Axion cosmology, lattice QCD and the dilute instanton gas

Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility $\chi(T)$ of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine $\chi(T)$ in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.Comment: 9 pages, 7 figure

Effective potential and vacuum stability

By following previous work on this subject, we investigate the issue of the instability of the electroweak vacuum against the top loop corrections by performing an accurate analysis of a Higgs-Yukawa model. We find that, when the physical cutoff is properly implemented in the theory, the potential does not exhibit any instability. Moreover, contrary to recent claims, we show that this instability cannot be understood in terms of the very insightful work of Wu and Weinberg on the non-convexity of the one-loop effective potential of a scalar theory. Some of the theoretical and phenomenological consequences of our results are briefly discussed.Comment: 10 pages, 4 figure

The running coupling of 8 flavors and 3 colors

We compute the renormalized running coupling of SU(3) gauge theory coupled to N_f = 8 flavors of massless fundamental Dirac fermions. The recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation. The results for the discrete beta-function show that it is monotonic without any sign of a fixed point in the range of couplings we cover. As a cross check the continuum results are compared with the well-known perturbative continuum beta-function for small values of the renormalized coupling and perfect agreement is found.Comment: 15 pages, 17 figures, published versio

On the charge density and asymptotic tail of a monopole

We propose a new definition for the abelian magnetic charge density of a nonabelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1=r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions

Carbonic anhydrase XII is a marker of good prognosis in invasive breast carcinoma

Hypoxia and pH influence gene expression in tumours, and it is becoming increasingly clear that the pattern of genes expressed by a tumour determines its growth and survival characteristics. Hypoxia-inducible factor-1 (HIF-1) is a key mediator of the cellular response to hypoxia and high HIF-1 expression has been identified as a poor prognostic factor in tumours. Recently, we identified the tumour-associated carbonic anhydrases (CA), CA9 and CA12 as hypoxia-inducible in tumour cell lines. Furthermore, we identified CA IX to be a poor prognostic factor in breast cancer. The aim of this study was to assess the prognostic significance of CA XII. CA XII expression was studied by immunohistochemistry in a series of 103 cases of invasive breast cancer and any association with recognised prognostic factors or relation with the outcome was examined. CA XII expression was present in 77 out of 103 (75%) cases and was associated with lower grade (P=0.001), positive estrogen receptor status (P<0.001), and negative epidermal growth factor receptor status (P<0.001). Furthermore, although CA XII expression was associated with an absence of necrosis (P<0.001), expression of CA XII in some high-grade tumours was induced in regions directly adjacent to morphological necrosis. Additionally, using univariate analysis, CA XII positive tumours were associated with a lower relapse rate (P=0.04) and a better overall survival (P=0.01). In conclusion, CA XII expression is influenced both by factors related to differentiation and hypoxia in breast cancer in vivo and CA XII expression is associated with a better prognosis in an unselected series of invasive breast carcinoma patients