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Cosmic Ray Test for Supersymmetry

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Cosmic Ray Test for Supersymmetry INSTITUTE FOR NUCLEAR STUDY INS-Rep.-560 UNIVERSITY OF TOKYO Nov. 1985 Tanashi, Tokyo 188 Japan Cosmic Ray Test for Supersynunetry Shoichi MIDORIKAWA end Seiji YOSHIMOTO INS-Rep.-560 Nov. 1985 Cosmic Ray Test for Supersymmetry Shcichi MIDORIKAWA and Seiji YOSHIMOTO Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188, Japan Abstract The photino can be the lightest supersymmetric particle and may be produced copiously in the stellar objects. He investigate the interactions of a light-photino with the matter and find that the production cross sections in resonance regions are the largest and that the production of fermions with their superpartners is important at higher energies. - 1 - Supersyinmetry seems to have viable features, and is helpful in solving many theoretical problems which have never been answered within the framework of the standard model. Although much effort has been made to search for super symmetry, no evidence has yet been found. The presently available experimental data give only lower bounds on the mass of superpartners of the particles (sparticles).2) It is known that extraterrestrial objects such as Cygnus X-3 are sources of high energy Y rays. These energies are beyond the ones which can be available in the terrestrial experiments. It is also plausible that the lightest superparticles are copiously produced in these stellar objects, and may be observed in the air shower and underground experiments. There are two candidates for the lightest sparticles. One is the scalar neutrino (c ) and the other is the photino (?). Although there have appeared some calculations about the photino-matter interactions in the literature, they are valid at rather low energies. In this article, we will derive the formula which can be applicable to the higher energies and will investigate the feasibility of detecting the signal of photinos in the apparatus of the DOMAND (Deep Underwater Muon and Neutrino Detector) type. In the following, we will assume that the photino is mass less or has a small mass compared with the ordinary particles. Before discussing the interactions of the photino with matter, let us recapitulate the interaction of the photon with matter. At lower energies, the photo-electric effect is the most important. As - 2 - energies grow, Compton scattering takes the dominant part. At higher energies, the cross section of electron pair production is the largest. In spite of the suppression factor a compared with the other processes, the reverse of the importance occurs because of the two factors. (1) For scattering processes, the cross section decreases eventually with the square of the center-of-mass energy as - s . On the other hand, in the pair production this factor is replaced by i , where ra is the mass of the produced particles. (2) Furthermore, the pair production is enhanced by the factor In (-I,). For more comprehensive reviews, readers should referred to, for example, ref. 7) and references therein. We will examine what kind of process will dominate in the photino-matter scattering. Can we also expect the similar mechanism as those discussed above in this case? The coupling of a photino (?) with matter Dirac spinors ^. =-j(l-T5)^ and ^R = -j(l+ y_) <li , of charge Qe, and their spin-0 partners ^ L and f R respectively are given in the following Lagrangian density: V2Q {Gtfoiff>"•?+**J} (1 > We will assume that the photino is a mass eigenstate. The first process we will consider is the analog of pair production of lepton slepton pairs (see Fig. 1). Let us define the momenta of the particle involved as I t i) — /L(p )+f*(k )+N(pf), (2a) - 3 - P - k'+p1 , P2 » ra^ , (2b) and P - P . (2c) where mc is the invariant mass squared of I ^, /. system, and k is the momentum of the exchanged photon. N is a target, whose mass is defined by p^ » pf » M . The region of k is determined in terms of 9, mc, and M as If the energy of the photino (u) is much larger than the mass of the slepton (m) , the dominant contribution to the cross section 2 121 I 2] 2 comes from k » - 'k i m. m. Furthermore, if k '. m «m 1 , we can use WeizsScker-Williams approximation. Thus we decompose the process + into two parts, i.e., y + 7~*/L I •, and N —•- N + y . The photon-photino scattering cross section, in the limit of |p"| »m (m is the miss of the lepton), is given by (4) where x = 5 (§ is the square of the center-of-mass energy). The main difference between pair production and the process described by eq. (4) lies in that in the latter case two mass scales, m and - 4 - m, appear and the mass ratio °f"5- works as an enhancement factor. By using the equivalent photon approximation, we obtain the cross section for y + N—•-/L t ^ t B as ,l Jo 3 4Z*a , ,u, fi I**! ll /EI • TT" ln(l'Lln<5='-Tj (5) where «> is the incident photino energy in the lab. frame, and Z is the atomic number. The cross sections are plotted in Fig. 2. As an illustration, let us consider the n^, ML production and choose the parameters such that Z « 1, ffl » 30 GeV, u • 10 TeV, then we have v{y + p -• nL + 5* + p) « 1.4x10 cm , which is comparable to the total cross sections of the neutrino nucleon scattering. Since 2£ will decay into 7L and 7. the final state contains u pair which can be distinguished from the neutrino reactions. Charge conjugation symmetry requires ,<y + N - /L + /* + m - "iy * N * /L + /L + N) (6) If the mass of J, and y_ are degenerate, we expect the u pair production cross sections four times as large as those discussed in (5). Next, we will examine the photino-lepton collision. The relevant Feynman diagrams are depicted in Fig. 3. Contrary to - 5 - Compton scattering, there is a resonance-production reaction y + / * /L at s =s m where ib is the mass of slepton /L> This is the analog of the so-called "Glashow resonance" (v + e • W ) ' in the electroweak theory. In estimating the cross sections we will modify the slepton propagator near the resonance into the Breit- Wigner form. p*-m*+imr where r is the decay width which will be discussed later. In the limit where the mass of /R is infinite, the cross sections of photino-lepton scattering is given by nciM, 2s (m*-m*). Ts 1 s+fll*-m') 1 s I (s-m1 )* L m2s-m* J * -2m1 ]»*-»•) s-m* (7) where s is the square of the center of mass energy. Since the slepton decays into a lepton and a photino, its width is given by - 6 - The cross sections in (7) have a peak near s » ft . Substituting (8) into (7) , we obtain at s » St2 4i where we have assumed A S>m . Notice that (9) is independent of a. As an illustration, let us substitute ft » 50 GeV into (9), then we obtain a i. 2.0x10 era, which is much larger than those estimated from (5). However( away from resonances (7) decreases and behaves as 1/s. In these higher energy regions, the / , /* production process is more important than the ~+« •* 7 +e process. The cross sections of (7) are plotted in Fig. 4. In the case whare photinos hit quarks, the similar resonances occur. However, if gluinos (§) are lighter than squarks (Q), the process of § •+ g + q occurs with the strength of gs- We will evaluate the cross sections of 7 + q* § + q process in the limit where the mass of q vanishes and the mass of qR becomes infinite. Then we obtain + q * § + q) ( 1 where C2 (N) is the Casimir operator, and for SU(N), C2(N) = j" , m is the mass of g, and M is the mjss of gL . If - 7 - total decay rate r . can be approximated by r (g -*• § + ql as (11) The cross sections (10) are also enhanced near the resonance region where S = M . In this region, the cross section is given by where we have neglected the gluino-mass. Comparing (12) with (9), we find that (12) is suppressed by a factor of 57 . The quarks are constituents of the nucleon. The total cross sections of the photino-nucleon processes are calculated by using the standard quark-parton model, O(Y + Nucleon* 9 + x' Zoiy + q - g + q;xs)f (x) . (13) The superposition in (13) smears the peak in (12). We show the numerical results in Fig. 5 with a parton distribution given in ref. 10). The dominant decay mode of the gluino is the three body decay into qqy. Thus, in the photino-nucleon scattering, we can see two jets as the final states: one coming from g is broad and the other coming from q is sharp. We have shown that near the resonance regions the photino- - 8 - matter scattering cross sections may be much more larger than the neutrino-matter cross sections. We can expect that supernovas such as Cygnus X-3 can be the sources of the light sparticles as well as the high energy y rays. Though a naive estimation of photino-flux is too small to be detected, the mechanism of photino production in steller objects is not well understood. Therefore we might have large enough flux to be detected. Recently, the anomalous largeu flux in cosmic rays from Cygnus X-3 has reported. If the sufficiently large flux of photino comes from Cygnus X-3, we can expect muons as many as electrons in the showers.
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