One-loop Results Research Articles

Nonrenormalization theorem for thed=1,N=8vector multiplet

Sigma models describing low energy effective actions on D0-brane probes with N=8 supercharges are studied in detail using a manifestly d=1, N=4 super-space formalism. Two 0+1 dimensional N=4 multiplets together with their general actions are constructed. We derive the condition for these actions to be N=8 supersymmetric and apply these techniques to various D-brane configurations. We find that if in addition to N=8 supersymmetry the action must also have Spin(5) invariance, the form of the sigma model metric is uniquely determined by the one-loop result and is not renormalized perturbatively or non-perturbatively.

On R4 threshold corrections in type IIB string theory and ( p, q)-string instantons

We obtain the exact non-perturbative thresholds of R 4 terms in type 1113 string theory compactified to eight and seven dimensions. These thresholds are given by the perturbative tree-level and one-loop results together with the contribution of the D-instantons and of the ( p, q)-string instantons. The invariance under U-duality is made manifest by rewriting the sum as a non-holomorphic-invariant modular function of the corresponding discrete U-duality group. In the eight-dimensional case, the threshold is the sum of an order-1 Eisenstein series for SL(2, Z) and an order-3/2 Eisenstein series for SL(3, Z) . The seven-dimensional result is given by the order-3/2 Eisenstein series for SL(5, Z) . We also conjecture formulae for the non-perturbative thresholds in lower-dimensional compactifications and discuss the relation with M-theory.

Higher-Order Corrections to Sirlin's Theorem inO(p6)Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.

D-instantons, strings and M-theory

The R4 terms in the effective action for M-theory compactified on a two-torus are motivated by combining one-loop results in type II superstring theories with the Sl(2, Z) duality symmetry. The conjectured expression reproduces precisely the tree-level and one-loop R4 terms in the effective action of the type II string theories compactified on a circle, together with the expected infinite sum of instanton corrections. This conjecture implies that the R4 terms in ten-dimensional string type II theories receive no perturbative corrections beyond one loop and there are also no non-perturbative corrections in the ten-dimensional IIA theory. Furthermore, the eleven-dimensional M-theory limit exists, in which there is an R4 term that originates entirely from the one-loop contribution in the type IIA theory and is related by supersymmetry to the eleven-form C(3) R4. The generalization to compactification on T3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed.

A simple approximation of the one-loop corrected cross section for e+e− → W+W− at LEP 2

Using the SU (2) gauge coupling, g W ± ( M W ± 2 ), at the high-energy scale of M W ± , defined by the (theoretical value of the) leptonic W -width, rather than using the low-energy value, defined via the Fermi coupling, G μ , in the Born approximation, and supplementing with Coulomb corrections and initial state radiation, errors with respect to the exact one-loop results for the differential cross section of e + e − → W + W − are below 1% at LEP 2 energies at all W + W − production angles. A similar procedure is suggested to incorporate leading bosonic loop effects into four-fermion production in the fermion-loop scheme. The resulting accuracy below 1% is sufficient for LEP 2 experiments.

Mass bounds in a Z 2 scalar-fermion model

The lattice regularized Z2 scalar-fermion model using staggered fermions in four dimensions is investigated in the broken symmetry phase. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type of Yukawa interaction. Triviality upper bound and vacuum stability lower bound on the mass of the scalar particle are numerically estimated. Qualitative agreement between Monte Carlo data and one-loop perturbative results is obtained. Systematic errors of the upper bound are estimated. At strong Yukawa coupling, we see some quantitative disagreements due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.

One-loop results for three-gluon vertex in arbitrary gauge and dimension

One-loop results for three-gluon vertex in arbitrary gauge and dimension

One-loop results for three-gluon vertex in arbitrary gauge and dimension

We review the calculation of one-loop contributions to the three-gluon vertex, for arbitrary (off-shell) external momenta, in arbitrary covariant gauge and in arbitrary space-time dimension. We discuss how one can get the results for all on-shell limits of interest directly from the general off-shell expression.

Square root singularity in boundary reflection matrix

Two-particle scattering amplitudes for integrable relativistic quantum field theory in 1+1 dimensions can normally have at most singularities of poles and zeros along the imaginary axis in the complex rapidity plane. It has been supposed that single-particle amplitudes of the exact boundary reflection matrix exhibit the same structure. In this paper, single-particle amplitudes of the exact boundary reflection matrix corresponding to the Neumann boundary condition for affine Toda field theory associated with twisted affine algebras a 2 n (2) are conjectured, based on one-loop result, as having a new kind of square root singularity.

Supergravity coupled to chiral and Yang-Mills matter at one loop

We present the full result for the divergent one-loop contribution to the effective boson Lagrangian for supergravity coupled to chiral and Yang-Mills supermultiplets. We also consider the specific case of dilaton couplings in effective supergravity Lagrangians from superstrings, for which the one-loop result is considerably simplified.

Meson loops in the Nambu-Jona-Lasinio model

The effects of meson loops in the vacuum sector of the Nambu-Jona-Lasinio model are calculated. Using the effective action formalism we take consistently all next-to-leading-order 1 N c terms into account. This leads to a symmetry-conserving approach, in which all features of spontaneously broken chiral symmetry, such as the Goldstone theorem, the Goldberger-Treiman and the Gell-Mann-Oakes-Renner relations are preserved. Contributions to 〈 qq〉 and F π are calculated, and are shown to be substantial, at the level of 30%, consistent with the 1 N c expansion. The leading non-analytic terms in the chiral expansion of 〈 qq〉 , F π and m π have the same form as the one-loop results of chiral perturbation theory.

Non-equilibrium symmetry restoration beyond one loop

We calculate the strength of symmetry restoration effects in highly non-equilibrium states which can arise, for example, during preheating after inflation. We show that in certain parameter range the one-loop results are unstable, requiring summation of multiloop diagrams. We solve this problem for the O( N) model in the large N-limit and show that the symmetry restoration may be less effective than what predicted by the one-loop estimate.

γγ → πππ to one loop in chiral perturbation theory

The γγ → π 0 π 0 π 0 and γγ → π + π − π 0 amplitudes are discussed in the general context of Chiral Perturbation Theory (ChPT) to O( p 6). Chiral loops are found to play a major role. This makes these processes a good test of ChPT, mainly in its anomalous sector. We correct earlier numerical results at tree level and determine the one-loop results as well.

Final state interactions and Khuri-Treiman equations in,ν → 3π decays

Using extended Khuri-Treiman equations, we evaluate the final state interactions due to two-pion rescatterings to the decays ν → π 0 π + π − and ν → π 0 π 0 π 0. As subtraction to the dispersion relation we take the one-loop chiral perturbation theory result of Gasser and Leutwyler. The calculated corrections are moderate and amount to about 14% in the amplitude at the center of the decay region. A careful analysis of the errors inherent to our approach is given. As a consequence, the experimental rate of the decay can only be reproduced if the double quark mass ratio Q −2 = [ (m d − m.) (m s − m ) ̂ ]·[ (m d + m u) (m s + m ) ̂ ] is increased from the usual value of 1 (24.1) 2 to 1 (22.4 ± 0.9) 2 . We have also calculated the ratio of the rates of the two decays and various Dalitz plot parameters. In particular, the linear slope a in the charged decay is different from the one-loop value and agrees better with experiment.

Bounds on the renormalized couplings in a Z2 Scalar-Fermion model

The triviality upper bound and the vacuum stability lower bound on the mass of the scalar particle is numerically investigated in a Z2 scalar-fermion model using staggered fermions. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type Yukawa interaction. Reasonable agreement between Monte Carlo data and one-loop perturbative results is obtained except that at strong Yukawa couplings, significant deviations arise due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.

Vector current correlator to two loops in chiral perturbation theory.

The isospin-breaking correlator of the product of flavor octet vector currents, ${\mathrm{\ensuremath{\Pi}}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}^{38}$(${\mathit{q}}^{2}$)= i\ensuremath{\int}${\mathit{d}}^{4}$x exp(iq\ensuremath{\cdot}x)〈0\ensuremath{\Vert}T[${\mathit{V}}_{\mathrm{\ensuremath{\mu}}}^{3}$ (x)${\mathit{V}}_{\ensuremath{\nu}}^{8}$(0)]\ensuremath{\Vert}0〉, is computed to next-to-next-to-leading (two-loop) order in chiral perturbation theory. Large corrections to both the magnitude and ${\mathit{q}}^{2}$ dependence of the one-loop result are found, and the reasons for the slow convergence of the chiral series for the correlator given. The two-loop expression involves a single O(${\mathit{q}}^{6}$) counterterm, present also in the two-loop expressions for ${\mathrm{\ensuremath{\Pi}}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}^{33}$(${\mathit{q}}^{2}$) and ${\mathrm{\ensuremath{\Pi}}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}^{88}$(${\mathit{q}}^{2}$), which counterterm contributes a constant to the scalar correlator ${\mathrm{\ensuremath{\Pi}}}^{38}$(${\mathit{q}}^{2}$), defined by ${\mathrm{\ensuremath{\Pi}}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}^{38}$(${\mathit{q}}^{2}$)\ensuremath{\equiv}(${\mathit{q}}_{\mathrm{\ensuremath{\mu}}}$${\mathit{q}}_{\ensuremath{\nu}}$-${\mathit{q}}^{2}$${\mathit{g}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$) ${\mathrm{\ensuremath{\Pi}}}^{38}$(${\mathit{q}}^{2}$). The feasibility of extracting the value of this counterterm from other sources is discussed. Analysis of the slope of the correlator with respect to ${\mathit{q}}^{2}$ using QCD sum rules is shown to suggest that, even to two-loop order, the chiral series for the correlator may not yet be well converged, and the physical origins of possible important O(${\mathit{q}}^{8}$) contributions discussed. \textcopyright{} 1996 The American Physical Society.

Polymer diffusion in quenched disorder: A renormalization group approach

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionw≔u−v≥0 and for small effective disorder coupling\(\bar v(l)\) on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as Open image in new window for\(\bar v(l) \ll 1\).

Strange mesonic transition form factor.

The strange-quark vector current {rho}-to-{pi} meson transition form factor is computed at one-loop order using strange meson intermediate states. A comparison is made with a {phi}-meson dominance model estimate. They find that one-loop contributions are comparable in magnitude to those predicted by {phi}-meson dominance. It is possible that the one-loop contribution can make the matrix element as large as those of the electromagnetic current mediating vector meson radiative decays. However, due to the quadratic dependence of the one-loop results on the hadronic form factor cut-off mass, a large uncertainty in the estimate of the loops is unavoidable. These results indicate that non-nucleonic strange quarks could contribute appreciably in moderate-{vert_bar}Q{sup 2}{vert_bar} parity-violating electron-nucleus scattering measurements aimed at probing the strange-quark content of the nucleon.

Self-energy of heavy quark

We demonstrate that to calculate the selfenergy of a heavy quark in the heavy quark limit (or the heavy fermion limit in what is called the Baryon Chiral Perturbation Theory), the use of standard dimensional regularization provides only the quantum limit: opposite to the heavy quark (or classical) limit that one wishes to obtain. We thus devised a standard ultraviolet/infrared regularization procedure in calculating the one- and two-loop contributions to the heavy quark self-energy in this limit. Then the one-loop result is shown to provide the standard classical Coulomb self-energy of a static colour source that is linearly proportional to the ultraviolet cutoff Λ. All the two-loop contributions are found to be proportional to Λ In (Λ/γ) where γ is the infrared cutoff. Often only the contribution from the bubble (light quarks, gluon and ghost) insertion to the gluon propagator has been considered as theO(α s ) correction to the Coulomb energy to this order. Our result shows that other contributions are of the same magnitude, thus have to be taken into account.

Higher-loop anomalies in chiral gravities

The one-loop anomalies for chiral W 3 gravity are derived using the Fujikawa regularisation method. The expected two-loop anomalies are then obtained by imposing the Wess-Zumino consistency conditions on the one-loop results. The anomalies found in this way agree with those already known from explicit Feynman diagram calculations. We then directly verify that the order ℏ 2 non-local BRST Ward identity anomalies, arising from the “dressing” of the one-loop results, satisfy Lam's theorem. It is also shown that in a rigorous calculation of Q 2 anomaly for the BRST charge, one recovers both the non-local as well as the local anomalies. We further verify that, in chiral gravities, the non-local anomalies in the BRST Ward identity can be obtained by the application of the anomalous operator Q 2, calculated using operator products, to an appropriately defined gauge fermion. Finally, we give arguments to show why this relation should hold generally in reparametrisation-invariant theories.