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Register a new userFalse Vacuum Decay in QCD within an Effective Lagrangian Approach
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Authors
Todd Fugleberg
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In an effective Lagrangian approach to QCD we nonperturbatively calculate an analytic approximation to the decay rate of a false vacuum per unit volume, $Gamma/V$. We do so for both zero and high temperature theories. This result is important for the study of the early universe at around the time of the QCD phase transition. It is also important in order to determine the possibility of observing this false vacuum decay at the Relativistic Heavy Ion Collider (RHIC). Previously described dramatic signatures of the decay of false vacuum bubbles would occur in our case as well.
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The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter $xi$ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge parameter even after the renormalization.
Using the well-known low-energy effective Lagrangian of QCD --valid for small (non-vanishing) quark masses and a large number of colors-- we study in detail the regions of parameter space where $CP$ is spontaneously broken/unbroken for a vacuum angle $theta= pi$. In the $CP$-broken region there are first order phase transitions as one crosses $theta=pi$, while on the (hyper)surface separating the two regions, there are second order phase transitions signaled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the $CP$ spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised when the QCD parameters fall in the above mentioned $CP$-broken region, in spite of the fact that the axion solves the strong-$CP$ problem. These latter results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.
We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the models target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions.
An effective Lagrangian approach based on the heavy quark and chiral symmetry is introduced to analyse the spectroscopy of open charm mesons. Strong two-body decay widths and ratios of branching fractions are computed, and this piece of information is used to assign quantum numbers to recently observed charmed states which still need to be properly classified.
We propose a simple non-perturbative formalism for false vacuum decay using functional methods. We introduce the quasi-stationary effective action, a bounce action that non-perturbatively incorporates radiative corrections and is robust to strong couplings. The quasi-stationary effective action obeys an exact flow equation in a modified functional renormalization group with a motivated regulator functional. We demonstrate the use of this formalism in a simple toy model and compare our result with that obtained in perturbation theory.
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