Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

We reassess the impact of short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude on the anomalous magnetic moment of the muon, $$a_\mu =(g-2)_\mu /2$$ a μ = ( g - 2 ) μ / 2 , by comparing different solutions that have recently appeared in the literature. In particular, we analyze the relevance of the exact axial anomaly and its impact on $$a_\mu $$ a μ and conclude that it remains rather limited. We show that all recently proposed solutions agree well within uncertainties on the numerical estimate of the impact of short-distance constraints on $$a_\mu $$ a μ , despite differences in the concrete implementation. We also take into account the recently calculated perturbative corrections to the massless quark loop to update our estimate and outline the path towards future improvements.

Updates on the QCD phase diagram from lattice

Different aspects of the phase diagram of strongly interacting matter described by quantum chromodynamics (QCD), which have emerged from the recent studies using lattice gauge theory techniques, are discussed. A special emphasis is given on understanding the role of the anomalous axial U(1) symmetry in determining the order of the finite temperature chiral phase transition in QCD with two massless quark flavors and tracing its origin to the topological properties of the QCD vacuum.

The two-loop perturbative correction to the (g − 2)μ HLbL at short distances

The short-distance behaviour of the hadronic light-by-light (HLbL) contribution to (g − 2)μ has recently been studied by means of an operator product expansion in a background electromagnetic field. The leading term in this expansion has been shown to be given by the massless quark loop, and the non-perturbative corrections are numerically very suppressed. Here, we calculate the perturbative QCD correction to the massless quark loop. The correction is found to be fairly small compared to the quark loop as far as we study energy scales where the perturbative running for the QCD coupling is well-defined, i.e. for scales μ ≳ 1 GeV. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .

NNLO charmed-meson fragmentation functions and their uncertainties in the presence of meson mass corrections

The main aim of this paper is to present new sets of non-perturbative fragmentation functions (FFs) for $$D^0$$D0 and $$D^+$$D+ mesons at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the $$\overline{\mathrm {MS}}$$MS¯ factorization scheme with five massless quark flavors. This new determination of FFs is based on the QCD fit to the experimental data for hadron production in the electron-positron single-inclusive annihilation (SIA). We discuss in detail the novel aspects of the methodology used in our analysis and the validity of obtained FFs by comparing with previous works in literature which have been carried out up to NLO accuracy. We will also incorporate the effect of charmed meson mass corrections into our QCD analysis and discuss the improvements upon inclusion of these effects. The uncertainties in the extracted FFs as well as in the corresponding observables are estimated using the “Hessian” approach. For a typical application, we use our new FFs to make theoretical predictions for the energy distributions of charmed mesons inclusively produced through the decay of unpolarized top quarks, to be measured at the CERN LHC. As a result of this analysis, suggestions are discussed for possible future studies on the current topic to consider any theory improvements and other available experimental observables.

Chiral symmetry breaking by monopole condensation

Under the assumption of Abelian dominance in QCD, we have shown that chiral condensate is locally present around each QCD monopole. The essence is that either charge or chirality of a quark is not conserved, when the low energy massless quark collides with QCD monopole. In reality, the charge is conserved so that the chirality is not conserved. Reviewing the presence of the local chiral condensate, we show by using chiral anomaly that chiral nonsymmetric quark pair production takes place when a color charge is putted in a vacuum with monopole condensation, while chiral symmetric pair production takes place in a vacuum with no monopole condensation. Our results strongly indicate that the chiral symmetry is broken by the monopole condensation.

FURTHER ANALYSIS OF EXCITATIONS OF QUARKS AT FINITE TEMPERATURE — MASS EFFECT AND POLE STRUCTURE

We calculate the spectral function of the massive quark at finite temperature ( T ) using a Yukawa model and show that the peak in the negative energy region among the three-peaks found in a previous work for the massless quark is largely suppressed. To explore the underlying mechanism of this behavior, we also investigate the pole structure of the retarded Green function of the quark. We will show the result only for the massless quark. We find the residues of the poles corresponding the three-peaks are all comparable at T ∼ mb. We also show that the multi-peak structure of the quark spectra is well described in the pole approximation which indicates that the quasi-particle picture is valid in this T region.