Pion Pair Production with Higher Order Radiative Corrections in Low Energy e+e- Collisions

The complete one-loop QED initial state, final state and initial--final state interference corrections to the process e+e- -> pi+pi- are presented. Analytic formulae are given for the virtual and for the real photon corrections. The total cross section, the pion angular distribution and the pi+pi- invariant mass distribution are investigated in the regime of experimentally realistic kinematical cuts. It is shown that in addition to the full one-loop corrections also two-loop initial state corrections and even the resummation of higher order soft photon logarithms can be necessary if at least per cent accuracy is required. For the data analysis we focus on an inclusive treatment of all photons. The theoretical error concerning our treatment of radiative corrections is then estimated to be less than 2 per mille for both the measurement of the total cross section and the pi+pi- invariant mass distribution. In addition we discuss the model uncertainty due to the pion substructure. Altogether the precision of the theoretical prediction matches the requirements of low energy e+e- experiments like the ones going on at DAFNE or VEPP-2M.Comment: 16 pages 9 figures 7 tables; 6 figs added+text; modified Eqs.(56,68), enhanced appendice

Majorana dimers and holographic quantum error-correcting codes

Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography

Signature of heavy Majorana neutrinos at a linear collider: Enhanced charged Higgs pair production

A charged Higgs pair can be produced at an ee collider through a t-channel exchange of a heavy neutrino (N) via e^+ e^- -> H^+ H^- and, if N is a Majorana particle, also via the lepton number violating (LNV) like-sign reaction e^\pm e^\pm \to H^\pm H^\pm. Assuming no a-priori relation between the effective eNH^+ coupling (\xi) and light neutrino masses, we show that this interaction vertex can give a striking enhancement to these charged Higgs pair production processes. In particular, the LNV H^-H^- signal can probe N at the ILC in the mass range 100 GeV < m_N < 10^4 TeV and with the effective mixing angle, \xi, in the range 10^{-4} < \xi^2 < 10^{-8} - well within its perturbative unitarity bound and the neutrinoless double beta decay (\beta\beta_{0\nu}) limit. The lepton number conserving (LNC) e^+ e^- \to H^+ H^- mode can be sensitive to, e.g., an O(10) TeV heavy Majorana neutrino at a 500 GeV International Linear Collider (ILC), if \xi^2 > 0.001.Comment: Latex, 5 pages, 3 figures. V2 as published in PR

Measuring the FSR--inclusive pi+pi- cross section

Final state radiation (FSR) in pion--pair production cannot be calculated reliably because of the composite structure of the pions. However, FSR corrections have to be taken into account for a precise evaluation of the hadronic contribution to g-2 of the muon. The role of FSR in both energy scan and radiative return experiments is discussed. It is shown how FSR influences the pion form factor extraction from experimental data and, as a consequence, the evaluation of a_mu^had. In fact the O(alpha) FSR corrections should be included to reach the precision we are aiming at. We argue that for an extraction of the desired FSR--inclusive cross section sigma^(gamma)_had a photon--inclusive scan measurement of the ``e+e- to pi+pi- + photons'' cross section is needed. For exclusive scan and radiative return measurements in contrast we have to rely on ad hoc FSR models if we want to obtain either sigma^(gamma)_had or the FSR--exclusive cross section sigma^(0)_had. We thus advocate to consider seriously precise photon--inclusive energy scan measurements at present and future low energy e+e- facilities. Then together with radiative return measurements from DAFNE and BABAR and forthcoming scan measurements at VEPP-2000 we have a good chance to substantially improve the evaluation of a_mu^had in the future.Comment: 18 pages, 13 Figure

Neutrino Masses and A TeV Scale Seesaw Mechanism

A simple extension of the Standard Model providing TeV scale seesaw mechanism is presented. Beside the Standard Model particles and right-handed Majorana neutrinos, the model contains a singly charged scalar, an extra Higgs doublet and three vector like singly charged fermions. In our model, Dirac neutrino mass matrix raises only at the loop level. Small but non-zero Majorana neutrino masses come from integrating out heavy Majorana neutrinos, which can be at the TeV scale. The phenomenologies of the model are investigated, including scalar mass spectrum, neutrino masses and mixings, lepton flavor violations, heavy neutrino magnetic moments as well as possible collider signatures of the model at the LHC.Comment: 13 pages, 4 figures. references adde

Left-right symmetry at LHC and precise 1-loop low energy data

Despite many tests, even the Minimal Manifest Left-Right Symmetric Model (MLRSM) has never been ultimately confirmed or falsified. LHC gives a new possibility to test directly the most conservative version of left-right symmetric models at so far not reachable energy scales. If we take into account precise limits on the model which come from low energy processes, like the muon decay, possible LHC signals are strongly limited through the correlations of parameters among heavy neutrinos, heavy gauge bosons and heavy Higgs particles. To illustrate the situation in the context of LHC, we consider the "golden" process $pp \to e^+ N$. For instance, in a case of degenerate heavy neutrinos and heavy Higgs masses at 15 TeV (in agreement with FCNC bounds) we get $\sigma(pp \to e^+ N)>10$ fb at $\sqrt{s}=14$ TeV which is consistent with muon decay data for a very limited $W_2$ masses in the range (3008 GeV, 3040 GeV). Without restrictions coming from the muon data, $W_2$ masses would be in the range (1.0 TeV, 3.5 TeV). Influence of heavy Higgs particles themselves on the considered LHC process is negligible (the same is true for the light, SM neutral Higgs scalar analog). In the paper decay modes of the right-handed heavy gauge bosons and heavy neutrinos are also discussed. Both scenarios with typical see-saw light-heavy neutrino mixings and the mixings which are independent of heavy neutrino masses are considered. In the second case heavy neutrino decays to the heavy charged gauge bosons not necessarily dominate over decay modes which include only light, SM-like particles.Comment: 16 pages, 10 figs, KL-KS and new ATLAS limits taken into accoun

Influence of the left-handed part of the neutrino mass matrix on the lepton number violating e-e- -> W-W- process

Influence of the neutrino mass submatrix $M_L$ on the e-e- -> W-W- process is discussed. Taking into account various possible CP signatures of heavy neutrinos it is shown that, in some cases, nonzero $M_L$ substantially changes predictions for maximum possible values of the e-e- -> W-W- cross section. A direct role of the $\omega^2$ parameter (coming from neutrinoless double beta decay) is clarified. The consequences of doubly charged Higgs particles $\delta^{--}$ with resonances even far away from energies of the future linear lepton collider ($\sqrt{s}=0.5-1$ TeV) are studied.Comment: revtex, epsfig, 5 figures, 9 pages. To appear in Phys.Rev.

Boundary theories of critical matchgate tensor networks

Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states

Evaluation of High Order Terms for the Hubbard Model in the Strong-coupling Limit

The ground-state energy of the Hubbard model on a Bethe lattice with infinite connectivity at half filling is calculated for the insulating phase. Using Kohn's transformation to derive an effective Hamiltonian for the strong-coupling limit, the resulting class of diagrams is determined. We develop an algorithm for an algebraic evaluation of the contributions of high-order terms and check it by applying it to the Falicov-Kimball model that is exactly solvable. For the Hubbard model, the ground-state energy is exactly calculated up to order t^12/U^11. The results of the strong-coupling expansion deviate from numerical calculations as quantum Monte Carlo (or density-matrix renormalization-group) by less than 0.13% (0.32% respectively) for U>4.76.Comment: 8 pages, 5 figures, 2 flowcharts, 1 tabl