We study the shift of the chiral condensate in a constant electromagnetic field in the context of chiral perturbation theory. Using the Schwinger proper-time formalism, we derive a one-loop expression correct to all orders in m 2 π /eH . Our result correctly reproduces a previously derived "low-energy theorem" for m π = 0. We show that it is essential to include corrections due to nonvanishing m π for a theorem of low energy to have any approximate regime of validity in the physical universe. We generalize these results to systems containing electric fields and discuss the regime of validity for the results. In particular, we discuss the circumstances in which the method formally breaks down due to pair creation in an electric field.
Bottom-up holographic models of QCD, inspired by the anti-de Sitter space/conformal field theory correspondence, have shown a remarkable degree of phenomenological success. However, they rely on a number of bold assumptions. We investigate the reliability of one of the key assumptions, which involves matching the parameters of these models to QCD at high 4D momentum q 2 and renormalization scale µ 2 . We show that this leads to phenomenological and theoretical inconsistencies for scale-dependent quantities such as qq .
The response of the QCD vacuum to very large static external magnetic fields (q B >> Lambda_QCD^2) is studied. In this regime, the magnetization of the QCD vacuum is naturally described via perturbative QCD. Combining pQCD and the Schwinger proper time formalism, we calculate the magnetization of the QCD vacuum due to a strong magnetic field at leading order (one-loop) to be proportional to B log B. We show that the leading perturbative correction (two-loop) vanishes.Comment: LaTeX: 6 pages, 1 figur
We examine the shift in the chiral condensate due to a constant electromagnetic field at O(p 6 ) using SU (2) chiral perturbation theory and a realistic Mπ = 140 MeV. We find that this value differs significantly from the value calculated using Mπ = 0, while the magnitude of the two-loop correction is unclear due to the uncertainty in the experimentally determined value of the relevant L6 LEC.
Quark-hadron duality implies that a process described in terms of quark loops should be the hadronic amplitude when averaged over a sufficient number of states. Ambiguities associated with the notion of quark hadron duality can be made arbitrarily small for highly excited mesons at large Nc. QCD is expected to form a string like description at large Nc yielding an exponentially increasing Hagedorn spectrum for high mass. It is shown that in order to reconcile quantum-hadron duality with a Hagedorn spectrum, the magnitude of individual coupling constants between highlying mesons in a typical decay process must be characteristically larger than the average of the coupling constants to mesons with nearby masses. The ratio of the square of the average coupling to the average of the coupling squared (where the average is over mesons with nearby masses) drops exponentially with the mass of the meson. Scenarios are discussed by which such a high precision cancellation can occur.It is well known that QCD in the limit of an infinite number of colors has an infinite number of infinitely narrow meson states [1]. The narrowness arises from the fact that meson-meson interactions are suppressed by powers of 1/N c . Clearly at finite N c the widths are finite due to decays. At large but finite N c , one expects that mesons of increasing mass become increasingly broad-eventually to the point where they are no longer discernable. It is not immediately clear what, if anything, one can deduce about multi-meson couplings from general considerations of large N c QCD. In this paper we show that we can infer important qualitative information about couplings of highly excited mesons at large but finite N c . In particular, one can show that the magnitude of the coupling constant for a typical three meson vertex involved in the decay process is much larger than the average of such coupling over a large number of mesons with the same quantum numbers and nearby masses. Indeed, at large N c the ratio of the square of the average coupling to the average of the coupling squared (where the average is over mesons with nearby masses) drops exponentially with the mass of the meson.This rather striking result can be derived from two well-founded pieces of physics which are thought to become exact at large N c . The first of these is quarkhadron duality-the general principle that the amplitude for a hadronic process smeared over a sufficient number of states will be equal to the amplitude as calculated from a (perturbative) quark process [2]. The second is the widely accepted view that at large N c and high excitations mesons can be represented by QCD strings [3,4]. We should note here that analogous arguments can be formulated for glueballs and one expects the same qualitative features.We wish to stress, that result here is by no means obvious. Clearly, a Hagedorn spectrum implies that any two-point correlation function of QCD composite operators will have couplings of the external couplings falling exponentially with the mass: the spectral stren...
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