Gluino contribution to the 3-loop quark mass anomalous dimension in the minimal supersymmetric standard model

We deduce the gluino contribution to the three-loop QCD quark mass anomalous dimension function within the minimal supersymmetric Standard Model (MSSM) from its standard QCD expression. This work is a continuation of the program of computation of MSSM renormalization group functions.     

The 16th moment of the three-loop anomalous dimension of the non-singlet transversity operator in QCD

We present the result of the three-loop anomalous dimension of non-singlet transversity operator in QCD for the Mellin moment N=16$N=16$. The obtained result coincides with the prediction from arXiv:1203.1022 and can serve as a confirmation of the correctness of the general expression for three-loop anomalous dimension of non-singlet transversity operator in QCD for the arbitrary Mellin moment.     

Three-loop mixing of dipole operators

We calculate the complete three-loop O(alpha(3)(s)) anomalous dimension matrix for the dimension-five dipole operators that arise in the standard model after integrating out the top quark and the heavy electroweak bosons. Our computation completes the three-loop anomalous dimension matrix of operators that govern low-energy |DeltaF| = 1 flavor-changing processes, and represents an important ingredient of the next-to-next-to-leading order QCD analysis of the B--> X(s)gamma decay.     

Supersymmetric QCD

We demonstrate the existence of a well-defined vacuum state in supersymmetric QCD with finite vacuum expectation values (VEVs) for scalars. Our results differ from those of several authors who find that a supersymmetric vacuum state exists only at infinite VEVs for the scalar fields. Our analysis is an application of previous results obtained using instantons in conjunction with the anomalous supersymmetry transformation laws found by Konishi.     

Higgs boson mass in supersymmetry to three loops

Within the minimal supersymmetric extension of the standard model, the mass of the light CP-even Higgs boson is computed to three-loop accuracy, taking into account the next-to-next-to-leading order effects from supersymmetric quantum chromodynamics. We consider two different scenarios for the mass hierarchies of the supersymmetric spectrum. Our numerical results amount to corrections of about 500 MeV, which is of the same order as the experimental accuracy expected at the CERN Large Hadron Collider.     

Calculation of the quark and gluon form factors to three loops in QCD

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al. for the three-loop form factors. In addition, we derive the subleading \( \mathcal{O}\left( \varepsilon \right) \) terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.     

Relation Between the Pole Mass and MS Mass of Top Quark in Supersymmetric QCD

We discuss the relation between the pole mass and MS mass of top quark in the framework of the supersymmetric QCD.We find that the supersymmetric contributions are comparable to those of the standard model.     

Anomaly constraints on supersymmetric effective lagrangians

In this paper we set constraints on the possible effective-lagrangian representations of supersymmetric gauge theories with spontaneously broken chiral flavor symmetries, by finding the conditions under which a Wess-Zumino term to represent the anomalous interactions can be constructed. We find that effective lagrangians for such theories are possible only for nonlinear sigma models defined on noncompact manifolds, and demonstrate the realization of this result in supersymmetric QCD. We also consider the Wess-Zumino term in the nonlinear realization of broken supersymmetry.     

Photon structure function in supersymmetric QCD revisited

We investigate the virtual photon structure function in the supersymmetric QCD (SQCD), where we have squarks and gluinos in addition to the quarks and gluons. Taking into account the heavy particle mass effects to the leading order in QCD and SQCD we evaluate the photon structure function and numerically study its behavior for the QCD and SQCD cases.     

Higgs self-coupling beta-function in the Standard Model at three loops

We present the results for three-loop beta-function for the Higgs self-coupling calculated within the unbroken phase of the Standard Model. We also provide the results for three-loop beta-function for Higgs mass parameter, which was easily extracted from our calculation. Our results coincide with that of recent paper of K. Chetyrkin and M. Zoller (2013) [1]. In addition, the expression for the Higgs field anomalous dimension is given.     

Spin structure of hadrons in supersymmetric quantum chromodynamics at short distances

We study the short-distance spin structure of nucleons in supersymmetric QCD. We calculate the Altarelli-Parisi spin transition coefficients ΔP _ba and corresponding anomalous Δ γ _ab ⁿ fora, b=quarks, gluons, gluinos and squarks and present the supersymmetric relations between them. Further analysis is divided into two parts: the parity conserving case and parity violating case, both following from the mass mixing in the squark sector. Solving theQ ²-evolution equations we determine the quark, gluon, gluino and squark spin distribution at variousQ ² above the threshold for production of supersymmetric partners. We also show the analytic solutions for the first moments in the nonsinglet and singlet sector. In particular the spin carried by the valence quarks turn out to vanish asymptotically except of one particular case of squark mixing.     

Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π⁰ → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π⁰ → γγ in SQCD.     

The spectrum of a class of supersymmetric theories with false vacua

The spectrum of a supersymmetric quantum mechanics model, whose potential has a steep supersymmetric minimum and a broad non-supersymmetric minimum, is analyzed. With the exception of the supersymmetric ground state, the low-energy spectrum is found to be determined entirely by the non-supersymmetric well. The model is motivated by effective lagrangians proposed for supersymmetric QCD. It is speculated that in an equivalent field theory exhibiting a supersymmetric true vacuum and a non-supersymmetric false vacuum, the false vacuum can play an important rôle in the physics, and that the lowest energy excitations are extended field configurations involving a new mass scale.     

The supersymmetric QCD and KL-KS mass difference

Assuming that globally supersymmetric QCD accounts for the discrepancy between the experimental value of the K_L-K_S mass difference and that obtained from the electroweak model, we extract constraints on the squark masses for different evaluations of the K^O$\text{K}$^O hadronic matrix element.     

New uncertainties in QCD—QED rescaling factors using quadrature method

In this paper we briefly outline the quadrature method for estimating uncertainties in a function which depends on several variables, and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of the fermion mass renormalisation. Our present calculation is found to be new and also reliable when compared to the earlier values employed by various authors     

Vanishing three-loop beta function in N = 4 supersymmetric Yang-Mills theory

We have calculated the beta function of the N = 4 supersymmetric Yang-Mills theory through three-loop order and find that it is zero. The calculation was performed using superspace techniques that also allowed the calculation of the complete three-loop chiral-multiplet propagator, which turned out to be quite simple. These results strongly support the speculations that the theory is finite order-by-order in perturbation theory.     

Leading logarithmic approximation in QCD

The leading logarithmic approximation (LLA) for the scattering amplitudes in QCD is reviewed. The double-logarithmic asymptotics of scattering amplitudes is obtained as a solution to nonlinear evolution equations in the infrared cutoff. The DGLAP equation describes an evolution of parton distributions with increasing parton virtuality. The evolution of the amplitudes with respect to the scale in the longitudinal subspace is given by the BFKL equation. The gluon and quarks in QCD lie on the Regge trajectories calculable in perturbation theory. Mesons and baryons are composite states of Reggeized quarks. Similarly the Pomeron and Odderon are colorless ground states of Reggeized gluons. In the case of multicolor QCD, the Reggeon field theory in LLA is completely integrable. The Reggeon interactions in QCD are derived from a gauge-invariant effective action. In particular, next-to-leading corrections to the BFKL equation in QCD and in supersymmetric gauge models are obtained in this way.     

Neutral current in the heavy top quark limit and the renormalization of the singlet axial current

We use a simple renormalization group argument to demonstrate that the large top mass limit of the axial neutral current in QCD is unambiguously determined by the renormalization of the singlet axial current which suggests a natural scheme independent normalization condition for the latter. By calculating the anomalous dimension of the singlet axial current at three-loop level in the scheme we derive the result for the top quark decoupling from the axial neutral current valid up to (and including) the terms of order _s ² .Work supported by DFG Grant Nr. Ku 502/3-1     

Dimensional regularization and supersymmetry

We examine in detail the techniques of supersymmetric dimensional regularization. A peculiar complementarity is found to be inherent in the regularization: its manifestly supersymmetric version is contradictory, while the removal of inconsistencies costs a lossof supersymmetry in higher orders. We analyse this phenomenon at the level of Feynman diagrams and discover an explicit example of supersymmetry breakdown in the three-loop approximation. In the light of this result, we reconsider the status of dimensional regularization in globally supersymmetric gauge theories.