Renormalization of Supersymmetric Field Theories in Loop Regularization with String-mode Regulators
Jian-Wei Cui, Yong Tang, Yue-Liang Wu
备注：
31 pages, 12 figures, the version to appear in PRD, an appendix is added for a proof of translational invariance of loop regularization and the consistency condition for the regularized logarithmic divergence is emphasized for preserving gauge symmetry in supersymmetric gauge theories
By applying the recently developed Loop Regularization(LR) with string-mode regulators to supersymmetric field theories, we explicitly verify the supersymmetric Ward identities in several supersymmetric models at one-loop level. It is interesting to observe that supersymmetry is a so remarkable symmetry that the supersymmetric Ward identities hold as long as a regularization scheme is realized in the exact four dimensional space-time with translational invariance for the momentum integration, and the gauge symmetry can be maintained once the regularization scheme preserves supersymmetry and satisfies the consistency condition for logarithmic divergences. As a manifest demonstration, we carry out a complete one-loop renormalization for the massive Wess-Zumino model by adopting the LR method, it is found that all the quadratic divergences cancel out and the relations among masses and coupling constants hold after renormalization, which agrees with the well-known non-renormalization theorem. It is concluded that the LR method preserves not only gauge symmetry but also supersymmetry. A simple and definite derivation of Majorana Feynman rules is found to be very useful.
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not self-consistent. A consistent regularization, which does not break the supersymmetry, is the higher covariant derivative regularization. However, the integrals obtained with this regularization can not be usually calculated analytically. We discuss application of this regularization to the calculations in supersymmetric theories. In particular, it is demonstrated th…
We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction…
By undertaking additional analyses postponed in a previous paper, we complete our construction of a manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. We present the following: An evaluation of the covariant gauge anomaly; a proof of the integrability of the covariant gauge current in anomaly-free cases; a calculation of a one-loop superconformal anomaly in the gauge supermultiplet sector. On the last point, we find that the ghost-anti-ghost supermultiplet and the Nakanishi-Lautrup supermultiplet give rise to BRST exact contributions which, due to…
We formulate a manifestly supersymmetric gauge covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has a covariant form and can emerge only in one-loop diagrams with all the external lines being the background gauge superfield. We also present several illustrative applications in the one-loop approximation: the self-energy part of the chiral multiplet and of the gauge multiplet; the super-chiral anomaly and the superconformal…
General issues concerning the regularization of supersymmetric theories using dimensional regularization and dimensional reduction are reviewed. Recent progress on problems of dimensional reduction related to factorization, supersymmetry, Higgs boson mass calculations, and mathematical consistency is discussed.
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There has been a controversial recent claim that the standard result on the Higgs to two photon decay rate is incorrect, with the use of dimensional regularization fingered as the alleged culprit. Given the great importance of the $H\to γγ$ process as a possible Standard Model Higgs discovery channel at the LHC if the Higgs mass is light, it is critical to find a way to check the correctness of the results of dimensional regularization for this process. Here we report the results of a perturbative calculation of the $H\to γγ$ decay amplitude using a spacetime lattice as a UV regulator, which i…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the supersymmetry-invariance of dimensional reduction in an easy manner. This method is applied to several supersymmetry identities at the one- and two-loop level, and thus the extent to which dimensional reduction is known to preserve supersymmetry is significantly enlarged.
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Finding an efficient and compelling regularization of soft and collinear degrees of freedom at the same invariant mass scale, but separated in rapidity is a persistent problem in high-energy factorization. In the course of a calculation, one encounters divergences unregulated by dimensional regularization, often called rapidity divergences. Once regulated, a general framework exists for their renormalization, the rapidity renormalization group (RRG), leading to fully resummed calculations of transverse momentum (to the jet axis) sensitive quantities. We examine how this regularization can be i…
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Two-loop QCD corrections to $ H \rightarrow b + \bar{b} + g $ at higher powers in the dimensional regulator
School of Physical Sciences, National Institute of Science Education and Research（国家科学教育研究中心物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立大学）；Theoretical Physics Division, Physical Research Laboratory（物理研究实验室理论物理部）；Department of Physics, Indian Institute of Technology Guwahati（古瓦哈提印度理工学院物理系）；The Institute of Mathematical Sciences（数学科学研究所）
本文计算了维度正则化参数 $\epsilon$ 高次幂下希格斯玻色子衰变到底夸克对和胶子（$H \rightarrow b + \bar{b} + g$）的两圈无质量QCD修正，通过将振幅投影到适当的洛伦兹结构上，并给出了形状因子的数值行为，这些振幅是计算强子对撞中底夸克湮灭产生希格斯加喷注的三圈虚修正的必要输入。
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve formally iterating the divergent interaction and then regularizing and renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be introduced, or dimensional regularization can be applied. We show that these two methods yield different results after renormalization. Furthermore, if a cutoff is used, the NN phase shift data cannot be repro…
In this review article we report on the newest developments in precision calculations in supersymmetric theories. An important issue related to this topic is the construction of a regularization scheme preserving simultaneously gauge invariance and supersymmetry. In this context, we discuss in detail dimensional reduction in component field formalism as it is currently the preferred framework employed in the literature. Furthermore, we set special emphasis on the application of multi-loop calculations to the analysis of gauge coupling unification, the prediction of thelightest Higgs boson mass…
In this proceeding I briefly review current status of the construction of nuclear electro-weak currents within chiral effective field theory. I show that gauge and chiral symmetry requirements lead to the well-known continuity equations for the current and charge operators which, however, get modified at higher orders. Regularization of the current will be also discussed. I demonstrate that implementation of a cutoff regulator in a naive way leads to violation of chiral symmetry. To respect the underlying symmetries I propose to use higher derivative regularization in the nuclear forces and cu…
