Infrared anomaly induced by spontaneous breakdown of supersymmetry

We apply the renormalization scheme of Zimmermann and Lowenstein to O'Raifeartaigh's model of a theory with spontaneous breakdown of supersymmetry. Within perturbation theory the BPHZL method together with the algebraic technique of Becchi, Rouet, Stora allows one to study rigorously the infrared properties of the model and to prove that in the supersymmetry Ward identity for Green functions, there shows up an anomalous contribution. It is indicated that the existence of this term is independent of the renormalization procedure.     

On the 1-Loop Renormalization of the Electroweak Standard Model and its Application to Leptonic Processes

A renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained as a simple substructure. Field renormalization respecting the gauge symmetry gives finite propagators and vertex functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators in the t'Hooft-Feynman gauge. We give a complete list of self energies and all renormalization constants also in the unphysical Higgs and ghost sector. Explicit results are given for the renormalized self energies, vertex functions and boxes that enter the evaluation of 1-loop radiative corrections to fermionic processes. We calculate the 1-loop radiative corrections to purely leptonic reactions like μ decay, vμ_μe scattering and μ pair production in e⁺e⁻annihilation. A test of the standard model is performed by comparing these low energy data with the results of the PP collider experiments for the W and Z boson masses.     

Renormalization group functions for the radiative symmetry breaking scheme

We obtain the renormalization group (RG) functions for the massless scalar field theory where symmetry breaking occurs radiatively. After obtaining the effective potential for the radiative symmetry breaking scheme by finite transformations for the classical field and coupling constant, we obtain the corresponding RG functions from that of the minimal subtraction (MS) scheme.     

“BEST” Homonuclear Adiabatic Decoupling for C- and N-Double-Labeled Proteins

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f_1rms as the main decoupling that is required for Bloch–Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch–Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or “BEST” decoupling for short, is constructed, which not only compensates the Bloch–Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.     

Open bosonic strings in general background fields

We discuss the renormalization properties of the 2 dim. field theory describing an open bosonic string in the background fields corresponding to its massless excitations. The relevant β-functions are calculated for gravitational, antisymmetric tensor and Yang-Mills background on 1-loop level, for pure Yang-Mills background an 2-loop level and in the Abelian case up to 3 loops. We find a renormalization scheme dependence starting at 2 loop order. Putting β to zero yields the equation of motion for the non-linear electrodynamics of Fradkin and Tseytlin.     

Perturbative series and the 1/N expansion for the QED β-function

A comparison of the 5-loop perturbative series and the 1/N expansion for the QED renormalization group β-function in the Minimal Subtraction scheme is performed. The good agreement between two expansions is found which proves that the MS β-function is adequately described by both series.     

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D₀ for different values of dimensions including the most important practical cases D₀ = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added.     

On dangerous irrelevant operators

The effects of dangerous irrelevant operators on various types of critical behavior are described, as particular cases of a systematic field theoretic renormalization group treatment. Starting from a general formulation, such cases as the tricritical crossover above three dimensions, hyperscaling above four, and symmetry-breaking by irrelevant operators are considered. The irrelevance discussed is either oftthe “strong type”, identifiable by dimensional analysis, or of the “weak type”, produced by the renormalization group.     

Isidor I. Rabi and CERN

Isidor I. Rabi (1898–1988) is the acknowledged “father of CERN,” today one of the most important particle-physics laboratories in the world. I explore his motives for promoting the idea in 1950 that Western Europe should build a “Brookhaven” with national governments replacing universities. I unravel the many ways in which a major accelerator facility in Geneva, Switzerland, could both stimulate European science and serve the interests of the American scientific community. Rabi was careful to avoid giving any official support to steps then under way in Europe to build a research reactor, even though Brookhaven National Laboratory on Long Island, New York, had one from the outset. I suggest that his main motive for doing so was that he wanted West Germany to be part of the collaborative venture. Rabi was well aware of the foreign-policy objectives of the U.S. State Department in the European theater in 1950, and he wanted to situate politically the new research center in the framework of the Marshall Plan for the postwar reconstruction of the continent, “remaking the Old World in the image of the New.”John Krige is Kranzberg Professor in the School of History,Technology and Society at the Georgia Institute of Technology. He has researched and published extensively on the place of science and technology in the postwar reconstruction of Western Europe, and the role of the United States therein.     

Multiparticle perturbation theory and an accurate calculation of parity nonconservation in cesium

A method of calculating higher-order correlation corrections, using Green's functions and the Feynman diagrammatic technique, is developed. A basis of the single-electron orbitals is computed using the relativistic Hartree-Fock method. The interaction of an atom with an external field is computed by solving the time-dependent Hartree-Fock equations. In the methodology presented, we consider all the second-order correlation corrections and the dominating classes of higher order diagrams: the screening of the Coulomb interaction of electrons, particle-hole interaction and mass operator iterations. The calculation of the energy levels, the intervals of hyperfine structure and the amplitudes of the allowed EI-transitions in C_s shows that the method developed ensures precision at the 0.1–1% level. A calculation of the parity nonconservation of the El-amplitude of the transition 6s–7s in Cs is produced. The result <6s¦D_z¦7s> = –(0.91 ± 0.01)·10^–11 i¦e¦a^B (–Q_W/N) is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 108–119, August, 1990.     

Spin alignment and parity violation effects inρ 0 production in neutrino and antineutrino charged-current interactions

Most of the measured events on hydrogen, deuterium and neon targets from BEBC at CERN and the 15-foot Bubble Chamber at Fermilab are combined to measure spin-density matrix elements for ⁰ production in the current-fragmentation region in neutrino and antineutrino charged-current interactions. The spin-alignment parameter is found to be 0.08±0.11 for neutrino and 0.41±0.11 for antineutrino interactions. The parity-odd density matrix element Im(₁₀+_–10) is consistent with zero in both reactions. In the combined neutrino and antineutrino data an indication of parity violation is observed: Im _1–1=0.38±0.16 atx _B >0.2,Q ²>8 GeV² andz>0.6.     

An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems

We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov–Arnold–Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

Trellis ternary line coding scheme for asynchronous optical CDMA systems

In this paper, we investigate the employment of a ternary line coding technique based on Ungerboeck's trellis-coded method in asynchronous optical CDMA systems. The ternary coding we use is predicated upon the equal-weight orthogonal (EWO) scheme. Each user transmits two mutually orthogonal signature sequences to represent “+1” and “−1”, respectively, and nothing is transmitted for “0”. The receiver employs a maximum-likelihood soft-decoder to select the path with minimum Euclidean distance as the preferred path. This trellis ternary coding scheme applies set partitioning with partially overlapping subsets to increase the free Euclidean distance, which considerably improves system performance. Furthermore, due to line coding technique, such scheme comprises sufficient clock information, and thus benefits for baseband timing extraction (i.e. clock recovery). Numerical results reveal that the proposed trellis ternary coding scheme can significantly reduce the error floor and allow more active users to be accommodated in the network.     

Nonlinear dynamics of soft boson collective excitations in hot QCD plasma III: Bremsstrahlung and energy losses

Within the framework of semiclassical approximation a general formalism for deriving an effective current generating bremsstrahlung of arbitrary number of soft gluons (longitudinal or transverse ones) in scattering of higher-energy parton off thermal parton in hot quark-gluon plasma with subsequent extension to two and more scatterers is obtained. For the case of static color centers, an expression for energy loss induced by usual bremsstrahlung of lowest-order with allowance for an effective temperature-induced gluon mass and finite mass of the projectile (heavy quark) is derived. The detailed analysis of contribution to radiation energy loss associated with existence of effective three-gluon vertex induced by hot QCD medium is performed. It is shown that in general, the bremsstrahlung associated with this vertex has no sharp direction (as in the case of usual bremsstrahlung) and therefore here, we can expect an absence of suppression effect due to multiple scattering. For the case of two-color static scattering centers it was shown that the problem of calculation of bremsstrahlung induced by four-gluon hard thermal loop (HTL) vertex correction can be reduced to the problem of the calculation of bremsstrahlung induced by three-gluon HTL correction. It was shown that for limiting value of soft gluon occupation number N_k 1/α_s all higher processes of bremsstrahlung of arbitrary number of soft gluons become of the same order in coupling, and the problem of resummation of all relevant contributions to radiation energy loss of fast parton, arises. An explicit expression for matrix element of two soft gluon bremsstrahlung in small angles approximation is obtained.     

Effective spin susceptibility, electron mass and Landé factor in two-dimensional (2D) Si inversion layers

We have studied the silicon (Si) band-structure, electron–electron and electron-ionized donor interaction effects on our accurate and approximate results (AcR and ApR) for renormalized effective spin susceptibitity (RESS), electron mass (EEM), Landé factor and spin polarization in the impure 2D Si (electron system), showing that:(i) our ApR, being strongly deviated from our AcR, reproduces approximately all the data obtained recently by Pudalov et al. (Phys. Rev. Lett. 88 (2002) 196404) [in particular, RESS =4.7 at the critical value of Wigner–Seitz radius r_s: r_s=r_c≈8.5 at which occur the “apparent” metal–insulator transition (MIT)] and can also be compared with other ApRs found in the recent literature,(ii) both the RESS and EEM produce physical singularities at the same critical value: r_s=r_c11.05661 (weakly disordered samples) at which occurs the “true” MIT; the existence of such two “apparent and true” critical values in this impure system agrees with a recent discussion by Abrahams et al. (Rev. Mod. Phys. 73 (2001) 251), and(iii) at r_s=r_c=8.5, at which occurs the “apparent” MIT, our AcR for effective spin polarization and the corresponding result, obtained using a disordered Hubbard model and a determinant quantum Monte Carlo method by Denteneer and Scalettar (Phys. Rev. Lett. 90 (2003) 246401), both give the same result: ξ_eff.=ξ_c0.31 at B0.4 T, which is found to be lower than the critical parallel magnetic field for full spin polarization, B_c=1.29 T, supporting thus the existence of such an “apparent” MIT.     

On the renormalization of the charm quartet model

Some aspects of the renormalization program for the charm quartet model are discussed, with special emphasis on the role played by the Cabibbo angle. The cancellation of divergences in the W-quarks and Higgs-quarks sector is examined by explicit calculations at the one-loop level, both in the unitary and 't Hooft-Feyman gauges. The main analysis is based on a renormalization scheme which allows for the most general counter-terms generated by the Yukawa couplings. A second approach, equivalent at the S-matrix level, is briefly discussed. As a byproduct of our work we verify that the standard perturbative analysis leads to the same expressions for the coefficients of the divergent parts in the renormalization of the gauge coupling g₀ as a recent current algebra formulation of the radiative corrections.     

Two-boson truncation of Pauli-Villars-regulated Yukawa theory

We apply light-front quantization, Pauli-Villars regularization, and numerical techniques to the nonperturbative solution of the dressed-fermion problem in Yukawa theory in 3 + 1 dimensions. The solution is developed as a Fock-state expansion truncated to include at most one fermion and two bosons. The basis includes a negative-metric heavy boson and a negative-metric heavy fermion to provide the necessary cancellations of ultraviolet divergences. The integral equations for the Fock-state wave functions are solved by reducing them to effective one-boson-one-fermion equations for eigenstates with J_z = 1/2. The equations are converted to a matrix equation with a specially tuned quadrature scheme, and the lowest mass state is obtained by diagonalization. Various properties of the dressed-fermion state are then computed from the nonperturbative light-front wave functions. This work is a major step in our development of Pauli-Villars regularization for the nonperturbative solution of four-dimensional field theories and represents a significant advance in the numerical accuracy of such solutions.