Off-shell photon distribution amplitudes in the low-energy effective theory of QCD

Based on the principle of Lorentz covariance the transition matrix elements from an off-shell photon state to the vacuum are decomposed into the light-cone photon distribution amplitudes (DAs), in which only two transversal DAs survive in the on-shell limit. The eight off-shell light-cone photon DAs corresponding to chiral odd and chiral even up to twist four, and the corresponding coupling constants are studied systematically in the instanton vacuum model of quantum chromodynamics (QCD). The various individual photon DAs multiplied by their corresponding coupling constants are expressed in terms of the correlation functions, which are connected with the spectral densities of an effective quark propagator and then evaluated in the low-energy effective theory derived from the instanton vacuum model of QCD. The explicit analytical expressions and the numerical results for the photon DAs and their coupling constants are given

Thermodynamics of scalar–tensor theory with non-minimally derivative coupling

With the usual definitions for the entropy and the temperature associated with the apparent horizon, we show that the unified first law on the apparent horizon is equivalent to the Friedmann equation for the scalar–tensor theory with non-minimally derivative coupling. The second law of thermodynamics on the apparent horizon is also satisfied. The results support a deep and fundamental connection between gravitation, thermodynamics, and quantum theory

On the effect of the degeneracy among dark energy parameters

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter <math><mrow><mi>w</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></math> and the fractional energy density <math><msub><mi mathvariant="italic">Ω</mi><mi mathvariant="italic">ϕ</mi></msub></math> . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of <math><mrow><mi>w</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></math> which reduce to the popular Chevallier–Polarski–Linder parametrization with an explicit degeneracy relation between <math><msub><mi>w</mi><mn>0</mn></msub></math> and <math><msub><mi>w</mi><mi>a</mi></msub></math> . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among <math><msub><mi>w</mi><mi>a</mi></msub></math> , <math><msub><mi>w</mi><mn>0</mn></msub></math> , and <math><msub><mi mathvariant="italic">Ω</mi><mrow><mi>m</mi><mn>0</mn></mrow></msub></math> . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between <math><msub><mi>w</mi><mn>0</mn></msub></math> and <math><msub><mi>w</mi><mi>a</mi></msub></math> for the two models are consistent with observational data. (2) The degeneracies have little effect on <math><msub><mi mathvariant="italic">Ω</mi><mrow><mi>m</mi><mn>0</mn></mrow></msub></math> . (3) The <math><mrow><mn>1</mn><mi mathvariant="italic">σ</mi></mrow></math> error of <math><msub><mi>w</mi><mn>0</mn></msub></math> was reduced about 30 % with the degeneracy relations

The general property of dynamical quintessence field

We discuss the general dynamical behaviors of quintessence field, in particular, the general conditions for tracking and thawing solutions are discussed. We explain what the tracking solutions mean and in what sense the results depend on the initial conditions. Based on the definition of tracking solution, we give a simple explanation on the existence of a general relation between <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>w</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math> and <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math> which is independent of the initial conditions for the tracking solution. A more general tracker theorem which requires large initial values of the roll parameter is then proposed. To get thawing solutions, the initial value of the roll parameter needs to be small. The power-law and pseudo-Nambu Goldstone boson potentials are used to discuss the tracking and thawing solutions. A more general <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>w</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math> – <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math> relation is derived for the thawing solutions. Based on the asymptotical behavior of the <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>w</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math> – <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math> relation, the flow parameter is used to give an upper limit on <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mi>w</mi></mrow><mrow><mi>ϕ</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math> for the thawing solutions. If we use the observational constraint <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>w</mi></mrow><mrow><mi>ϕ</mi><mn>0</mn></mrow></msub><mo>&lt;</mo><mo>−</mo><mn>0.8</mn></math> and <math altimg="si5.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.2</mn><mo>&lt;</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mi>m</mi><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>0.4</mn></math> , then we require <math altimg="si6.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≲</mo><mn>1</mn></math> for the inverse power-law potential <math altimg="si7.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>p</mi><mi>l</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mi>n</mi></mrow></msup></math> with tracking solutions and the initial value of the roll parameter <math altimg="si8.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>1.3</mn></math> for the potentials with the thawing solutions

Critical phenomena of static charged AdS black holes in conformal gravity

The extended thermodynamics of static charged AdS black holes in conformal gravity is analyzed. The P–V criticality of these black holes has some unusual features. There exists a single critical point with critical temperature Tc and critical pressure Pc . At fixed T>Tc (or at fixed P>Pc ), there are two zeroth order phase transition points but no first order phase transition points. The systems favors large pressure states at constant T , or high temperature states at constant P

The phase-space analysis of scalar fields with non-minimally derivative coupling

We perform a dynamical analysis for the exponential scalar field with non-minimally derivative coupling. For the quintessence case, the stable fixed points are the same with and without the non-minimally derivative coupling. For the phantom case, the attractor with dark energy domination exists for the minimal coupling only. For the non-minimally derivative coupling without the standard canonical kinetic term, only the de Sitter attractor exists, and the dark matter solution is unstable

Entropy bound of horizons for charged and rotating black holes

We revisit the entropy product, entropy sum and other thermodynamic relations of charged and rotating black holes. Based on these relations, we derive the entropy (area) bound for both event horizon and Cauchy horizon. We establish these results for variant class of 4-dimensional charged and rotating black holes in Einstein(–Maxwell) gravity and higher derivative gravity. We also generalize the discussion to black holes with NUT charge. The validity of this formula, which seems to be universal for black holes with two horizons, gives further clue on the crucial role that the thermodynamic relations of multi-horizons play in black hole thermodynamics and understanding the entropy at the microscopic level

Electric fields and chiral magnetic effect in Cu+Au collisions

The non-central Cu+Au collisions can create strong out-of-plane magnetic fields and in-plane electric fields. By using the HIJING model, we study the general properties of the electromagnetic fields in Cu+Au collisions at 200 GeV and their impacts on the charge-dependent two-particle correlator γq1q2=〈cos⁡(ϕ1+ϕ2−2ψRP)〉 (see main text for definition) which was used for the detection of the chiral magnetic effect (CME). Compared with Au+Au collisions, we find that the in-plane electric fields in Cu+Au collisions can strongly suppress the two-particle correlator or even reverse its sign if the lifetime of the electric fields is long. Combining with the expectation that if γq1q2 is induced by elliptic-flow driven effects we would not see such strong suppression or reversion, our results suggest to use Cu+Au collisions to test CME and understand the mechanisms that underlie γq1q2

Quadratic thermal terms in the deconfined phase from holography

Recent lattice simulation has uncovered many interesting properties of SU( N ) gauge theory at finite temperature. Especially, above the deconfinement phase transition all the thermodynamic quantities acquire significant quadratic contributions in inverse temperature. Such a term is also found to dominate the logarithm of the renormalized Polyakov loop. Using the Hawking-Page transition in Anti-de Sitter space as an example, we show how such contributions can be naturally generated in the holographic approach

Perturbations of single-field inflation in modified gravity theory

In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form f(R) . Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the “real” ones as we always do for pure f(R) theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there is large parameter space in these models, we show that it is easy to fit the data very well