Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions

We show that the critical mass M_c=8π of bacterial populations in two dimensions in the chemotactic problem is the counterpart of the critical temperature T_c=GMm/4k_B of self-gravitating Brownian particles in two-dimensional gravity. We obtain these critical values by using the Virial theorem or by considering stationary solutions of the Keller-Segel model and Smoluchowski-Poisson system. We also consider the case of one-dimensional systems and develop the connection with the Burgers equation. Finally, we discuss the evolution of the system as a function of M or T in bounded and unbounded domains in dimensions d=1, 2 and 3 and show the specificities of each dimension. This paper aims to point out the numerous analogies between bacterial populations, self-gravitating Brownian particles and, occasionally, two-dimensional vortices.     

The influence of substrate temperature and annealing on the properties of pulsed laser-deposited YIG films on fused quartz substrate

Yttrium iron garnet (YIG) thin films were deposited on fused quartz substrate at different substrate temperatures (T_s) varying from room temperature (RT) to 850 °C using pulsed laser deposition (PLD) technique. All the films in the as-deposited state were X-ray amorphous and non-magnetic at RT. The film deposited at RT after annealing at temperatures T_a?700 °C showed both X-ray peaks and the magnetic order. The films deposited at higher T_s (500–850 °C) and then annealed at 700 °C resulted in better-quality films with higher 4πM_s value. The highest value of magnetization was for the sample deposited at 850 °C and annealed at 700 °C, which is 68% of the bulk 4πM_s value.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.     

Surface demagnetizing field as a source of uniaxial surface anisotropy in GdCoMo thin amorphous films

Surface magnetic anisotropy energy was studied for (Gd_0.26Co_0.74)_0.96Mo_0.04 and (Gd_0.29Co_0.71)_0.96Mo_0.04 thin amorphous films by means of microwave spectroscopy at the X-band within the temperature range 4–295 K. Excitations of surface spin waves were observed in the spin wave resonance spectra. The experiment was performed in a rotating external magnetic field. The angular dependence of the resonance field for the uniform mode (spin wave vector k=0) and the surface mode made it possible to determine the surface uniaxial anisotropy constant K_s and its temperature dependence. An inhomogeneity of the saturation magnetization M_s within a close-to-surface layer of thickness d can generate the surface anisotropy energy with anisotropy constant K_s given by the formula: K_s=4πM^b_s (M^b_s−M^surf_s)d, where the indexes b and surf correspond to the bulk and surface values, respectively. The temperature dependence of K_s calculated by means of the formula agrees qualitatively with temperature dependence of K_s found in the experiment.     

Unruh effect and holography

We study the Unruh effect on the dynamics of quarks and mesons in the context of AdS₅/CFT₄ correspondence. We adopt an AdS₅ metric with the boundary Rindler horizon extending into a bulk Rindler-like horizon, which yields the thermodynamics with Unruh temperature verified by computing the boundary stress tensor. We then embed in it a probe fundamental string and a D7 brane in such a way that they become the dual of an accelerated quark and a meson in Minkowski space, respectively. Using the standard procedure of holographic renormalization, we calculate the chiral condensate, and also the spectral functions for both the accelerated quark and meson. Especially, we extract the corresponding strength of random force of the Langevin dynamics and observe that it can characterize the phase transition of meson melting. This result raises an issue toward a formulation of complementarity principle for the Rindler horizon. We find most of the dynamical features are qualitatively similar to the ones in the thermal bath dual to the AdS black hole background, though they could be quite different quantitatively.     

Dynamical and Bose-Einstein correlations of centrally produced pion pairs in hadron-hadron collisions

We calculate dynamical and Bose-Einstein inclusive correlations of pion pairs (as functions of the invariant pair mass M_ππ) from the decay of independently produced clusters, whose finite size is explicitly taken into account. We show that recent pp bubble chamber data from FNAL on the correlation functions C₂(M_ππ) for centrally produced π⁺π^? and π^?π^? pairs can be understood within this picture. Some implications for Hanbury-Brown-Twiss type analyses are discussed.     

Exclusive radiativeB-decays in the light-cone QCD sum rule approach

We discuss vector, axial-vector, scalar and pseudoscalar two-point functions at low and intermediate energies. We first review what is known from chiral perturbation theory, as well as from a heat kernel expansion within the context of an extended Nambu-Jona-Lasinio (ENJL) model. We derive then these two-point functions to all orders in the momenta and to leading order in 1/N _c within the framework of this model. We find an improved high-energy behaviour and a general way of parametrizing them that shows relations between some of the two-point functions, which are also valid in the presence of gluonic interactions. The similarity between the shape of the experimentally known spectral functions and the ones we derive, is greatly improved with respect to those predicted by the usual constituent quark like models. We also obtain the scalar massM _s =2M _Q independent of the regularization scheme. In the end, we calculate fully an example of a nonleptonic matrix element in the ENJL-model, theπ ⁺?π ⁰ electromagnetic mass difference and find good agreement with the measured value.

     

Decay constants of heavy mesons from a QCD relativistic potential model

We compute masses and leptonic decay constants of charmed and beauty pseudoscalar and vector mesons by using a QCD-inspired relativistic potential model. We obtain results in agreement with the available experimental data; as for the pseudoscalar meson decay constants, we predict f_D=1.38f_π,f_Ds=1.51f_π,f_B=1.75f_π,f_Bs=1.86f _π.     

A measurement of the QCD colour factors and a limit on the light gluino

Using data collected from 1992 to 1995 with the ALEPH detector at LEP, a measurement of the colour factor ratios C _A/C _F and T _F /C _F and the strong coupling constant α _s = C _F α _s(M_Z)/(2π) has been performed by fitting theoretical predictions simultaneously to the measured differential two-jet rate and angular distributions in four-jet events. The result is found to be in excellent agreement with QCD, {fx4-1} Fixing C _A/C _F and T _F/C _F to the QCD values permits a determination of α _s(M_Z) and η _f, the number of active flavours. With this measurement the existence of a gluino with mass below 6.3 GeV/c² is excluded at 95% confidence level.     

The speed of sound in hadronic matter

We calculate the speed of sound c _s in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form ρ(m)～m ^?a exp?{bm}, which leads to singular behavior at the critical temperature T _c =1/b. With a=4 the pressure and the energy density remain finite at T _c , while the specific heat diverges there. As a function of the temperature, the corresponding speed of sound initially increases similarly to that of an ideal pion gas, until near T _c resonance effects dominate, which causes c _s to vanish as (T _c ?T)^1/4. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around T _c , the actual critical behavior in these models is no longer present.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

Particle composition at high transverse momenta in p-p-collisions in the central region at the CERN ISR

Preliminary measurements have been made at centre of mass energies √s = 31 and 44 GeV of the π, K and p production ratios at 90° for p_T between 2.0 and 3.5 GeV/c. The (K+p)/π ratio is given down to p_T = 1.4 GeV/c. No strong energy dependence is observed for these transverse momenta.     

Finite temperature behavior of gauge hierarchy models with quantum mechanical resuscitation

We investigate the finite temperature behavior of Dimopoulos and Georgi's hierarchy model where the grand unification scale M_G is naturally generated by the quantum corrections. Owing to the particular form, M²π²(e²lnπ ? 1), of the scalar potential, the first order GUT phase transition takes place at the critical temperature T_c ～ 10^9?12GeV much lower than M_G. If M_G should be of O(M_P) (Planck mass), the universe may undergo an inflationary stage to expand enough. Baryon number asymmetry might be produced by the decay of colored scalars with a mass of 10^10?12 GeV.     

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM ₀, its value at zero momentum, and by the strong coupling constant α _s and bare quark massm ₀. In the limiting case of no explicit chiral symmetry breaking. i.e.,m ₀=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm ₀, α _s andM ₀ well in step with other estimates. This makes possible a calculation off _π, the pion decay constant, in reasonable agreement with experiment.     

Limits on low scale gravity from e+e−→W+W−, ZZ and γγ

It has been proposed recently that the scale of quantum gravity (“the string scale”) can be M_S∼few TeV with n≥2 extra dimensions of size R≲mm so that, at distances greater than R, Newtonian gravity with M_Pl∼10¹⁸ GeV is reproduced if M_Pl²∼RⁿM_Sⁿ⁺². Exchange of virtual gravitons in this theory generates higher-dimensional operators involving SM fields, suppressed by powers of M_S. We discuss constraints on this scenario from the contribution of these operators to the processes e⁺e⁻→W⁺W⁻, ZZ, γγ. We find that LEP2 can place a limit M_S≈1 TeV from e⁺e⁻→W⁺W⁻, ZZ, γγ.     

Study of double pomeron exchange in pp collisions at √s=31GeV

The reaction pp→ppπ⁺π^? at √s=31GeV was studied at the Split Field Magnet Facility of the CERN-ISR. Selecting events with two leading protons of x>0.9 and a rapidity gap Δy>2 between the protons and both pions a sample of 720 events is obtained representing a cross section of 25±10μb. The mass distribution of the dipion system, x and p_T distributions for the protons are presented and analyzed for the presence of double pomeron exchange.     

Pion-pion phase shift and K2π decay

We remark that, using the Cabibbo transformation properties for the weak Hamiltonian we can obtain Δ₀ = δ₀⁽⁰⁾ (s = M_K⁽²⁾ (s = M_K²) from the experimental decay rates for K_s → 2π, K⁺ → π⁰π⁺, obtaining δ₀ = 58.0° ± 4.6°. This result implies in particular a value of ≈ 0.6 for the S-wave isospin zero scattering length, in accordance with K_e4 results but in violent disagreement with Weinberg's calculation.     

Effective field theory for massive gravitons and gravity in theory space

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M_Pl and a mass m_g, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above m_g. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ∼(m_g⁴M_Pl)^1/5 for the Fierz-Pauli theory, but can be raised to Λ∼(m_g²M_Pl)^1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.