اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSymmetry of anomalous dimension matrices explained
117
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
Three-loop counterterms for the Standard Model (SM) revealed that the matrix of anomalous dimensions ($gamma$) of quarks is divergent in the $d to 4$ limit unless a carefully chosen non-Hermitian square-root of $Z$ matrix is used in the textbook form
ula for $gamma$. Here, an alternative prescription is given, which expresses $gamma$ and $beta$ functions directly in terms of counterterms (instead of $sqrt{Z}$ and conventional `bare couplings) and produces finite results. In the SM, this prescription $automatically$ reproduces results obtained previously by adjusting $sqrt{Z}$.
We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a
closely related quantity in terms of an effective coupling defined by the light-like cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory, and use this observation to predict the non-planar $n_{f}$-dependent terms of the four-loop cusp anomalous dimension.
We review the current status of calculations of the HQET field anomalous dimension and the cusp anomalous dimension. In particular, we give the results at 4 loops for the quartic Casimir contribution, and for the full QED case, up to $varphi^6$ in th
e small angle expansion. Furthermore, we discuss the leading terms in the anti-parallel lines limit at four loops.
The anomalous dimension of spin-1/2 baryon operators in QCD is derived at leading 1/Nf order using the minimal subtraction scheme. A residual ambiguity, originating from the presence of evanescent operators in dimensional regularization, is parametri
zed by a function of the renormalized coupling. Our result is shown to agree with previous 2 and 3 loop calculations performed in two different renormalization schemes.
The Birkhoffs theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. It can be proven that a similar theorem holds for unitary matrices with equal line sums for prime dimensions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
