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

Shcichi MIDORIKAWA and Seiji YOSHIMOTO

Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188, Japan

Abstract

The photino can be the lightest supersymmetric and may be produced copiously in the stellar objects. He investigate the interactions of a light-photino with the and find that the production cross sections in resonance regions are the largest and that the production of with their 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 . 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

(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 (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 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 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 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_)

  • 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 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 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

    ,

    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 , the similar resonances occur. However, if (§) 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 -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 -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 as many as in the showers. But the zenith angle distribution of the secondary muons must be flat since the u,7 production cross section is 10" cm forW » 30 GeV.

    The authors should like to thank Prof. H. Terazawa for careful reading of the manuscript. One of us (S.H.) should like to thank Profs. K. Akama, K. Hidaka and T. Shimada for valuable comments and helpful discussions. The numerical calculation is performed with FACOM M380 at INS.

    - 9 - References

    1) D. V. Nanopoulos and A. Savoy-Navarro ed. , Phys. Rep. 105 (1964) 1: S. Dawson, B. Eichten, and C. Quigg, Phys. Rev. D31 (1985) 1581: H. E. Haber and G. L. Kane, Phys. Rep. 1_T7 (1985) 75. 2) S. Yamada, talk presented at 1985 INS International Symposium (1985), to be published in the Proceedings: S. Komamiya, talk presented at 1985 International Symposium on Lepton and Photon Interactions at High Energies (1985), to be published in the Proceedings. 3) M. Samorski and W. Stamm, Astrophys. J. 26J3 (1983) L17: J. Lloyd-Evans et al., 3_0S_ (1983) 784. 4) R. W. Robinett, Phys. Rev. Lett. 55 (1985) 469: E. W. Kolb, M. S. Turner and T. P. Walker, Phys. Rev. D32 (1985) 1145: F. Wilczek, Phys. Rev. Lett. 55_ (1985) 1252. 5) V. J. Stenger, Nature 312 (1985) 411. 6) P. Fayet, Phys. Lett. 86B (1979) 272. 7) w. Heitler, The Quantum Theory of Raidation (Clarendon, Oxford, 1954): H. Terazawa, Rev. Mod. Phys. 45_ (1973) 615. 8) C. F. von Weizsacker, Z. Phys. ji£ (1934) 612: E. J. Williams, Phys. Rev. £5 (1934) 729. 9) S. L. Glashow, Phys. Rev. U8_ (1960) 316: J. Bahcall and S. Frantschi, Phys. Rev. 135B (1964) 788:

    -10- V. S. Berezinsky, D. Cline, and D. Schramra, Phys. Lett. 7BB

    (1978) 635:

    V. S. Berezinsky and V: L. Ginzberg, Mon. Net. Roy. Astron.

    Soc. !£! (1981) 3:

    R. W. Brown and F. W. Stecker, Phys. Rev. D26 (1982) 373.

    10) M. Gldck, E. Hoffman, and E. Reya, Z. Phys. C13 (1982) 119.

    11) M. Marshak et al., Phys. Rev Lett. 5.4 (1985) 2079:

    G. Battistoni et al., Phys. Lett. 155B (1985) 465.

    -11- Figure Captions

    Fig. 1. Diagrams for f + N * /T + 7* + N.

    Fig. 2. Cross sections for y +p-*-UT+u? + Pas a function of

    the incident photino energy. The solid line is a result

    with A - 30 GeV and the dashed line with ill • 50 GeV.

    Fig. 3. Diagrams for y + I •<• y + £ •

    Fig. 4. Cross sections for 9 + * "* Y + e as a function of the

    incident photino energy. The solid and dashed lines are

    results with ft • 30 GeV and 50 GeV, respectively.

    Fig. 5. Cross sections for y + Nucleon •*• y + X, as a function of

    the incident photino energy. The solid line is the

    result with M - 30 GeV and m• 5 GeV, and the dashed

    line with M » 50 GeV and m« 5 GeV, respectively.

    -12- N N

    Fig.1

    -13- CM u

    10

    -14- 11

    Fig. 3

    -15- 10

    10 icr 9 1CP 10 E(GeV)

    -16- 10"36

    r37 10

    CM E u 10"•3' 8

    10"39

    10 10 10b 108 109 E(GeV ) Fig. 5

    -17-