arXiv subjects

H. B. O'Connell

Publications and source records attributed to H. B. O'Connell.

At least 19 recordsLinked to original sources

arXiv2008

The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach

We readdress the problem of finding a simultaneous description of the pion form factor data in e+e- annihilations and in tau decays. For this purpose, we work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical rho, omega and phi fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the 4--momentum flowing into the vector meson lines. This allows us to define a dynamical, i.e. s-dependent, vector meson mixing scheme. The model is overconstrained by extending the framework in order to include the description of all meson radiative (V P gamma and P gamma gamma couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking (omega/ phi --> pi+ pi-) decay modes. The model provides a simultaneous, consistent and good description of the e+e- and tau dipion spectra. The expression for pion form factor in the latter case is derived from those in the former case by switching off the isospin breaking effects specific to e+e- and switching on those for tau decays. Besides, the model also provides a good account of all decay modes of the form V P gamma, Pgamma gamma as well as the isospin breaking decay modes. It leads us to propose new reference values for the rho^0 --> e+ e- and omega --> pi+ pi- partial widths which are part of our description of the pion form factor. Other topics (phi --> K anti K, the rho meson mass and width parameters) are briefly discussed. Therefore, we confirm the 3.3 sigma discrepancy between the theoretical estimate of a_mu based on e+e- and its direct BNL measurement.

hep-ph↗

arXiv2003

Anomalous $η/η^\prime$ Decays: The Triangle and Box Anomalies

We examine the decay modes $η/\etp\ra π^+ π^- γ$ within the context of the Hidden Local Symmetry (HLS) Model. Using numerical information derived in previous fits to $VPγ$ and $Ve^+e^-$ decay modes in isolation and the $ρ$ lineshape determined in a previous fit to the pion form factor, we show that all aspects of these decays can be predicted with fair accuracy. Freeing some parameters does not improve the picture. This is interpreted as a strong evidence in favor of the box anomaly in the $η/\etp$ decays, which occurs at precisely the level expected. We also construct the set of equations defining the amplitudes for $η/\etp\ra π^+ π^- γ$ and $ η/\etp \ra \ggam $ at the chiral limit, as predicted from the anomalous HLS Lagrangian appropriately broken. This provides a set of four equations depending on only one parameter, instead of three for the traditional set. This is also shown to match the (two--angle, two--decay--constant) $η-\etp$ mixing scheme recently proposed and is also fairly well fulfilled by the data. The information returned from fits also matches expectations from previously published fits to the $VPγ$ decay modes in isolation.

nucl-th↗

arXiv2003

The Pion Form Factor Within the Hidden Local Symmetry Model

We analyze a pion form factor formulation which fulfills the Analyticity requirement within the Hidden Local Symmetry (HLS) Model. We show that it implies an $s$--dependent dressing of the $ρ-γ$ VMD coupling and an account of several coupled channels. The corresponding function $F_π(s)$ provides nice fits of the pion form factor data from $s=-0.25$ to $s=1$ GeV$^2$. It is shown that the coupling to $K \bar{K}$ has little effects, while $\omg π^0$ improves significantly the fit quality below the $ϕ$ mass. All parameters, except for the subtraction polynomial coefficients are fixed from the rest of the HLS phenomenology. The fits show consistency with the expected behaviour of $F_π(s)$ at $s=0$ up to ${\cal O} (s^2)$ and with the phase shift data on $δ_1^1(s)$ from threshold to somewhat above the $ϕ$ mass. The $\omg$ sector is also examined in relation with recent data from CMD--2.

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arXiv2002

Isospin Symmetry Breaking within the HLS Model: A Full ($ρ, ω, ϕ$) Mixing Scheme

We study the way isospin symmetry violation can be generated within the Hidden Local Symmetry (HLS) Model. We show that isospin symmetry breaking effects on pseudoscalar mesons naturally induces correspondingly effects within the physics of vector mesons, through kaon loops. In this way, one recovers all features traditionally expected from $ρ-\omg$ mixing and one finds support for the Orsay phase modelling of the $e^+e^- \ra π^+ π^-$ amplitude. We then examine an effective procedure which generates mixing in the whole $ρ$, $\omg$, $ϕ$ sector of the HLS Model. The corresponding model allows us to account for all two body decays of light mesons accessible to the HLS model in modulus and phase, leaving aside the $ρ\ra ππ$ and $K^* \ra K π$ modes only, which raise a specific problem. Comparison with experimental data is performed and covers modulus and phase information; this represents 26 physics quantities successfully described with very good fit quality within a constrained model which accounts for SU(3) breaking, nonet symmetry breaking in the pseudoscalar sector and, now, isospin symmetry breaking.

nucl-th↗

arXiv2001

VMD, the WZW Lagrangian and ChPT: The Third Mixing Angle

We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian ${\cal L}^{(0)}+{\cal L}^{(1)}$. This allows to rely on radiative decays of light mesons ($VPγ$ and $P γγ$) in order to extract some numerical information of relevance to ChPT: a value for $Λ_1=0.20 \pm 0.04$, a quark mass ratio of $\simeq 21.2 \pm 2.4$, and a negligible departure from the Gell-Mann--Okubo mass formula. The mixing angles are $θ_8=-20.40^\circ \pm 0.96^\circ$ and $θ_0=-0.05^\circ \pm 0.99^\circ$. We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle $θ_P$ is actually quite appropriate and algebraically related to the $η/η'$ mixing pattern presently preferred by the ChPT community. For instance the traditional $θ_P$ is functionally related to the ChPT $θ_8$ and fulfills $θ_P \simeq θ_8/2$. The vanishing of $θ_0$, supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3) $\ra$ SU(3)$\times$ U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs.

hep-ph↗

arXiv2000

An Effective Approach to VMD at One Loop Order and the Departures from Ideal Mixing for Vector Mesons

We examine the mechanisms producing departures from ideal mixing for vector mesons within the context of the Hidden Local Symmetry (HLS) model. We show that kaon loop transitions between the ideal combinations of the $ω$ and $ϕ$ mesons necessitate a field transformation in order to get the mass eigenstates. It is shown that this transformation is close to a rotation for processes involving, like meson decays, on--shell $ω$ and $ϕ$ mesons. The HLS model predicts a momentum dependent, slowly varying mixing angle between the ideal states. We examine numerically the consequences of this for radiative and leptonic decays of light mesons. The mean $ω-ϕ$ mixing angle is found smaller than its ideal value; this is exhibited separately in radiative and in leptonic decays. Effects of nonet symmetry breaking in the vector sector are compared to those produced by the field rotation implied by the HLS model.

nucl-th↗

arXiv1999

Radiative Decays, Nonet Symmetry and SU(3) Breaking

We re-examine the problem of simultaneously describing in a consistent way all radiative and leptonic decays of light mesons (V -> P gamma, P -> V gamma, P -> gamma gamma, V -> e^+ e^-). For this purpose, we rely on the Hidden Local Symmetry model in both its anomalous and non--anomalous sectors. We show that the SU(3) symmetry breaking scheme proposed by Bando, Kugo and Yamawaki, supplemented with nonet symmetry breaking in the pseudoscalar sector, allows one to reach a nice agreement with all data, except for the K^{*+/-} radiative decay. An extension of this breaking pattern allows one to account for this particular decay mode too. Considered together, the whole set of radiative decays provides a pseudoscalar mixing angle theta_P ~ -11^o and a value for theta_V which is ~ 3^o from that of ideal mixing. We also show that it is impossible, in a practical sense, to disentangle the effects of nonet symmetry breaking and those of glue inside the eta', using only light meson decays.

hep-ph↗

arXiv1999

Vector meson dominance and the rho meson

We discuss the properties of vector mesons, in particular the rho^0, in the context of the Hidden Local Symmetry (HLS) model. This provides a unified framework to study several aspects of the low energy QCD sector. Firstly, we show that in the HLS model the physical photon is massless, without requiring off field diagonalization. We then demonstrate the equivalence of HLS and the two existing representations of vector meson dominance, VMD1 and VMD2, at both tree level and one loop order. Finally the S matrix pole position is shown to provide a model and process independent means of specifying the rho mass and width, in contrast to the real axis prescription currently used in the Particle Data Group tables.

hep-ph↗

arXiv1999

Extracting Br(omega->pi^+ pi^-) from the Time-like Pion Form-factor

We extract the G-parity-violating branching ratio Br(omega->pi^+ pi^-) from the effective rho-omega mixing matrix element Pi_{rho omega}(s), determined from e^+e^- -> pi^+ pi^- data. The omega->pi^+ pi^- partial width can be determined either from the time-like pion form factor or through the constraint that the mixed physical propagator D_{rho omega}^{mu nu}(s) possesses no poles. The two procedures are inequivalent in practice, and we show why the first is preferred, to find finally Br(omega->pi^+ pi^-) = 1.9 +/- 0.3%.

hep-ph↗

arXiv1998

Hidden Symmetry and Georgi's Vector Limit

We study the generation of vector meson masses in the Hidden Local Symmetry (HLS) model of low energy QCD. After demoting the HLS to a hidden global symmetry (HGS), the rho is explicitly shown to be massless for any value of the HS parameter "a" and the chiral partner of the pion appears as the Goldstone boson associated with the spontaneous breaking of the HGS, closely resembling the predictions of Georgi's vector limit.

hep-ph↗

arXiv1998

SU(3) breaking and Hidden Local Symmetry

We study the various existing implementations of SU(3) breaking in the Hidden Local Symmetry model for the low energy hadronic sector following a mechanism originally proposed by Bando, Kugo and Yamawaki (BKY). We pay particular attention to hermiticity and current conservation. Following this, we present a new method for including symmetry breaking effects which preserves the BKY mas s relation among vector mesons. Symmetry breaking (SB) necessarily requires a transformation of the pseudoscalar fields, which, following BKY, we refer to a s field renormalization. We examine the consequences of propagating this throug h all Lagrangian terms including the anomalous ones. We thus explore the consequences of these various SB schemes for both charged and neutral pseudoscalar decay constants as measured in weak and anomalous decays respectively.

hep-ph↗

arXiv1998

Extracting the rho-omega mixing amplitude from the pion form-factor

We re-examine and extend a recent analysis which showed that the rho-omega mixing amplitude cannot be unambiguously extracted from the pion electromagnetic form-factor in a model independent way. In particular, we focus on the argument that the extraction is sensitive to the presence of any intrinsic omega_I -> 2pi coupling. Our extended analysis confirms the original conclusion, with only minor, quantitative differences. The extracted mixing amplitude is shown to be sensitive to both the intrinsic coupling omega_I -> 2pi and to the value assumed for the mass of the neutral rho meson.

hep-ph↗

arXiv1998

Rho-omega Mixing and the Pion Electromagnetic Form-Factor

The suggestion of momentum dependence in the amplitude for rho-omega mixing has generated concern over related implications for vector meson dominance and the photon-rho coupling. We discuss two established representations of vector meson dominance and show that one of these is completely consistent with such a coupling. We then apply it to a calculation of the pion electromagnetic form-factor. Our analysis leads to a new value for the on-shell rho-omega mixing amplitude of (-3800 +/- 370) MeV^2.

hep-ph↗

arXiv1998

Vector Meson Mixing and Charge Symmetry Violation

We discuss the consistency of the traditional vector meson dominance (VMD) model for photons coupling to matter, with the vanishing of vector meson-meson and meson-photon mixing self-energies at q^2=0. This vanishing of vector mixing has been demonstrated in the context of rho-omega mixing for a large class of effective theories. As a further constraint on such models, we here apply them to a study of photon-meson mixing and VMD. As an example we compare the predicted momentum dependence of one such model with a momentum-dependent version of VMD discussed by Sakurai in the 1960's. We find that it produces a result which is consistent with the traditional VMD phenomenology. We conclude that comparison with VMD phenomenology can provide a useful constraint on such models.

hep-ph↗

arXiv1998

Constraints on the momentum dependence of rho-omega mixing

Within a broad class of models we show that the amplitude for rho^0-omega mixing must vanish at the transition from timelike to spacelike four momentum. Hence in such models the mixing is either zero everywhere or is necessarily momentum-dependent. This lends support to the conclusions of other studies of rho-omega mixing and calls into question standard assumptions about the role of rho-omega mixing in the theoretical understanding of charge-symmetry breaking in nuclear systems.

hep-ph↗

arXiv1998

Rho-Omega Mixing and the Pion Form Factor in the Time-like Region

We determine the magnitude, phase, and $s$-dependence of $ρ$-$ω$ ``mixing'' in the pion form factor in the time-like region through fits to $e^+e^- \ra π^+ π^-$ data. The associated systematic errors in these quantities, arising from the functional form used to fit the $ρ$ resonance, are small. The systematic errors in the $ρ$ mass and width, however, are larger than previously estimated.

hep-ph↗

arXiv1998

Rho-Omega Mixing and Direct CP Violation in Hadronic B-Decays

The extraction of CKM-matrix-element information from hadronic B-decays generally suffers from discrete ambiguities, hampering the diagnosis of physics beyond the Standard Model. We show that a measurement of the rate asymmetry, which is CP-violating, in $B^{\pm}\toρ^{\pm}ρ^0(ω)\toρ^{\pm}π^+π^-$, where the invariant mass of the $π^+π^-$ pair is in the vicinity of the $ω$ resonance, can remove the mod($π$) uncertainty in $α\equiv arg [-V_{td} V_{tb}^\ast/(V_{ud}V_{ub}^\ast)]$ present in standard analyses.

hep-ph↗

arXiv1998

New results in rho^0 meson physics

We compare the predictions of a range of existing models based on the Vector Meson Dominance hypothesis with data on e^+ e^- -> pi^+ pi^$ and e^+ e^- -> mu^+ mu^- cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these models is capable of providing an accurate representation of the full range of experimental data. We find that, of the models considered, only that proposed by Bando et al. is able to consistently account for all information, provided one allows its parameter "a" to vary from the usual value of 2 to 2.4. Our fit with this model gives a point-like coupling (gamma pi^+ π^-) of magnitude ~ -e/6, while the common formulation of VMD excludes such a term. The resulting values for the rho mass and pi^+ pi^- and e^+e^- partial widths as well as the branching ratio for the decay omega -> pi^+ pi^- obtained within the context of this model are consistent with previous results.

hep-ph↗