Radius of convergence in lattice QCD at finite μB with rooted staggered fermions

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity eμ/T. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around μ=0. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We show that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. This is a cutoff effect that potentially affects all estimates of the radius of convergence with the standard staggered rooting. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial and, therefore, of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at Nt=4. We perform a finite-volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be μB/T≈2 and roughly temperature independent. Our simulations are performed at strange quark chemical potential μs=0, but the method can be straightforwardly extended to strangeness chemical potential μS=0 or strangeness neutrality

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

On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres

We study the time-dependent dynamics of a collection of N collapsing/expanding D0-branes in type IIA String Theory. We show that the fuzzy-S^3 and S^5 provide time-dependent solutions to the Matrix Model of D0-branes and its DBI generalisation. Some intriguing cancellations in the calculation of the non-abelian DBI Matrix actions result in the fuzzy-S^3 and S^5 having the same dynamics at large-N. For the Matrix model, we find analytic solutions describing the time-dependent radius, in terms of Jacobi elliptic functions. Investigation of the physical properties of these configurations shows that there are no bounces for the trajectory of the collapse at large-N. We also write down a set of useful identities for fuzzy-S^3, fuzzy-S^5 and general fuzzy odd-spheres.Comment: 35 pages, latex; v2: discussion in Appendix B on the large-N limit of the associator is modified, main results of paper unchange

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

Atrial fibrillatory rate as predictor of recurrence of atrial fibrillation in horses treated medically or with electrical cardioversion

Background The recurrence rate of atrial fibrillation (AF) in horses after cardioversion to sinus rhythm (SR) is relatively high. Atrial fibrillatory rate (AFR) derived from surface ECG is considered a biomarker for electrical remodelling and could potentially be used for the prediction of successful AF cardioversion and AF recurrence. Objectives Evaluate if AFR was associated with successful treatment and could predict AF recurrence in horses. Study design Retrospective multicentre study. Methods Electrocardiograms (ECG) from horses with persistent AF admitted for cardioversion with either medical treatment (quinidine) or transvenous electrical cardioversion (TVEC) were included. Bipolar surface ECG recordings were analysed by spatiotemporal cancellation of QRST complexes and calculation of AFR from the remaining atrial signal. Kaplan-Meier survival curve and Cox regression analyses were performed to assess the relationship between AFR and the risk of AF recurrence. Results Of the 195 horses included, 74 received quinidine treatment and 121 were treated with TVEC. Ten horses did not cardiovert to SR after quinidine treatment and AFR was higher in these, compared with the horses that successfully cardioverted to SR (median [interquartile range]), (383 [367-422] vs 351 [332-389] fibrillations per minute (fpm), P < .01). Within the first 180 days following AF cardioversion, 12% of the quinidine and 34% of TVEC horses had AF recurrence. For the horses successfully cardioverted with TVEC, AFR above 380 fpm was significantly associated with AF recurrence (hazard ratio = 2.4, 95% confidence interval 1.2-4.8, P = .01). Main limitations The treatment groups were different and not randomly allocated, therefore the two treatments cannot be compared. Medical records and the follow-up strategy varied between the centres. Conclusions High AFR is associated with failure of quinidine cardioversion and AF recurrence after successful TVEC. As a noninvasive marker that can be retrieved from surface ECG, AFR can be clinically useful in predicting the probability of responding to quinidine treatment as well as maintaining SR after electrical cardioversion