Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed.Comment: 54 pages, 24 figure

Exploring Takfir, Its Origins and Contemporary Use: The Case of Takfiri Approach in Daesh’s Media

Muslims have been the primary targets of Daesh’s attacks since 2014 in different countries such as Afghanistan, Iraq, and Syria. These attacks were based on its takfiri ideology. As Daesh official media and documents indicate, kufr (unbelief, infidelity) in Daesh’s approach is not limited to non-Muslims (original disbelievers), but Muslims are the most significant parts of kuffar (unbelievers) in its view and defined as incidental disbelievers. Through studying Daesh’s official documents and various Arabic, English, and Persian media productions, in an explanatory research, this article attempts to display Daesh’s takfiri approach toward Muslims and explains its historical and ideological roots, difference with Al-Qaeda’s takfiri approach, different approaches to takfir inside Daesh, main targets of Daesh’s takfir, and the reasons behinds its takfiri view. This article displays that for Daesh, the Muslims are limited only to Sunni Muslims who are accepting and following its approach. Other Sunni and non-Sunni Muslims are thus kuffar. This study also shows that the assertion of takfir has become a method for Daesh to discredit its opponents, such as Shi’a Muslims and other Muslim groups