Singularity-free Next-to-leading Order ΔS=1\Delta S= 1 Renormalization Group Evolution and ϵK′/ϵK\epsilon_{K}^{\prime}/\epsilon_{K} in the Standard Model and Beyond

The standard analytic solution of the renormalization group (RG) evolution for the $\Delta S = 1$ Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of $\epsilon_K^{\prime}$, the measure of direct $CP$ violation in $K\to \pi\pi$ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio $\epsilon_{K}^{\prime}/\epsilon_{K}$ (with $\epsilon_{K}$ quantifying indirect $CP$ violation) in the Standard Model (SM) at NLO to $\epsilon_{K}^{\prime}/\epsilon_{K} = (1.06 \pm 5.07) \times 10^{-4}$, which is $2.8\,\sigma$ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: If the new contribution is generated at the scale of 1-10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50-100 %. Our solution contains a term of order $\alpha_{EM}^2/\alpha_s^2$, which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.Comment: 42 pages, 2 figures, 6 tables; formulae corrected, numerical results almost unchanged, to be published in JHE

Creating a Safe Space in a Small Town for the LGBTQ+ community

Goal Statement: To create awareness in small town regarding effects of intentional and unintentional oppression and establish safe spaces for members of the LGBTQ+ community. Significant Findings: Members of small towns learn from generations that preceded them. While cultural views have evolved and become more inclusive over the decades, small towns lagged in acceptance. These lead to microaggressions against the LGBTQ+ by community members who do not realize actions and comments can lead to internal conflicts because they see these comments as a normalcy within their community. Members of the LGBTQ+ community then repress their identity until the reach a point in their life that they are comfortable with themselves if they reach that point at all. The LGBTQ+ community should feel safe during all aspects of their life and have trusted individuals that they can reach out to. Objectives/Strategies/Interventions/Next Steps: Religion is a staple of the community with many institutions throughout town. It is important to identify which establishments and allies and help members of the religious LGBTQ+ community find these resources. Youth should also establish a safe space within their educational setting. Offering education to teachers through mentoring programs with fellow teachers who identify as allies, the forgiveness approach to bullying to empower the victims will help members of the community have individuals they can reach out to. Community awareness can be achieved by normalizing varieties of sexual orientations and gender identities by engaging residents in discussions through community events throughout the year

Library Catalog in Transition

This article describes the history of the card catalog, along with the many problems inherent in the system as it was being practiced in 1981. Added to these issues were antiquated subject headings and imposing storage issues. The author suggests that the card catalog will eventually be rightfully replaced fully by computer catalogs

Some functions of universities in the United States today

Thesis (M.A.)--Boston University, 1949. This item was digitized by the Internet Archive

Our Digital Footprint: Protecting the Next Generation of Field Personnel

https://place.asburyseminary.edu/firstfruitspapers/1055/thumbnail.jp

The Montana Family Farmer under Chapter 12 Bankruptcy

The Montana Family Farmer Under Chapter 12 Bankruptc

Commercial Bad Faith: Tort Recovery for Breach of Implied Covenant in Ordinary Commercial Contracts

Commercial Bad Faith: Tort Recovery for Breach of Implied Covenant in Ordinary Commercial Contract