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Basics of a Photon Collider

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Basics of a Photon Collider BASICS OF A PHOTON COLLIDER Valeriy G. Serbo Novosibirsk State University, Novosibirsk, Russia Based on papers: V. Budnev, I. Ginzburg, G. Meledin and V. Serbo \The Two-Photon Particle Production Mechanism", Physics Reports 15C (1975) 181; I. Ginzburg, G. Kotkin, V. Serbo and V. Telnov \Photon Colliders", review for Physics Reports (under prepara- tion) \The Photon Collider at TESLA", IJMP A 19 (2004) 5097 1 Contents: 1. Introduction 1.1. The subject 1.2. Interaction of photons in the Maxwell theory and QED 2. Collisions of equivalent photons at e+e¡ storage rings 3. Results obtained in virtual γ¤γ¤ collisions 4. Linear e§e¡ collider 5. Photon collider on a base of a linear e§e¡ collider 5.1. Idea of high-energy γγ and γe colliders with real photons 5.2. Scheme of a photon collider 5.3. Compton scattering 6. Physics of γγ interactions 7. Conclusions 2 1. Introduction 1.1. The subject This small review is devoted to γγ collisions including methods of creating the col- liding γγ beams of high energy and physical problems which can be solved or clari¯ed in such collisions. It is a new and promising area in high energy physics connected with the fun- damental problems of strong and electro-weak interactions. 3 Our knowledge about elementary particles and their interactions is mainly obtained from par- ticle collisions. Most of fundamental results in particle physics has been obtained from experiments at the pp; pp;¹ e+e¡ and ep colliders. Principal characteristics of colliders are: the energy in the center-of-mass system (c.m.s) Ecm; luminosity of a collider L which determines col- lision rate N_ of events with the cross section σ by relation: N_ = L σ ; types of colliding particles. 4 The progress on high-energy colliders can be seen from the Table: Collider Type Ecm, TeV Start date Spp¹S pp¹ 0.6 1981 TEVATRON pp¹ 2 1987 LHC pp 14 2007 HERA ep 0.31 1992 SLC e+e¡ 0.1 1989 LEP-I e+e¡ 0.1 1989 LEP-II e+e¡ 0.2 1999 Linear collider e+e¡ 0.5 201? Photon collider γγ; γe 0.4 201?+? Muon collider ¹+¹¡ 0.1¥ 3 ?? Up to now and in the nearest future,the pp and pp¹ colliders are the machines with the highest energy. That is why such epochal discoveries as W and Z bosons (responsible for weak interaction) and t quark had been performed at the Spp¹S and the TEVATRON, respectively. 5 For detail study of new phenomena, it is im- portant not only the energy but also types of colliding particles. The e+e¡ colliders, being less energetic then pp colliders, have some advantages over proton colliders due to much lower background and simpler initial state. Well known example | the study of Z boson. About thirty years ago a new ¯eld of particle physics has appeared | photon-photon interactions Since that time the two-photon physics is ac- tively investigated in a number of accelerators. 6 A. Sessler \Gamma-Ray Colliders and Muon Colliders" Physics Today (March 1998, p. 48) \In high-energy physics, almost all of the pre- sent accelerators are colliding-beam machines. In recent decades these colliders have produced epochal discoveries: Stanford SPEAR electron- positron collider unveiled the charmed-quark meson and ¿ lepton in 1970s. In the realm of high-energy proton-antiproton colliders, the Super Proton Synchrotron at CERN gave us the W§ and Z0 vector bosons of electroweak uni¯cation in 1990s, and in 1999s the Teva- tron at Fermilab ¯nally unearthed the top quark, which is almost 200 times heavier than the proton." 7 \...What about other particles? Beam physi- cists are now actively studying schemes for col- liding photons with one another and schemes for colliding a beam of short-lived ¹+ leptons with a beam of their ¹¡ antiparticles. If such schemes can be realized, they will pro- vide extraordinary new opportunities for the investigation of high-energy phenomena. These exotic collider ideas ¯rst put forward in Russia more that 20 years ago..." 8 1.2. Interaction of photons in the Maxwell theory and QED In the classical Maxwell theory of electromagnetism, photons do not interact with each other. In quantum electrodynamics (QED) photons can interact via virtual e+e¡ pairs. For example, an elastic γγ scattering is described by Feynman diagrams of the following Fig. γ γ e + crossed γ γ 2 At low energies, ! ¿ mec where ! is the photon c.m.s. energy, this cross section is very small µ ¶6 2 2 ! σγγ!γγ = 0:031® re : mec2 9 The maximal value of the cross section is achie- 2 ved at the c.m.s. photon energy ! » mec and is large enough: à !2 4 ~ 2 2 ¡30 2 max σγγ!γγ » ® = ® re » 4 ¢ 10 cm : mec 2 At high energies, ! À mec , this cross section decreases à ! 2 2 2 2 mec σγγ!γγ »= 4:7 ® r : e ! For example, for visible light, ! » 1 eV, ¡65 2 σγγ!γγ » 10 cm : It is too small to be measured even with the most powerful modern lasers, though there were such attempts [D. Bernard, 2000]. 10 11 12 13 At energies ! > mc2, two photons can produce a pair of charged particles. The cross section of the characteristic process γγ ! ¹+¹¡ (Fig. a) γ µ+ µ+ γ a) + γ µ− γ µ− e+ µ+ * * γ , Z b) µ− e− 2 2 4 is equal to (at s = (2!) À 4m¹c ) m2c4 s σ = 4¼r2 e ln : γγ!¹+¹¡ e 2 4 s m¹c It is larger than the \standard" cross section for the production of the same pair in the e+e¡ colli- sions via a virtual photon only (Fig. b) 2 2 4 4¼re me c σ + ¡ + ¡ = : e e !¹ ¹ 3 s 14 15 2. Collisions of equivalent photons at e+e¡ storage rings Unfortunately, there are no sources of intense high-energy photon beams (like lasers at low energies). However, there is indirect way to get such beams | to use equivalent photons which accompanied fast charged particles. Namely this methods was used during last three decades for investigation of two-photon physics at e+e¡ storage rings. The essence of the equivalent photon approach can be explained in the following way: Fermi (1924); WeizsÄacker and Williams (1934) 16 The electromagnetic ¯eld of an ultra-relativistic electron is similar to the ¯eld of a light wave. There- fore, this ¯eld can be described as a flux of the equivalent photons with energy distribution dnγ=d!. The number of these photons per one electron with the energy E is determined by dia- gram of virtual bremsstrahlung -e - E HH HH HH ! HHj and it is equal to 2® E d! dnγ » ln ¼ ! ! or approximately d! dnγ » 0:03 : ! At the e+e¡ colliders the equivalent photons also collide and can produce some system of particles X (see Fig. a, where γ¤ denotes the equivalent photon) e+e¡ ! e+e¡γ¤γ¤ ! e+e¡X: 17 e− e− e+ γ* q = (ω ,q ) X (C=−1) 1 1 1 γ*, Z* X (C=+1) e− γ* q = ( ω , q 2 2 2) e+ e+ b) a) Thus, this process is directly connected with the subprocess γ¤γ¤ ! X. Strictly speaking, the equivalent photons are not real photons, they are virtual ones. The 4- 2 momentum squared of such a photon qi (which is equal to m2c2 for usual particle) is not equal 2 zero, qi 6= 0, but it is very small. For large part 2 2 2 of the cross section jqi j ¿ me c , therefore, the most of equivalent photons are almost real. The cross section for two-photon production of e+e¡ in collisions of two fast particles with charges + ¡ Z1e and Z2e, i.e. for the Z1Z2 ! Z1Z2e e pro- cess, was calculated by Landau and Lifshitz in 1934. 18 At ¯rst sight, the cross sections of the two-photon processes at e+e¡ colliders (Fig. a) are very small since they are the 4-order processes: 4 σtwo¡phot / ® ; while for the annihilation processes of (Fig. b) the cross sections 2 σannih / ® : However, the annihilation cross sections decre- ase with increase of the energy ~2c4 σ » ®2 ; s = (2E)2; annih s while the two-photon cross sections increase ~2 σ » ®4 lnn s : two¡phot 2 2 mcharc Here n = 3 ¥ 4 depending on the process, and the characteristic mass mchar is constant (for example, + ¡ mchar » m¹ for X = ¹ ¹ and mchar » m¼ for X = hadrons). p As a result, already at s > 2 GeV σe+e¡!e+e¡¹+¹¡ > σe+e¡!¹+¹¡: 19 20 Another example, at the LEP-II electron-posi- p tron collider with the energy s = 200 GeV, the number of events for two-photon production of hadrons with the invariant mass Wγγ > 2 GeV was by a three order of magnitude larger than that in the annihilation channel: 106 + − + −γ* γ * + − + − e e e e e e µ µ 5 10 + − + −γ*γ* + − W > 2 GeV e e e e e e hadrons 104 103 pb) 2 σ ( 10 101 + − e+ e− W W 100 e+ e− hadrons + − 0 0 10−1 e e Z Z 50 100 500 1000 s (GeV) At e+e¡ storage rings the two-photon processes e+e¡ ! e+e¡e+e¡ had been observed for the ¯rst time in 1970 (Novosibirsk). 21 The importance of two-photon processes for the lepton and hadron production at e+e¡ stor- age rings had been emphasized in the papers: Arteage-Romero, Jaccarini, Kessler and Parisi (1969, Paris); Balakin, Budnev and Ginzburg (1070, Novosibirsk); Brodsky, Kinoshita and Terazawa (1970, SLAC).
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