We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm) 3 and (11 fm) 3 and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of Nt = 8. The disconnected chiral susceptibility, χ disc shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous cross-over for mπ = 135 MeV. The peak location determines a pseudo-critical temperature Tc = 155(1)(8) MeV. Chiral SU (2)L ×SU (2)R symmetry is fully restored above 164 MeV, but anomalous U (1)A symmetry breaking is non-zero above Tc and vanishes as T is increased to 196 MeV.PACS numbers: 11.15. Ha, 12.38.Gc As the temperature of the QCD vacuum is increased above the QCD energy scale Λ QCD = 300 MeV, asymptotic freedom implies that the vacuum breaking of chiral symmetry must disappear and the familiar chirally-asymmetric world of massive nucleons and light pseudoGoldstone bosons must be replaced by an SU (2) L × SU (2) R symmetric plasma of nearly massless up and down quarks and gluons. Predicting, observing and characterizing this transition has been an experimental and theoretical goal since the 1980's. General principles are consistent with this being either a first-order transition for sufficiently light pion mass or a second-order transition in the O(4) universality class at zero pion mass with cross-over behavior for non-zero m π . While second order behavior is commonly expected, first-order behavior may be more likely if anomalous U (1) A symmetry is partially restored at T c resulting in an effectiveThe importance of the SU (2) L × SU (2) R chiral symmetry of QCD for the phase transition has motivated the widespread use of staggered fermions in lattice studies of QCD thermodynamics because this formulation possesses one exact chiral symmetry at finite lattice spacing, broken only by the quark mass. However, the flavor symmetry of the staggered fermion formulation is complicated showing an SU L (4) × SU R (4) "taste" symmetry that is broken by lattice artifacts and made to resemble the physical SU (2) L × SU (2) R symmetry by taking the square root of the Dirac determinant, a procedure believed to have a correct but subtle continuum limit for non-zero quark masses.

We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: 24 3 × 8 and 32 3 × 8, where the larger volume varies in linear size between 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, 16 3 ×8 volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the SU (2) L × SU (2) R and U (1) A symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, T c , of approximately 165 MeV consistent with previous results and strong finite volume dependence below T c . Clear evidence is seen for U (1) A symmetry breaking above T c which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U (1) A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N τ = 8 and spatial extent N σ = 16 in a temperature range of T = 139 − 195 MeV, corresponding to lattice spacings of a ≈ 0.12 − 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m π = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U (1) A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U (1) A and chiral symmetry restoration via Banks-Casher relations.

Translational and rotational excitation of the CO 2 (00 0 0) vibrationless state in the collisional quenching of highly vibrationally excited perfluorobenzene: Evidence for impulsive collisions accompanied by large energy transfers Classical trajectory calculations of the rate of collisional energy transfer between a bath gas and a highly excited polyatomic method, and the average energy transferred per collision, as functions of the bath gas translational energy and temperature, are reported. The method used is that of Lim and Gilbert [J. Phys. Chem. 94, 72 (1990)], which requires only about 500 trajectories for convergence, and generates extensive data on the collisional energy transfer between Xe and azulene, as a function of temperature, initial relative translational energy (E T)' and azulene initial internal energy (E'). The observed behavior can be explained qualitatively in terms of the Xe interacting in a chattering collision with a few substrate atoms, with the collision duration being much too brief to permit ergodicity but with a general tendency to transfer energy from hotter to colder modes (both internal and translational). At thermal energies, trajectory and experimental data show that the root-mean-squared energy transfer per collision, (ali 2) 112, is relatively less dependent on E' than the mean energy transfer (ali). The calculated temperature dependence is weak: (AE 2) 112 0:: To. 3 , corresponding to (AE down) 0:: To. 23 • Values for the calculated average rotational energy transferred per collision (data currently only available from trajectories, and required for falloff calculations for radical-radical and ion-molecule reactions) are of the order of k B T, and similar to those for the internal energy; there is extensive collision-induced internal-rotational energy transfer. The biased random walk "model B," as discussed in text, is found to be in accord with much of the trajectory data and with experiment. This suggests that energy transfer is through pseudorandom mUltiple interactions between the bath gas and a few reactant atoms; the "kick" given by the force at the turning point of each atom-atom encounter governs the amount of energy transferred. Moreover, a highly simplified version of this model explains why average energies transferred per collision for simple bath gases have the order-of-magnitude values seen experimentally, an explanation which has not been provided hitherto.

The relaxation of highly vibrationally excited methylpyrazine (C5N2H6) by collisions with CO2 molecules has been investigated over the temperature range 243–364 K using diode laser transient absorption spectroscopy. Particular focus is placed on understanding both the dynamical features and the kinetics of collisions which are accompanied by large energy transfers into the CO2 rotational and translational degrees of freedom. Vibrationally hot methylpyrazine (E′=40 987 cm−1) was prepared by 248 nm excimer laser pumping, followed by rapid radiationless transitions to the ground electronic state. The nascent rotational population distributions (J=58–80) of the 0000 ground state of CO2 resulting from collisions with hot methylpyrazine were probed at short times following the excimer laser pulse. Doppler spectroscopy was used to measure the distributions of CO2 recoil velocities for individual rotational levels of the 0000 state. In addition, the temperature dependence of the state resolved, absolute rate constants for collisions populating high J states of CO2 was determined. The rotational population distributions, distributions of recoil velocities, and quenching rates for production of CO2 high J states (J=58–80) exhibit a very weak temperature dependence. The slight temperature dependence indicates that CO2 molecules which scatter into high J states of the ground vibrationless level originate from rotational levels near the mean of the precollision thermal rotational distribution. A gap law model is used to estimate the average initial rotational state and velocity of the CO2 bath, which allows for the calculation of the energy transfer magnitudes, ΔE. The measured energy transfer probabilities which are indexed by final bath state are resorted as a function of ΔE to create the energy transfer distribution function, P(E,E′) from E′−E∼1500–6000 cm−1. P(E,E′) is fit to both single exponential and biexponential functions to extract a value for the average energy transferred in a single collision of methylpyrazine and CO2. This average energy transfer value is compared to donor loss energy transfer studies as well as previous bath energy gain studies on the pyrazine/CO2 and C6F6/CO2 systems. On average, methylpyrazine donates more energy per collision to CO2 than pyrazine but not as much as C6F6; however, methylpyrazine has the lowest probability for single collision energy transfers larger than 2000 cm−1 of the three molecules studied using this technique.