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Register a new userS-matrix approach to the Z resonance
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T. Riemann
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The proposed $e^+e^-$-collider FCC-ee aims at an unprecedented accuracy for $e^+e^-$ collisions into fermion pairs at the $Z$ peak, based on about $10^{13}$ events. The S-matrix approach to the $Z$ boson line shape allows the model-independent quantitative description of the reaction $e^+e^- to {bar f}f$ around the $Z$ peak in terms of few parameters, among them the mass $M_Z$ and width $Gamma_Z$ of the $Z$-boson. While weak and strong corrections remain black, a careful theoretical description of the photonic interactions is mandatory. I introduce the method and describe applications and the analysis tool SMATASY/ZFITTER.
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The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic ${alpha}^N$ order terms, it is necessary to know the open string (tree level) $(N+2)$-point amplitude of massless bosons, at least expanded at that order in $alpha$. In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring $n$-point amplitude is needed to find all the ${alpha}^N$ order terms. In this `revisited S-matrix approach we have checked that, at least up to ${alpha}^4$ order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian. The sort of results that we obtain seem to agree completely with the ones achieved by the method of BPS configurations, proposed about ten years ago. By means of the KLT relations, our results can be mapped to the NS-NS sector of the low energy effective lagrangian of the type II string theories implying that there one can also find kinematical constraints in the $N$-point amplitudes and that important informations can be inferred, at least up to ${alpha}^4$ order, by only using the (tree level) 4-point amplitude.
The experimental data on pi N scattering in the elastic energy region T_pi < 250 MeV are analyzed within the multichannel K-matrix approach with effective Lagrangians. Isospin invariance is not assumed in this analysis and the physical values for masses of the involved particles are used. The corrections due to pi^+- pi^0 and p-n mass differences are calculated and found to be in a reasonable agreement with the NORDITA results. Analysis shows the good description of the all experimental observables. From the data, new values for mass and width of the Delta^0 and Delta^{++} resonances were obtained. The isospin symmetric version gives phase shifts values close to the new solution for the pi-N elastic scattering amplitude FA02 by the GW group based on the latest experimental data. Our analysis leads to a considerably smaller < 1% isospin violation in the energy interval T_pi ~ 30-70 MeV as compared to 7% in some older analyses, however, it does confirm recent calculations based on chiral perturbation theory.
The gluino contributions to the $C_{7,8}$ Wilson coefficients for $b->s gamma$ are calculated within the unconstrained MSSM. New stringent bounds on the $delta^{RL}_{23}$ and $delta^{RR}_{23}$ mass insertion parameters are obtained in the limit in which the SM and SUSY contributions to $C_{7,8}$ approximately cancel. Such a cancellation can plausibly appear within several classes of SUSY breaking models in which the trilinear couplings exhibit a factorized structure proportional to the Yukawa matrices. Assuming this cancellation takes place, we perform an analysis of the $b->s gamma$ decay. We show that in a supersymmetric world such an alternative is reasonable and it is possible to saturate the $b->s gamma$ branching ratio and produce a CP asymmetry of up to 20%, from only the gluino contribution to $C_{7,8}$ coefficients. Using photon polarization a LR asymmetry can be defined that in principle allows for the $C_{7,8}$ and $C_{7,8}$ contributions to the $b->s gamma$ decay to be disentangled. In this scenario no constraints on the ``sign of $mu$ can be derived.
In the past year, in arXiv:1208.6066 we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the ${alpha}^N$ terms of the OSLEEL using open superstring $n$-point amplitudes in which $n$ is very much lower than $(N+2)$ (which is the order of the required amplitude to obtain those ${alpha}^N$ terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger in arXiv:1106.2645, using the Pure Spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4, 5, 6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the $alpha$ expansions for these amplitudes up to ${alpha}^6$ order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.
A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schrodinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $rtoinfty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}rm{N}$, the resonance $^{15}rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}rm{Be}$ and $^{11}rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{rm F}$
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