Divergences in anomalous dimension matrices of quarks at three loops: Explanation and simple solution

Symmetry of anomalous dimension matrices explained

In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and show that it is only true in a subset of all possible orthonormal bases, but that this subset is the natural one to use for physical calculations.

Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops

We compute the complete O(α s) anomalous dimension matrix relevant for the b → sγ, b → sg and b → sll transitions in the standard model and some of its extensions. For radiative decays we confirm the results of Misiak and Münz, and of Chetyrkin, Misiak and Münz. The O(α s) mixing of four-quark into semileptonic operators is instead a new result and represents one of the last missing ingredients...

Three-loop Cusp Anomalous Dimension and a Conjecture for N Loops

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Destabilizing Divergences in Supergravity Theories at Two Loops

We examine the stability of the mass hierarchy in hidden-sector supergravity theories. We show that a quadratically divergent tadpole can appear at two loops, even in minimal supergravity theories, provided the theory has a gaugeand global-symmetry singlet with renormalizable couplings to the visible fields. This tadpole can destabilize the hierarchy. We also find a quadratically divergent two-...