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The Proton Radius Puzzle refers to the ~7{\sigma} discrepancy that exists between the proton charge radius determined from muonic hydrogen and that determined from electronic hydrogen spectroscopy and electron-proton scattering. One possible partial resolution to the puzzle includes errors in the extraction of the proton radius from ep elastic scattering data. This possibility is made plausible by certain fits which extract a smaller proton radius from the scattering data consistent with that determined from muonic hydrogen. The reliability of some of these fits that yield a smaller proton radius was studied. We found that fits of form factor data with a truncated polynomial fit are unreliable and systematically give values for the proton radius that are too small. Additionally, a polynomial fit with a \chi^2_{reduced} ~ 1 is not a sufficient indication for a reliable result.

We investigate the renormalization of the quark-mixing matrix in the Electroweak Standard Model. We show that the corresponding counterterms must be gauge independent as a consequence of extended BRS invariance. Using rigid SU(2)_L symmetry, we proof that the ultraviolet-divergent parts of the invariant counterterms are related to the field renormalization constants of the quark fields. We point out that for a general class of renormalization schemes rigid SU(2)_L symmetry cannot be preserved in its classical form, but is renormalized by finite counterterms. Finally, we discuss a genuine physical renormalization condition for the quark-mixing matrix that is gauge independent and does not destroy the symmetry between quark generations., Comment: 20 pages, LaTeX, minor changes, references added

Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a manifest supersymmetric formulation the anomaly appears in two other identities: The first one describes the non-renormalization of the topological term, the second relates the renormalization of the gauge coupling to the renormalization of the complex supercoupling. Only one of the two identities can be maintained in perturbation theory. We discuss the two versions and derive the respective beta function of the local supercoupling, which is non-holomorphic in the first version, but directly related to the coupling renormalization, and holomorphic in the second version, but has a non-trivial, i.e.anomalous, relation to the beta function of the gauge coupling., Comment: References corrected

In this letter we apply the methods of our previous paper hep-th/0108045 to noncommutative fermions. We show that the fermions form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations into a field-dependent part and a \theta-part implies the Seiberg-Witten differential equations for the fermions., Comment: 7 pages, LaTeX

We show that the noncommutative Yang-Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The noncommutative Yang-Mills action is invariant under combined conformal transformations of the Yang-Mills field and of the noncommutativity parameter \theta. The Seiberg-Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action., Comment: 20 pages, LaTeX. v2: Streamlined proofs and extended discussion of Lorentz transformations

The renormalization of softly broken SQED is related to the one of supersymmetric QED by using the construction with a local gauge supercoupling and by taking into account softly broken anomalous axial U(1) symmetry. From this extended model one obtains the non-renormalization theorems of SQED and the counterterms of the soft breaking parameters as functions of the supersymmetric counterterms. Due to the Adler-Bardeen anomaly of the axial current an invariant regularization scheme does not exist, and therefore the $\beta$-functions of soft breaking parameters are derived from an algebraic construction of the Callan-Symanzik equation and of the renormalization group equation. We obtain the soft $\beta$-functions in terms of the gauge $\beta$-function and of the anomalous dimension of the supersymmetric matter mass. In particular, we find that the X-term of the scalar mass $\beta$-function as well as the gauge $\beta$-function in $l\geq 2$ are due to the Adler-Bardeen anomaly of the axial symmetry., Comment: 28 pages

The non-renormalization theorem of chiral vertices and the generalized non-renormalization theorem of the photon self energy are derived in SQED on the basis of algebraic renormalization. For this purpose the gauge coupling is extended to an external superfield. This extension already provides detailed insight into the divergence structure. Moreover, using the local supercoupling together with an additional external vector multiplet that couples to the axial current, the model becomes complete in the sense of multiplicative renormalization, with two important implications. First, a Slavnov--Taylor identity describing supersymmetry, gauge symmetry, and axial symmetry including the axial anomaly can be established to all orders. Second, from this Slavnov-Taylor identity we can infer a Callan-Symanzik equation expressing all aspects of the non-renormalization theorems. In particular, the gauge $\beta$-function appears explicitely in the closed form., Comment: Latex, 47 pages

The renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking is presented using spurion fields for introducing the breaking terms. It is proven that renormalization of the fields and parameters in the classical action yields precisely the correct counterterms to cancel all divergences. In the course of the construction of higher orders additional independent parameters appear, but they can be shown to be irrelevant in physics respects. Thus, the only parameters with influence on physical amplitudes are the supersymmetric and the well-known soft breaking parameters., Comment: 29 pages, published in The European Physical Journal C

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov--Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms., Comment: 38 pages, 4 figures

The non-renormalization theorems of chiral vertex functions are derived on the basis of an algebraic analysis. The property, that the interaction vertex is a second supersymmetry variation of a lower dimensional field monomial, is used to relate chiral Green functions to superficially convergent Green functions by extracting the two supersymmetry variations from an internal vertex and transforming them to derivatives acting on external legs. The analysis is valid in the massive as well as in the massless model and can be performed irrespective of properties of the superpotential at vanishing momentum., Comment: 20 pages, Latex, added acknowledgments

Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge parameter dependence algebraically. As application we discuss the anomaly coefficient in the Slavnov-Taylor identity, $S$-matrix elements, the vector two-point-function and the coefficients of renormalization group and Callan-Symanzik equation., Comment: 6, MPI-PhT/94-34, BUTP-94/15