arXiv subjects
Publications and source records attributed to Gilberto Colangelo.
We derive an asymptotic formula a la Luscher for the finite volume correction to the pion decay constant: this is expressed as an integral over the < 3 π| A_μ|0 > amplitude after proper subtraction of the pion pole contribution. We analyze the formula numerically at leading and next-to-leading order in the chiral expansion.
I present a method for evaluating the hadronic vacuum polarization contribution below 1 GeV to a_μwhich relies on analyticity, unitarity and chiral symmetry, as well as on data. The main advantage is that in the region just above threshold, where data are either scarce or have large errors, these theoretical constraints are particularly strong, and therefore allow us to reduce the uncertainties with respect to a purely data-based evaluation. Some preliminary numerical results are presented as illustration of the method.
We determine the relative pion mass shift $M_π(L)/M_π-1$ due to the finite spatial extent $L$ of the box by means of two-flavor chiral perturbation theory and the one-particle Lüscher formula. We use as input the expression for the infinite volume $ππ$ forward scattering amplitude up to next-to-next-to-leading order and can therefore control the convergence of the chiral series. A comparison to the full leading order chiral expression for the pion mass in finite volume allows us to check the size of subleading terms in the large-$L$ expansion.
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral perturbation theory, e.g., this means that one can obtain the series of leading chiral logs by calculating only one loop diagrams. We discuss also the renormalization group equations for the subleading divergences, and the crucial role of counterterms that vanish at the equations of motion. Finally, we show that the renormalization group equations obtained here apply equally well also to renormalizable theories.
We discuss the recent literature on the treatment of final state interactions in K -> pi pi. Various approaches are compared and particular emphasis is given to the possibility of combining dispersive methods with lattice input. Recent results on the dependence of various quantities on the quark masses at order p^6 in the chiral expansion are presented and the relevance for the lattice calculations is discussed.
These lectures provide an elementary introduction to Chiral Perturbation Theory, focused on the sector of pseudoscalar meson interactions. Basic concepts and technical methods of this approach are discussed on general grounds and with the help of a few specific examples.
I briefly review the current status of chiral perturbation theory in the meson sector. Emphasis is given on the quest for higher precision. I discuss two examples: one where it is difficult to make a good prediction (K_L -> pi^0 gamma gamma), and where CHPT, even when pushed to higher orders, cannot yield an increase in accuracy. The second one is pi pi scattering where a very sharp prediction can be made by combining CHPT at the two-loop level with dispersion relations
I describe the current status of the theory of pi pi scattering, reviewing in particular recent work on the numerical solution of Roy equations and on the matching between these and the chiral representation. I discuss numerical results on the scattering lengths and other threshold parameters.
I present a quick overview of the current status of Chiral perturbation theory in the meson sector. To illustrate the successes and some problems in the description of the phenomenology, I focus on a few selected examples that are relevant for DAFNE.
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.
We analyze the contributions to rare kaon decays mediated by flavor-changing Z-penguin diagrams in a generic low-energy supersymmetric extension of the Standard Model. In order to perform a model-independent analysis we expand the squark mass matrices around the diagonal, following the so called mass-insertion approximation. We argue that in the present case it is necessary to go up to the second order in this expansion to take into account all possible large effects. The current bounds on such second-order term, which was neglected in previous analyses, are discussed in detail and the corresponding upper bounds for the rare kaon decay rates are derived. As a result, we show that supersymmetric effects could lead to large enhancements of K -> pi nu{\bar nu} and K_L -> pi^0 e^+ e^- branching ratios.
We calculate the divergences of the generating functional of quenched Chiral Perturbation Theory at one loop, and renormalize the theory by an appropriate definition of the counterterms. We show that the quenched chiral logarithms can be reabsorbed in the renormalization of the B_0 parameter which, at lowest order, is proportional to the vacuum expectation value of the scalar quark density. Finally, we calculate several quantities at one loop to analyze the modifications induced by quenching in the finite part of the one-loop corrections. We point out that some of the finite loop corrections may diverge in the chiral limit.
We calculate the divergences of the generating functional of quenched Chiral Perturbation Theory to one loop for a generic number of flavours. The flavour number dependence of our result enlightens the mechanism of quark loop cancellation in the quenched effective theory for any Green function or S matrix element. We also apply our results to $ππ$ scattering and evaluate the coefficient of the chiral log in the S-wave scattering lengths for the quenched case.
We review a variety of topics related to hadronic structure functions in exclusive semihadronic tau decays. We introduce the concept of structure functions and summarize the most important concepts. We then calculate the decay $τ\to 3 πν_τ$ for very small hadronic invariant mass to one loop in Chiral Perturbation Theory. New interesting features emerge with respect to the known results at tree level, in particular for the structure functions $w_D$ and $w_E$. We discuss the prospects for experimental verification of our predictions. Finally, we discuss various issues at higher $Q^2$, related to hadronic resonance physics. Here we consider $2π$, $πK$, $3 π$, $K πK$ and $πK π$ hadronic final states.
I compare the lattice calculation of Fukugita et al. for the pion S-wave scattering lengths to the predictions of Chiral Perturbation Theory to two loop accuracy. I find good agreement, despite the use of the quenched approximation in the lattice calculation.
By using the Renormalization Group Equations in Chiral Perturbation Theory, one can calculate the double chiral logs that appear at two loops in any matrix element. We calculate them in the $ππ$ scattering amplitude, where they represent the potentially largest two loop contribution. It is shown that their correction is reasonably small.