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©2003 Elsevier Science B.V. All rights reserved., We present an equivalence theorem for the longitudinal components of the gauge bosons in a compactified five-dimensional extension of the Standard Model, whose spontaneous symmetry breaking is driven either by one Higgs in the bulk or by one on a brane or by both together. We also show some implications for the unitarity bounds on Higgs masses., Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1997 The American Physical Society. J.R.P would like to thank the Theory Group at Berkeley for their kind hospitality, the Jaime del Amo fundation for financial support, as well as M.J. Herrero and H.J. He for helpful discussions on the subject. This work has been partially supported by the Ministerio de Educación y Ciencia (Spain) Grant No. CICYT AEN93-0776)., In this work we study the applicability of the equivalence theorem, either for unitary models or within an effective Lagrangian approach. There are two types of limitations: the existence of a validity energy window and the use of the lowest order in the electroweak constants. For the first kind, we consider some methods, based on dispersion theory or the large N limit, that allow us to extend the applicability. For the second, we obtain numerical estimates of the effect of neglecting higher orders in the perturbative expansion. [S0556-2821(97)04421-4]., Ministerio de Educación y Ciencia (Spain), CICYT, Jaime del Amo fundation, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

We outline the concrete steps involved in building prescriptive master integrand bases for scattering amplitudes beyond the planar limit. We highlight the role of contour choices in such bases, and illustrate the full process by constructing a complete, triangle power-counting basis at two loops for six particles. We show how collinear contour choices can be used to divide integrand bases into separately finite and divergent subspaces, and how double-poles can be used to further subdivide these spaces according to (transcendental) weight. Complete details of the basis constructed for six particles is provided in the supplementary material.

Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth order in the charges (two-loop order) in a classical regime analogous to the post-Minkowskian expansion in General Relativity. We employ modern scattering amplitude tools and extract classical observables by both eikonal methods and the formalism of Kosower, Maybee, and O'Connell (KMOC). In addition, we provide a simplified approach to extracting the radial action beyond the conservative sector.

We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric (1

We derive closed formulas for the first examples of nonalgebraic, elliptic "leading singularities" in planar, maximally supersymmetric Yang-Mills theory and show that they are Yangian invariant.

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of 'power-counting' for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all 'leading-(transcendental-)weight' contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory - for generic helicities and arbitrary multiplicity.

We reproduce the two-loop seven-point remainder function in planar, maximally supersymmetric Yang-Mills theory by direct integration of conformally-regulated chiral integrands. The remainder function is obtained as part of the two-loop logarithm of the MHV amplitude, the regularized form of which we compute directly in this scheme. We compare the scheme-dependent anomalous dimensions and related quantities in the conformal regulator with those found for the Higgs regulator.

© The Author(s) 2019. We thank prof. W. Ochs for his comments and for providing us with the data of his updated (-+-) solution. JRP and AR are supported by the Spanish project FPA2016-75654-C2-2-P. This project has received funding from the European Union's Horizon 2020 research and innovation program under Grant agreement No.824093. AR would also like to acknowledge the financial support of the Universidad Complutense de Madrid through a predoctoral scholarship. JRE is supported by the Swiss National Science Foundation, project No. PZ00P2_174228., We provide global parameterizations of pi pi -> pi pi scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of pi pi -> pi pi, both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 GeV. Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the sigma/f(0)(500), f(0)(980) and rho(770) pole parameters., Unión Europea. H2020, Ministerio de Economía y Competitividad (MINECO)/FEDER, Swiss National Science Foundation (SNSF), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© American Physical Society. This work was supported by the German Bundesministerium für Bildung und Forschung, the U.S. Department of Energy under Grants No. DE-AC05-06OR23177 and No. DE-FG02-87ER40365, Research Foundation—Flanders (FWO), PAPIIT-DGAPA (UNAM, Mexico) under Grants No. IA101717 and No. IA101819, CONACYT(Mexico)underGrantNo.251817,U.S.National Science Foundation under Grant No. PHY-1415459,Ministerio de Ciencia, Innovación y Universidades (Spain) Grants No. FPA2016-77313-P and No. FPA2016-75654-C2-2-P, and Universidad Complutense de Madrid., We perform an analysis of the three-pion system with quantum numbers J(PC) = 1(++) thornthorn produced in the weak decay of tau leptons. The interaction is known to be dominated by the axial meson alpha(1) (1260). We build a model based on approximate three-body unitary and fix the free parameters by fitting it to the ALEPH data on tau- -> pi(-)pi(+)pi(-)nu(tau) decay. We then perform the analytic continuation of the amplitude to the complex energy plane. The singularity structures related to the pi pi subchannel resonances are carefully addressed. Finally, we extract the alpha(1) (1260) pole position m(p)((a1(1260)) - i Gamma((a1(1260))(p) /2 with m(p)((a1(1260)) = (1209 +/- 4(-9)(+12)) MeV, Gamma((a1(1260))(p) = (576 +/- 11(-20)(+89)) MeV., Ministerio de Ciencia e Innovación (MICINN), German Bundesministerium fur Bildung und Forschung, Research Foundation-Flanders (FWO), Universidad Complutense de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and the harmonic approximation (HA) for strong interactions. Diffusion Monte Carlo method is used to obtain the ground-state properties in a non-perturbative manner. We report the dependence of the Bertsch parameter on the interaction strength and construct a Padé approximant which fits the numerical data and reproduces correctly the asymptotic limits of weak and strong interactions. We find good agreement with beyond-mean field theory for the energy and the condensate fraction. The pair distribution function and the static structure factor are reported for a number of characteristic interactions. We demonstrate that the system experiences a gas-solid phase transition as a function of the dimensionless interaction strength. A peculiarity of the system is that by changing the density it is not possible to induce the phase transition. We show that the low-lying excitation spectrum contains plasmons in both phases, in agreement with the Bogoliubov and HA theories. Finally, we argue that this model can be interpreted as a realization of the unitary limit of a Bose system with the advantage that the system stays in the genuine ground state contrarily to the metastable state realized in experiments with short-range Bose gases., Postprint (published version)

This thesis provides an overview of the standard randomized benchmarking protocol, the extension to interleaved randomized benchmarking and the related unitarity randomized benchmarking, used to characterize noisy implementations of quantum gates from the Clifford group. It contains a brief overview of the textbook and literature preliminaries that are needed to understand the description and proof of these protocols. It outlines how previous work has reduced the number of random sequences needed in standard randomized benchmarking. Then it presents the new result of reduced number of sequences for unitarity randomized benchmarking and discusses the implication of these new results.

Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average) an entropy of 3.9 ± 2.5 bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of “hidden information” in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation, we adopt a variant of the “average subsystem” approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows “young” black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.

We introduce a notion of position-space cuts of eikonal diagrams, the set of diagrams appearing in the perturbative expansion of the correlator of a set of straight semi-infinite Wilson lines. The cuts are applied directly to the position-space representation of any such diagramand compute its imaginary part to the leading order in the dimensional regulator. Our cutting prescription thus defines a position-space analog of the standard momentum-space Cutkosky rules. Unlike momentum-space cuts which put internal lines on shell, position-space cuts constrain a number of the gauge bosons exchanged between the energetic partons to be lightlike, leading to a vanishing and a non-vanishing imaginary part for space-and timelike kinematics, respectively.

We further develop the formalism for taking position-space cuts of eikonal diagrams introduced in ref. [1]. These cuts are applied directly to the position-space representation of any such diagram and compute its discontinuity to the leading order in the dimensional regulator. We provide algorithms for computing the position-space cuts and apply them to several two-and three-loop eikonal diagrams, finding agreement with results previously obtained in the literature. We discuss a non-trivial interplay between the cutting prescription and non-Abelian exponentiation. We furthermore discuss the relation of the imaginary part of the cusp anomalous dimension to the static interquark potential.

We investigate the many-body properties of two distinct degenerate systems with strong interactions, namely that of a quark-gluon plasma and of an atomic Bose gas. In the first part of this thesis, the temperature dependence of the thermodynamic potential of quantum chromodynamics is studied. In particular, the specific heat and the quark effective mass are calculated for imbalanced quark matter in the limit of a large number of quark flavors (large-Nf), which corresponds to the random phase approximation. Also, a generalization of the Landau effective-mass relation for the imbalanced case within relativistic Landau-Fermi liquid theory is derived. The effects of imbalance is expected to have important consequences on the properties of quark matter in the core of neutron stars. In the second part, we develop an analytical approach for the description of the crossover of an atomic Bose gas from small to infinitely large scattering length (unitarity). We obtain several properties of the Bose gas as a function of interaction strength, such as the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. It is shown how the approach can be systematically improved with renormalization-group methods and that it reduces to the Bogoliubov theory in the weak-coupling limit.

The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the Large Hadron Collider and may also provide deeper insights into the theoretical foundations of quantum field theory. In this thesis we develop a new method for computing two-loop amplitudes, based on unitarity rather than Feynman diagrams. In this approach, the two-loop amplitude is first expanded in a linearly independent basis of integrals. The process dependence thereby resides in the coefficients of the integrals. These expansion coefficients are then the object of calculation. Our main results include explicit formulas for a subset of the integral coefficients, expressing them as products of tree-level amplitudes integrated over specific contours in the complex plane. We give a general selection principle for determining these contours. This principle is then applied to obtain the coefficients of integrals with the topology of a double box. We show that, for four-particle scattering, each double-box integral in the two-loop basis is associated with a uniquely defined complex contour, referred to as its master contour. We provide a classification of the solutions to setting all propagators of the general double-box integral on-shell. Depending on the number of external momenta at the vertices of the graph, these solutions are given as a chain of pointwise intersecting Riemann spheres, or a torus. This classification is needed to define master contours for amplitudes with arbitrary multiplicities. We point out that a basis of two-loop integrals with as many infrared finite elements as possible allows substantial technical simplications, in terms of obtaining the coefficients of the integrals, as well as for the analytic evaluation of the integrals themselves. We compute two such integrals at four points, obtaining remarkably compact expressions. Finally, we provide a check on a recently developed recursion relation for the all-loop integrand of the amplitudes of N=

Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed employing the recently proposed Grassmannian integral in N=4 super Yang-Mills theory. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.

This thesis deals with different aspects of string and /p/-brane theories. One of the motivations for string theory is to unify the forces in nature and produce a quantum theory of gravity. /p/-branes and related objects arise in string theory and are related to a non-perturbative definition of the theory. The results of this thesis might help in understanding string theory better. The first part of the thesis introduces and discusses relevant topics for the second part of the thesis which consists of five papers. In the three first papers we develop and treat a perturbative approach to relativistic /p/-branes around stretched geometries. The unperturbed theory is described by a string- or particle-like theory. The theory is solved, within perturbation theory, by constructing successive canonical transformations which map the theory to the unperturbed one order by order. The result is used to define a quantum theory which requires for consistency d = 25 + p dimensions for the bosonic /p/-branes and d = 11 for the supermembrane. This is one of the first quantum results for extended objects beyond string theory and is a confirmation of the expectation of an eleven-dimensional quantum membrane. The two last papers deal with a gauged WZNW-approach to strings moving on non-trivial space-times. The groups used in the formulation of these models are connected to Hermitian symmetric spaces of non-compact type. We have found that the GKO-construction does not yield a unitary spectrum. We will show that there exists, however, a different approach, the BRST approach, which gives unitarity under certain conditions. This is the first example of a difference between the GKO- and BRST construction. This is one of the first proofs of unitarity of a string theory in a non-trivial non-compact space-time. Furthermore, new critical string theories in dimensions less then 26 or 10 is found for the bosonic and supersymmetric string, respectively.

Time-frequency distributions are used in the analysis and processing of nonstationary signals. The Wigner-Ville distribution (WVD) is a fundamental time-frequency distribution uniquely satisfying many desirable mathematical properties. The realisation of this distribution for hardware or software platforms requires a discrete version. Historically the majority of the work on deriving discrete versions of the WVD has focused on creating alias-free distributions, often resulting in a loss of some desirable properties. Here a new discrete time and frequency WVD will be presented for nonperiodic signals and will be examined both in terms of its properties and aliasing. In particular unitarity, an assumed property for optimum time-frequency detection and signal estimation, and invertibility, a useful property especially for time-frequency filtering, will be examined. An efficient implementation of the distribution using standard real-valued fast Fourier transforms will also be presented.

©1996 Published by Elsevier Science. This work has been supported in part by the Ministerio de Education y Ciencia (Spain) (CICYTAEN95-1285-E) and COLCIENCIAS (Columbia). J.R.P. would like to thank the Theoretical Group at Berkeley for their kind hospitality, as well as the Jaime de1 Amo Foundation for a fellowship. Partial support by US DOE under contract DE-ACO3-76SFOOO98 is gratefully acknowledged., In this paper we study the large N limit of the Standard Model Higgs sector with N lambda, Ng(2) and Ng('2) constant and N being the number of would-be Goldstone bosons, Despite the simplicity of this method at leading order, its results satisfy simultaneously important requirements such as unitarity and the low-energy theorems in contrast with other more conventional approaches. Moreover, it is fully compatible with the Equivalence Theorem and it yields a consistent description of the Higgs boson mass and width, Finally we have also included a phenomenological discussion concerning the applications of this method to the LHC., Ministerio de Education y Ciencia (Spain), CICYT, COLCIENCIAS (Columbia), US DOE, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators give a representation of the canonical commutation relations with two degrees of freedom. If the charge of the particle is not an integer (the case corresponding to the Aharonov–Bohm effect), then the representation is inequivalent to the Schrödinger representation. It is shown that the inequivalent representation induces infinite-dimensional Hilbert space representations of the quantum group Uq(sl2). Some properties of these representations of Uq(sl2) are investigated.

A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators give a representation of the canonical commutation relations with two degrees of freedom. If the charge of the particle is not an integer (the case corresponding to the Aharonov–Bohm effect), then the representation is inequivalent to the Schrödinger representation. It is shown that the inequivalent representation induces infinite-dimensional Hilbert space representations of the quantum group Uq(sl2). Some properties of these representations of Uq(sl2) are investigated.

In this paper we apply a simple phenomenological model to describe the scattering amplitudes of strongly interacting longitudinal gauge bosons at the future pp colliders, LHC and SSC. The model is based on the use of the well-known techniques from chiral effective Lagrangians and chiral perturbation theory, supplemented by a unitarization method for the scattering amplitudes. The generality of the approach allows one to deal with various physical situations in the unknown symmetry breaking sector of the Standard Model. In particular we mimic the two typical scenarios for the symmetry breaking sector: one of Higgs-type and the other of QCD-type. Two different unitarization methods have been implemented for comparison: the Pade approximants method and the K-matrix method. The first one permits the incorporation of the possibility of dynamical resonances as it can develop poles for the various different (I,J)-channels. A systematic study of strongly interacting signals for both LHC and SSC is presented, and their rates and efficiencies are compared., Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

The aim of the lecture series presented at the International School of Physics Enrico Fermi, Varenna, Italy, is to present the main steps to follow in the standard proof of dispersion relations. Seven papers which were presented in course number 29 are contained in this book. These papers are: (1) The Role of Invariance Principles in Natural Philosophy, by E. P. Wigner; (2) The Proof of Dispersion Relations, by M. Froissart; (3) Causality, RMatrix, and Collision Matrix, by E. P. Wigner; (4) Dispersion Relations and Applications, by D. Y. Wong; (5) The Nonrelativistic Angular-Momentum Plane, by R. G. Newton; (6) Production Amplitudes, by P. V. Landshoff; and (7) High-Energy Scattering and Dispersion Theory, by R. Oehme. (Author), Proceedings of the International School of Physics 'Enrico Fermi,' Course 29, held at Varenna, Italy, 15 Jul-3 Aug 63. Available from Academic Press, 111 Fifth Avenue, New York 3, N. Y.

The Coulomb T-matrix is examined in a two body and a three body Hilbert space. The purpose is to demonstrate how this function may be used to construct the Faddeev three body kernel. In the process the apparent paradox of the indefiniteness of the Coulomb T-matrix on the energy shell is resolved. The question of off shell unitarity is discussed. (Author)

The deuteron form factor is calculated in a one-pionexchange (OPE) approximation using single-variable unsubtracted dispersion relations in the squared-momentum-transfer variable. As a first step, the imaginary parts of the form factors are presented in terms of the four invariants of the deuteron-nucleon (d-N) vertex. The resulting equations are compared in detail with similar expressions obtained from the Jankus potential theory, and a clear understanding of the precise way in which the d-N invariants play the role of the deuteron wave function emerges, enabling us to obtain relativistic wave functions. This comparison also shows the presence of new relativistic terms not included in the Jankus results (in particular, a new term appears in the magnetic moment). Then, the imaginary parts of the d-N vertex invariants are calculated numerically. In this calculation the OPE contribution in its anamalous region is calculated exactly, while the contributions above the normal threshold are obtained by an educated guess based on sum rules which the invariants are assumed to satisfy. Finally, using these results, the form factors are calculated numerically. With the assumption of unsubtracted dispersion relations, it is necessary to assume only the charge and mass of the deuteron, and the pion-nucleon coupling constant, in order to completely determine the form factors. The numerical results for the magnetic and quadrupole moments agree with experiment to within 2%; the D-state probability if 5.5% but is not very reliably determined, and the other results, while less good, are still quite reasonable. (Author), Pub. in The Physical Review v136 n1B pB140-61 Oct 12 1964 (Copies not available to DDC or Clearinghouse customers).

The formal theory of scattering processes is extended to include multiplechannel scattering (rearrangement collisions). First, the singlechannel case is reviewed. The multiple-channel case then is developed, in close analogy with the simpler case. The multiple-channel generalizations of the operator identities and the relations among the matrix elements that replace the familiar single-channel forms are derived. Timereversibility, reciprocity, and unitarity are suitably defined for single-channel and multichannel collisions ard are shown to have the property that any two implies the third. The generalization to particles with spin is discussed and some remarks are made on the application to complex potentials (optical model), where time-reflection invariance implies only reciprocity. The theory of resonance scattering, in which the target and the incident particle can form a compound system of finite lifetime, is discussed, particularly as it applies to the scattering of electrons by molecules at energies close to the resonant energies of the negative molecular ion. (Author)

Weinberg's derivation of Feynman rules for finite dimensional representation of the Lorentz group is generalized for massive particles to infinite dimensional irreducible representations of the Lorentz group. Following Feldman and Matthews, local and causal infinite dimensional fields, quantised by a commutator, are written down for irreducible unitary representations of the principal series of SL(2,C). Feynman rules for those infinite dimensional fields are stated and three point functions and pole diagrams are given explicitly for arbitrary unitary irreducible representations of the principal series of SL(2,C). (Author)

It is shown that one can in principle constrain the CP-violating parameter δ from measurements of four independent |Vij|2’s, or three |Vij|2’s and a ratio of two of them, in the leptonic sector. To quantify our approach, using unitarity, we derive simple expressions in terms of four independent |Vij|2’s for cos δ, and an expression for sin 2δ from J2. Thus, depending on the values for |Vij| and their accuracy, we can set meaningful limits on |δ|. To illustrate numerically, if |Vμ1|2 is close to 0.1 with a 10% precision, and if |Ve3|2 is larger than 0.005 and for values of |Ve2|2 and |Vμ3|2 that stay within ±0.1 of the current experimental data leads to a bound: π/2≤|δ|≤π. Alternatively, a certain combination of parameters with values of |Ve3|2 larger than 0.01 leads to a closed bound of 73≤|δ|≤103. In general, we find that it is better to use |Vμ1|2 or |Vτ1|2 as the fourth independent |Vij|2 and that, over most of the parameter space, δ is least sensitive to |Ve3|2. With just three independent measurements (solar, atmospheric, and reactor), it is impossible to set limits on the CP phase. In this respect, we study the use of ultrahigh energy cosmic ray neutrino fluxes as the additional fourth information. We find that within the SM, neutrino fluxes of all three flavors will be very similar but that pushing current neutrino data to their extreme values still allowed, ratios of cosmic neutrino fluxes can differ by up to 20%; such large discrepancies could imply negligibly small CP violation. We also study a nonradiative neutrino decay model and find that the neutrino fluxes can differ by a factor of up to 3 within this model and that an accuracy of 10% on the neutrino fluxes is sufficient to set interesting limits on δ.