On ambiguities and divergences in perturbative renormalization group functions

There is an ambiguity in choosing field-strength renormalization factors in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved β-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa β-functions and provide the first calculation of the flavor-improved 3-loop SM β-functions in the gaugeless limit.

Three-loop vertex integrals at symmetric point

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the ε-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.

Uprooted Speakers’ Grassroots English: Metalinguistic Perspectives of Asylum Seekers in Germany

This chapter discusses metalinguistic discourse produced by asylum seekers from English-speaking West Africa in Germany, with a focus on the role of English in participants’ communicative environment and the values and affordances ascribed to different varieties of English. The chapter argues that, in this specific context, a) English loses much of its communicative range but retains important identity-related functions, and b) the values associated with different varieties of English reflect global relationships in the World system of Englishes. African varieties are linked to in-group functions and receive differential evaluation, with Nigerian English being constructed as more standard-distant than Ghanaian English, whereas the English of German interlocutors is associated with the prestige varieties American and British English. Particularly surprising is the frequent equation of Gambian English with Jamaican ways of speech, a pattern accounted for not in terms of linguistic similarity but of the global circulation of reggae and dancehall culture. The chapter thus contributes to the sociolinguistics of globalization and the study of language, mobility, and migration.

The Integral Role of Organisational Governance in Promoting Interprofessional Education in Rural Settings

One of the key challenges with implementing and sustaining interprofessional education initiatives is the lack of governance structures and processes to guide them. This case study presents a process evaluation of an intersectoral advisory group that facilitated a novel interprofessional clinical education model in rural health settings in the state of Queensland, Australia. The group consisted of health and academic partners to guide the implementation and promote sustainability of this new model. The advisory group process was evaluated mid-way and at conclusion of the group functions, using focus group discussions. The focus group audio recordings were transcribed verbatim and subjected to inductive content analysis. Categories were developed for reporting. Three broad categories were identified: Characteristics of the group, functions of the group and multifaceted communication within the group and between sectors. By identifying and mapping the processes used by a strategic, high-level intersectoral advisory group consisting of members from the health and academic fields, key recommendations have been formulated to guide similar work in the future.

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

We extract the $$\varepsilon $$ ε -expansion from the recently obtained seven-loop g-expansion for the renormalization group functions of the O(N)-symmetric model. The different series obtained for the critical exponents $$\nu ,\ \omega $$ ν , ω and $$\eta $$ η have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for $$N=0,1,2,3$$ N = 0 , 1 , 2 , 3 and 4. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent $$\alpha $$ α for the XY model. We found the result $$-0.0123(11)$$ - 0.0123 ( 11 ) which is compatible with the famous experimental result of $$-0.0127(3)$$ - 0.0127 ( 3 ) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value $$-0.007(3)$$ - 0.007 ( 3 ) . For the challenging case of resummation of the $$\varepsilon $$ ε -expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.

Computational and photophysical characterization of a Laurdan malononitrile derivative

The malononitrile group is considered one of the strongest natural electron-withdrawing groups in a chemist's arsenal. However, surprisingly little is known about how this group functions in push-pull fluorophores. In...

Analisis Cara Kerja Perancangan E-Report Menggunakan Framework Codeigniter Untuk Laporan Keseharian Siswa

This research aims to develop an electronic reporting application that helps schools manage and share student daily information at school with parents. Making it easier for student guardians to supervise their children at school. This is implemented using the applied methodology used in solving practical problems in the modern world. In its application, a web-based application was built that was designed using the MVC (Model View Controller) method which aims to group functions into a unit in accordance with their respective types such as data, display and controller so as not to be scattered. Which is implemented with the Codeigniter framework which has very good documentation, small files, good performance and easy to integrate. So as to produce a Website-based E-report system using the MVC Method that can provide services in managing data such as adding, viewing, editing, and deleting data about the daily lives of students in schools stored in the database.

The all-loop perturbative derivation of the NSVZ $$\beta $$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions

The perturbative all-loop derivation of the NSVZ $$\beta $$ β -function for $${{\mathcal {N}}}=1$$ N = 1 supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum superfields. These singularities originate from integrals of double total derivatives and determine all contributions to the $$\beta $$ β -function starting from the two-loop approximation. Their sum is expressed in terms of the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields. This allows obtaining the NSVZ equation in the form of a relation between the $$\beta $$ β -function and these anomalous dimensions for the renormalization group functions defined in terms of the bare couplings. It holds for an arbitrary renormalization prescription supplementing the higher covariant derivative regularization. For the renormalization group functions defined in terms of the renormalized couplings we prove that in all loops one of the NSVZ schemes is given by the HD + MSL prescription.

Renormalization of scalar field theories in rational spacetime dimensions

We renormalize various scalar field theories with a $$\phi ^n$$ϕn self interaction such as $$n=5$$n=5, 7 and 9 in their respective critical dimensions which are non-integer. The renormalization group functions for the O(N) symmetric extensions are also computed.

Six-dimensional ultraviolet completion of the ℂℙ(N) σ model at two loops

We extend the recent one-loop analysis of the ultraviolet completion of the [Formula: see text] nonlinear [Formula: see text] model in six dimensions to two-loop order in the [Formula: see text] scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and [Formula: see text]-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the [Formula: see text] expansion of the respective large [Formula: see text] exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop [Formula: see text] renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.