The Lamb Shift in Dimensional Regularization
We present a simple derivation of the Lamb shift using effective field theory techniques and dimensional regularisation.
hep-ph↗
arXiv subjects
J. Soto
Publications and source records attributed to J. Soto.
Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
We propose an effective field theory for heavy quark-antiquark bound states once the soft gluons have been integrated out. We also give new results for the matching between QCD (QED) and NRQCD (NRQED).
hep-ph↗
Heavy Quarkonium and nonperturbative corrections
We analyse the possible existence of non-perturbative contributions in heavy $\bar Q Q$ systems ($\bar Q$ and $Q$ need not have the same flavour) which cannot be expressed in terms of local condensates. Starting from QCD, with well defined approximations and splitting properly the fields into large and small momentum components, we derive an effective lagrangian where hard gluons (in the non-relativistic aproximation) have been integrated out. The large momentum contributions (which are dominant) are calculated using Coulomb type states. Besides the usual condensate corrections, we see the possibility of new non-perturbative contributions. We parametrize them in terms of two low momentum correlators with Coulomb bound state energy insertions $E_n$. We realize that the Heavy Quark Effective lagrangian can be used in these correlators. We calculate the corrections that they give rise to in the decay constant, the bound state energy and the matrix elements of bilinear currents at zero recoil. We study the cut-off dependence of the new contributions and we see that it matches perfectly with that of the large momentum contributions. We consider two situations in detail: i) $E_n>> Λ_{QCD}$ ($M_Q \rightarrow \infty$) and ii) $E_n << Λ_{QCD}$, and briefly discuss the expected size of the new contributions in $Υ$ , $J/Ψ$ and $B_{c}^{\ast}$ systems.
hep-ph↗
Heavy Quark Hadronic Lagrangian for S-wave Quarkonium
We use Heavy Quark Effective Theory (HQET) techniques to parametrize certain non-perturbative effects related to quantum fluctuations that put both heavy quark and antiquark in quarkonium almost on shell. The large off-shell momentum contributions are calculated using Coulomb type states. The almost on-shell momentum contributions are evaluated using an effective 'chiral' lagrangian which incorporates the relevant symmetries of the HQET for quarks and antiquarks. The cut-off dependence of both contributions matches perfectly. The decay constants and the matrix elements of bilinear currents at zero recoil are calculated. The new non-perturbative contributions from the on-shell region are parametrized by a single constant. They turn out to be $O(α^2/Λ_{QCD} a_{n})$, $a_{n}$ being the Bohr radius and $α$ the strong coupling constant, times the non-perturbative contribution coming from the multipole expansion (gluon condensate). We discuss the physical applications to $Υ$, $J/Ψ$ and $B_{c}$ systems.
hep-ph↗
Matching the HQET to Coulomb Type Bound States
We show that the infinite imaginary anomalous dimensions of certain heavy quark-antiquark currents in the HQET arise due to an inappropriate commutation of two limits, namely coinciding velocities and infinite cut-off. This commutation is not apparent when dimensional regularization is used, but it can be made manifest in a cut-off regularization. We argue that operators containing heavy quark and antiquark fields with the same velocity in the HQET must not be matched to perturbative QCD but to Coulomb-type bound state contributions. We show how to do so at one loop level.
hep-ph↗
Extra symmetries in the effective theory of heavy quarks
Extra symmetries are shown to exist in the effective theory of heavy quarks when both quarks and anti-quarks with the same velocity are included. These symmetries mix the quark with the anti-quark sector and they resemble axial-type of symmetries. Together with the known flavor and spin symmetries they form a $u(4)$ algebra when a single flavor is considered. It is shown that the full $U(4)$ set of symmetries breaks spontaneously down to $ U(2) \otimes U(2)$. The Goldstone modes corresponding to the spontaneously broken currents are identified. Finally, the precise connection of this theory with the fundamental QCD is derived and it is investigated under some approximations. Some physical processes where these extra symmetries may be relevant are pointed out.
hep-ph↗
Anomalies in the effective theory of heavy quarks
The question of the anomalies in the effective theory of heavy quarks is investigated at two different levels. Firstly, it is shown that none of the symmetries of this effective theory contains an anomaly. The existence of a new `$ γ_ 5 $'-symmetry is pointed out and shown to be also anomaly free. Secondly, it is shown that the chiral anomaly of QCD is not reproduced in the effective lagrangian for the heavy quarks, thus contradicting 't Hooft's anomaly matching condition. Finally, the effective theory of heavy quarks is derived from the QCD lagrangian in such a way that the terms leading to the anomaly are included. For this derivation the generating functional method is used.
hep-ph↗