Higher - Order Qed Effects and Nonlinear Qed

After a brief review of higher-order QED effects, a survey is made of novel aspects of QED with emphasis on recent experimental results in strong-field QED: nonlinear Compton scattering and multiphoton pair creation by light. 1 Higher-Order QED Effects Quantum Electrodynamics (QED) describes the interactions between charged particles that are mediated by quanta (photons) of the electromagnetic field. The simplest QED processes involve only a single photon, as represented by exchange and annihilation diagrams (Fig. 1). These processes involve two vertices of the form γee (where e represents an electric charge, not necessarily an electron). The process that consists only of emission of a real photon by a charged particle is forbidden by energy-momentum conservation. We may then say that higher-order QED is any process that involves more than two γee vertices. Higher-order QED processes are often divided into two groups: tree and loop. Loop processes involve one or more virtual pairs of charged particles; examples are shown in Fig. 2. Tree processes, such as that of Fig. 3, have no loops. Higher-order QED tree processes are often called radiative corrections. Any basic interaction can be modified by the emission of one or more photons, and the probability of emission of a soft photon approaches unity. Hence, the empirical measurement of the “basic” processes is dependent on an extrapolation to the improbable case of no radiative Figure 1: The simplest QED processes: one-photon exchange and annihilation. Figure 2: Examples of 10th-order loop processes (⇔ 10 extra vertices). corrections. A contemporary example of the effect of initial-state radiative corrections is shown in Fig. 3. Figure 3: Initial-state radiative corrections to the reaction e+e− → Z. The rate for a tree process with n γee vertices is proportional to α, where α = e/h̄c ≈ 1/137 is the QED fine structure constant. Hence, it is usually the case that very high order tree processes are suppressed compared to lower-order processes. However, there are regimes in which this is not the case. Processes in very strong electromagnetic fields can favor larger numbers of photons, as has been shown some years ago in atomic physics 6, 10) (Fig. 4). In sec. 3 we present first evidence for such effects in elementary particle physics. Higher-order QED loop processes are studied in four classic tests: 17, 28) • Hydrogen Lamb Shift: σ∆E(2S1/2 − 2P1/2) = 2 ppm [Theory limited by uncertainty in proton radius]. • Muonium hyperfine splitting: 24) Expt. − Theory ≈ 0.25 ppm [muon mass, O(α3) terms, hadronic (+ weak) loops]. New LAMPF data being analyzed; error → 0.1 ppm. Figure 4: a) Observation of photon emission at up to the 46th harmonic in laser-plasma interactions. b) Multiphoton ionization of atoms in which up to 22 photons were absorbed. • e anomalous magnetic moment: Expt. − Theory ≈ 25 ppb [α, O(α5) terms]. • μ anomalous magnetic moment: 13, 25) Expt. − Theory ≈ 10 ppm [O(α5) terms, hadronic (+ weak) loops]. New BNL expt. starts in Fall 1998; error → 0.5 ppm. 26) Trouble spot: the observed orthopositronium decay rate differs from theory by 6 σ; but the theory is incomplete at relative O(α2). 30) Summation an infinite class of loop corrections to the γee vertex results in the “running” of the coupling constant: α(Q) = α0 1− α0 3π ln ( Q2 Λ2 ) . (1) For example, when extrapolated to the Z-pole, 12) one obtains α−1(M2 Z) = 128.93±0.02; half of the change from the value of 137 at low Q is due to hadronic corrections. Direct evidence for the running of the coupling constant has recently been obtained by the TOPAZ group 34) by comparing e+e− → μ+μ− to e+e− → e+e−μ+μ−; they found α−1(Q2 = (57.77 GeV/c)) = 128.5±1.8, while the theory predicts a value of 129.6. As first remarked by Landau, the form of eq. (1) is such that the coupling α grows arbitrarily large as Q approaches the pole at Λ exp(3π/α0). One way to avoid this singularity is to invoke chiral symmetry breaking. 18) This phenomenon is associated with the possibility of a QED phase transition at strong coupling, as has been suggested by lattice gauge theory calculations. 1, 2, 29) Could a variant of a QED phase transition occur in strong fields as well as at strong coupling? A possibly relevant measure of electromagnetic field strength is the so-called QED critical field, 20, 43, 45) Ecrit = mc eh̄ = mc eλC = 1.3× 10 V/cm = 4.3× 10 Gauss, (2) above which spontaneous pair creation occurs. No theory of a strong-field QED phase change exists. During the 1980’s, the “evidence” for positron peaks in low-energy heavyion collisions (Darmstadt) was sometimes associated with a QED phase change, but the evidence is now largely withdrawn. 44, 48) The Landau pole problem can also be avoided via grand unification and strings. An elegant variant of grand unification invokes supersymmetry to bring the running of the coupling constants αQED, αstrong and αweak together at a common energy. 15, 32) This prediction is one of the most far-reaching applications of higher-order QED. A subclass of loop processes involves “boxes”, fermion loops coupled to four photons (Fig. 5). Delbrück scattering and photon splitting in the field of a nucleus have been measured, 22) but light-by-light scattering of real photons has not yet been observed in the laboratory. Figure 5: QED box processes: Delbrück scattering, light-by-light scattering and photon splitting. An application of light-by-light scattering is finite-temperature QED, in which the frequency of the Planck spectrum is slightly shifted. 3, 41) The effect, however, is small: ∆λ λ ∝ α ( kT mc2 )4 ≈ 10−35 ( T 300K )4 . (3) A recent experiment 14) can be said to have observed an effect of finite-temperature QED, as shown in Fig. 6. Figure 6: Evidence for Compton scattering of the LEP electron beam off the thermal photons inside the beam pipe. The well-known success of QED in describing higher-order effects remains an inspiration for theories of other interactions, both elementary and complex. 21) 2 Novel Aspects of QED Prior to the Maxwellian synthesis of electromagnetism, the Navier-Stokes equation of hydrodynamics was a candidate for the “theory of everything”; but it didn’t predict sonoluminescence. 16) The latter is the phenomenon in which an imploding bubble of gas inside a liquid converts a large fraction of the initial acoustic energy into visible light by a process that is not well understood. 40) [It is likely that the eV-scale photons of sonoluminescence are what makes liquid nitroglycerine explode when dropped. 23)] Several recent speculations relate sonoluminescence to QED process: • Preparata et al.: 9) a QED theory of water vapor predicts emission of light when water vapor condenses at density near 1 g/cm. • Schwinger: 46) a bubble is an electromagnetic cavity; an imploding bubble will radiate away the changing, trapped zero-point energy. This is a dynamic manifestation of the Casimir effect. 31) • Liberati et al.: 35) an imploding bubble ⇒ rapidly changing index of refraction ⇒ associated radiation. This relates to an earlier idea: • Yablonovitch: 52) an accelerating boundary across which the index of refraction changes is a realization of the Hawking-Unruh effect, leading to conversion of QED vacuum fluctuations into real photons. In 1974, Hawking noted that an observer outside a black hole experiences a bath of thermal radiation of temperature