Higher twists and αs(MZ)\alpha_s(M_Z) extractions from the NNLO QCD analysis of the CCFR data for xF3xF_3 structure function

A detailed next-to-next-to-leading order (NNLO) QCD analysis is performed for the experimental data of the CCFR collaboration for the $xF_3$ structure function. Theoretical ambiguities of the results of our NNLO fits are estimated by application of the Pad\'e resummation technique and variation of the factorization and renormalization scales. The NNLO and N$^3$LO $\alpha_s(Q^2)$ $\bar{MS}$-matching conditions are used. In the process of the fits we are taking into account of twist-4 $1/Q^2$-terms. We found that the amplitude of the $x$-shape of the twist-4 factor is decreasing in NLO and NNLO, though some remaining twist-4 structure seems to retain in NNLO in the case when statistical uncertainties are taken into account. The question of the stability of these results to the application of the [0/2] Pad\'e resummation technique is considered. Our NNLO results for $\alpha_s(M_Z)$ values, extracted from the CCFR $xF_3$ data, are $\alpha_s(M_Z)=0.118 \pm 0.002 (stat) \pm 0.005 (syst)\pm 0.003 (theory)$ provided the twist-4 contributions are fixed through the infrared renormalon model and $\alpha_s(M_Z)=0.121^{+0.007}_{0.010}(stat)\pm 0.005 (syst) \pm 0.003 (theory)$ provided the twist-4 terms are considered as free parameters.Comment: 33 pages LaTeX, 3 ps figures; minor misprints are eliminated, 2 new referencies are added; accepted for publication in Nucl. Phys.

Summing up the perturbation series in the Schwinger Model

Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation shows the complete agreement between nonperturbative and perturbative approaches.Comment: 10 pages (in REVTEX

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Subgraphs in random networks

Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find new scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree distribution, \gamma, as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime the subgraph number of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where \alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and \alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and \gamma_c=s+1. We find that certain subgraphs appear much more frequently than in Erdos networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.Comment: 8 pages, 5 figure

The T=0 neutron-proton pairing correlations in the superdeformed rotational bands around 60Zn

The superdeformed bands in 58Cu, 59Cu, 60Zn, and 61Zn are analyzed within the frameworks of the Skyrme-Hartree-Fock as well as Strutinsky-Woods-Saxon total routhian surface methods with and without the T=1 pairing correlations. It is shown that a consistent description within these standard approaches cannot be achieved. A T=0 neutron-proton pairing configuration mixing of signature-separated bands in 60Zn is suggested as a possible solution to the problem.Comment: 9 ReVTex pages, 10 figures, submitted to Phys. Rev.

Psychology and aggression

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68264/2/10.1177_002200275900300301.pd

Two-loop O(GF2MH4){\rm O}\left(G_F^2M_H^4\right) corrections to the fermionic decay rates of the Higgs boson

We calculate the dominant ${\rm O}\left(G_F^2M_H^4\right)$ two-loop electroweak corrections to the fermi\-onic decay widths of a heavy Higgs boson in the Standard Model. Use of the Goldstone-boson equivalence theorem reduces the problem to one involving only the physical Higgs boson $H$ and the Goldstone bosons $w^\pm$ and $z$ of the unbroken theory. The two-loop corrections are opposite in sign to the one-loop electroweak corrections, exceed the one-loop corrections in magnitude for $M_H>1114\ {\rm GeV}$, and increase in relative magnitude as $M_H^2$ for larger values of $M_H$. We conclude that the perturbation expansion in powers of $G_FM_H^2$ breaks down for $M_H\approx 1100\ {\rm GeV}$. We discuss briefly the QCD and the complete one-loop electroweak corrections to $H\rightarrow b\bar{b}, \,t\bar{t}$, and comment on the validity of the equivalence theorem. Finally we note how a very heavy Higgs boson could be described in a phenomenological manner.Comment: 24 pages, RevTeX file, 4 figures in a separate compressed uuencoded Postscript file or available by mail on request. Fig. 1 not included see Figs. 1, 2 in Phys. Rev. D 48, 1061 (1993