Chiral Perturbation Theory Lagrangian Research Articles

Electroweak single-pion production off the nucleon: From threshold to high invariant masses

[Background] Neutrino-induced single-pion production (SPP) provides an important contribution to neutrino-nucleus interactions, ranging from intermediate to high energies. There exists a good number of low-energy models in the literature to describe the neutrinoproduction of pions in the region around the Delta resonance. Those models consider only lowest-order interaction terms and, therefore, fail in the high-energy region (pion-nucleon invariant masses, $W$>2 GeV). [Purpose] Our goal is to develop a model for electroweak SPP off the nucleon, which is applicable to the entire energy range of interest for present and future neutrino-oscillation experiments. [Method] We start with the low-energy model of [Phys.Rev.D76,033005(2007)], which includes resonant contributions and background terms derived from the pion-nucleon Lagrangian of chiral-perturbation theory. Then, from the background contributions, we build a high-energy model using a Regge approach. The low- and high-energy models are combined, in a phenomenological way, into a hybrid model. [Results] The Hybrid model is identical to the low-energy model in the low-W region, but, for W>2 GeV, it implements the desired high-energy behavior dictated by Regge theory. We have tested the high-energy model by comparing with one-pion production data from electron and neutrino reactions. The Hybrid model is compared with electron-proton scattering data, with neutrino SPP data and with the predictions of the NuWro Monte Carlo event generator. [Conclusions] Our model is able to provide satisfactory predictions of the electroweak one-pion production cross section from pion threshold to high $W$. Further investigation and more data are needed to better understand the mechanisms playing a role in the electroweak SPP process in the high-W region, in particular, those involving the axial current contributions.

Renormalization of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons

Starting from a relativistic Lagrangian for pseudoscalar Goldstone bosons and vector mesons in the antisymmetric tensor representation, a one-loop calculation is performed to pin down the divergent structures that appear for the effective low-energy action at chiral orders Q^2 and Q^4. The corresponding renormalisation-scale dependences of all low-energy constants up to chiral order Q^4 are determined. Calculations are carried out for both the pseudoscalar octet and the pseudoscalar nonet, the latter in the framework of chiral perturbation theory in the limit of a large number of colours.

A method to prove the minimality of the order p6 chiral Lagrangian

In this talk, a method to find relations between the operators in the the mesonic Lagrangian of Chiral Perturbation Theory at order p6 is presented, which can be used to establish the minimality of the Lagrangian operator basis. As an example, we apply the method to the two-flavour case in the absence of scalar and pseudo-scalar sources (s=p=0), and conclude that the minimal Lagrangian contains 27 independent operators.

On the minimality of the order p6 chiral Lagrangian

A method to find relations between the operators in the mesonic Lagrangian of Chiral Perturbation Theory at order p6 is presented. The procedure can be used to establish if the basis of operators in the Lagrangian is minimal. As an example, we apply the method to the two-flavor case in the absence of scalar and pseudo-scalar sources (s=p=0), and conclude that the minimal Lagrangian contains 27 independent operators.

Chiral sum rules and vacuum condensates from tau-lepton decay data

QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension $d=2$ and $d=4$. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension $d=6$ and $d=8$, as well as the chiral correlator at zero momentum, proportional to the counter term of the ${\cal{O}}(p^4)$ Lagrangian of chiral perturbation theory, $\bar{L}_{10}$. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations. We find no compelling indications of duality violations in the kinematic region above $s \simeq 2.2$ GeV$^2$ after using pinched integration kernels.

Chiral effective theories from holographic QCD with scalars

We develop a method for integrating out the heavy Kaluza-Klein modes of scalar type as well as those of vector and axial-vector types, in a class of hard-wall bottom-up approaches of holographic QCD models, including the Dirac-Born-Infeld and Chern-Simons parts. By keeping only the lowest-lying vector mesons, we first obtain an effective chiral Lagrangian of the vector mesons based on the hidden local symmetry, and all the low-energy constants in the HLS Lagrangian are expressed in terms of holographic integrals and, consequently, are fully determined by the holographic geometry and a few constants of mesons. We find that the Gell-Mann--Oakes--Renner relation is manifestly reproduced at the lowest order of derivative expansion. We also explicitly show that a naive inclusion of the Chern-Simons term cannot reproduce the desired chiral anomaly in QCD, and hence, some counterterms should be provided: This implies that the holographic QCD models of hard-wall type cannot give definite predictions for the intrinsic parity-odd vertices involving vector and axial-vector mesons. After integrating out the vector mesons from the HLS Lagrangian, we further obtain the Lagrangian of chiral perturbation theory for pseudoscalar mesons with all the low-energy constants fully determined.

Relations between anomalous and even-parity sectors in AdS/QCD

We derive the O(p6) Chiral Perturbation Theory Lagrangian in the massless quark limit for a class of gravity dual models of Quantum Chromodynamics with the chiral symmetry broken through boundary conditions. The odd O(p6) couplings are related to the O(p4) low-energy constants (LEC's) in the even-parity sector. Some combinations of even O(p6) couplings are found to be universal and independent of the peculiarities of the model. These relations turn out to be the manifestation at low energies of a broader relation between anomalous and even-parity amplitudes.

Extracting information on renormalized coupling constants of contact interactions of the chiral perturbation theory lagrangian from the phase-shift analysis of πN scattering

The analytic approach to the construction of the effective theory of strong interactions in the low-energy range is developed and its application to pion-nucleon scattering is considered. A model-independent definition of renormalized coupling constants of contact interactions of the effective chiral perturbation theory Lagrangian is proposed. With the help of the available data of pion-nucleon phase-shift analysis the information on these constants is extracted.

Magnetized baryonic matter in holographic QCD

We investigate the properties of the Sakai-Sugimoto model at finite magnetic field and baryon chemical potentials. We show that in a finite magnetic field, there exists a spatially homogeneous configuration carrying a finite-baryon number density. At a low magnetic field and baryon chemical potential, the equation of state of the matter coincides with that obtained from the chiral perturbation theory Lagrangian with an anomalous term. We discuss the behavior of the system at larger magnetic fields.

A rational approximation to [formula omitted] and its [formula omitted] low-energy constant

Using a sequence of rational approximants and the large-Nc limit of QCD, we estimate the value of the low-energy constant C87 which appears in the Lagrangian of Chiral Perturbation Theory at O(p6).

Effective action and holography in 5D gauge theories

We apply the holographic method to 5D gauge theories on the warped interval. Our treatment includes the scalars associated with the fifth gauge field component, which appear as 4D Goldstone bosons in the holographic effective action. Applications are considered to two classes of models in which these scalars play an important role. In the Composite-Higgs (and/or Gauge-Higgs Unification) scenario, the scalars are interpreted as the Higgs field and we use the holographic recipe to compute its one-loop potential. In AdS/QCD models, the scalars are identified with the mesons and we compute holographically the Chiral Perturbation Theory Lagrangian up to p^4 order. We also discuss, using the holographic perspective, the effect of including a Chern-Simons term in the 5D gauge Lagrangian. We show that it makes a Wess-Zumino-Witten term to appear in the holographic effective action. This is immediately applied to AdS/QCD, where a Chern-Simons term is needed in order to mimic the Adler-Bardeen chiral anomaly.

Three-point Green Functions in the resonance region : LEC's

Using the 1 / N C expansion scheme and truncating the hadronic spectrum to the lowest-lying multiplets of resonances we develop a procedure to implement QCD information on the non-perturbative regime populated by resonances through the use of three-point Green Functions of QCD currents. The process implies to enforce on these functions the constraints provided by their asymptotic behaviour ruled by QCD using their OPE or associated form factors. As a result we are able to determine several couplings of the O ( p 6 ) Chiral Perturbation Theory Lagrangian and, in consequence, to address phenomenological issues such as the SU ( 3 ) breaking in K l 3 decays.

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.

The anomalous chiral Lagrangian of order $p^6$

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$ . The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavors, 23 terms for three and 5 for two flavors. In the two flavor case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.

Electromagnetic couplings of the chiral perturbation theory Lagrangian from the perturbative chiral quark model

We apply the perturbative chiral quark model to the study of the low-energy pi-N interaction. Using an effective chiral Lagrangian we reproduce the Weinberg-Tomozawa result for the S-wave pi-N scattering lengths. After inclusion of the photon field we give predictions for the electromagnetic O(p^2) low-energy couplings of the chiral perturbation theory effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e^2) radiative corrections to the pi-N scattering amplitude. Finally, we estimate the leading isospin-breaking correction to the strong energy shift of the pi(-)p atom in the 1s state, which is relevant for the experiment "Pionic Hydrogen" at PSI.

Rare decayD0→γγ

We present a calculation of the rare decay mode D^0 -> gamma gamma, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Perturbation Theory Lagrangian with a strong g coupling as recently determined by CLEO from the D^* -> D pi width, we consider both the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one-loop pi, K diagrams. The loop contributions which are proportional to g and contain the a_1 Wilson coefficient are found to dominate the decay amplitude, which turns out to be mainly parity violating. The branching ratio is then calculated to be (1.0+-0.5)x10^(-8). Observation of an order of magnitude larger branching ratio could be indicative of new physics.

φ→π+π−decay within a chiral unitary approach

Starting from the chiral perturbation theory Lagrangian, but keeping different masses for the charged and neutral mesons ${(m}_{u}\ensuremath{\ne}{m}_{d}),$ and using a previously developed nonperturbative unitary scheme that generates the lightest meson-meson resonances, we construct $K\overline{K}\ensuremath{\rightarrow}K\overline{K}$ and $K\overline{K}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in the vector channel. This allows us to obtain the kaon-loop contribution to $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\rho}$ mixing and study the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay. The dominant contribution to this decay comes from the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ process. However, there can be large interferences with the subdominant contributions coming from $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\rho}$ and $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\omega}$ mixing, or of these two contributions among themselves. As a consequence, a reliable measurement of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay could be used to differentiate between some $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\omega}$ mixing scenarios proposed in the literature.

Pion-nucleon scattering and the nucleonΣterm in an extended linearΣmodel

A modified linear $\ensuremath{\Sigma}$ model that allows for ${g}_{A}=1.26$ by addition of vector and pseudovector $\ensuremath{\pi}N$ coupling terms was discussed by Bjorken and Nauenberg and by Lee. In this extended linear $\ensuremath{\Sigma}$ model the elastic $\ensuremath{\pi}N$ scattering amplitudes satisfy the relevant chiral low-energy theorems, such as the Weinberg-Tomozawa relation for the isovector $\ensuremath{\pi}N$ scattering length and in some cases Adler's ``consistency condition.'' The agreement of the isospin symmetric $\ensuremath{\pi}N$ scattering length with experiment is substantially improved in this extended $\ensuremath{\Sigma}$ model as compared with the original linear one. We show that the nucleon sigma term $({\ensuremath{\Sigma}}_{N})$ in the linear and the extended $\ensuremath{\Sigma}$ models with three different kinds of chiral symmetry breaking terms are identical. Within the tree approximation the formal operator expression for the ${\ensuremath{\Sigma}}_{N}$ term and the value extracted from the $\ensuremath{\pi}N$ scattering matrix coincide. Large values of ${\ensuremath{\Sigma}}_{N}$ are easily obtained without any $s\overline{s}$ content of the nucleon. Using chiral rotations the Lagrangian of this extended \ensuremath{\Sigma} model reproduces the lowest-order $\ensuremath{\pi}N$ chiral perturbation theory Lagrangian.

The mesonic chiral lagrangean of order p6

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic even-intrinsic-parity sector at order $p^6$. The Lagrangian contains 112 in principle measurable + 3 contact terms for the general case of $n$ light flavours, 90+4 for three and 53+4 for two flavours. The equivalence between equations of motion and field redefinitions to remove spurious terms in the Lagrangians is shown to all orders in the chiral expansion. We also discuss and implement other methods for reducing the number of terms to a minimal set.

DecayD0→K¯*0π−e+νein the context of chiral perturbation theory

We study the decay ${D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}$, using $\mathrm{SU}{(2)}_{L}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{R}$ chiral perturbation theory for heavy charmed mesons and vector mesons, in the kinematic regime where $\frac{{p}_{M}\ifmmode\cdot\else\textperiodcentered\fi{}{p}_{\ensuremath{\pi}}}{{m}_{M}}$ (here $M={D}^{0} or {\overline{K}}^{*0}$) is much smaller than the chiral symmetry-breaking scale ${\ensuremath{\Lambda}}_{{\ensuremath{\chi}}^{\mathrm{SB}}}$ (${\ensuremath{\Lambda}}_{{\ensuremath{\chi}}^{\mathrm{SB}}}\ensuremath{\sim}1$ GeV). We present the leading diagrams and amplitude, and calculate the rate, in the region where, to leading order in our calculations, the ${\overline{K}}^{*0}$ is at zero recoil in the ${D}^{0}$ rest frame. The rate thus calculated is given in terms of a known form factor and depends on the $D{D}^{*}\ensuremath{\pi}$ coupling constant ${g}_{D}$ of the heavy (charmed) meson chiral perturbation theory Lagrangian. A measurement of the above decay, in the aforementioned kinematic regime, can result in the extraction of an experimental value for ${g}_{D}$, accurate at the level of our approximations, and gives us a measure of the validity of approaches based on chiral perturbation theory in studying similar processes.