Nonlinear Chiral Lagrangian Research Articles

Top\u2013antitop production from W^+_L W^-_L and Z_L Z_L scattering under a strongly interacting symmetry-breaking sector

By considering a non-linear electroweak chiral Lagrangian, including the Higgs, coupled to heavy quarks, and the equivalence theorem, we compute the one-loop scattering amplitudes W^+W^-rightarrow tbar{t}, ZZrightarrow tbar{t} and hhrightarrow tbar{t} (in the regime M_t^2/v^2ll sqrt{s}M_t/v^2ll s/v^2 and to NLO in the effective theory). We calculate the scalar partial-wave helicity amplitudes which allow us to check unitarity at the perturbative level in both M_t/v and s/v. As with growing energy perturbative unitarity deteriorates, we also introduce a new unitarization method with the right analytical behavior on the complex s-plane and that can support poles on the second Riemann sheet to describe resonances in terms of the Lagrangian couplings. Thus we have achieved a consistent phenomenological description of any resonant tbar{t} production that may be enhanced by a possible strongly interacting electroweak symmetry breaking sector.

Proximity off0(1500)andf0(1710)to the scalar glueball

Within a nonlinear chiral Lagrangian framework, the underlying mixings among quark-antiquark, four-quark and glue components of $f_0(1500)$ and $f_0(1710)$ are studied in a global picture that includes all isosinglet scalar mesons below 2 GeV. The quark components are introduced in the Lagrangian in terms of two separate nonets (a quark-antiquark nonet and a four-quark nonet) which can mix with each other and with a scalar glueball. The free parameters of the Lagrangian are studied by a simultaneous fit to more than 20 experimental data and constraints on the mass spectrum, decay widths, and decay ratios of the isosinglet scalars below 2 GeV. Moreover, constraints on the mass spectrum and decay widths of isodoublet and isovector scalars below 2 GeV as well as pion-pion scattering amplitude are also taken into account. The insights gained in this global picture, due to the complexities of the mixings as well as the experimental uncertainties, are mainly qualitative but are relatively robust, and reveal that the lowest scalar glueball hides between $f_0(1500)$ and $f_0(1710)$, resulting in a considerable mixing with various quark components of these two states. The overall current experimental and theoretical uncertainties do not allow to pin down the exact glue components of isosinglet states, nevertheless it is shown that the $f_0(1500)$ and $f_0(1710)$ have the highest glue component. While this global study does not allow precision predictions for each individual state, it provides useful "family" correlations among the isosinglet states that are found insightful in probing the substructure of all scalars, in general, and the isosinglets, in particular. The overall estimate of the scalar glueball mass is found to be $1.58 \pm 0.18$ GeV.

Probing the substructure off0(1370)

Within an effective nonlinear chiral Lagrangian framework the substructure of $f_0(1370)$ is studied. The investigation is conducted in the context of a global picture of scalar mesons in which the importance of the underlying connections among scalar mesons below and above 1 GeV is recognized and implemented. These connections are due to the mixings among various quark-antiquarks, four-quarks and glue components and play a central role in understanding the properties of scalar mesons. Iterative Monte Carlo simulations are first performed on the 14-dimensional parameter space of the model and sets of points in this parameter space (the global sets) that give an overall agreement with all experimental data on mass spectrum, various decay widths and decay ratios of all isosinglet scalar states below 2 GeV are determined. Then within each global set, subsets that give closest agreement for the properties of $f_0(1370)$ are studied. Unlike the properties of other isosinglet states that show a range of variation within each global set, it is found that there is a clear signal for $f_0(1370)$ to be predominantly a quark-antiquark state with a substantial $s {\bar s}$ component, together with small remnants of four-quark and glue components.

Phenomenology and cosmology of an electroweak pseudo-dilaton and electroweak baryons

Abstract In many strongly-interacting models of electroweak symmetry breaking the lowest-lying observable particle is a pseudo-Goldstone boson of approximate scale symmetry, the pseudo-dilaton. Its interactions with Standard Model particles can be described using a low-energy effective nonlinear chiral Lagrangian supplemented by terms that restore approximate scale symmetry, yielding couplings of the pseudo-dilaton that differ from those of a Standard Model Higgs boson by fixed factors. We review the experimental constraints on such a pseudo-dilaton in light of new data from the LHC and elsewhere. The effective nonlinear chiral Lagrangian has Skyrmion solutions that may be identified with the ‘electroweak baryons’ of the underlying strongly-interacting theory, whose nature may be revealed by the properties of the Skyrmions. We discuss the finite-temperature electroweak phase transition in the low-energy effective theory, finding that the possibility of a first-order electroweak phase transition is resurrected. We discuss the evolution of the Universe during this transition and derive an order-of-magnitude lower limit on the abundance of electroweak baryons in the absence of a cosmological asymmetry, which suggests that such an asymmetry would be necessary if the electroweak baryons are to provide the cosmological density of dark matter. We revisit estimates of the corresponding spin-independent dark matter scattering cross section, with a view to direct detection experiments.

A mixing scheme for the structure of [formula omitted] and [formula omitted

Within the framework of a nonlinear chiral Lagrangian we explore the nontrivial nature of f 0 ( 600 ) and f 0 ( 1370 ) in terms of quarkonium, tetraquark and gluonium components. The mass constraints are obtained and the strong and radiative partial widths are calculated to demonstrate and discriminate these components. The static properties of f 0 ( 1500 ) and glueball are also studied. Our results are confronted with the experimental and theoretical data available as well as the upcoming measurements.

Comparison of scalar resonances using two unitarisation procedures in ππ and πK scattering

We review two previous approaches to studying pseudoscalar meson-meson scattering amplitudes to beyond 1 GeV using non-linear and linear chiral Lagrangians. In these approaches we use two different unitarisation techniques - a generalised Breit Wigner prescription and K-matrix unitarization respectively. We report some new findings on K-matrix unitarisation of ππ and π K scattering in the non-linear chiral Lagrangian approach and make some related remarks about the light scalar mesons.

κK*0γ-vertex in light cone QCD sum rules

We investigate the $\ensuremath{\kappa}{K}^{*0}\ensuremath{\gamma}$-vertex in the framework of light cone QCD sum rules. We estimate the coupling constant ${\mathrm{g}}_{\ensuremath{\kappa}{K}^{*0}\ensuremath{\gamma}}$, and compare our result with that used in the nonlinear chiral Lagrangian approach using the vector-meson dominance model in the SU(3) limit.

Chiral Lagrangian Treatment of 0++ Mesons and 0++Glueballs

Within the framework of a nonlinear chiral Lagrangian the mass spectraand the decay properties of 0++ states below 2 GeV are studied.Assuming that f0(980), a0(980), K*0(1430), andf0(1500) comprise an SU(3) nonet, we make a detailed predictionabout the static properties of the 0++ mesons. The substructureanalysis of these states in terms of two- and four-quark components aswell as a glueball component is carried out. We also consider theinteraction Lagrangian and provide a preliminary study of the strong andradiative decays of the 0++ mesons. The scalar glueball masses andpartial widths are also presented. In view of the fact that few data of 0++mesons are clearly given in the present PDG (Particle Data Group) list and that thefour-quark content of mesons is a hot issue both experimentally andtheoretically, the predicted results of the paper may be helpful forupcoming experimental and theoretical studies of these mesons.

Mass uncertainties off0(600)andf0(1370)and their effects on determination of the quark and glueball admixtures of theI=0scalar mesons

Within a nonlinear chiral Lagrangian framework the correlations between the quark and glueball admixtures of the isosinglet scalar mesons below 2 GeV and the current large uncertainties on the mass of the f0(600) and the f0(1370) are studied. The framework is formulated in terms of two scalar meson nonets (a two-quark nonet and a four-quark nonet) together with a scalar glueball. It is shown that while some properties of these states are sensitive to the mass of f0(600) and f0(1370), several relatively robust conclusions can be made: The f0(600), the f0(980), and the f0(1370) are admixtures of two and four quark components, with f0(600) being dominantly a non-strange four-quark state, and f0(980) and f0(1370) having a dominant two-quark component. Similarly, the f0(1500) and the f0(1710) have considerable two and four quark admixtures, but in addition have a large glueball component. For each state, a detailed analysis providing the numerical estimates of all components is given. It is also shown that this framework clearly favors the experimental values: m[f0(600)] < 700 MeV and m[f0(1370)] = 1300-1450 MeV. Moreover, an overall fit to the available data shows a reciprocal substructure for the f0(600) and the f0(1370), and a linear correlation between their masses of the form m [f0(1370)] = 0.29 m[f0(600)] + 1.22 GeV. The scalar glueball mass of 1.5-1.7 GeV is found in this analysis.

PROBING THE QUARK AND GLUEBALL ADMIXTURES OF THE SCALAR MESONS

A nonlinear chiral Lagrangian framework for scalar mesons below 2 GeV [the I =l/2 states: κ(900) and [Formula: see text]; the I=1 states: a0(980) and a0(1450); and the I=0 states: α(550), f0(980), f0(1370), f0(1500) and f0(1710)] is presented. This framework is formulated in terms of two meson nonets with a mixing mechanism dictated by SU (3) symmetry and its breakdown.

Chiral dynamics from AdS space

We study the low energy dynamics of pions in a gravity dual of chiral symmetry breaking. The string theory construction consists of a probe D7 brane in the Constable Myers non-supersymmetric background, which has been shown to describe chiral symmetry breaking in the pattern of QCD. We expand the D7 brane's Dirac Born Infeld action for fluctuations that correspond to the Goldstone mode and show that they take the form of a non-linear chiral lagrangian. We numerically compute the quark condensate, pion decay constant and higher order Gasser Leutwyler coefficients. We find their form is consistent with naive dimensional analysis estimates. We also explore the gauging of the quark's chiral symmetries and the vector meson spectrum.

ISOSINGLET SCALAR MESONS BELOW 2 GeV AND THE SCALAR GLUEBALL MASS

A collective treatment of the I=0 scalar mesons below 2 GeV [σ(550), f0(980), f0(1370), f0(1500) and f0(1710)] in a nonlinear chiral Lagrangian framework that is constrained by the mass and the partial decay widths of the I=1/2,1 scalars [κ(900), [Formula: see text], a0(980) and a0(1450)] is presented. The sub-structure of these states in terms of two and four quark components, as well as a glueball component is explored, and its correlation with the mass of f0(1370) is studied. Consistency with the available experimental data suggests that the σ(550) is dominantly a nonstrange four-quark state, whereas the sub-structure of other I=0 states are sensitive to the input mass of f0(1370). This investigation estimates the scalar glueball mass in the range 1.47–1.64 GeV.

Low energyK¯Ninteractions and Faddeev calculation of theK−dscattering length in isospin and particle bases

$\overline{K}N$ interactions are investigated via an effective nonlinear chiral meson-baryon Lagrangian. The adjustable parameters are determined by a fitting procedure on the ${K}^{\ensuremath{-}}p$ threshold branching ratios and total cross-section data for ${p}_{K}^{lab}\ensuremath{\leqslant}250\phantom{\rule{0.3em}{0ex}}\text{MeV}∕c$. We produce predictions for the $\ensuremath{\Sigma}\ensuremath{\pi}$ mass spectrum, and scattering lengths ${a}_{{K}^{\ensuremath{-}}p}$, ${a}_{n}({K}^{\ensuremath{-}}n\ensuremath{\rightarrow}{K}^{\ensuremath{-}}n)$, ${a}_{n}^{\ensuremath{\circ}}({\overline{K}}^{\ensuremath{\circ}}n\ensuremath{\rightarrow}{\overline{K}}^{\ensuremath{\circ}}n)$, and ${a}_{ex}({K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{\ensuremath{\circ}}n)$. The $\overline{K}N$ amplitudes thus obtained, as well as those for other two-body channels ($\ensuremath{\pi}N$, $NN$, and $YN$), are used as input to predict the scattering length ${A}_{{K}^{\ensuremath{-}}d}$, for which we have devised a relativistic version of the three-body Faddeev equations. Results for all two- and three-body coupled channels are reported both in isospin and particle bases. All available $\overline{K}N$ data are well reproduced and our best results for the ${K}^{\ensuremath{-}}p$ and ${K}^{\ensuremath{-}}d$ scattering lengths are ${a}_{{K}^{\ensuremath{-}}p}=(\ensuremath{-}0.90+i0.87)$ fm and ${A}_{{K}^{\ensuremath{-}}d}=(\ensuremath{-}1.80+i1.55)$ fm.

Effects of light scalar mesons inη→3πdecay

We study the role of a possible nonet of light scalar mesons in the still interesting � ! 3� decay process, with the primary motivation of learning more about the scalars themselves. The framework is a conventional non-linear chiral Lagrangian of pseudoscalars and vectors, extended to include the scalars. The parameters involving the scalars were previously obtained to fit the s-wave �� and �K scatterings in the region up to about 1 GeV as well as the strong decay � ' ! ���. At first, one might expect a large enhancement from diagrams including a light �(560). However there is an amusing cancellation mechanism which prevents this from occurring. In the simplest model there is an enhancement of about 13 per cent in the � ! 3� decay rate due to the scalars. In a more complicated model which includes derivative type symmetry breakers, the cancellation is modified and the scalars contribute about 30 percent of the total decay rate (although the total is not significantly changed). The vectors do not contribute much. Our model produces a reasonable estimate for the related a0(980) f0(980) mixing strength, which has been a topic of current debate. Promising directions for future work along the present line are suggested.

How reliable is the mean-field nuclear matter description for supporting chiral effective Lagrangians?

The link between non-linear chiral effective Lagrangians and the Walecka model description of bulk nuclear matter is questioned. This fact is by itself due to the Mean Field Approximation (MFA) which innuclear mater makes the picture of a nucleon-nucleon interaction based on scalar (vector) meson exchange equivalent to the description of a nuclear matter based on attractive and repulsive contact interactions. We present a linear chiral model where this link between the Walecka model and an underlying to chiral symmetry realization still holds, due to MFA.

Low energy pion-hyperon interaction

We study the low energy pion-hyperon interaction considering effective nonlinear chiral invariant Lagrangians including pions, \ensuremath{\rho} mesons, \ensuremath{\sigma} mesons, hyperons, and corresponding resonances. Then we calculate the S- and P-wave phase shifts, total cross sections, angular distributions, and polarizations for the momentum in the center-of-mass frame up to $k=400$ MeV. With these results we discuss the $\mathrm{CP}$ violation in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Xi}}\ensuremath{\Lambda}\ensuremath{\pi}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}\ensuremath{\Xi}\ensuremath{\pi}$ weak decays.

In-mediumππcorrelation induced by partial restoration of chiral symmetry

The purposes of the present paper are twofold: Firstly, we show that the near-threshold enhancement in the I = J = 0 channel in nuclear matter takes place irrespective of the representations (linear or non-linear) of chiral symmetry, if the effect of partial restoration of chiral symmetry in the medium is properly incorporated. Secondly, we show that L (2) , which is a next-to-leading order term in the non-linear chiral lagrangian in the heavy-baryon formalism, gives relevant vertices for the near-threshold enhancement in the I=J=0 channel. Such vertices have not been taken into account in previous calculations of the in-medium ππ scattering in the non-linear lagrangian approaches. Let us first consider the ππ scattering in nuclear matter in the SU(2) LσM to demonstrate the essential idea of the near-threshold enhancement. The following argument is slightly different from the original one [4] but is easy to be generalized to the non-linear case. The lagrangian adopted in [4] is the standard Gell-Mann-Levy model with a minor modification

Chiral Lagrangian treatment ofπηscattering

We study $\ensuremath{\pi}\ensuremath{\eta}$ scattering in a model which starts from the tree diagrams of a non-linear chiral Lagrangian including appropriate resonances. Previously, models of this type were applied to $\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K$ scattering and were seen to require the existence of light scalar $\ensuremath{\sigma}(560)$ and $\ensuremath{\kappa}(900)$ mesons and to be consistent with the ${f}_{0}(980).$ The present calculation extends this to include the ${a}_{0}(980),$ thereby completing a possible nonet of light scalars, all ``seen'' in the same manner. We note that, at the initial level, the $\ensuremath{\pi}\ensuremath{\eta}$ channel is considerably cleaner than the $\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K$ channels for the study of light scalars. This is because the large competing effects of vector meson exchange and ``current-algebra'' contact terms are absent. The simplicity of this channel enables us to demonstrate the closeness of our exactly crossing symmetric amplitude to a related exactly unitary amplitude. The calculation is also extended to higher energies in order to let us discuss the role played by the ${a}_{0}(1450)$ resonance.

The role of tensor forces in nucleon-nucleon scattering within nonlinear chiral Lagrangian approach

The role of tensor forces in nucleon-nucleon scattering within nonlinear chiral Lagrangian approach

In-medium effects on theφmeson

The temperature dependence of the $\ensuremath{\varphi}$ meson mass and its decay width $(\ensuremath{\varphi}\ensuremath{\rightarrow}K\mathrm{K\ifmmode\bar\else\textasciimacron\fi{}})$ have been studied from an effective nonlinear chiral Lagrangian in SU(3). The effective mass has been obtained from the pole position of the full propagator. The width has also been calculated. It has been found that the mass decreases with temperature very slowly whereas the decay width increases quite sharply. Possible consequences on the QGP signals are discussed.