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E. de Rafael

Publications and source records attributed to E. de Rafael.

At least 19 recordsLinked to original sources
arXiv2003

Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD

We present new results for the matrix elements of the Q_6 and Q_4 penguin operators, evaluated in a large-Nc approach which incorporates important O(N_c^2\frac{n_f}{N_c}) unfactorized contributions. Our approach shows analytic matching between short- and long-distance scale dependences within dimensional renormalization schemes, such as MS-bar. Numerically, we find that there is a large positive contribution to the Delta I =1/2 matrix element of Q_6 and hence to the direct CP-violation parameter epsilon'/epsilon. We also present results for the Delta I = 1/2 rule in K -> pi pi amplitudes, which incorporate the related and important ``eye-diagram'' contributions of O(N_c^2\frac{1}{N_c}) from the Q_2 operator (i.e. the penguin-like contraction). The results lead to an enhancement of the Delta I = 1/2 effective coupling. The origin of the large unfactorized contributions which we find is discussed in terms of the relevant scales of the problem.

hep-ph↗
arXiv2002

Electroweak Hadronic Contributions to the muon g-2

We reanalyze the two-loop electroweak hadronic contributions to the muon g-2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Green's function.

hep-ph↗
arXiv2002

Hadronic light-by-light scattering contribution to the muon g-2: an effective field theory approach

The hadronic light-by-light contribution to a_{mu}, the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a_{mu}, and to a sizeable reduction of the discrepancy between the present experimental value of a_{mu} and its theoretical counterpart in the standard model.

hep-ph↗
arXiv2001

Testing an approximation to large-Nc QCD with a toy model

We consider a simple model of large-Nc QCD defined by a spectrum consisting of an infinite set of equally spaced zero-width vector resonances. This model is an excellent theoretical laboratory for investigating certain approximation schemes which have been used recently in calculations of hadronic parameters, such as the Minimal Hadronic Approximation. We also comment on some of the questions concerning issues of local duality versus global duality and finite-energy sum rules.

hep-ph↗
arXiv2001

A Critical Reassessment of Q7 and Q8 Matrix Elements

We compare recent theoretical determinations of weak matrix elements of the electroweak penguin operators Q7 and Q8. We pay special attention to the renormalization scheme dependence of these determinations as well as to the influence of higher dimension operators in the different approaches.

hep-ph↗
arXiv2000

Minimal Hadronic Ansatz to Large-Nc QCD and Hadronic tau Decay

I report on some recent work done in collaboration with Santi Peris and Boris Phily (hep-ph/0007338) where, using the Aleph data on vector and axial-vector spectral functions, we test simple duality properties of QCD in the large-Nc limit which emerge in the approximation of a {\it minimal hadronic ansatz} of a spectrum of narrow states. These duality properties relate the short- and long-distance behaviours of specific correlation functions, which are order parameters of spontaneous chiral symmetry breaking, in a way that we find well supported by the data.

hep-ph↗
arXiv2000

Tests of large-Nc QCD from hadronic tau decay

We use the Aleph data on vector and axial-vector spectral functions to test simple duality properties of QCD in the large Nc limit, which emerge in the approximation of a minimal hadronic ansatz of a spectrum of narrow states. These duality properties relate the short- and long-distance behaviours of specific correlation functions, which are order parameters of spontaneous chiral symmetry breaking, in a way that we find well supported by the data.

hep-ph↗
arXiv1999

A New Approach to Weak Amplitudes in Large-Nc QCD

We report on some recent progress made in understanding weak matrix elements of mesons in the context of the next-to-leading order of the large-Nc approximation to QCD. Specifically, we first use the example of the weak contributions to the pi^+ - pi^0 mass difference to exhibit how a systematic matching can be achieved analytically between short distances and long distances within our large-Nc framework. We are then also able to compute matrix elements of the operator Q_7, as they turn out to depend on the same QCD correlator as the previous pion mass difference. As a final example we determine the chiral counterterms governing the pseudoscalar decay into a lepton pair, where we briefly comment also on the special case K_L -> mu^+ mu^-.

hep-ph↗
arXiv1999

Decay of pseudoscalars into lepton pairs and large-Nc QCD

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colours Nc. When further restricted to the lowest meson dominance approximation to large-Nc QCD, our results agree well with the available experimental data.

hep-ph↗
arXiv1999

Matrix Elements of Electroweak Penguin Operators in the 1/Nc Expansion

It is shown that the K -> pi pi matrix elements of the four-quark operator Q_7, generated by the electroweak penguin-like diagrams of the Standard Model, can be calculated to first non-trivial order in the chiral expansion and in the 1/Nc expansion. Although the resulting B factors B_7^(1/2) and B_7^(3/2) are found to depend only logarithmically on the matching scale, mu, their actual numerical values turn out to be rather sensitive to the precise choice of mu in the GeV region. We compare our results to recent numerical evaluations from lattice-QCD and to other model estimates.

hep-ph↗
arXiv1998

The electroweak pi^+ - pi^0 mass difference and weak matrix elements in the 1/Nc expansion

The pi^+ - pi^0 mass difference generated by the electroweak interactions of the Standard Model is expressed, to lowest order in the chiral expansion and to leading order in alpha, in terms of an integral involving the same correlation function Pi_{LR}(Q^2) which governs the well known electromagnetic pi^+ - pi^0 mass difference. We calculate this contribution within the framework of QCD in the limit of a large number of colours $N_c$. We show how this calculation, which requires non-trivial contributions from next-to-leading terms in the 1/Nc expansion, provides an excellent theoretical laboratory for studying issues of long- and short-distance matching in calculations of weak matrix elements of four-quark operators. The electroweak pi^+ - pi^0 mass difference turns out to be a physical observable which is under good analytical control and which should, therefore, be an excellent testground of numerical evaluations in lattice-QCD and of model calculations in general.

hep-ph↗
arXiv1998

Matching Long and Short Distances in Large-Nc QCD

It is shown, with the example of the experimentally known Adler function, that there is no matching in the intermediate region between the two asymptotic regimes described by perturbative QCD (for the very short-distances) and by chiral perturbation theory (for the very long-distances). We then propose to consider an approximation of large-Nc QCD which consists in restricting the hadronic spectrum in the channels with J^P quantum numbers 0^-, 1^-, 0^+ and 1^+ to the lightest state and treating the rest of the narrow states as a perturbative QCD continuum; the onset of this continuum being fixed by consistency constraints from the operator product expansion. We show how to construct the low-energy effective Lagrangian which describes this approximation. The number of free parameters in the resulting effective Lagrangian can be reduced, in the chiral limit where the light quark masses are set to zero, to just one mass scale and one dimensionless constant to all orders in chiral perturbation theory. A comparison of the corresponding predictions, to O(p^4) in the chiral expansion, with the phenomenologically known couplings is also made.

hep-ph↗
arXiv1997

Patterns of Spontaneous Chiral Symmetry Breaking in the Large-Nc Limit of QCD-Like Theories

It is shown that in vector-like gauge theories, such as QCD, and in the limit of a large number of colours Nc, the ordering pattern of narrow vector and axial-vector states at low energies is correlated with the size of the possible local order parameters of chiral symmetry breaking. This has implications on the underlying dynamics of spontaneous chiral symmetry breaking in QCD, and also on possible values of the parameter S for oblique electroweak corrections, the analogue of the QCD low energy constant L10.

hep-ph↗
arXiv1997

How small can the light quark masses be?

We derive lower bounds for the combination of light quark masses m_s +m_u and m_d +m_u. The derivation is based on first principles: the analyticity properties of two-point functions of local current operators and the positivity of the corresponding hadronic spectral functions. The bounds follow from the restriction of the sum over all possible hadronic states which can contribute to the hadronic spectral functions to those with the lowest invariant mass. These hadronic contributions are well known phenomenologically, either from experiment or from chiral perturbation theory calculations. The results we find cast serious doubts on the reliability of some of the lattice QCD determinations which have been recently reported.

hep-ph↗
arXiv1997

Electroweak Effective Charges and their relation to Physical Cross Sections

In quantum electrodynamics with fermions f = e,μ..., knowledge of the vacuum polarization spectral function determined from the tree level e^+e^- -> f^+f^- cross sections, together with a single low energy measurement of the fine structure constant α, enables the construction of the one-loop effective charge α_eff(q^2) for all q^2. It is shown how an identical procedure can be followed in the electroweak sector of the Standard Model to construct three gauge-, scale- and scheme-independent one-loop electroweak effective charges and an effective weak mixing angle from the tree level e^+e^- -> W^+W^-, ZH and e^+ν_e -> W^+Z, W^+γ, W^+H differential cross sections, together with three low energy measurements, which may be chosen to be αand the masses of the W and Z bosons. It is found that the corresponding proper self-energy-like functions thus constructed are identical to those obtained in the pinch technique framework. In this way, it is shown how the concept of effective charges in the electroweak Standard Model is as well-defined and unique as in quantum electrodynamics.

hep-ph↗
arXiv1997

Low-Energy QCD and Ultraviolet Renormalons

We discuss the contribution of ultraviolet (UV) renormalons in QCD to two-point functions of quark current operators. This explicitly includes effects due to the exchange of one renormalon chain as well as two chains. It is shown that, when the external euclidean momentum of the two-point functions becomes smaller than the scale $Λ_L$ associated with the Landau singularity of the QCD one-loop running coupling constant, the positions of the UV renormalons in the Borel plane become true singularities in the integration range of the Borel transform. This introduces ambiguities in the evaluation of the corresponding two-point functions. The ambiguities associated with the leading UV renormalon singularity are of the same type as the contribution due to the inclusion of dimension d=6 local operators in a low-energy effective Lagrangian valid at scales smaller than $Λ_L$. We then discuss the inclusion of an infinite number of renormalon chains and argue that the previous ambiguity hints at a plausible approximation scheme for low-energy QCD, resulting in an effective Lagrangian similar to the one of the extended Nambu-Jona-Lasinio (ENJL) model of QCD at large N_c.

hep-ph↗
arXiv1996

On Renormalons and Landau Poles in Gauge Field Theories

It is shown that the commonly accepted relationship between the Landau singularity in the running coupling constant of QED or QCD and the renormalon singularities in the Borel sums of perturbation theory expansions is only a particular feature of the restriction of the perturbative $β$--function to the one loop level.

hep-ph↗