Direct Measurement of the Chudakov Effect

Abstract

Experimental results for the restricted energy loss of pairs created from 1-178 GeV photons in a thin Au target and subsequently passing a CCD detector are presented. It is shown that pairs-when detected close to the creation vertex-suffer a reduced energy loss due to the internal screening of the charges constituting the pair. Furthermore, the ability to measure directly the energy of the pair by calorimetry enables a comparison with theory as a function of energy. The observed phenomenon is in good qualitative agreement with general expectations from the Chudakov effect but indicates a quantitative disagreement with either of two mutually disagreeing theories. DOI: 10.1103/PhysRevLett.100.164802 PACS numbers: 41.60.ÿm, 07.85.Fv, 29.40.Vj, 95.30.Gv In the preparatory phase of the CERN NA63 experiment, we have investigated the reduced energy deposition from a positron-electron pair in the vicinity of their creation point. This reduction is due to the internal screening of charges, the so-called Chudakov (or King-Perkins-Chudakov) effect [1,2].By taking into account the density effect, a considerable contribution to the ionization energy loss originates from transverse distances b q ' v=! p , where v is the particle speed through the medium with plasma frequency ! p . If a penetrating assembly of separate charges is internally spaced less than this distance, the ionization is influenced by interference terms. This can be the case, e.g., for an energetic hydrogen molecule that is stripped upon entry to the substance, but it can also be an effect present for an electron-positron pair where each participating charge screens the charge of the other as seen from the relevant distance b q in the medium. Because of the Lorentz transformation of angles to the laboratory system, the electron and positron emitted in the pair creation process from a photon of energy @! appear with an approximate angle of 1= mc 2 =E e ' 2mc 2 =@! to the photon momentum @k in the frame of the laboratory. Thus, by defining E e =@! and p @!=mc 2 , we get an opening angle of the pairthe so-called Borsellino angle [3]. The energy loss thus diminishes close to the creation point if the created pair is sufficiently energetic and therefore forward directed. This is the so-called Chudakov effect. In a sense, the Chudakov effect is the pair production analogue of the more familiar density effect in radiation emission.A closely related effect -to both the density effect ([4], Chap. 13.5) and the Chudakov effect-has recently been calculated for Cherenkov radiation emission from e e ÿ pairs in the vicinity of the creation point [5,6]. This internal screening effect may affect decisively the behavior of the Cherenkov emission in neutrino-induced electromagnetic showers. A similar reduction may apply in the case of vacuum-assisted photoionization [7], where the created pair that knocks out the electron may suffer internal screening, leading to a lower photoionization cross section. Finally, the radiation emission from relativistic positronium may be in...

Measurements and theories of the King–Perkins–Chudakov effect

“…(6) can be approximated by K 0 ðxÞ ' lnð1=xÞ (neglecting a constant term which may be significant for not too small values of s) which results in 6), are quite different. This is exactly the region that was probed experimentally in [19], and the aim of the following is to discuss which of these theories -for all practical purposes covering the different theoretical approaches -achieves the best agreement with measurements.…”

“…For more precise measurements with pairs of known energy, the KPC effect must be investigated in an accelerator-based beam. Before [19], there existed one such proposal for a measurement in an accelerator environment [23]. That proposal, however, neglected the inherent noise contribution from thin solid-state detectors, originating from the capacitance.…”

The influence of non-parallelism of electron and positron velocities upon high-energy e+e− pair ionization loss in thin plate

“…The solid line on Fig. 2 shows the considered dependence for 100 GeV pair (the pairs of such energy were obtained, for instance, in the experiment [9]) calculated for the most probable angle of pair divergence # = 2/c [17] while the dashed curve shows this dependence calculated with the use of approximation in which the electron and the positron velocities are considered parallel (the #-dependent terms in the expression before the cosine function in (7) are set to equal zero while in the cosine argument the quantity z 1 # = s 1 is understood as the transverse separation between the particles in the plate). For the chosen values of the energy of the pair and the angle of its divergence the distance Z 0 within which the interference effects influence upon the pair ionization loss is about 10 m. The figure presents the region of distances up to 2 mm on which the influence of non-parallelism of the particle's velocities upon the pair ionization loss is most noticeable.…”

“…Let us also note that the problem statement considered in [11] and [14] probably better corresponds to the experimental situation of the first accelerator-based investigation of pair ionization loss [9,10] in which the pairs loss was measured in thin silicon detector situated on different distances from golden foils in which the pairs were created by high-energy photons. Taking into account the contribution from transition radiation leads to somewhat better description of the obtained here results than the one provided by theories of pair ionization loss in boundless medium [1][2][3][4][5].…”

“…Ionization energy loss of an ultra relativistic electron-positron pair created by a high-energy photon in substance has been studied in series of works both theoretically [1][2][3][4][5] and experimentally [6][7][8][9][10]. Its main peculiarity is associated with existence of socalled Chudakov effect which consists in reduction of pair ionization loss in the vicinity of its creation point comparing to the sum of losses of electron and positron which traverse the substance separately one from another.…”