Revisiting the Naturalness Problem -- Who is afraid of quadratic divergences? --

It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences, which can always be absorbed into a position of the critical surface, should be simply subtracted in model constructions. Such a picture gives another justification to the argument that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.Comment: 22 pages, 6 figures, version published in Phys. Rev.

QED vertex form factors at two loops

We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$. The calculation is carried out within the continuous $D$-dimensional regularization scheme, with a single continuous parameter $D$, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences. The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 53 pages, 3 figure

Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q^2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 38 pages, 6 figures, typos corrected, version accepted by Nucl. Phys.

Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field models

In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified nuclear Skyrme interaction, and proposed a strategy to treat such a divergence. In the present work, we extend the same strategy to the case of the full nuclear Skyrme interaction. Moreover we show that, in spite of the strong divergence ($\sim$ $\Lambda^5$, where $\Lambda$ is the momentum cutoff) related to the velocity-dependent terms of the interaction, the adopted cutoff regularization can be always simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratio. This paves the way to applications to finite nuclei.Comment: 15 figure

Vertex diagrams for the QED form factors at the 2-loop level

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared electron mass $m_e^2=a$. We identify all the Master Integrals (MI's) of the problem and write the differential equations in $Q^2$ which they satisfy. The equations are expanded in powers of $\epsilon = (4-D)/2$ and solved by the Euler's method of the variation of the constants. As a result, we obtain the coefficients of the Laurent expansion in $\epsilon$ of the MI's up to zeroth order expressed in close analytic form in terms of Harmonic Polylogarithms.Comment: A few misprints have been corrected. The results are now available at http://pheno.physik.uni-freiburg.de/~bhabha, as FORM input file

Amine-oxide adsorbents for post-combustion CO₂ capture

Amine functionalized silicas are promising chemisorbent materials for post-combustion CO₂ capture due to the high density of active sites per unit mass of adsorbent that can be obtained by tuning the synthesis protocol, thus resulting in high equilibrium CO₂ adsorption capacities. However, when compared to physisorbents, they have a few disadvantages. Firstly, oxidative degradation of the amine groups reduces the lifetime of these adsorbent materials. Furthermore, rapid heat release following the reaction between amines and CO₂ results in large local temperature spikes which may adversely affect adsorption equilibria and kinetics. Thirdly, there is a lack of fundamental understanding of CO₂-amine adsorption thermodynamics, which is key to scaling up these materials to an industrial-scale adsorption process. In this dissertation the qualitative and quantitative understanding of these three critical aspects of aminosilica adsorbents have been furthered so these materials can be better evaluated and further tuned as adsorbents for post-combustion CO₂ capture applications.Ph.D

Dimensional Reduction applied to QCD at three loops

Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $\beta$ function and the anomalous dimension of the quark masses are derived to three-loop order. Special emphasis is put on the proper treatment of the so-called $\epsilon$-scalars and the additional couplings which have to be considered.Comment: 13 pages, minor changes, references adde

Higher loop corrections to a Schwinger--Dyson equation

We consider the effects of higherloop corrections to a Schwinger--Dyson equations for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess--Zumino model as a laboratory. We obtain the dominant contributions of the three and four loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.Comment: 12 pages, 2 imbedded TiKZ pictures. A few clarifications matching the published versio

The Casimir energy of skyrmions in the 2+1-dimensional O(3)-model

One-loop quantum corrections to the classical vortices in 2+1 dimensional O(3)-models are evaluated. Skyrme and Zeeman potential terms are used to stabilize the size of topological solitons. Contributions from zero modes, bound-states and scattering phase-shifts are calculated for vortices with winding index n=1 and n=2. For both cases the S-matrix shows a pronounced series of resonances for magnon-vortex scattering in analogy to the well-established baryon resonances in hadron physics, while vortices with n>2 are already classically unstable against decay. The quantum corrections destabilize the classically bound n=2 configuration. Approximate independence of the results with respect to changes in the renormalization scale is demonstrated.Comment: 24 pages LaTeX, 14 figure