Polarization tensor of magnetized quark-gluon plasma at nonzero baryon density

We derive a general expression for the absorptive part of the one-loop photon polarization tensor in a strongly magnetized quark-gluon plasma at nonzero baryon chemical potential. To demonstrate the application of the main result in the context of heavy-ion collisions, we study the effect of a nonzero baryon chemical potential on the photon emission rate. The rate and the ellipticity of photon emission are studied numerically as a function the transverse momentum (energy) for several values of temperature and chemical potential. When the chemical potential is small compared to the temperature, the rates of the quark and antiquark splitting processes (i.e., $$q\rightarrow q +\gamma $$ q → q + γ and $${\bar{q}}\rightarrow {\bar{q}} +\gamma $$ q ¯ → q ¯ + γ , respectively) are approximately the same. However, the quark splitting gradually becomes the dominant process with increasing the chemical potential. We also find that increasing the chemical potential leads to a growing total photon production rate but has only a small effect on the ellipticity of photon emission. The quark-antiquark annihilation ($$q+{\bar{q}}\rightarrow \gamma $$ q + q ¯ → γ ) also contributes to the photon production, but its contribution remains relatively small for a wide range of temperatures and chemical potentials investigated.

Laser Transmission Welding of Semi-Crystalline Polymers and Their Composites: A Critical Review

The present review provides an overview of the current status and future perspectives of one of the smart manufacturing techniques of Industry 4.0, laser transmission welding (LTW) of semi-crystalline (SC) polymers and their composites. It is one of the most versatile techniques used to join polymeric components with varying thickness and configuration using a laser source. This article focuses on various parameters and phenomena such as inter-diffusion and microstructural changes that occur due to the laser interaction with SC polymers (specifically polypropylene). The effect of carbon black (size, shape, structure, thermal conductivity, dispersion, distribution, etc.) in the laser absorptive part and nucleating agent in the laser transmissive part and its processing conditions impacting the weld strength is discussed in detail. Among the laser parameters, laser power, scanning speed and clamping pressure are considered to be the most critical. This review also highlights innovative ideas such as incorporating metal as an absorber in the laser absorptive part, hybrid carbon black, dual clamping device, and an increasing number of scans and patterns. Finally, there is presented an overview of the essential characterisation techniques that help to determine the weld quality. This review demonstrates that LTW has excellent potential in polymer joining applications and the challenges including the cost-effectiveness, innovative ideas to provide state-of-the-art design and fabrication of complex products in a wide range of applications. This work will be of keen interest to other researchers and practitioners who are involved in the welding of polymers.

A conformal dispersion relation: correlations from absorption

We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its “absorptive part”, defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the “inverted” conformal block with the ordinary conformal block.

Kinematical Theory of Scattering

The chapter introduces the kinematical theory of scattering, which is based on the Born approximation. It is shown that the neutron scattering response function can be written as the time Fourier transform of a correlation function, or intermediate scattering function. Several general properties of the correlation function are derived, and the response function is shown to satisfy the Principle of Detailed Balance. The distinction between static and dynamic correlations is explained, and their correspondence to elastic and inelastic scattering is established. The meaning of the static approximation is explained, and the link between the dynamical part of the response function and the absorptive part of the generalized susceptibility via the Fluctuation-Dissipation theorem is established. Some general sum rules are proved, and a spectral-weight function is defined. Response functions are obtained for some simple models.

Magnetic Scattering: General Properties

The basic theory of magnetic scattering is presented. A response function for magnetic scattering is defined, and expressed in terms partial response functions. The relation between the partial response functions and the correlation function for components of the magnetization is obtained, and the dynamical part of the partial reponse functions is linked via the fluctuation-dissipation theorem to the absorptive part of the generalized susceptibility. It is shown how the dipole approximation can be used to simply the magnetic scattering operator for localized electrons, and the magnetic form factor is introduced. Examples of the use of the dipole magnetic form factor, as well as more general anisotropic magnetic form factors, are given. A comparison with the X-ray atomic form factor is given. Various sum rules for the magnetic response function and generalized susceptibility are obtained.

Froissart bound for/from CFT Mellin amplitudes

We derive bounds analogous to the Froissart bound for the absorptive part of CFT_dd Mellin amplitudes. Invoking the AdS/CFT correspondence, these amplitudes correspond to scattering in AdS_{d+1}d+1. We can take a flat space limit of the corresponding bound. We find the standard Froissart-Martin bound, including the coefficient in front for d+1=4 being \pi/\mu^2π/μ2, \muμ being the mass of the lightest exchange. For d>4d>4, the form is different. We show that while for CFT_{d\leq 6}CFTd≤6, the number of subtractions needed to write a dispersion relation for the Mellin amplitude is equal to 2, for CFT_{d>6}CFTd>6 the number of subtractions needed is greater than 2 and goes to infinity as d goes to infinity.

WEAK ANNIHILATION TOPOLOGIES AND FINAL STATE INTERACTIONS IN $B^+ \rightarrow D^+_s\phi$ DECAY

In this research, the hadronic decay of [Formula: see text] is analyzed by using "QCD factorization" (QCDF) method and final state interaction (FSI). First, the [Formula: see text] decay is calculated via QCDF method and only the annihilation graphs exist in that method. Then, FSI is considered to solve the [Formula: see text] decay as a sizable correction and the D+*K0, D0*K+ and [Formula: see text] via the exchange of [Formula: see text], K-(*) and [Formula: see text] mesons are chosen for the intermediate states. To estimate the intermediate states amplitudes, QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of [Formula: see text] decay is less than 1.9×10-6 and our results according to QCDF method and FSI effects are 0.16×10-6 and 1.86×10-6, respectively.

THE FORM FACTOR OF ργ*→π0IN THE FINITE-WIDTH LIGHT-CONE LOCAL DUALITY SUM RULE

The form factor of the transition ργ*→π0is investigated by analyzing the γγ*→π0transition in the framework of the light-cone local duality quantum chromodynamics sum rules. Both finite- and zero-width forms for the low-energy physical absorptive part of the γγ*→π0transition are considered. The numerical results for the transition form factor Fρπ(Q2) in the asymptotic form and the CZ one of the pion distribution amplitude are obtained respectively, the difference between the finite- and zero-width form is not big but still distinguishable. It is found that the results for the form factor Fρπ(Q2) from CZ, asymptotic and the flat pion DAs are compatible with the predictions of perturbative QCD. Our results will be helpful to distinguish the shape of the pion DA of twist-two, when the concrete information of the experimental data for the transition ργ*→π0are provided.

STUDIES OF Λ(1405) WITH K-MESIC ATOMS

Experimental tests of the Λ(1405) properties are suggested. These could reflect the position and shape of this state in the [Formula: see text] channel. The first test consists in precise determinations of the level widths in the highest accessible K -mesic atom states. One needs to study the dependence of these widths on the binding energy of the valence protons in the involved nuclei. The second test consists in the measurement of radiative transitions from the P-wave atomic hydrogen levels to the Λ(1405) state. In both cases one can study the absorptive part of [Formula: see text] scattering amplitude in the subthreshold region.