalar form factors and to unknown meson to meson transition form factors at a large momentum transfer squared equal to the D0 mass squared. A good overall agreement to the Belle Dalitz plot density distribution is achieved. Another set of parameters fits equally well the BABAR Collaboration Dalitz plot model. The branching fractions of the dominant channels compare well with those of the isobar Belle or BABAR models.The lower-limit values of the branching fractions of the annihilation amplitudes are significant. Built upon experimental data from other processes, the unitary K pi and pi pi scalar form factors, entering our decay amplitude and satisfying analyticity and chiral symmetry constraints, are furthermore constrained by the present Dalitz plot analysis. Our decay amplitude could be a useful input for determinations of D0-D0bar mixing parameters and of the CKM angle gamma (or phi3).

Unified dispersive approach to real and virtual photon-photon scattering at low energy

Previous representations of pion pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitariy, chiral symmetry and soft photon constraints are generalized to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the $\pi\pi$ phase-shifts, on pion form factors and on pion polarizabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalized polarizabilies, to vector meson radiative decays, and to the $\sigma\gamma$ electromagnetic form factor. Finally, and evaluation of the contribution of $\gamma\pi\pi$ states in the hadronic vacuum polarization to the muon $g-2$ is given, which should be less model dependent than previous estimates.

Chiral color quark symmetry and possible constraints on the G′-boson mass from tevatron and LHC data

A gauge model featuring a chiral color symmetry of quarks was considered, and possible manifestations of this symmetry in proton-antiproton and proton-proton collisions at the Tevatron and LHC energies were studied. The cross section \(\sigma _{t\bar t}\) for the production of \(t\bar t\) quark pairs at the Tevatron and the forward-backward asymmetry \(A_{FB}^{p\bar p}\) in this process were calculated and analyzed with allowance for the contributions of the G′-boson predicted by the chiral color symmetry of quarks, the G′-boson massmG′ and the mixing angle θG being treated as free parameters of the model. Limits on mG′ versus θG were studied on the basis of data from the Tevatron on \(\sigma _{t\bar t}\) and \(A_{FB}^{p\bar p}\), and the region compatible with these data within one standard deviation was found in the mG′-θG plane. The region ofmG′-mass values that is appropriate for observing the G′-boson at LHC is discussed.

Kπform factors and final state interactions inD+→K−π+π+decays

We present a model for the decay ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorization approach. Hadronic final state interactions are taken into account through the $K\ensuremath{\pi}$ scalar and vector form factors fulfilling analyticity, unitarity, and chiral symmetry constraints. The model has only two free parameters that are fixed from experimental branching ratios. We show that the modulus and phase of the $S$ wave thus obtained agree nicely with experiments up to 1.55 GeV. We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. Allowing for a global phase difference between the $S$ and $P$ waves of $\ensuremath{-}65\ifmmode^\circ\else\textdegree\fi{}$, the Dalitz plot of the ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$ decay, the $K\ensuremath{\pi}$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.

CPviolation and kaon-pion interactions inB→Kπ+π−decays

We study $CP$ violation and the contribution of the strong kaon-pion interactions in the three-body $B\ensuremath{\rightarrow}K{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays. We extend our recent work on the effect of the two-pion $S$- and $P$-wave interactions to that of the corresponding kaon-pion ones. The weak amplitudes have a first term derived in QCD factorization and a second one as a phenomenological contribution added to the QCD penguin amplitudes. The effective QCD coefficients include the leading order contributions plus next-to-leading order vertex and penguins corrections. The matrix elements of the transition to the vacuum of the kaon-pion pairs, appearing naturally in the factorization formulation, are described by the strange $K\ensuremath{\pi}$ scalar ($S$-wave) and vector ($P$-wave) form factors. These are determined from Muskhelishvili-Omn\`es coupled channel equations using experimental kaon-pion $T$-matrix elements, together with chiral symmetry and asymptotic QCD constraints. From the scalar form factor study, the modulus of the ${K}_{0}^{*}(1430)$ decay constant is found to be $(32\ifmmode\pm\else\textpm\fi{}5)\text{ }\text{ }\mathrm{MeV}$. The additional phenomenological amplitudes are fitted to reproduce the $K\ensuremath{\pi}$ effective mass and helicity angle distributions, the $B\ensuremath{\rightarrow}{K}^{*}(892)\ensuremath{\pi}$ branching ratios and the $CP$ asymmetries of the recent data from Belle and BABAR collaborations. We use also the new measurement by the BABAR group of the phase difference between the ${B}^{0}$ and ${\overline{B}}^{0}$ decay amplitudes to ${K}^{*}(892)\ensuremath{\pi}$. Our predicted ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}_{0}^{*}(1430){\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}_{0}^{*}(1430)\ensuremath{\rightarrow}{K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ branching fraction, equal to $(11.6\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, is smaller than the result of the analyzes of both collaborations. For the neutral ${B}^{0}$ decays, the predicted value is $(11.1\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. In order to reduce the large systematic uncertainties in the experimental determination of the $B\ensuremath{\rightarrow}{K}_{0}^{*}(1430)\ensuremath{\pi}$ branching fractions, a new parametrization is proposed. It is based on the $K\ensuremath{\pi}$ scalar form factor, well constrained by theory and experiments other than those of $B$ decays.

STATUS OF CHIRAL DOUBLERS OF HEAVY-LIGHT HADRONS IN LIGHT OF RECENT BABAR, CLEO, BELLE AND SELEX Ds STATES

We explain the main idea of the chiral doublers scenario, originating from simultaneous constraints of chiral symmetry and of heavy quark spin symmetry on effective theories of heavy-light hadrons. In particular we discuss chiral doublers for mesons, chiral doublers for excited mesons, chiral doublers for baryons and chiral doublers for excited baryons. We point out the arguments why new states Ds(2317) and Ds(2457) might be viewed as chiral doublers of Ds and [Formula: see text]. Then we comment on non-strange mesons D0(2308) and D′1(2427) observed by Belle and Focus, and on Θc(3099) signal observed by H1. Finally, we point out that very recent discovery by SELEX of Ds(2632), if confirmed by other experiments and if spin-parity of this state is 1-, may be interpreted as a signal for chiral doubler of Ds1(2536). Such an identification implies another narrow, spin-parity 2-Ds state ca 37 MeV above the new 1-, corresponding to chiral partner of Ds2.

Progress in the calculation of nucleon form factors and parton distribution functions

Even though current lattice calculations are limited to unrealistically large quark masses, it is possible to implement the model independent constraints of chiral symmetry in extrapolations to the physical region. We discuss the role of the Δ-isobar in the extrapolation of the moments of spin dependent parton distribution functions. Unlike the unpolarised case, the Δ plays a crucial role for the isovector spin dependent distributions. We also present initial results for the extrapolation of isovector nucleon form factors, finding reasonably good agreement with experimental data.

Chiral extrapolation of hadronic observables

One of the great challenges of lattice QCD is to produce unambiguous predictions for the properties of physical hadrons. We review recent progress with respect to a major barrier to achieving this goal, namely the fact that computation time currently limits us to large quark mass. Using insights from the study of the lattice data itself, together with the general constraints of chiral symmetry, we demonstrate that it is possible to extrapolate accurately and in an essentially model independent manner from the mass region where calculations will be performed within the next five years to the chiral limit.

FOOTPRINTS OF A BROAD σ(600) IN WEAK-INTERACTION PROCESSES

We explore how chiral-symmetry constraints on weak-interaction matrix elements point toward the existence of an intermediate-state σ in several different weak-interaction processes. Particular attention is directed toward recent evidence for a σ within three-body nonleptonic weak decays.

Constraining quark-hadron duality at largeNc

Quark-meson duality for two-point functions of vector and axial-vector QCD currents is investigated in the large-${N}_{c}$ approximation. We find that the joint constraints of duality and chiral symmetry suggest degeneracy of excited vector and axial-vector mesons in the large-${N}_{c}$ limit. We compare model-independent constraints with expectations based on the Veneziano-Lovelace-Shapiro string model. Several models of duality are constructed, and phenomenological implications are discussed.

Sigma-term physics in the perturbative chiral quark model

We apply the perturbative chiral quark model at one loop to analyze meson-baryon sigma terms. Analytic expressions for these quantities are obtained in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). Our result for the $\ensuremath{\pi}N$ sigma term ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}\ensuremath{\approx}45 \mathrm{MeV}$ is in good agreement with the value deduced by Gasser, Leutwyler, and Sainio using dispersion-relation techniques and exploiting the chiral symmetry constraints.

Chiral three-nucleon forces from p-wave pion production.

Production of p-wave pions in nucleon-nucleon collisions is studied according to an improved power counting that embodies the constraints of chiral symmetry. Contributions from the first two nonvanishing orders are calculated. We find reasonable convergence and agreement with data for a spin-triplet cross section in pp-->pppi(0), with no free parameters. Agreement with existing data for a spin-singlet cross section in pp-->pnpi(+) constrains a short-range operator shown recently to contribute significantly to the three-nucleon potential.

Incorporating chiral symmetry in extrapolations of octet baryon magnetic moments

We explore methods of extrapolating lattice calculations of hadronic observables to the physical regime, while respecting the constraints of chiral symmetry and heavy quark effective theory. In particular, we extrapolate lattice results for magnetic moments of the spin-1/2 baryon octet to the physical pion mass and compare with experimental measurements. The success previously reported for extrapolations of the nucleon magnetic moments carries over to the Σ baryons. A study of the residual discrepancies in the Ξ baryon moments suggests that it is important to have new simulation data with a more realistic strange quark mass.

Dispersive and chiral symmetry constraints on the light meson form factors

The form factors of the light pseudoscalar mesons are investigated in a dispersive formalism based on hadronic unitarity, analyticity and the OPE expansion of the QCD Green functions. We propose generalizations of the original mathematical techniques, suitable for including additional low energy information provided by experiment or Chiral Perturbation Theory (CHPT). The simultaneous treatment of the electroweak form factors of the $\pi$ and K mesons allows us to test the consistency with QCD of a low energy CHPT theorem. By applying the formalism to the pion electromagnetic form factor, we derive quite strong constraints on the higher Taylor coefficients at zero momentum, using information about the phase and the modulus of the form factor along a part of the unitarity cut.

Dispersive and chiral symmetry constraints on the light meson form factors

The form factors of the light pseudoscalar mesons are investigated in a dispersive formalism based on hadronic unitarity, analyticity and the OPE expansion of the QCD Green functions. We propose generalizations of the original mathematical techniques, suitable for including additional low energy information provided by experiment or Chiral Perturbation Theory (CHPT). The simultaneous treatment of the electroweak form factors of the $\pi$ and $K$ mesons allows us to test the consistency with QCD of a low energy CHPT theorem. By applying the formalism to the pion electromagnetic form factor, we derive quite strong constraints on the higher Taylor coefficients at zero momentum, using information about the phase and the modulus of the form factor along a part of the unitarity cut.

Master formulae approach to photon fusion reactions

We analyze the γγ → ππ, KK, ηη, πη reactions through S = 2 GeV , using the master formula approach to QCD with three flavors. In this approach, the constraints of broken chiral symmetry, unitarity and crossing symmetry are manifest in all channels. The pertinent vacuum correlators are analyzed at tree level using straightforward resonance saturation methods. A one-loop chiral power counting analysis at threshold is also carried out and compared to standard chiral perturbation theory. Our results are in overall agreement with the existing data in all channels. We predict the strange meson polarizabilities and a very small cross section for γγ → ηη.

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f 0 and a 0 resonances. The ππ → ππ, ππ → K K phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π 0 η and K K mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f 0 and a 0 resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below s ≃ 1.2 GeV.

Electromagnetic mass differences of pions and kaons

We use the Cottingham method to calculate the pion and kaon electromagnetic mass differences with as few model dependent inputs as possible. The constraints of chiral symmetry at low energy, QCD at high energy and experimental data in between are used in the dispersion relation. We find excellent agreement with experiment for the pion mass difference. The kaon mass difference exhibits a strong violation of the lowest order prediction of Dashen's theorem, in qualitative agreement with several other recent calculations.