arXiv subjects

S. Bertolini

Publications and source records attributed to S. Bertolini.

15 recordsLinked to original sources

arXiv2003

Fermion Masses and Mixings in the Little Flavon Model

We present a complete analysis of the fermion masses and mixing matrices in the framework of the little flavon model. In this model textures are generated by coupling the fermions to scalar fields, the little flavons, that are pseudo-Goldstone bosons of the breaking of a global SU(6) symmetry. The Yukawa couplings arise from the vacuum expectation values of the flavon fields, their sizes controlled by a potential a la Coleman-Weinberg. Quark and lepton mass hierarchies and mixing angles are accomodated within the effective approach in a natural manner.

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arXiv2003

The little flavons

Fermion masses and mixing matrices can be described in terms of spontaneously broken (global or gauge) flavor symmetries. We propose a little-Higgs inspired scenario in which an SU(2)xU(1) gauge flavor symmetry is spontaneously (and completely) broken by the vacuum of the dynamically induced potential for two scalar doublets (the flavons) which are pseudo-Goldstone bosons remaining after the spontaneous breaking--at a scale between 10 and 100 TeV--of an approximate SU(6) global symmetry. The vacuum expectation values of the flavons give rise to the texture in the fermion mass matrices. We discuss in detail the case of leptons. Light-neutrino masses arise by means of a see-saw-like mechanism that takes place at the same scale at which the SU(6) global symmetry is broken. We show that without any fine tuning of the parameters the experimental values of the charged-lepton masses,the neutrino square mass differences and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix are reproduced.

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arXiv1999

Estimating epsilon'/epsilon. A Review

The real part of epsilon'/epsilon measures direct CP violation in the decays of the neutral kaons in two pions. It is a fundamental quantity which has justly attracted a great deal of theoretical as well as experimental work. Its determination may answer the question of whether CP violation is present only in the mass matrix of neutral kaons (the superweak scenario) or also at work directly in the decays. After a brief historical summary, we discuss the present and expected experimental sensitivities. In the light of these, we come to the problem of estimating epsilon'/epsilon in the standard model. We review the present (circa 1998) status of the theoretical predictions of epsilon'/epsilon. The short-distance part of the computation is now known to the next-to-leading order in QCD and QED and therefore well under control. On the other hand, the evaluation of the hadronic matrix element of the relevant operators is where most of the theoretical uncertainty still resides. We analyze the results of the currently most developed calculations. The values of the B_i parameters in the various approaches are discussed, together with the allowed range of the relevant combination of the Cabibbo-Kobayashi-Maskawa entries Im V_{td}V^*_{ts}. We conclude by summarizing and comparing all up-to-date predictions of epsilon'/epsilon. Because of the intrinsic uncertainties of the long-distance computations, values ranging from 10^{-4} to a few times 10^{-3} can be accounted for in the standard model. Since this range covers most of the present experimental uncertainty, it is unlikely that new physics effects can be disentangled from the standard model prediction. For updates on the review and additional material see http://www.he.sissa.it/review/.

hep-ph↗

arXiv1999

Estimating epsilon'/epsilon in the Standard Model

I discuss the comparison of the current theoretical calculations of epsilon'/epsilon with the experimental data. Lacking reliable ``first principle'' calculations, phenomenological approaches may help in understanding correlations among different contributions and available experimental data. In particular, in the chiral quark model approach the same dynamics which underlies the Delta I = 1/2 selection rule in kaon decays appears to enhance the K -> pi pi matrix element of the Q_6 gluonic penguin, thus driving epsilon'/epsilon in the range of the recent experimental measurements.

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arXiv1998

$ε'/ε$ at $O(p^4)$ in the Chiral Expansion

After updating the determination of the combination of Kobayashi-Maskawa elements $ \Im V_{td}V^*_{ts}$ according to our new estimate of the parameter $\hat B_K$, we study the CP-violating ratio $ε'/ε$ by means of hadronic matrix elements computed to $O(p^4)$ in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some $O(p^2)$ terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio $ε'/ε$ is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find $ε'/ε= 1.7 ^{+1.4}_{-1.0} \times 10^{-3}$. Values positive and of the order of $10^{-3}$ are therefore preferred.

hep-ph↗

arXiv1998

The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion

We calculate the hadronic matrix elements to $O(p^4)$ in the chiral expansion for the ($ΔS =1$) $K^0 \to 2 π$ decays and the ($ΔS=2$) $\bar K^0$-$K^0$ oscillation. This is done within the framework of the chiral quark model. The chiral coefficients thus determined depend on the values of the quark and gluon condensates and the constituent quark mass. We show that it is possible to fit the $ΔI =1/2$ rule of kaon decays with values of the condensates close to those obtained by QCD sum rules. The renormalization invariant amplitudes are obtained by matching the hadronic matrix elements and their chiral corrections to the short-distance NLO Wilson coefficients. For the same input values, we study the parameter $\hat B_K$ of kaon oscillation and find $\hat B_K = 1.1 \pm 0.2$. As an independent check, we determine $\hat B_K$ from the experimental value of the $K_L$-$K_S$ mass difference by using our calculation of the long-distance contributions. The destructive interplay between the short- and long-distance amplitudes yields $\hat B_K = 1.2 \pm 0.1$, in agreement with the direct calculation.

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arXiv1997

The $b\to sγγ$ transition in softly broken supersymmetry

We study the effect of supersymmetric contributions to the effective quark transition $b\to sγγ$, including leading order QCD effects. We apply the discussion to the decay $B_s\toγγ$. Even though one-particle irreducible contributions could play a role, numerical cancelations make the amplitude for the two-photon emission strongly correlated to the $b\to sγ$ amplitude which is sharply constrained by experiment. A quite general statement follows: as long as non-standard physics effects appear only in the matching of the Wilson coefficients of the standard effective operator basis, the deviations from the standard model expectations of the decay rates induced by $b\to sγγ$ are bound to follow closely the corresponding deviations on $b\to sγ$. Effects of new physics are therefore bound to be small.

hep-ph↗

arXiv1997

The Physics of $K^0 -\bar K^0$ Mixing: $\widehat{B}_K$ and $ΔM_{LS}$ in the Chiral Quark Model

We compute the $\widehat B_K$ parameter and the mass difference $ΔM_{LS}$ of the $K^0-\bar K^0$ system by means of the chiral quark model. The chiral coefficients of the relevant $ΔS=2$ and $ΔS=1$ chiral lagrangians are computed via quark-loop integration. We include the relevant effects of one-loop corrections in chiral perturbation theory. The final result is very sensitive to non-factorizable corrections of $O(α_S N)$ coming from gluon condensation. The size of the gluon condensate is determined by fitting the experimental value of the amplitude $K^+ \to π^+π^0$. By varying all the relevant parameters we obtain $\widehat{B}_K= 0.87 \pm 0.33\ .$ We evaluate within the model the long-distance contributions to $ΔM_{LS}$ induced by the double insertion of the $ΔS = 1$ chiral lagrangian and study the interplay between short- and long-distance amplitudes. By varying all parameters we obtain $ΔM_{LS}^{th}/ΔM_{LS}^{exp} = 0.76 ^{+0.64}_{-0.34} .$ Finally, we investigate the phenomenological constraints on the Kobayashi-Maskawa parameter Im $λ_t$ entering the determination of $ε'/ε$.

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arXiv1996

A New Estimate of $\varepsilon '/\varepsilon$

We discuss a new estimate of $\varepsilon '/\varepsilon$ in the kaon system. The present approach is based on the evaluation of the hadronic matrix elements of the \mbox{$ΔS =1$} effective quark lagrangian by means of the chiral quark model, with the inclusion of meson one-loop renormalization and NLO Wilson coefficients. The estimate here reviewed is fully consistent with the $ΔI =1/2$ selection rule in $K\to ππ$ decays, which is well reproduced within the same framework.

hep-ph↗

arXiv1996

The $ΔS = 1$ Weak Chiral Lagrangian as the Effective Theory of the Chiral Quark Model

We use the chiral quark model to estimate the coefficients of the weak chiral lagrangian as obtained from the bosonization of the ten relevant operators of the $ΔS = 1$ effective quark lagrangian. All contributions of order $N_c^2$ as well as $N_c$ and $α_s N_c$ are included. The chiral coefficients are given in terms of $f_π$, the quark and gluon condensates and the scale-dependent NLO Wilson coefficients of the corresponding operators. In addition, they depend on the constituent quark mass $M$, a parameter characteristic of the model. The $γ_5$-scheme dependence of the chiral coefficients, computed via dimensional regularization, and the Fierz transformation properties of the operator basis are discussed in detail. We apply our result to the evaluation of the hadronic matrix elements for the decay $K^0 \rightarrow 2 π$, consistently including the renormalization induced by the meson loops. The effect of this renormalization is sizable and introduces a long-distance scale dependence that matches in the physical amplitudes the short-distance scale dependence of the Wilson coefficients.

hep-ph↗

arXiv1996

A New Estimate of $\varepsilon '/\varepsilon$

We discuss direct $CP$ violation in the standard model by giving a new estimate of $\varepsilon'/\varepsilon$ in kaon decays. Our analysis is based on the evaluation of the hadronic matrix elements of the \mbox{$ΔS =1$} effective quark lagrangian by means of the chiral quark model, with the inclusion of meson one-loop renormalization and NLO Wilson coefficients. Our estimate is fully consistent with the $ΔI =1/2$ selection rule in $K\to ππ$ decays which is well reproduced within the same framework. By varying all parameters in the allowed ranges and, in particular, taking the quark condensate---which is the major source of uncertainty---between $(-200\ {\rm MeV})^3$ and $(-280\ {\rm MeV})^3$ we find $$ -5.0 \times 10^{-3}\ <\varepsilon'/\varepsilon <\ 1.4 \times 10^{-3}\ .$$ Assuming for the quark condensate the improved PCAC result \mbox{$\vev{\bar qq} = -(221\: \pm 17\ {\rm MeV})^3$} and fixing $Λ_{\rm QCD}^{(4)}$ to its central value, we find the more restrictive prediction $$\varepsilon '/\varepsilon = ( 4 \pm 5 ) \,\times \,10^{-4}\ , $$ where the central value is defined as the average over the allowed values of Im $λ_t$ in the first and second quadrants. In these estimates the relevant mixing parameter Im $λ_t$ is self-consistently obtained from $\varepsilon$ and we take $m_t^{\rm pole} = 180 \pm 12$ GeV. Our result is, to a very good approximation, renormalization-scale and $γ_5$-scheme independent.

hep-ph↗

arXiv1996

The $ΔI = 1/2$ Selection Rule

We compute the isospin $I= 0$ and 2 amplitudes for the decay of a kaon into two pions by estimating the relevant hadronic matrix elements in the chiral quark model. The results are parametrized in terms of the quark and gluon condensates and of the constituent quark mass $M$. The latter is a parameter characteristic of the model, that we restrict by matching the results in the two $γ_5$-schemes (HV and NDR) of dimensional regularization. We find that, for values of these parameters within the current determinations, the $ΔI= 1/2$ selection rule is well reproduced by means of the cumulative effects of short-distance NLO Wilson coefficients, penguin diagrams, non-factorizable soft-gluon corrections and meson-loop renormalization.

hep-ph↗

arXiv1994

Studying $\varepsilon '/\varepsilon$ in the Chiral Quark Model: $γ_5$-Scheme Independence and NLO Hadronic Matrix Elements

We study the $CP$-violating, $|ΔS| =1$ parameter $\varepsilon '/\varepsilon$ by computing the hadronic matrix elements in the chiral quark model. We estimate the coefficients of the next-to-leading order terms in the chiral expansion that correspond to the operators $Q_6$ and $Q_{11}$. We consider the impact of these corrections on the value of $\varepsilon '/\varepsilon$. We also investigate the possibility that the chiral quark model might drastically reduce the dimensional regularization $γ_5$-scheme dependence of current evaluations of $\varepsilon '/\varepsilon$.

hep-ph↗

arXiv1994

The Relevance of the Dipole Penguin Operators in $ε'/ε$

The standard model contribution to $ε'/ε$ of the magnetic- and electric-dipole penguin operators $Q_{11} = \frac{g_s}{16π^2} \, m_s \: \bar{s}\, σ_{μν} t^a G^{μν}_a (1-γ_5 )\, d $ and $Q_{12} = \frac{eQ_d}{16π^2}\, m_s \: \bar{s}\, σ_{μν} F^{μν} (1-γ_5 )\, d $ is discussed. While the electromagnetic penguin $Q_{12}$ seems to have a vanishingly small matrix element, we find that the gluonic dipole operator $Q_{11}$ may give a contribution to $ε'/ε$ comparable to that of other operators so far considered, and should therefore be consistently included in the analysis.

hep-ph↗

arXiv1993

On soft breaking and CP phases in the supersymmetric standard model

We consider a class of N=1 supersymmetric extensions of the Standard Model in which the soft breaking sector is CP conserving at the GUT scale. We study the question of whether the presence of explicit CP violation in the Yukawa sector of the theory induces through renormalization effects CP violating phases in the soft terms, which could lead to observable effects. A clear pattern appears in the structure of phases in the soft sector. In particular, the inclusion of intergenerational mixing induces large phases in the flavour mixing entries of the trilinear soft breaking terms, whereas the diagonal entries remain real. A mechanism is proposed for generating through chargino exchange a contribution to the neutron electric dipole moment which can be a few orders of magnitude larger that that of the Standard Model, although still out of reach of experimental tests. We comment on the possible relevance of these phases for baryogenesis at the weak scale in minimal supersymetric scenarios, recently considered in the literature.

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