Loop Amplitude Research Articles

Less suppressed μ→eγ and τ→μγ loop amplitudes and extra dimension theories

When μeγ (or τμγ) loop involves a vector boson, the amplitude is suppressed by more than two powers of heavy particle masses. However we show that the scalar boson loop diagrams are much less damped. Particularly, the loop amplitude in which the intermediate fermion and scalar boson have comparable masses is as large as possible, as allowed by the decoupling theorem. Such a situation is realized in the “universal extra dimension theory”, and can yield a large enough rate for μeγ to be detectable in current experiments. Our investigation involves precise calculation of the scalar boson loop's dependence on the masses of the intermediate states.

Remarks on the calculations of charged open string amplitudes: the 1-loop tadpole

In string theory, there are various physical situations where the world-sheet fields have a shifted moding. For instance, this is the case for the twisted closed string in Z_N orbifold or for the charged open string in a constant electro-magnetic field. Because of this feature, it is quite challenging to give explicit formulae describing the string interaction, even for the bosonic case. In this note, we focus on the case of the charged open bosonic string and construct the 1-loop tadpole which is an object generating all 1-point functions from the annulus in the presence of an external field. In the operator formalism, this represents one of the basic building blocks for the construction of a general loop amplitude.

PHOTON-PAIR CONVERSION INTO NEUTRINOS IN A STRONG MAGNETIC FIELD

A general analysis of the three-vertex loop amplitude in a strong magnetic field, based on the asymptotic form of the electron propagator in the field, is performed. In order to investigate the photon–neutrino process [Formula: see text], the vertex combinations of the scalar–vector–vector (SVV), pseudoscalar–vector–vector (PVV), three-vector (VVV), and axial-vector–vector–vector (AVV) types are considered. It is shown that only the SVV amplitude grows linearly with the magnetic field strength, while in the other amplitudes, PVV, VVV and AVV, the linearly growing terms are canceled. The process [Formula: see text] is investigated in the left–right-symmetric extension of the standard model of electroweak interaction, where the effective scalar νν e e coupling could exist. Possible astrophysical manifestations of the considered process are discussed.

Relating the RNS and pure spinor formalisms for the superstring

Recently, the superstring was covariantly quantized using the BRST-like operator $Q = \oint \lambda^\alpha d_\alpha$ where $\lambda^\alpha$ is a pure spinor and $d_\alpha$ are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and $\eta_0$ ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a $b$ ghost in the pure spinor formalism which might be useful for loop amplitude computations.

The long span problem in the analysis of conductor vibration damping

In analysis of vibration damping of overhead spans, expected severity is determined on the basis of the balance of vibration power supplied by the wind through vortex shedding against dissipation by self damping in the conductor and by damping devices. Conventional practice is to approximate the vibration of the span as a series of sine-shaped loops, all of equal amplitude, for purposes of estimating wind input and self damping. However, for long spans requiring efficient damping, most of the loops are not sine shaped, and loop amplitude varies along the span. The effects of these differences are explored by representing the vibration as opposite-moving waves that grow as they travel. Nonlinearity in the wind excitation and self damping functions is taken into account. Results show that so-called long span effects significantly reduce required span-end damping in long spans.

Soft-QCD effects in B⇒ γγ decay: quark level form factors

Soft-QCD effects of quark-level form factors in γγ decay of B s -mesons via D D ̄ intermediate states, suggested by Ellis et al., are examined in the “Salpeter” model [reinterpreted in terms of the Markov-Yukawa Transversality Principle (MYTP)] when formulated on a covariant light front (null-plane). The gluonic kernel in the infrared regime which generates the constituent mass via standard DBχS, is calibrated to both q q ̄ and qqq spectra, meson mass splittings, pion form factor, and other parameters. With this check, an exact evaluation of the D D ̄ γ vertex form factor F( α) (normalized to F(0)=1), gives a multiplicative effect of F 2( α) on the B s ⇒ γγ amplitude via D-meson triangle loop, where α = ( p 2+ M 2)/ M 2 is the off-shellness parameter of the exchanged D-meson of mass M and 4-momentum p μ , and is a variables of the (internal) loop integration. Unfortunately, the F 2( α) effect decreases the loop amplitude by a factor of 30 w.r.t. the point hadron value, resulting in a reduction of 3 orders of magnitude in long distance (hadronic) contributions to the B s ⇒ γγ decay rate, thus greatly impairing the visibility of such modes.

The strangeness magnetic moment of the proton in the chiral quark model

The strangeness magnetic moment of the proton is shown to be small in the chiral quark model. The dominant loop contribution is due to kaons. The K ∗ loop contributions are proportional to the difference between the strange and light constituent quark masses or m K ∗ −2 and therefore small. The loop fluctuations that involve radiative transitions between K ∗ mesons and kaons are small, when the cutoff scale in the loops is taken to be close to the chiral symmetry restoration scale. The net loop amplitude contribution to the strangeness magnetic moment of the proton is about −0.05, which falls within the uncertainty range of the experimental value.

Magnetic hysteresis based on dipolar interactions in granular magnetic systems

The magnetic hysteresis of granular magnetic systems is investigated in the high-temperature limit $(T\ensuremath{\gg}$ blocking temperature of magnetic nanoparticles). Measurements of magnetization curves have been performed at room temperature on various samples of granular bimetallic alloys of the family ${\mathrm{Cu}}_{100\ensuremath{-}x}{\mathrm{Co}}_{x} (x=5--20 \mathrm{at}.%)$ obtained in ribbon form by planar flow casting in a controlled atmosphere, and submitted to different thermal treatments. The loop amplitude and shape, which are functions of sample composition and thermal history, are studied taking advantage of a novel method of graphical representation, particularly apt to emphasize the features of thin, elongated loops. The hysteresis is explained in terms of the effect of magnetic interactions of the dipolar type among magnetic-metal particles, acting to hinder the response of the system of moments to isothermal changes of the applied field. Such a property is accounted for in a mean-field scheme, by introducing a memory term in the argument of the Langevin function which describes the anhysteretic behavior of an assembly of noninteracting superparamagnetic particles. The rms field arising from the cumulative effect of dipolar interactions is linked by the theory to a measurable quantity, the reduced remanence of a major symmetric hysteresis loop. The theory's self-consistence and adequacy have been properly tested at room temperature on all examined systems. The agreement with experimental results is always striking, indicating that at high temperatures the magnetic hysteresis of granular systems is dominated by interparticle, rather than single-particle, effects. Dipolar interactions seem to fully determine the magnetic hysteresis in the high-temperature limit for low Co content $(x<~10).$ For higher concentrations of magnetic metal, the experimental results indicate that additional hysteretic mechanisms have to be introduced.

Infrared behavior of graviton-graviton scattering

The quantum effective theory of general relativity, independent of the eventual full theory at high energy, expresses graviton-graviton scattering at one loop order O(E^4) with only one parameter, Newton's constant. Dunbar and Norridge have calculated the one loop amplitude using string based techniques. We complete the calculation by showing that the 1/(d-4) divergence which remains in their result comes from the infrared sector and that the cross section is finite and model independent when the usual bremsstrahlung diagrams are included.

Probing the interface potential in stick/slip friction by a lateral force modulation technique

The influence of the shape of the interaction potential is investigated on details in stick/slip friction as encountered between an AFM tip and a substrate. Based on qualitative arguments of stick/slip systems, a novel technique is introduced in which the AFM tip is brought into a lateral resonance mode. In comparison to a direct measurement in the stick/slip signal, we suggest that the method is preferable to highlight these non-linear characteristics. In combination with the shape of the surface potential involved in stick/slip friction, this modulation diminishes the friction loop amplitude in a controlled way. Furthermore, a partial stick/slip behavior is observed above a certain threshold level of driving amplitude, where the tip alternates periodically between a zero-friction and a non-zero-friction state.

Multiloop f3 amplitudes from bosonic string theory

We show how the multiloop amplitudes of f3 theory (in the world-line formulation of Schmidt and Schubert_ are recovered from the N-tachyon (h + 1)-loop amplitude in bosonic string theory in the α′ → 0 limit, if one keeps the tachyon coupling constant fixed. In this limit the integral over string moduli space receives contributions only from those corners where the world-sheet resembles a f3 particle diagram. Technical issues involved are a proper choice of local world-sheet coordinates, needed to take the string amplitudes off-shell, and a formal procedure for introducing a free mass parameter M2 instead of the tachyonic value −4/α′.

Low-energy dynamics of the γγ → ππ reaction in the NJL model

We calculate the one-quark-loop amplitude for the low energy $\gamma\gamma\to\pi\pi$ collision in the context of the Nambu and Jona-Lasinio model with scalar and pseudoscalar four quark couplings to all orders in the external momenta. We show that the NJL predictions for the $\gamma\gamma\to\pi^+\pi^-$ reaction are not far from the Born amplitude, which is close to the data, and is compatible with the chiral perturbation theory estimations. We determine the corrections given by the NJL model in leading order of $1/N_c$ to the chiral loop amplitude for $\gamma\gamma\to\pi^0\pi^0$. Numerical results for the $\gamma\gamma\rightarrow\pi\pi$ cross sections and for pion polarizabilities are given.

Strong changes in the magnetic properties of ultrathin Co/Cu(001) films due to submonolayer quantities of a nonmagnetic overlayer.

We have studied the evolution of the magnetic properties of the Co/Cu(001) system as a Cu overlayer is deposited, using the magneto-optical Kerr effect (MOKE) in situ. We observe striking, nonmonotonic variations in the coercive field ${\mathit{H}}_{\mathit{c}}$, the M-H loop amplitude ${\mathit{M}}_{\mathrm{max}}$, and the ratio of remanent to saturation magnetization S upon the deposition of submonolayer quantities of Cu. We propose that the observed effects arise due to overlayer-induced changes in the electronic structure. As a consequence both the magnetic anisotropy of the films and the magneto-optical response vary strongly. We show that the entire Co film is affected, in that a single Cu atom at the surface can affect the behavior of more than 40 Co atoms throughout the thickness of the film, illustrating the importance of the segregation of substrate atoms during the growth of such films. Distinct behavior occurs according to the range of overlayer thickness, implying that separate physical mechanisms dominate for different coverages. At submonolayer thicknesses we propose that a step-induced uniaxial magnetic anisotropy term is very strongly modified by the presence of a partial Cu overlayer. Concurrent changes in the magneto-optical signal are attributed to the electronic structure of the partial Cu/Co interface. For overlayer thicknesses in the monolayer range, electronic effects associated with the completed interface occur, in particular a reduction of the Curie temperature ${\mathit{T}}_{\mathit{C}}$ and a possible suppression of the magnetic moment of the Co atoms.

Some experimental results about the correlation between Barkhausen noise and the fatigue life of steel specimens

The results of Barkhausen Noise (BN) measurements during pulsating axial fatigue tests on notched steel specimens are reported. The aim of these measurements was to study the cyclic signal in the first stage of the fatigue process, in order to find a correlation between this magnetic parameter and the fatigue life of the specimens. The hysteresis loop of the BN intensity versus the applied load, during the initial stage of the process up to the crack nucleation, for different load levels has been studied. The loop amplitude is found to change significantly during the life period investigated, according to the load level. This behaviour is connected to the degree of cyclic plastic deformation and reflects the micro-structural settling phenomena that happen during the first stage of the fatigue process. The loop amplitude measured at the first cycle of each specimen has been related to the corresponding failure cycles number, showing a possible way for the prediction of the fatigue life.

Heavy fermion production and the symmetry breaking sector of the electroweak interactions

We point out that heavy fermion production through the fusion of the longitudinal gauge bosons might be relevant in probing the strongly interacting symmetry breaking sector of the electroweak interactions, by showing the dependence of the one loop amplitude for ( w +w −→ tt ) on the symmetry breaking mechanism. The one loop amplitude for ( w +w −→ tt ) is calculated for the standard model and extended technicolour theory. Techni-rho meson exchange is also briefly discussed. We find that at m t =150 GeV the cross section of top pair production in e + e − collisions is comparable in order of magnitude to that of the longitudinal gauge boson scattering.

Critical current relaxation in epitaxial thin YBaCuO films in changing and constant field

Abstract The magnetic hysteresis loop (MHL) amplitude increases with the sweep rate of the external magnetic field Be. Each MHL recorded with a sweep rate dB e dt can be labeled with an “effective” time tmo which represents the time needed for the relaxation at constant Be of magnetic moment M from the critical state Me to the value Mo of a given MHL. The dependence of M on dB e dt provides essentially the same information as magnetic relaxation experiments at constant Be. The determination of tMo from a general dependence of M on sweep rate dB e dt or on rate of relaxation dM dt is described and applied to experimental data obtained for an epitaxial YBa2Cu3O7 thin film. In comparison with conventional relaxation at constant magnetic field MHL experiments make it possible to drastically extend the time window of relaxation processes towards shorter times (down to 10−2s or less). Combination of both methods enables more precise tests of existing models on vortex motion in layered superconductors.

Extension of the time window for investigation of relaxation effects in high- Tc superconductors

Measurements of the dependence of the magnetic hysteresis loop amplitude in a superconductor on the magnetic field sweep rate d H e/d t are shown to provide essentially the same information as magnetic relaxation experiments (flux-creep) at fixed external field H e. For practical reasons, however, magnetic hysteresis loop measurements are better suited to investigate fast flux-line movements than conventional flux-creep measurements. From the general flux movement differential equation it is shown that each magnetic hysteresis loop recorded at a given d H e/d t can be labelled by an effective time t M 0 so that this experimental information can be used to extend the time window of flux-creep measurements to short times. This method is applied to the experimental data obtained on a YBa 2Cu 3O 7 single crystal. In this way the time window is extended to less than 10 -2 s which is valuable for a more precise check of existing theoretical models for the activation energy of flux motion. It is found that the experimental data are well described by using an activation energy U( j)=( U c / μ)[( j c / j) μ -1] with μ=0.74 at 16 K and 1.8 T.

Loop gas model for open strings

The open string with one-dimensional target space is formulated in terms of an SOS, or loop gas model on a random surface. We solve an integral equation for the loop amplitude with Dirichlet and Neumann boundary conditions imposed on different pieces of its boundary. The result is used to calculate the mean values of order and disorder operators, to construct the string propagator and find its spectrum of excitations. The latter is not sensitive either to the string tension λ or to the mass μ of the “quarks” at the ends of the string. As in the case of closed strings, the SOS formulation allows us to construct a Feynman-diagram technique for the string interaction amplitudes.

A bag model calculation of the electroweaks?d? loop

We consider the CP-conserving electroweak transitionss→dγ. To include confinement effects below the charm scale, we perform the loop calculations within the bag model. According to the calculation, confinement effects are rather important and give amplitudes three orders of magnitude bigger than that obtained from the free quark loop, which is ∼eG F m c 2 /M W 2 . Moreover, the amplitude is of the same order of magintude as the perturbative two loop amplitude ∼eG F α s ln(m c /μ). For the decay modeΩ−→γΞ− we obtain a branching ratio 4.4·10−5. Other radiative decays of strange baryons are known to be dominated by pole diagrams.

Operator formulation of superstring multiloop amplitudes

An operator formulation of the superstring is presented, where the covariantized picture-changing operator is inserted to each 3-string vertex and the {ital b} ghost into each propagator. In this formalism, all spin structure can be treated equally at the same time, and the {ital g}-loop amplitude is explicitly calculable from its building blocks, i.e., the propagators and the 3-string vertices. The resulting amplitude agrees with the standard one obtained by applying the techniques of algebraic geometry in the functional formalism.