Supersymmetric QCD: Exact Results and Strong Coupling

We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. We demonstrate that infrared divergences do not occur in the perturbation expansion about the instanton, but explain that there is no reason to think this captures all contributions from the sector with unit topological charge. That one expects additional contributions is illustrated by dilute gas corrections. These are infrared divergent, and so difficult to define, but if non-zero give order one, holomorphic, corrections to the leading result. Exploiting an earlier analysis of Davies et al, we demonstrate that in the theory compactified on a circle of radius beta, due to infrared effects, finite contributions indeed arise which are not visible in the formal limit that beta goes to infinity.Comment: 28 pages, two references added, one typo correcte

Uncertainties in Coupling Constant Unification

The status of coupling constant unification in the standard model and its supersymmetric extension are discussed. Uncertainties associated with the input coupling constants, $m_{t}$, threshold corrections at the low and high scales, and possible nonrenormalizable operators are parametrized and estimated. A simple parametrization of a general supersymmetric new particle spectrum is given. It is shown that an effective scale $M_{SUSY}$ can be defined, but for a realistic spectrum it may differ considerably from the typical new particle masses. The implications of the lower (higher) values of $\alpha_{s}(M_{Z})$ suggested by low-energy ($Z$-pole) experiments are discussed.Comment: LaTex, 51 pages, 6 figures (available upon request), UPR-0513

Quantum Symmetries and Marginal Deformations

We study the symmetries of the N=1 exactly marginal deformations of N=4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup. However, a closer look from the perspective of quantum groups reveals that the Lagrangian is in fact invariant under a certain Hopf algebra which is a non-standard quantum deformation of the algebra of functions on SU(3). Our discussion is motivated by the desire to better understand why these theories have significant differences from N=4 SYM regarding the planar integrability (or rather lack thereof) of the spin chains encoding their spectrum. However, our construction works at the level of the classical Lagrangian, without relying on the language of spin chains. Our approach might eventually provide a better understanding of the finiteness properties of these theories as well as help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added an appendix, fixed minor typo

The association between family and community social capital and health risk behaviours in young people: an integrative review

Background: Health risk behaviours known to result in poorer outcomes in adulthood are generally established in late childhood and adolescence. These ‘risky’ behaviours include smoking, alcohol and illicit drug use and sexual risk taking. While the role of social capital in the establishment of health risk behaviours in young people has been explored, to date, no attempt has been made to consolidate the evidence in the form of a review. Thus, this integrative review was undertaken to identify and synthesise research findings on the role and impact of family and community social capital on health risk behaviours in young people and provide a consolidated evidence base to inform multi-sectorial policy and practice.<p></p> Methods: Key electronic databases were searched (i.e. ASSIA, CINAHL, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, Embase, Medline, PsycINFO, Sociological Abstracts) for relevant studies and this was complemented by hand searching. Inclusion/exclusion criteria were applied and data was extracted from the included studies. Heterogeneity in study design and the outcomes assessed precluded meta-analysis/meta-synthesis; the results are therefore presented in narrative form.<p></p> Results: Thirty-four papers satisfied the review inclusion criteria; most were cross-sectional surveys. The majority of the studies were conducted in North America (n=25), with three being conducted in the UK. Sample sizes ranged from 61 to 98,340. The synthesised evidence demonstrates that social capital is an important construct for understanding the establishment of health risk behaviours in young people. The different elements of family and community social capital varied in terms of their saliency within each behavioural domain, with positive parent–child relations, parental monitoring, religiosity and school quality being particularly important in reducing risk.<p></p> Conclusions: This review is the first to systematically synthesise research findings about the association between social capital and health risk behaviours in young people. While providing evidence that may inform the development of interventions framed around social capital, the review also highlights key areas where further research is required to provide a fuller account of the nature and role of social capital in influencing the uptake of health risk behaviours.<p></p&gt

Equilibrium analysis in multi-echelon supply chain with multi-dimensional utilities of inertial players

In a supply chain, the importance of information elicitation from the supply chain players is vital to design supply chain network. The rationality and self-centredness of these players causes the information asymmetry in the supply chain and thus situation of conflict and non-participation of the players in the network design process. In such situations, it is required to analyse the supply chain players’ behaviour in order to explore potential for coordination through incentives. In this paper, a novel approach of social utility analysis is proposed to elicit the information for supply chain coordination among the supply chain players in a dyadic relationship – supplier and buyer. In principal, we consider a monopsony situation where buyer is a dominant player. With the objective of maximizing the social utility, efforts have been made to value behavioural issues in supply chain. On the other hand, the reluctance of player due to the information asymmetry is measured in the form of inertia – an offset to the supply chain profit. The suppliers’ behaviour is analysed with three distinct level of risk for two types of the product in procurement process. The useful insight from this paper is in supplier selection process where the reluctance of supplier offsets supply chain profit. The paper provides recommendations to supply chain managers for efficient decision-making ability in supplier selection process

Search for CP violation in D+→ϕπ+ and D+s→K0Sπ+ decays

A search for CP violation in D + → ϕπ + decays is performed using data collected in 2011 by the LHCb experiment corresponding to an integrated luminosity of 1.0 fb−1 at a centre of mass energy of 7 TeV. The CP -violating asymmetry is measured to be (−0.04 ± 0.14 ± 0.14)% for candidates with K − K + mass within 20 MeV/c 2 of the ϕ meson mass. A search for a CP -violating asymmetry that varies across the ϕ mass region of the D + → K − K + π + Dalitz plot is also performed, and no evidence for CP violation is found. In addition, the CP asymmetry in the D+s→K0Sπ+ decay is measured to be (0.61 ± 0.83 ± 0.14)%

Study of Bc+B_c^+ decays to the K+K−π+K^+K^-\pi^+ final state and evidence for the decay Bc+→χc0π+B_c^+\to\chi_{c0}\pi^+

A study of $B_c^+\to K^+K^-\pi^+$ decays is performed for the first time using data corresponding to an integrated luminosity of 3.0 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of $7$ and $8$ TeV. Evidence for the decay $B_c^+\to\chi_{c0}(\to K^+K^-)\pi^+$ is reported with a significance of 4.0 standard deviations, resulting in the measurement of $\frac{\sigma(B_c^+)}{\sigma(B^+)}\times\mathcal{B}(B_c^+\to\chi_{c0}\pi^+)$ to be $(9.8^{+3.4}_{-3.0}(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times 10^{-6}$. Here $\mathcal{B}$ denotes a branching fraction while $\sigma(B_c^+)$ and $\sigma(B^+)$ are the production cross-sections for $B_c^+$ and $B^+$ mesons. An indication of $\bar b c$ weak annihilation is found for the region $m(K^-\pi^+)<1.834\mathrm{\,Ge\kern -0.1em V\!/}c^2$, with a significance of 2.4 standard deviations.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-022.html, link to supplemental material inserted in the reference