Lifetime of a Disoriented Chiral Condensate

The lifetime of a disoriented chiral condensate formed within a heat bath of pions is calculated assuming temperatures and densities attainable at present and future heavy-ion colliders. A generalization of the reduction formula to include coherent states allows us to derive a formula for the decay rate. We predict the half-life to be between 4 and 7 fm/c, depending on the assumed pion density. We also calculate the lifetime in the presence of higher resonances and baryons, which shortens the lifetime by at most 20%. PACS numbers: 25.75.-q, 11.30.Rd, 12.38.Mh Typeset using REVTEX Formation of hot and dense matter in heavy-ion collisions has the possibility of creating a phase where chiral symmetry is restored. As this matter cools and expands, the vacuum could relax into the “wrong” zero temperature ground state. Subsequent shifting of the vacuum back into alignment with the outside world could then lead to an excess of low momentum pions [1] in a single direction in isospin space [2]. This excess is called a disoriented chiral condensate (DCC) and many studies have looked into whether its presence could be a signal of chiral symmetry restoration in heavy-ion collisions. Most of the discussion has centered around the details of formation of such regions [1–6]. There has been a general consensus that these regions could be numerous and large enough with the conditions at RHIC and the LHC to be detected. While the idea of DCC-formation is appealing, the physics governing the chiral phase transition is not known well enough to make reliable predictions about the possible formation of these condensates. Experiment is needed to establish their existence. The ability to detect a DCC from hadronic observables in heavy-ion collisions depends on the condensate lifetime. An early estimate [4] gave a half-life of τ ∼ 3 fm/c. A more recent calculation [5] has found a damping rate of γ ∼ 1 (fm/c). This roughly corresponds to a half-life of τ ∼ 1/γ ∼ 1 fm/c, which would be short enough to jeopardize the definiteness of the signal. This calculation was based on the O(4) sigma model in the symmetric phase. However, after formation, the DCC lives in the phase of spontaneously broken chiral symmetry. Characteristic of this phase is the suppression of S-wave scattering among pions, which should protect the low momentum pion modes in the DCC. Indeed, an extension of Ref. [5] to the broken phase produces smaller damping rates [6]. The purpose of this letter is to provide a reliable estimate of the lifetime of a DCC state in the hadronic (chirally broken) phase. Defining the DCC to be a coherent state of pions with low momenta, we derive a general formula for the decay rate in the presence of other hadrons. The effect of higher resonances as well as that of baryons to the DCC lifetime is also estimated. Our calculation is constrained by data at every point possible. Assuming the formation of a DCC, interactions with the thermal heat bath can enhance or deplete the number of pions in the condensate. In a heavy-ion collision, pions are the most abundant thermal particles, and so their interactions with the DCC is expected to give the dominant contribution to the decay rate. The DCC can be written as a coherent state [2,4]