Simplification of Flavour Combinatorics in the Evaluation of Hadronic Processes

A serious computational problem in the evaluation of hadronic collision processes is connected with the large number of partonic subprocesses included in the calculation. These are from the quark and gluon content of the initial hadrons, and from CKM quark mixing. For example, there are 180 subprocesses which contribute to the $W$+2jets process, and 292 subprocesses in $W$+3jets production at the LHC, even when quarks from only the first two generations are taken into account. We propose a simple modification of the rules for evaluation of cross sections and distributions, which avoids multiplication of channels from the mixture of quark states. The method is based on a unitary rotation of down quarks, thus, transporting the mixing matrix elements from vertices of Feynman diagrams to the parton distribution functions (PDF). As a result, one can calculate cross sections with significantly fewer subprocesses. For the example mentioned above, with the new rules, one need evaluate only 21 and 33 subprocesses respectively. The matrix elements of the subprocesses are calculated without quark mixing but with a modified PDF convolution which depends on the quark mixing angle, and on the topologies of gauge invariant classes of diagrams. The proposed method has been incorporated into the CompHEP program and checked with various examples.Comment: 10 pages (standard LaTeX code), 3 figures, 2 table

Pedicle screw fixation in spinal disorders: A European view

Continuing controversy over the use of pedicular fixation in the United States is promoted by the lack of governmental approval for the marketing of these devices due to safety and efficacy concerns. These implants have meanwhile become an invaluable part of spinal instrumentation in Europe. With regard to the North American view, there is a lack of comprehensive reviews that consider the historical evolution of pedicle screw systems, the rationales for their application, and the clinical outcome from a European perspective. This literature review suggests that pedicular fixation is a relatively safe procedure and is not associated with a significantly higher complication risk than non-pedicular instrumentation. Pedicle screw fixation provides short, rigid segmental stabilization that allows preservation of motion segments and stabilization of the spine in the absence of intact posterior elements, which is not possible with non-pedicular instrumentation. Fusion rates and clinical outcome in the treatment of thoracolumbar fractures appear to be superior to that achieved using other forms of treatment. For the correction of spinal deformity (i.e., scoliosis, kyphosis, spondylolisthesis, tumor), pedicular fixation provides the theoretical benefit of rigid segmental fixation and of facilitated deformity correction by a posterior approach, but the clinical relevance so far remains unknown. In low-back pain disorders, a literature analysis of 5,600 cases of lumbar fusion with different techniques reveals a trend that pedicle screw fixation enhances the fusion rate but not clinical outcome. The most striking finding in the literature is the large range in the radiological and clinical results. For every single fusion technique poor and excellent results have been described. This review argues that European spine surgeons should begin to back up the evident benefits of pedicle screw systems for specific spinal disorders by controlled prospective clinical trials. This may prevent forthcoming medical licensing authorities from restricting the use of pedicle screw devices and dictating the practice of spinal surgery in Europe in the near futur

Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain

We study the generating function of the spin-spin correlation functions in the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without magnetic field. We have found its fundamental functional relations from those for general correlation functions, which originate in the quantum Knizhink-Zamolodchikov equation. Using these relations, we have calculated the explicit form of the generating functions up to n=6. Accordingly we could obtain the spin-spin correlator up to k=5.Comment: 10 page

Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain

We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length $m$. On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.Comment: 35 page

Exact evaluation of density matrix elements for the Heisenberg chain

We have obtained all the density matrix elements on six lattice sites for the spin-1/2 Heisenberg chain via the algebraic method based on the quantum Knizhnik-Zamolodchikov equations. Several interesting correlation functions, such as chiral correlation functions, dimer-dimer correlation functions, etc... have been analytically evaluated. Furthermore we have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a result the exact von Neumann entropy for the reduced density matrix on six lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author

Dynamical correlation functions of the XXZ spin-1/2 chain

We derive a master equation for the dynamical spin-spin correlation functions of the XXZ spin-1/2 Heisenberg finite chain in an external magnetic field. In the thermodynamic limit, we obtain their multiple integral representation.Comment: 25 page

Energy scales in a stabilized brane world

Brane world gravity looks different for observers on positive and negative tension branes. First we consider the well-known RS1 model with two branes embedded into the AdS_5 space-time and recall the results on the relations between the energy scales for an observer on the negative tension brane, which is supposed to be "our" brane. Then from the point of view of this observer we study energy scales and masses for the radion and graviton excitations in a stabilized brane world model. We argue that there may be several possibilities leading to scales of the order 1-10 TeV or even less for new physics effects on our brane. In particular, an interesting scenario can arise in the case of a "symmetric" brane world with a nontrivial warp factor in the bulk, which however takes equal values on both branes.Comment: 15 pages, corrected typos, enlarged conten

Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet

We exactly evaluate the third neighbor correlator and all the possible non-zero correlators <S^{alpha}_j S^{beta}_{j+1} S^{gamma}_{j+2} S^{delta}_{j+3}> of the spin-1/2 Heisenberg $XXX$ antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.Comment: 4 page