Low-energy QCD and ultraviolet renormalons

We discuss the contribution of ultraviolet (UV) renormalons in QCD to two-point functions of quark current operators. This explicitly includes effects due to the exchange of one renormalon chain as well as two chains. It is shown that, when the external Euclidean momentum of the two-point functions becomes smaller than the scale AL associated with the Landau singularity of the QCD one-loop running coupling constant, the positions of the UV renormalons in the Borel plane become true singularities in the integration range of the Bore] transform. This introduces ambiguities in the evaluation of the corresponding two-point functions. The ambiguities associated with the leading UV renormalon singularity are of the same type as the contribution due to the inclusion of dimension d = 6 local operators in a low-energy effective Lagrangian valid at scales smaller than AL. We then discuss the inclusion of an infinite number of renormalon chains and argue that the previous ambiguity hints at a plausible approximation scheme for low-energy QCD, resulting in an effective Lagrangian similar to the one of the extended Nambu-Jona-Lasinio (ENJL) model of QCD at large N_c.     

Perturbative QCD analysis of local duality in a fixed w2 framework

We study the Q2 dependence of large x F2 nucleon structure function data, with the aim of providing a perturbative QCD based, quantitative analysis of parton-hadron duality. As opposed to previous analyses at fixed x, we use a framework in fixed W2. We uncover a breakdown of the twist-4 approximation with a renormalon type improvement at O(1/Q(4)) which affects the initial evolution of parton distributions.     

Resummations with renormalon effects for the hadronic vacuum polarization contribution to the muon (g−2)

The hadronic vacuum polarization contribution to the muon (g−2) value is calculated by considering a known dispersion integral which involves the R_e⁺e⁻(s) ratio. The theoretical part stemming from the region below 1.8 GeV is the largest contribution in our approach, and is calculated by using a contour integral involving the associated Adler function D(Q²). In the resummations, we explicitly take into account the exactly known renormalon singularity of the leading infrared renormalon in the usual and in the modified Borel transform of D(Q²), and map further away from the origin the other renormalon singularities by employing judiciously chosen conformal transformations. The renormalon effect increases the predicted value of the hadronic vacuum polarization contribution to the muon (g−2), and therefore diminishes the difference between the recently measured and the SM/QCD-predicted value of (g−2). It is also shown that the total QED correction to the hadronic vacuum polarization is very small, about 0.06%.     

Evolution of parton densities beyond leading order: The non-singlet case

We develop a technique, based explicitly on the factorization properties of mass singularities, which allows one to calculate the evolution of parton densities beyond leading order. We present the results for the evolution of hadronic structure functions as well as for parton fragmentation functions into hadrons. Within our scheme the predictions for a particular process are obtained by convoluting a universal parton density with a “short-distance” cross section specific to the process. As an application, we calculate the QCD predictions for the Q² dependence of deep inelastic lepton-hadron scattering and of one-particle iclusive e⁺ e^? annihilation cross sections. Our results for electroproduction agree with those obtained with the operator product expansion technique. Physical quantities in scattering are related to the corresponding ones in annihilation by analytic continuation, whereas the Gribov-Lipatov relation is strongly violated.     

Evolving dark energy with w not = -1

Theories of evolving quintessence are constructed that generically lead to deviations from the w = -1 prediction of nonevolving dark energy. The small mass scale that governs evolution, m(phi) approximately = 10(-33) eV, is radiatively stable, and the "Why now?" problem is solved. These results rest on seesaw cosmology: Fundamental physics and cosmology can be broadly understood from only two mass scales, the weak scale nu and the Planck scale M. Requiring a scale of dark energy rho(DE)(1/4) governed by nu2/M and a radiatively stable evolution rate m(phi) given by nu4/M3 leads to a distinctive form for the equation of state w(z). Dark energy resides in the potential of a hidden axion field that is generated by a new QCD-like force that gets strong at the scale lambda approximately = nu2/M approximately = rho(DE)(1/4). The evolution rate is given by a second seesaw that leads to the axion mass m(phi) approximately = lambda2/f, with f approximately = M.     

The renormalon contribution to the current product j μ5 j S

The product of an axialvector and a scalar current and its relation to the chiral-odd distribution function h ₁ is discussed in the framework of the renormalon approach. Using a bag-model calculation for h ₁, we calculate its intrinsic uncertainty due to renormalon poles. The result is given as a function of Bjorken-x as well as for the first moments separately. Received: 9 November 1998 / Revised version: 22 January 1999     

Where to look for solving the gauge hierarchy problem?

A mass of the Higgs boson close to 126 GeV may give a hint that the standard model of particle physics is valid up to the Planck scale. We discuss perspectives for the solution of the gauge hierarchy problem at high scales. Scenarios with an ultraviolet fixed point have predicted a Higgs boson mass very close to 126 GeV if the fixed point value of the quartic scalar coupling is small. In this case the top quark pole mass should be close to 172 GeV.     

Charm-quark contribution to KL-->mu+mu- at next-to-next-to-leading order

We calculate the charm-quark contribution to the decay K(L)-->mu(+)mu(-) in next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P(c) from +/-22% down to +/-7%, corresponding to scale uncertainties of +/-3% and +/-6% in the short-distance part of the branching ratio and the determination of the Wolfenstein parameter rho[over] from K(L)-->mu(+)mu(-) The error in P(c)=0.115+/-0.018 is now in equal shares due to the combined scale uncertainties and the current uncertainty in the charm-quark mass. We find B(K(L)-->mu(+)mu(-)) SD=(0.79+/-0.12)x10(-9), with the present uncertainty in the Cabibbo-Kobayashi-Maskawa element V(td) being the dominant individual source in the quoted error.     

The decay π → eνγ: PCAC quark model

We reexamine the PCAC sum rule for radiative pion decay, allowing for a singular short-distance behaviour of the axial divergence. It is shown that the sum rule of Das, Mathur and Okubo follows from a weak form of PCAC even if the axial divergence is allowed to have dimension three, appropriate for free (or asymptotically free) quarks. We find no quark mass corrections.     

High-energy behavior of jet and lepton-pair production

The cross section for jet and lepton-pair production at large transverse momenta has been studied to all orders in QCD perturbation theory. Appropriate moments of these cross sections are seen to factorize short-distance from long-distance dependence, and scale breaking is governed by the anomalous dimensions of twist-two operators.     

Estimation of the large order behavior of the plaquette

The universality of vacuum condensate can be exploited to relate the infrared renormalon caused large order behaviors of different processes. As an application the normalization constant of the large order behavior of the average plaquette is estimated using the Adler function.     

IR-renormalon contributions to the structure functions g 3 and g 5

We calculate the leading 1/N _f perturbative contributions to the polarized nonsinglet structure functions g ₃ and g ₅ to all orders in α_s. The contributions from the first renormalon pole are determined. It is a measure for the ambiguity of the perturbative calculation and is hypothetically assumed to dominate the power corrections. The corrections Δg ₃ and Δg ₅ are given as functions of the Bjorken variable x and turn out to be negligible. The anomalous dimensions of the leading twist operators are obtained in the next-to-leading order. Received: 10 June 1998 / Revised version: 25 September 1998     

Small <Emphasis Type="Italic">x</Emphasis> behavior of parton distributions: a study of higher twist effects

We review the double asymptotic scaling phenomenon for the structure functions of the deepinelastic scattering process. We present an analytical parameterization of the contributions from the twist-two operators of the Wilson operator product expansion and power suppressed terms. Higher twist corrections to F ₂ at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. Higher twist terms are estimated using two different approaches: one motivated by BFKL and the other motivated by the renormalon formalism. The results of the latter approach are in very good agreement with deep inelastic scattering data from HERA. The text was submitted by the authors in English.     

Correlator of heavy- quark currents at small q2 in the large-$\beta_0$ limit

The correlator of vector heavy-quark currents at small q ² is considered in the large- limit. The leading IR renormalon ambiguity of the sum of the perturbative series is canceled by the UV renormalon ambiguity of the gluon condensate. The asymptotic behavior of the perturbative series is obtained in a model-independent way, up to a single unknown normalization factor. Gluon-virtuality distribution functions for the perturbative correction are calculated.Received: 3 December 2004, Published online: 21 February 2005     

Contributions of renormalon singularities

On the basis of some simple examples we suggest a general method for discussing the contribution of renormalons to the Borel transform based on the general analytical structure of the renormalization group β function. No simple principal value or contour integral Borel representation seems to be possible. Instead a splitting of the Borel transform at each renormalon singularity seems to be necessary making the infinite sum over renormalons possibly difficult to define.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.     

用短程飞行时间吸收谱对铯磁光阱中冷原子温度的测量

介绍采用短程飞行时间吸收谱测量铯原子磁光阱(MOT) 中冷原子温度的基本原理及实验实现.与通常的飞行时间方法不同，采用短程飞行时间吸收谱来测量MOT 中冷原子云的温度.在MOT 区域正下方若干毫米处入射一束圆柱状共振探测光束(实验中对于h=3mm，5mm，8mm的情况均作了研究)，释放冷原子云，在其膨胀和自由下落过程中穿过探测光束，即可由光电探测器测得飞行时间吸收谱，由此推得MOT中冷原子的温度. 关键词： 磁光阱 冷原子 飞行时间 短程飞行时间 铯原子