Predictions Of Chiral Perturbation Theory Research Articles

Determination of the ΔS= 1 weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions

A new method to determine the low-energy couplings of the Delta S = 1 weak Hamiltonian is presented. It relies on a matching of the topological poles in 1/m(2) of three-point correlators of two pseudoscalar densities and a four-fermion operator, measured in lattice QCD, to the same observables computed in the is an element of-regime of chiral perturbation theory. We test this method in a theory with a light charm quark, i.e. with an SU(4) flavour symmetry. Quenched numerical measurements are performed in a 2 fm box, and chiral perturbation theory predictions are worked out up to next-to-leading order. The matching of the two sides allows to determine the weak low-energy couplings in the SU( 4) limit. We compare the results with a previous determination, based on three-point correlators containing two left-handed currents, and discuss the merits and drawbacks of the two procedures.

Role of theσresonance in determining the convergence of chiral perturbation theory

The dimensionless parameter $\ensuremath{\xi}={M}_{\ensuremath{\pi}}^{2}/(16{\ensuremath{\pi}}^{2}{F}_{\ensuremath{\pi}}^{2})$, where ${F}_{\ensuremath{\pi}}$ is the pion decay constant and ${M}_{\ensuremath{\pi}}$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $\ensuremath{\sigma}$-resonance is different. We first confirm that the leading low-energy constants appearing in the chiral Lagrangian are the same when calculated from the $p$-regime and the $ϵ$-regime as expected. However, $\ensuremath{\xi}\ensuremath{\lesssim}0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $\ensuremath{\xi}>0.0035$ the data begin to deviate dramatically from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $\ensuremath{\sigma}$-resonance in our model. Our findings may be useful for lattice QCD studies.

Modeling pion physics in theϵ-regime of two-flavor QCD using strong coupling lattice QED

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with $U(1)$ gauge fields. For massless quarks, this theory has an $S{U}_{L}(2)\ifmmode\times\else\texttimes\fi{}S{U}_{R}(2)\ifmmode\times\else\texttimes\fi{}{U}_{A}(1)$ symmetry. By adding a four-fermion term we can break the ${U}_{A}(1)$ symmetry and thus incorporate the physics of the QCD anomaly. We can also tune the pion decay constant $F$, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy pion physics in a setting similar to lattice QCD from first principles. However, unlike lattice QCD, a major advantage of our model is that we can easily design efficient algorithms to compute a variety of quantities in the chiral limit. Here we show that the model reproduces the predictions of chiral perturbation theory in the $ϵ$-regime.

First observation and measurement of the decay [formula omitted

Using the full data set of the NA48/2 experiment, the decay K±→π±e+e−γ is observed for the first time, selecting 120 candidates with 7.3±1.7 estimated background events. With K±→π±πD0 as normalisation channel, the branching ratio is determined in a model-independent way to be Br(K±→π±e+e−γ,meeγ>260 MeV/c2)=(1.19±0.12stat±0.04syst)×10−8. This measured value and the spectrum of the e+e−γ invariant mass allow a comparison with predictions of chiral perturbation theory.

Electroweak Radiative Corrections to Muon Capture

Electroweak radiative corrections to muon capture on nuclei are computed and found to be sizable. They enhance the capture rates for hydrogen and helium by 2.8% and 3.0%, respectively. As a result, the value of the induced pseudoscalar coupling, g(P)(exp), extracted from a recent hydrogen 1S singlet capture experiment is increased by about 21% to g(P)(exp)=7.3+/-1.2 and brought into good agreement with the prediction of chiral perturbation theory, g(P)(theory)=8.2+/-0.2. Implications for helium capture rate predictions are also discussed.

Dynamical twisted mass fermions with light quarks

We present results of dynamical simulations of Nf=2 degenerate Wilson twisted mass quarks at maximal twist in the range of pseudo scalar masses 300 MeV≲mPS≲550 MeV. Reaching such small masses was made possible owing to a recently developed variant of the HMC algorithm. The simulations are performed at one value of the lattice spacing a≲0.1 fm. In order to have O(a) improvement and aiming at small residual O(a2) cutoff effects, the theory is tuned to maximal twist by requiring the vanishing of the untwisted quark mass. Precise results for the pseudo scalar decay constant and the pseudo scalar mass are confronted with chiral perturbation theory predictions and the low energy constants F, l¯3 and l¯4 are evaluated with small statistical errors.

Low Q2measurements of the neutron and 3He spin structure

Thomas Jefferson National Accelerator Facility experiment E97-110 was performed to provide a precise measurement of the extended Gerasimov-Drell-Hearn integral and of moments of the neutron and of the 3He spin structure functions. The momentum transfer range 0.02 < Q2 < 0.3 (GeV/c)2 will allow us to test predictions of Chiral Perturbation Theory, and chek the GDH sum rule by extrapolating the integral to the real photon point. The data have been taken in Hall A using a highly polarized electron beam and a polarized 3He target. The status of the data analysis is discussed, and preliminary results are shown.

Hadron spectrum, quark masses, and decay constants from light overlap fermions on large lattices

We present results from a simulation of quenched overlap fermions with Luescher-Weisz gauge field action on lattices up to 24{sup 3}48 and for pion masses down to {approx_equal}250 MeV. Among the quantities we study are the pion, rho, and nucleon masses; the light and strange quark masses; and the pion decay constant. The renormalization of the scalar and axial vector currents is done nonperturbatively in the RI-MOM scheme. The simulations are performed at two different lattice spacings, a{approx_equal}0.1 fm and {approx_equal}0.15 fm, and on two different physical volumes, to test the scaling properties of our action and to study finite volume effects. We compare our results with the predictions of chiral perturbation theory and compute several of its low-energy constants. The pion mass is computed in sectors of fixed topology as well.

K→ππAmplitudes from Lattice QCD with a Light Charm Quark

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K-->pipi amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.

Recent Results in Rare and Semileptonic Kaon Decays from NA48

Recent results are presented on rare neutral kaon decays from the NA48/1 collaboration, and on semileptonic charged kaon decays from the NA48/2 collaboration. Using data taken on 2002, NA48/1 has measured the CP conserving component of the decay K 0 → π 0 π + π − . For the λ parameter describing this decay the values Re ( λ ) = 0.038 ± 0.008 s t a t ± 0.006 s y s t and Im ( λ ) = − 0.013 ± 0.005 s t a t ± 0.004 s y s t have been obtained. This is consistent with previous measurements and with chiral perturbation theory predictions. NA48/1 has also measured the BR ( K s → π ± e ∓ ν ) = ( 6.8 ± 0.2 s t a t ± 0.2 s y s t ) 10 −4 , consistent with Δ S = Δ Q . Using data collected during eight hours minimum bias run on 2003, the NA48/2 collaboration has measured BR ( K ± → π 0 e ± ν ) = ( 5.14 ± 0.02 s t a t ± 0.06 s y s t ) 10 −2 , where the channel K ± → π 0 π ± has been used as normalization. From the same data sample, the ratio of K ± → π 0 μ ± ν to K ± → π 0 e ± ν has been obtained. This results on BR ( K ± → π 0 μ ± ν ) = ( 3.462 ± 0.018 s t a t ± 0.006 s y s t ± 0.011 λ + , λ 0 ± 0.068 n o r m ) . From semileptonic decays the value of the CKM matrix element V u s can be extracted. The values of V u s | f + ( 0 ) | obtained by NA48/2 from electron and muon channels are compatible. The result on K 0 → π 0 π + π − is final, and all the other results presented here are preliminary.

A new determination of the γπ → ππ anomalous amplitude via πe- → π-e-π0 data

We discuss the reaction π-e- → π-e-π0 with the purpose of obtaining information on the γπ → ππ anomalous amplitude $ \cal {F}$ 3π. We compare a full calculation at $ \cal {O}$ (p6) in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia et al. By integrating our theory results using Monte Carlo techniques, we obtain σ = 2.05 nb at $ \cal {O}$ (p6) and σ = 2.17 nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross-section of σ = (2.11±0.47) nb. On the basis of the ChPT results one would extract from the experimental cross-section as amplitudes $ \cal {F}$ 3π(0)extr = (9.9±1.1) GeV-3 and $ \cal {F}$ 3π(0)extr = (9.6±1.1) GeV-3, respectively, which have to be compared with the low-energy theorem $ \cal {F}$ 3π = e/(4π2Fπ3) = 9.72GeV-3. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain $ \cal {F}$ 3π with smaller uncertainty.

An exploratory lattice study of [formula omitted][formula omitted] decays at next-to-leading order in the chiral expansion

We present the first direct evaluation of Δ I = 3 / 2 K → π π matrix elements with the aim of determining all the low-energy constants at NLO in the chiral expansion. Our numerical investigation demonstrates that it is indeed possible to determine the K → π π matrix elements directly for the masses and momenta used in the simulation with good precision. In this range however, we find that the matrix elements do not satisfy the predictions of NLO chiral perturbation theory. For the chiral extrapolation we therefore use a hybrid procedure which combines the observed polynomial behavior in masses and momenta of our lattice results, with NLO chiral perturbation theory at lower masses. In this way we find stable results for the quenched matrix elements of the electroweak penguin operators ( 〈 π π | O 8 | K 0 〉 I = 2 = ( 0.68 ± 0.09 ) GeV 3 and 〈 π π | O 7 | K 0 〉 I = 2 = ( 0.12 ± 0.02 ) GeV 3 in the NDR- MS ¯ scheme at the scale 2 GeV), but not for the matrix elements of O 4 (for which there are too many low-energy constants at NLO for a reliable extrapolation). For all three operators we find that the effect of including the NLO corrections is significant (typically about 30%). We present a detailed discussion of the status of the prospects for the reduction of the systematic uncertainties.

Radiative K e3 decays revisited

Motivated by recent experimental results and ongoing measurements, we review the chiral perturbation theory prediction for radiative Ke3 decays (neutral kaons). Special emphasis is given on the stability of the inner bremsstrahlung-dominated relative branching ratio vs. the Ke3 form factors, and on the separation of the structure dependent amplitude in differential distributions over the phase space. For the structure dependent terms, an assessment of the order p^6 corrections is given. In particular, a full next-to-leading order calculation of the axial component is performed. The experimental analysis of the photon energy spectrum is discussed, and other potentially useful distributions are introduced.

Detecting chiral singularities in lattice QCD at strong coupling

We study the difficulties associated with detecting chiral singularities in strongly coupled lattice QCD at fixed nonzero tempearture. We show that the behavior of the chiral condensate, the pion mass and the pion decay constant, for small masses, are all consistent with the predictions of Chiral Perturbation Theory. However, the values of the quark masses that we need to demonstrate this are much smaller than those being used in dynamical QCD simulations.

Measurement of electric and magnetic polarizabilities with Primakoff reaction at COMPASS

The COMPASS spectrometer is well suited to perform precise measurements of the pion polarizabilities via the Primakoff reaction π(Z,A)→π+(Z,A)+ψ. The electric\((\bar \alpha _\pi )\) and magnetic\((\bar \beta _\pi )\) polarizabilities characterize the response of the response of the pion quark substructure to the electromagnetic field of the ψ during the πψ scattering. The results of a simulation for the foreseen 2004 setup are presented. The measurement of the pion polarizabilities allows for a test of the chiral perturbation theory (χPT) predictions.

Connecting lattice QCD with chiral perturbation theory at strong coupling

We study the difficulties associated with detecting chiral singularities predicted by chiral perturbation theory (ChPT) in lattice QCD. We focus on the physics of the remnant O(2) chiral symmetry of staggered fermions in the strong coupling limit using the recently discovered directed path algorithm. Since it is easier to look for power-like singularities as compared to logarithmic ones, our calculations are performed at a fixed finite temperature in the chirally broken phase. We show that the behavior of the chiral condensate, the pion mass and the pion decay constant, for small masses, are all consistent with the predictions of ChPT. However, the values of the quark masses that we need to demonstrate this are much smaller than those being used in dynamical QCD simulations. We also need to use higher order terms in the chiral expansion to fit our data.

The nucleon mass in Nf=2 lattice QCD: finite size effects from chiral perturbation theory

In the framework of relativistic SU(2) f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O( p 4). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N f =2 simulations of the UKQCD and QCDSF Collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD Collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.

The nucleon mass in Nf=2 lattice QCD: finite size effects from chiral perturbation theory

In the framework of relativistic SU(2) f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O ( p 4 ). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N f =2 simulations of the UKQCD and QCDSF Collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD Collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.

Scalar meson dynamics in chiral perturbation theory

A comparison of the linear sigma model (L$\sigma$M) and Chiral Perturbation Theory (ChPT) predictions for pion and kaon dynamics is presented. Lowest and next-to-leading order terms in the ChPT amplitudes are reproduced if one restricts to scalar resonance exchange. Some low energy constants of the order $p^4$ ChPT Lagrangian are fixed in terms of scalar meson masses. Present values of these low energy constants are compatible with the L$\sigma$M dynamics. We conclude that more accurate values would be most useful either to falsify the L$\sigma$M or to show its capability to shed some light on the controversial scalar physics.

First observation of the KS→π0γγ decay

Using the NA48 detector at the CERN SPS, 31 KS→π0γγ candidates with an estimated background of 13.7±3.2 events have been observed. This first observation leads to a branching ratio of BR(KS→π0γγ)z>0.2=(4.9±1.6stat±0.9syst)×10−8 in agreement with Chiral Perturbation Theory predictions.