The Form Factors and Quantum Equation of Motion in the sine-Gordon Model

Using the methods of the 'form factor program' exact expressions of all matrix elements are obtained for several operators of the quantum sine-Gordon model alias the massive Thirring model. A general formula is presented which provides form factors in terms of an integral representation. In particular charge-less operators as for example the current of the topological charge, the energy momentum tensor and all higher currents are considered. In the breather sector it is found the quantum sine-Gordon field equation holds with an exact relation between the 'bare' mass and the normalized mass. Also a relation for the trace of the energy momentum is obtained. All results are compared with Feynman graph expansion and full agreement is found.Comment: TCI-LaTeX, 21 pages with 2 figur

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references adde

Large scale analytic calculations in quantum field theories

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.Comment: 25 pages Latex, 1 style fil

Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representations of the scalar products of Bethe states of the model.Comment: Latex file, 28 pages, based on the talk given by W. -L. Yang at Statphys 24, Cairns, Australia, 19-23 July, 201

Measurement of the Dipion Mass Spectrum in X(3872) -> J/Psi Pi+ Pi- Decays

We measure the dipion mass spectrum in X(3872)--> J/Psi Pi+ Pi- decays using 360 pb-1 of pbar-p collisions at 1.96 TeV collected with the CDF II detector. The spectrum is fit with predictions for odd C-parity (3S1, 1P1, and 3DJ) charmonia decaying to J/Psi Pi+ Pi-, as well as even C-parity states in which the pions are from Rho0 decay. The latter case also encompasses exotic interpretations, such as a D0-D*0Bar molecule. Only the 3S1 and J/Psi Rho hypotheses are compatible with our data. Since 3S1 is untenable on other grounds, decay via J/Psi Rho is favored, which implies C=+1 for the X(3872). Models for different J/Psi-Rho angular momenta L are considered. Flexibility in the models, especially the introduction of Rho-Omega interference, enable good descriptions of our data for both L=0 and 1.Comment: 7 pages, 4 figures -- Submitted to Phys. Rev. Let

Measurement of B(t->Wb)/B(t->Wq) at the Collider Detector at Fermilab

We present a measurement of the ratio of top-quark branching fractions R= B(t -> Wb)/B(t -> Wq), where q can be a b, s or a d quark, using lepton-plus-jets and dilepton data sets with integrated luminosity of ~162 pb^{-1} collected with the Collider Detector at Fermilab during Run II of the Tevatron. The measurement is derived from the relative numbers of t-tbar events with different multiplicity of identified secondary vertices. We set a lower limit of R > 0.61 at 95% confidence level.Comment: 7 pages, 2 figures, published in Physical Review Letters; changes made to be consistent with published versio

Search for Higgs Boson Decaying to b-bbar and Produced in Association with W Bosons in p-pbar Collisions at sqrt{s}=1.96 TeV

We present a search for Higgs bosons decaying into b-bbar and produced in association with W bosons in p-pbar collisions at sqrt{s}=1.96 TeV. This search uses 320 pb-1 of the dataset accumulated by the upgraded Collider Detector at Fermilab. Events are selected that have a high-transverse momentum electron or muon, missing transverse energy, and two jets, one of which is consistent with a hadronization of a b quark. Both the number of events and the dijet mass distribution are consistent with standard model background expectations, and we set 95% confidence level upper limits on the production cross section times branching ratio for the Higgs boson or any new particle with similar decay kinematics. These upper limits range from 10 pb for mH=110 GeV/c2 to 3 pb for mH=150 GeV/c2.Comment: 7 pages, 3 figures; updated title to published versio

Search for ZZ and ZW Production in ppbar Collisions at sqrt(s) = 1.96 TeV

We present a search for ZZ and ZW vector boson pair production in ppbar collisions at sqrt(s) = 1.96 TeV using the leptonic decay channels ZZ --> ll nu nu, ZZ --> l l l' l' and ZW --> l l l' nu. In a data sample corresponding to an integrated luminosity of 194 pb-1 collected with the Collider Detector at Fermilab, 3 candidate events are found with an expected background of 1.0 +/- 0.2 events. We set a 95% confidence level upper limit of 15.2 pb on the cross section for ZZ plus ZW production, compared to the standard model prediction of 5.0 +/- 0.4 pb.Comment: 7 pages, 2 figures. This version is accepted for publication by Phys. Rev. D Rapid Communication

Search for Second-Generation Scalar Leptoquarks in ppˉ\bm{p \bar{p}} Collisions at s\sqrt{s}=1.96 TeV

Results on a search for pair production of second generation scalar leptoquark in $p \bar{p}$ collisions at $\sqrt{s}$=1.96 TeV are reported. The data analyzed were collected by the CDF detector during the 2002-2003 Tevatron Run II and correspond to an integrated luminosity of 198 pb$^{-1}$. Leptoquarks (LQ) are sought through their decay into (charged) leptons and quarks, with final state signatures represented by two muons and jets and one muon, large transverse missing energy and jets. We observe no evidence for $LQ$ production and derive 95% C.L. upper limits on the $LQ$ production cross sections as well as lower limits on their mass as a function of $\beta$, where $\beta$ is the branching fraction for $LQ \to \mu q$.Comment: 9 pages (3 author list) 5 figure