Chiral Perturbation Theory Calculations Research Articles

The effect of the energy functional on the pasta-phase properties of catalysed neutron stars

Nuclear pasta, that is an inhomogeneous distribution of nuclear matter characterised by non-spherical clustered structures, is expected to occur in a narrow spatial region at the bottom of the inner crust of neutron stars, but the width of the pasta layer is strongly model dependent. In the framework of a compressible liquid-drop model, we use Bayesian inference to analyse the constraints on the sub-saturation energy functional and surface tension imposed by both ab-initio chiral perturbation theory calculations and experimental measurements of nuclear masses. The posterior models are used to obtain general predictions for the crust-pasta and pasta-core transition with controlled uncertainties. A correlation study allows us to extract the most influential parameters for the calculation of the pasta phases. The important role of high-order empirical parameters and of the surface tension is underlined.

Extracting the spin polarizabilities of the proton by measurement of Compton double-polarization observables

The Compton double-polarization observable $\Sigma_{2z}$ has been measured for the first time in the $\Delta(1232)$ resonance region using a circularly polarized photon beam incident on a longitudinally polarized target at the Mainz Microtron. This paper reports these results, together with the model-dependent extraction of four proton spin polarizabilities from fits to additional asymmetry data using dispersion relation and chiral perturbation theory calculations, with the former resulting in: $\gamma_{E1E1} = -3.18 \pm 0.52$, $\gamma_{M1M1} = 2.98 \pm 0.43$, $\gamma_{E1M2} = -0.44 \pm 0.67$ and $\gamma_{M1E2} = 1.58 \pm 0.43$, in units of $10^{-4}~\mathrm{fm}^{4}$.

Effects of nonequilibrated topological charge distributions on pseudoscalar meson masses and decay constants

We study the effects of failure to equilibrate the squared topological charge $Q^2$ on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle $\theta$. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively-valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste-violations are important are also presented. The derived $Q^2$ dependence is compared to that of simulations using the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated $Q^2$, or to make estimates of the systematic error coming from the failure to equilibrate $Q^2$. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

Feynman\u2013Hellmann theorem for resonances and the quest for QCD exotica

The generalization of the Feynman–Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in chiral perturbation theory and by large-N_c arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible.

Measurements of double-polarized compton scattering asymmetries and extraction of the proton spin polarizabilities.

The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to extract the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the Δ(1232) region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a dispersion model calculation yields γ(E1E1)=-3.5±1.2, γ(M1M1)=3.16±0.85, γ(E1M2)=-0.7±1.2, and γ(M1E2)=1.99±0.29, in units of 10(-4) fm(4).

Detailed study of the Ke4 decay mode properties

The NA48/2 collaboration at CERN has accumulated an unprecedented statistics of the semileptonic Ke4 charged kaon decay in the “charged pions” (Ke4(+-)) mode K±→π+π−eν and in the “neutral pions” (Ke4(00)) mode K±→π0π0eν with respectively <1% and ∼1% background contamination, allowing a detailed study of the decay properties.More than one million Ke4(+-) decays have been analyzed leading to the improved determination of the branching ratio and detailed studies of the form factors. The resulting BR(K±e4(+−))=(4.257±0.004stat±0.016syst±0.031ext)×10−5 is 3 times more precise than the corresponding PDG value and the error is dominated by the external uncertainty from the branching ratio of the normalization decay mode. It has been possible to obtain the absolute value of the form factor fs=5.705±0.017exp±±0.017syst±0.031ext and we can now translate into absolute form all the relative form factors previously published by NA48/2. This result complements the study of the S and P wave hadronic form factors obtained by NA48/2 in a simultaneous analysis of the ππ scattering length obtained from the same data sample.Concurrently, 65,210 K± decays into π0π0e±ν have been collected, increasing the world available statistics by several orders of magnitude. A study of the differential rate provides the first measurement of the form factors. The achieved precision makes possible also the observation of small effects such as the evidence for a cusp-like structure in the distribution of the π0π0 invariant mass squared around the threshold 4mπ+2. Using a model independent description of the form factors we have obtained the final result, inclusive of radiative decays, BR(K±e4(00))=(2.552±0.010stat±0.010syst±0.032ext)×10−5, also dominated by the external uncertainty from the branching ratio of the normalization decay mode, and improving the world average precision by an order of magnitude.The detailed study of form factors is sensitive to small isospin symmetry breaking effects and brings new inputs to low energy QCD description and crucial tests of predictions from Chiral Perturbation Theory and lattice QCD calculations.

Implications of the Oklo Phenomenon in a Chiral Approach to Nuclear Matter

It has been customary to use data from the Oklo natural nuclear reactor to place bounds on the change that has occurred in the electromagnetic fine structure constant $\alpha$ over the last 2 billion years. Alternatively, an analysis could be based on a recently proposed expression for shifts in resonance energies which relates them to changes in both $\alpha$ and the average $m_q$ of the $u$ and $d$ current quark masses, and which makes explicit the dependence on mass number $A$ and atomic number $Z$. (Recent model independent results on hadronic $\sigma$-terms suggest sensitivity to the strange quark mass is negligible.) The most sophisticated analysis, to date, of the quark mass term invokes a calculation of the nuclear mean-field within the Walecka model of quantum hadrodynamics. We comment on this study and consider an alternative in which the link to low-energy quantum chromodynamics (QCD) and its pattern of chiral symmetry-breaking is more readily discernible. Specifically, we investigate the sensitivity to changes in the pion mass $M_\pi$ of a single nucleon potential determined by an in-medium chiral perturbation theory ($\chi$PT) calculation which includes virtual $\mathrm{\Delta}$-excitations. Subject to some reasonable assumptions about low-energy constants (LECs), we confirm that the $m_q$-contribution to resonance shifts is enhanced by a factor of 10 or so relative to the $\alpha$-term and deduce that the Oklo data for Sm imply that $|m_q(\mathrm{Oklo})- m_q(\mathrm{now})| \lesssim 10^{-9}m_q(\mathrm{now})$.

Two-loop sunset integrals at finite volume

We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Theory (χPT) calculation of the pseudoscalar meson masses and decay constants at next-to-next-to-leading order, including the case of Partially Quenched χPT. We also provide numerical implementations of the finite-volume sunset integrals, and review the results for one-loop integrals at finite volume.

The advanced nucleon electromagnetic structure model and prediction of hyperon electromagnetic form factors

The advanced Unitary and Analytic model of electromagnetic structure of nucleons is applied for sophisticated prediction of hyperon electromagnetic form factors in space-like and time-like regions simultaneously. The static parameters of hyperons are predicted and compared with chiral perturbation theory calculations.

Hadron Structure in Chiral Perturbation Theory

We present our predictions for meson form factors for the SU(3) octet and investigate their impact on the pion electroproduction cross sections. The electric and magnetic polarizabilities of the SU(3) octet of mesons and baryons are analyzed in detail. These extensive calculations are made possible by the recent implementation of semi-automatized calculations in fully-relativistic chiral perturbation theory, which allows evaluation of polarizabilities from Compton scattering up to next-to-the-leading order.

Determination of SU(2) chiral perturbation theory low energy constants from a precise description of pion-pion scattering threshold parameters

We determine the values of the one- and two-loop low energy constants appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion scattering. For this we use a recent and precise sum rule determination of some scattering lengths and slopes that appear in the effective range expansion. In addition we provide sum rules for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the $S$, $P$, $D$, and $F$ waves are consistent with previous determinations but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.

Thresholdπ0photoproduction in relativistic chiral perturbation theory

We present a calculation of $\pi^0$ photoproduction on the proton in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including chiral order $q^4$. With the results we analyze the latest $\pi^0$ photoproduction data in the threshold region obtained at the Mainz Microtron. In the calculation of observables and the fit of the low-energy constants, we take $S$, $P$, and $D$ waves into account. We compare the results for the multipoles with the corresponding single-energy analysis. Furthermore, we also fit the $O(q^4)$ heavy-baryon chiral perturbation theory calculation and compare both results. We provide predictions for several polarization observables for future experiments. Finally, we discuss the $\beta$ parameter of the unitarity cusp which is related to the breaking of isospin symmetry.

ChPT calculations of pionic formfactors

An overview on chiral perturbation theory calculations of form factors is presented. The main focus is given on the form factors related to the lightest meson, pion, namely: pion decay constant, pion vector and scalar form factor, radiative pion decay and transition form factor. A pure calculation within the effective theory can be extended using further methods, as resonance chiral theory and leading logarithm calculations.

The Kπ form factors from Analyticity and Unitarity

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic Kl3 decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of Kπ form factors up to an energy tin = 1GeV2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.

Neutral Pion Decay

The study of π0 decay has played an important role in the development of particle physics: The π0→γγ decay provides key insights into the anomaly sector of quantum chromodynamics. In this review, the historical progression of π0 discovery, lifetime measurements, and theory are presented. A new measurement of the π0 radiative width via the Primakoff effect has been made at JLab. The result, Γ(π0→γγ)=7.82±0.14(stat.)±0.17(syst.) eV, is a factor of 2.1 more precise than the currently accepted value, and it is in agreement with the chiral anomaly prediction and with next-to-leading-order chiral perturbation theory calculations. Primakoff experiments at higher energies to measure the η and η′ radiative widths are also discussed.

Axial couplings in heavy-hadron chiral perturbation theory at the next-to-leading order

We present calculations of axial-current matrix elements between various heavy-meson and heavy-baryon states to the next-to-leading order in heavy-hadron chiral perturbation theory in the $p$-regime. When compared with data from lattice computations or experiments, these results can be used to determine the axial couplings in the chiral Lagrangian. Our calculation is performed in partially quenched chiral perturbation theory for both $\mathrm{SU}(4|2)$ and $\mathrm{SU}(6|3)$. We incorporate finite-size effects arising from a single Goldstone meson wrapping around the spatial volume. Results for full QCD with two and three flavors can be obtained straightforwardly by taking the sea-quark masses to be equal to the valence-quark masses. To illustrate the impact of our chiral perturbation theory calculation on lattice computations, we analyze the SU(2) full-QCD results in detail. We also study one-loop contributions relevant to the heavy-hadron strong-decay amplitudes involving final-state Goldstone bosons, and demonstrate that the quark-mass dependence of these amplitudes can be significantly different from that of the axial-current matrix elements containing only single-hadron external states.

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

We improve our description of pion-pion scattering data by imposing additional requirements to our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of Forward Dispersion Relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy Kl4 decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous Chiral Perturbation Theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

Dynamical polarizabilities of an SU(3) octet of baryons

We present calculations and an analysis of the spin-independent dipole electric and magnetic dynamical polarizabilities for the lowest in mass SU(3) octet of baryons. These extensive calculations are made possible by the recent implementation of semi-automatized calculations in chiral perturbation theory which allows evaluating dynamical spin-independent electromagnetic polarizabilities from Compton scattering up to next-to-the-leading order. Our results are in good agreement with calculations performed for nucleons found in the literature. The dependences for the range of photon energies up to , covering the majority of the meson photoproduction channels, are analyzed. The separate contributions into polarizabilities from the various baryon–meson clouds are studied.

MOMENTS OF SPIN STRUCTURE FUNCTIONS: SUM RULES AND POLARIZABILITIES

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight into some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e., the Bjorken, Burkhardt–Cottingham, Gerasimov–Drell–Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g1 at low momentum transfer of 0.05–0.1 GeV2 but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability δLT. The Burkhardt–Cottingham sum rule has been verified with good accuracy in a wide range of Q2 assuming that no singular behavior of the structure functions is present at very high excitation energies.