Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
SEARCH FOR SUPERSYMMETRY AT THE ~p COLLIDER ¢r
John ELLIS, John S. HAGELIN Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94305, USA
and
D.V. NANOPOULOS and M. SREDNICKI Theory Division, CERN, CH-1211 Geneva 23, Switzerland
Received 25 April 1983
Many models of broken supersymmetry predict the existence of supersymmetric fermions x -+,° with masses less than the W e and Z °. Often there are two light neutral fermions ×o, even in models with large gaugino masses. The W -+ have large branching ratios for decays into X -+ + ×0, with the X +- subsequently decaying into ×o plus hadrons or leptons. We propose looking at the CERN ~p collider for W +- production and decay into supersymmetric fermions, a likely signature being "zen" events with one broadened hadronic jet system recoiling against invisible missing transverse energy.
The CERN Op collider has already started making its anticipated discoveries [ 1,2]. What other adventures may be in store for our experimental colleagues? One possibility is the discovery of supersymmetry [3] . Broken super- symmetric theories are currently the focus of considerable interest, and strategies have been proposed [4] to look in h a d r o n - h a d r o n collisions for strongly interacting supersymmetric particles such as gluinos and squarks. There should in addit ion be many color singlet supersymmetric fermions X -+,0 coupled to the W -+ and the Z 0, and it has been pointed out [ 5 - 7 ] that in many theories at least one particle of each charge should be lighter than the in- termediate vector bosons.
In this paper we explore the phenomenology of such fermions in some detail. We discuss the charged and neu- tral fermion mass matrices, pointing out that there may be light X +,0 even in theories with large gauglno masses. We delineate the areas of parameter space allowed by present experimental searches and by cosmology [8,9]. We point out that in much of the allowed domain one and often two W -+ ~ X -+ + X 0 decay channels are open. The branching ratios are expected to be several percent [6 ,7] , while the forward-backward decay asymmetry is model- dependent. Decays involving the lightest neutral supersymmetric fermion, which is probably predominant ly a pho- tino ~', are likely to have a distinctive signature. The charged fermion X +- would recoil against large missing trans- verse energy, just like the e -+ in the W +- events already observed [1,2] . The ×-+ would then decay into X 0 and a pair of charged and neutral conventional leptons or two collimated hadronic jets. Thus a likely signature would be "zen" events *~ of the type shown in fig. 1 : a broadened hadronic jet system in one hemisphere with invisible transverse energy to balance it. We also consider the possibility of similar events from Z 0 -~ X 0 + X 0', X O' ~ X 0 + X
decays, but find that these neutral zen events are suppressed in the cosmologically allowed domains. There could be other sources of zen events, for example, W +- decays into heavy leptons or Z 0 decays into sneutrinos as dis- cussed in ref. [11] .
Work supported by the Department of Energy, contract DE-AC03-76SF00515. ,1 This terminology is motivated by the zen koan: "You can make the sound of two hands clapping. Now what is the sound of
one hand?" See ref. [10] for important background information.
Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
Fig. 1. Zen event signature, with a charged susy fermion ×+ decaying into a spray of hadrons on one side of the beam axis denoted by ®, and transverse energy-momentum balanced by two light neutral supersymmetric fermions ×o.
We consider a minimal susy model with two light doublets of Higgs chiral superfields H 1 and H 2 of weak hy- percharge + 1 respectively [3 ,5 ,12-15] . The mass matrices for the charged and neutral susy fermions - gauginos and shiggses - are determined by the lagrangian terms
~ i ~ i _ M2 ~ a ~ a _ Ml"~"g ' (1) £E + ee0.H1H 2
where W a and B denote SU(2) and U(1) gauge superfields respectively, the tildes denote fermionic components and fij(a) are doublet (triplet) SU(2) indices. Th e quantities e, M 2 and M 1 are mass parameters that are generally expected to be O(mw). We shall assume
M 1 = { (or I/°~2)M2' (2)
where eei =-g2/47r, i = 1 ,2 ,3 are the gauge coupling constants, which holds to leading order in the renormalization group equations [ 12 ] if SU(2) X U(1) is eventually embedded in a unifying non-abelian group. When combined with the conventional Higgs-gauge field couplings the full mass matrix for the left-handed charged fermion fields becomes (" ('~+, H~) , (3)
g201 -- H 2
where (01H 0 210) = o "m 2 =,,2t'02 + o2)/2. This matrix is diagonalized by rotations through angles 0+ among 1,2" W 62t 1 the positvel~} and negatively charged fields respectively, where
tan0_+ = [b e + (b 2 + 4a2) 1/2]/2a+_, (4a)
with
a+ = M2g2o I -- eg2o 2 2 2 _ v~) . , b+ = M 2 - e 2 + g2(°2
= M2g2o 2 - eg2o 1
The charged fermion masses are
rn 1 = M 2 cos 0+ cos 0_ - g2o2 cos 0+ sin 0_ - g2ol sin 0+ cos 0_ - e s in 0 + s in 0 _ ,
(4b)
m 2 = M 2 s i n 0 + s i n 0 _ + g 2 o 2 s i n 0 + c o s 0 _ + g 2 o l c o s 0 + s i n 0 - c c o s 0 + c o s 0 . (5)
Note that in the limit M2, e -+ 0 the charged mass eigenstates become the Dirac fermions (H2 ' ~r+) and (~/- , ~ ) (swiggses) with masses
g202 , g2ol ,
respectively, while in the limit M 2 ~ 0% e -+ 0 the eigenmasses become
(6a)
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Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
Fig. 2. Charged and neutral mass eigenstates for plausible ranges of lel/m W and M2/mw, assuming (a) u 1 = 02, e > 0 ; (b) o I = 02, e < 0; (c) 01 = 402, e > 0; (d) 01 = 4v2, e < 0. Solid lines correspond to the lightest neutral eigenstate; dashed lines to the next- to-lightest neutral eigenstate. Dotted lines denote the lightest charged eigenstate.
M2, g2olU2/M 2. (6b)
Fig. 2 displays the mass o f the lightest charged fermion ×+- for ranges o f the unknown parameters ( c , M 2 , v 1/02):
since H 1 gives masses to the charge 2/3 quarks and r n c ~ ms, m t ~ m b it may well be that u 1 > / v 2 . We see that m + ~< m . . . . in most o f the range o f parameters except possibly i f b o t h M ~ and e are much greater than M W.
X-There areW- four neutral susy fermions which mix , namely ~ 3 , ' ~ 0 , H7 anal HT" Their mixing mat r ix ,2 is
:2 -g2OllV~ glOl/N/'~
l-g:,v,/,,/: o \ g2u2/V'~ e
which in terms o f the convenient combina t ions
0 g2v2/N/~l/W3 I -glv:d"/2/l /
glOl/V ~ e ItHT ] -.lOi/,i o I l
(7)
,2 Here we correct errors in ref. [5].
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Volume 127B, number 3,4 PHYSICS LETTERS
XO = (01~ 7 _ 02~O)/u, '~'0 =(02~ 7 + Ul~7)/O, [where we have introduced o = (02 + 02) 1/2 ] becomes
The Higgs combinations X0 and "~0 are approximate mass eigenstates in the limit M 2 + co but e small. Fig. 2 dis- plays the two lightest neutral fermion masses. We see that in general the lightest neutral fermion is lighter than the lightest charged fermion. This is favored by cosmology, since the lightest supersymmetric particle is essential- ly stable, and if it were charged it would dissipate and condense in conventional matter with a density far above experimental upper limits on stable exotic relics from the big bang [16]. We also see from fig. 2 that in general there are two light neutral fermions, one of which is predominantly the photino when M2, e "~ m w , while the other is mainly a shiggs as seen in eq. (10c).
There are significant constraints on the parameters M 2 and e which come from particle physics [17] and cosmology [8,9 ]. No new charged fermion has been seen [ 17 ] with a mass less than about 20 GeV and we shall take this as a lower limit on mx+ , though it has been argued [ 15 ] that a light charged supersymmetric fermion might have escaped detec- tion. Cosmology imposes an upper limit of at most 2 × 10 -29 gm/cc on the possible density ,3 of stable heavy neutral fermions [ 16 ]. Their density is reduced to acceptable levels only if they annihilate sufficiently efficiently, and it has recently been pointed out [8] that the annihilation of Majorana fermions like ours is strongly suppressed by P-wave phase space at low temperature. The effective interaction for annihilation into Dirac fermions ffhas the general form
£ = ~7~,),5 ~ fTu(AP L + BPR)f , (1 1)
where A, B receive contributions from intermediate Z ° and sfermion~' exchange in the s and t channels respec- tively. If we define an arbitrar z neutral Majorana fermion
+ + +
- + o 2 )
and use a convention where Qf = Tf 3 + ½ Yf then the Z 0 and sfermion exchange contributions to A and B are
A z = (7 2 - a 2)[(gl sin 0 w + g2 COS Ow)/4M ~ ] (½ YfLgl sin O w - T3fLg2 cos OwL (13a)
B z = (7 2 - 6 2) [(gl sin 0 w +g2 cos Ow)/8a 2 ] YfRgl sin 0W, (1 3b)
,3 This bound comes from the overall density of the universe and is very conservative. One can argue that massive neutral fermions probably condense into galaxies in which case a more stringent limit coming from missing galactic matter could be applied. See ref. [9] for more details.
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Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
IO
03
0.01
O.I
0.01 0.01
?)): ~
- y , I
I r I I
!
I I
1 I I 0.1 I 0 .01
i~2/mw
( b )
, , a " -A\ I
i i I 0.1 b IO
M 2 / m w
Fig. 3. Domains of parameter space consistent with cosmology (solid) and PEP/PETRA limits (dashed). Also shown are the do- mains in which one (hatched) and two (cross-hatched) W -+ ~ ×-+ + ×0 decay modes are kinematically allowed. The labels (a) to (d) correspond to those in fig. 2.
A • f = (T3LOtg2 1 2 2 + ~ Y fL3g l ) /2m"(L, B~f = - ( ~ Y fR3g l )2 /Zm~R , (13c,d)
where addi t ional small cont r ibut ions to Af ~, B T involving shiggs couplings propor t iona l to fermion masses are
omi t t ed for s implici ty o f presenta t ion , 4 . The gaugino couplings (13c,d) can be larger than the shiggs couplings
(13a,b) i f m?. < m Z (as al lowed by existing constraints [ 17 ] ), and thus the gauginos potent ia l ly annihilate more eff ic ient ly . We find that to be consistent wi th cosmology , the lightest susy particle should not be p redominan t ly
a shiggs, but should be a phot ino or conta in gaugino components . Fig. 3 shows the ranges o f M 2 and e which are consistent wi th cosmology if rn~ ~, ~ 20 GeV which is the most favorable case for annihi lat ion and hence yields
the most conservative bounds. ~7'e refer the interested reader elsewhere [9] for a more comple te s tudy o f the cos- mological constraints on susy particles.
~_4 These additional shiggs contributions to the sfermion exchange diagram cannot in general be cast into an effective interaction of the form (11) : while the contribution quadratic in the shiggs couplings can, the shiggs-gaugino interference term cannot. We have included the shiggs-shiggs contribution in computing the bounds in fig. 3, and found that it becomes important for the annihilation of neutral shiggses if o 1 = vz, since the Z ° contribution to the annihilation cross section vanishes in this limit (~2 - ~2).
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Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
There are substantial regions of the experimentally and cosmologically allowed domains in fig. 3 for which the decays W -+ -~ X -+ + X 0 are kinematically accessible [6] . Indeed, there are sizeable regions with two available decay modes involving predominant ly photino and shiggs states respectively, which are also shown in fig. 3. We have studied the branching ratios and forward-backward asymmetries for W -+ decay into these modes for general val- ues of the parameters e , M 2 and v 1/v 2. If we define a neutral mass eigenstate as in (11) and take the charged Dirac eigenstates from eq. (4): , os0/C°s° (sin0 +co0 ) X1 s i n 0 + - - i ] X2 = + ~ + , (14)
sin 0+W + cos0+H 1
then, for example, the left- and right-handed couplings o f the W - to the X1 X 0 combination are (in units of g2/ v% ,s
gL = W"2cos0_~ -- s in0_6 , gR = - - V ~ c o s 0 + a + sin0+3,. (15)
The branching ratio for W -+ -+ X -+ + ×0 is simply
is a final state three-momentum. Defining "forward" to be when a negative particle emerges in the direction o f the proton beam, the f o r w a r d -
backward asymmetry is
f I do - fO_l da Pmw(g 2 - g2R) A = - , (17)
do +~P ) + 2gLgRm+_m O]
so that the electron asymmetry defined by (17) is expected to be + 3/4. Fig. 4 shows how R and A vary for W +- decays into X -+ + the lightest X 0, generally predominantly a ~. The rates for W + -+ X + + ×0' are not shown: they are generally larger because the SU(2) gauge coupling to the shiggs is larger than the electromagnetic coupling of the photino. We have chosen to emphasize decays into the lightest neutral fermion because they are more experi- mentally accessible, as we will see in a moment . We see that the W -+ X 0 -+ X +- + rates are a substantial fraction R of the W +- -+ e + + v branching ratio which is expected to be about 8% in the standard model. The susy fermions have an essentially null fo rward-backward asymmetry if v 1 ~ 02, but may have a substantial negative asymme- try if 01 >~ 02. These results can be related intuitively to the W and H contents o f the charged mass eigenstates. They contrast with the asymmetry of +3/4 expected for the electron or for a further sequential heavy lepton, and can in principle be used to distinguish between them and susy particles if one can construct a measure o f the X -+ charge, for example by weighting suitably the charges of its decay products as functions of their momenta [ 18].
The charged susy fermions X -+ are expected to decay via W +- or sfermion exchange into some X ° + (ev,/xv, rv, or q~). The lifetime is not expected to be long enough for the X +- decay path to be observable. The final state par- ticle distributions should resemble those in conventional heavy lepton decay, though the Michel parameter will
A heavier X , if produced, would decay into not in general correspond to pure (V - A) or (V + A) interactions. • 0' the lighter ×0 + (vV, £+£- , or qEt). This can occur via sfermion exchange, or via Z 0 exchange since the Z 0 couplings
,s If a charged or neutral eigenstate corresponds to a negative eigenvalue of the mass matrices (3) or (9), it is necessary to intro- duce a relative minus sign between the top (left) and bottom (right) Weyl components of the Dirac spinor to obtain the phys- ical mass eigenstate. This would flip the relative sign ofg L and gR in (15).
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Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
I0
I
0.1
0.01
i . , - . • ../ -
- , / ,ool :. : / / I . " . : / /
.... /./..... "13 ....:///
I ..,'""i/f/ / ......
I
0.1
(a)
(c)
r ~ ' . . . i l l - - " , . - I \'-&
, . . " '%:..X.. ,,o • . . L .....
\ "°'..o
I I
~ "..~:.
+1/3 ';2"% 3
b'3 7 I/2
r/3
0.01 I I I I O.OI 0.1 I 0.01 0.1 I I0
Me/mw M~/mw
Fig. 4. Rates and forward-backward asymmetries for zen events in the allowed regions of fig. 3. Dotted lines are rates normalized to the eu rate. Dashed lines represent forward-backward asymmetries. The labels (a) to (d) correspond to those in figs. 2 and 3.
to X 0 and X 0' are not diagonal (and in fact become purely off-diagonal if o 1 = 02). The Z 0 contribution requires a shiggs component in the predominantly photino X 0 eigenstate, but otherwise gives a contribution to the X 0' rate which is typical of a heavy lepton. A potentially larger contribution to the X 0' decay rate comes from sfermion exchange, which occurs either through the gaugino component of ×0' or directly through the shiggs-fermion cou- pling cc m f / M w . Since there is typically ample phase space for X 0' --* X 0 + X decay, it is unlikely that the X O' would live long enough for its decay to provide a separated vertex, so we shall not examine this possibility further.
The promising signature to search for experimentally at the ~p collider is likely to be W ± ~ X +- + lightest X 0, X ± -+ lightest X 0 + (~q). Fig. 4 shows that these events may occur with a rate close to that for W ± -* e±v decay. Comparison of figs. 2 and 4 shows that in the interesting region the X ± typically has a mass 0(30) GeV, while the lightest X 0 has a mass O(10) GeV. The X +- is therefore usually produced relativistically with a transverse energy 0 ( 4 0 - 5 0 ) GeV, and with a recoil transverse energy 0 ( 3 0 - 4 0 ) GeV. The X ± decays into a missing neutral with transverse energy O(15) GeV and two hadronic jets with invariant mass 0(20) GeV and total transverse energy 0(25) GeV. The resulting event signature is shown in fig. 1 : two collimated jets coalescing into a broadened ha- dronic jet on one side of the beam axis with a net missing recoil energy of 0(25) GeV on the opposite side. These are what we call "zen events". If the X* mass is increased, the two hadronic jets become more splayed out, until in an idealized case the X ± becomes nonrelativistic in the W ± rest frame, and the typical azimuthal angle between the two hadronic jets may apporach 120 °. In this case the event structure resembles more closely the form already
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Volume 127B, number 3,4 PHYSICS LETTERS 28 July 1983
discussed by other authors [4] in connection with gluino or squark pair-production. It is a general feature of su- persymmetric theories that one expects events with large amounts of missing transverse energy-momentum which do not contain leptons. In this respect they resemble heavy lepton production events, and we note parenthetical- ly that a search for zen events can also be interpreted as a search for heavy leptons with masses between the pres- ent experimental limit [ 17 ] of about 18 GeV and mw. Ways of distinguishing between heavy leptons and susy fermions include the fo rward-backward product ion asymmetry, the Michel decay parameter p which must be 3/4 for a conventional sequential heavy lepton but could be 0 for X -+ decay thus modifying the final state jet ener- gy distributions, and the possibility of unconventional decay branching ratios due to sfermion exchange diagrams.
We have also studied the decay of the Z 0 into light neutral susy fermions. In general, there are three kinemat- ically allowed modes: Z 0 -+ X 0 X 0, Z 0 -+ xOx O' and Z 0 ~ xO'x °' where X 0 and X 0' are respectively the lightest and next-to-lightest neutral susy fermion. We have previously observed that cosmological arguments prefer a light pho- tino to a light shiggs. Furthermore, since Z 0 ~ ' ~ ' i s strongly suppressed relative to Z 0 -+ HH, this implies F(Z 0
xOx °) ~ F(Z ° ~ ×OxO') "~ P(Z ° -+ xO'xO'). The most likely mode for susy Z ° decay is therefore Z ° -+ xO'x °', where both of the X 0' decay into X 0 plus quarks or leptons. The experimental signature for such a process is un- fortunately less distinctive in ~p collisions than a bona fide zen event. However e+e - ~ X0'X 0' through a virtual Z 0 could be looked for at present day as well as forthcoming e+e - machines. The cross section for this process is
1 2sin2Ow,geA --½, or simply (3, 2 -- ~ 2)2 in units of a conventional neutrino cross section if whereg~ = - ~ + = m~o, "~ s. Typically we find that (3, 2 - 52) 2 is O(1) in the cosmologically allowed domain, except when 01 = 02 where (3, 2 - ~ 2) vanishes identically.
We note that for total center-of-mass energies far below the Z 0 resonance, a second product ion mechanism for neutral susy fermions due to selectron exchange can be important if the selectron is light enough [ 15,19]. Since the electron-shiggs coupling is negligible, this mechanism requires a significant gaugino component within the final state fermions, so that in general one expects o~,(e+e - ~ ×OxO ) ~ o~,(e+e - ~ xO× 0') >> o~,(e+e - ~ xO'×O'). It is quite possible that the ×0' can contain sufficient gaugino components for this mechanism to produce observ- able e+e - ~ xOx O' zen events at present energies, as discussed in ref. [15] .
We conclude that the rate of zen events from W -+ decay and the magnitude of their missing energy-momentum seems to place them well within the reach of experiments [1,2] with the CERN ~p collider in the near future. Let us hope our experimental colleagues are lucky enough to make another exciting discovery.
We would like to acknowledge useful discussions with H.E. Haber, H. Kowalski and A. Savoy-Navarro, and we thank J. Prentki for stressing to us the potential of the ~p collider for searching for susy particles.
References
[1] G. Arnison et al., Phys. Lett. 122B (1983) 103. [2] M. Banner et al., Phys. Lett. 122B (1983) 476. [3] For a recent review see: P. Fayet, Proc. Intern. High energy physics Conf. (Paris, July 1982). [4] I. Hinchliffe and L. Littenberg, in: Proc. D.P.F. Summer Study on Elementary particle physics and future facilities (Snow-
mass, 1982), eds. R. Donaldson, R. Gustafson and F. Paige (APS, 1982) p. 242. [5] J. Ellis and G.G. Ross, Phys. Lett. l17B (1982) 397;
J. Ellis, L.E. Ibfi~ez and G.G. Ross, CERN preprint TH-3382 (1982). [6] S. Weinberg, Phys. Rev. Lett. 50 (1983) 387. [7] A.H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49 (1982) 970. [8] H. Goldberg, Noertheastern preprint NUB-2592 (1983). [9] J. Ellis, J.S. Hagelin, D.V. Nanopoulos, K. Olive and M. Srednicki, in preparation.
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[10] F. Capra, The tao of physics (Shambhala. Berkeley, 1975) p. 48ff. [ 11] R.M. Barnett, K. Lackner and H.E. Haber, Phys. Lett. 126B (1983) 64. [12] K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Prog. Theor. Phys. 68 (1982) 927. [13] L. Alvarez-Gaum6, J. Polchinski and M.B. Wise, Harvard preprint HUTP-82/A063 (1983). [14] J. Ellis, J.S. Hagelin, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. 125B (1983) 275. [15] J.-M. Fr~re and G.L. Kane, University of Michigan preprint UM-TH 83-2 (1983). [16] S. Wolfram, Phys. Lett. 82B (1979) 65;
P.F. Smith and J.R.J. Bennett, Nucl. Phys. B149 (1979) 525. [17] K.H. Lau, SLAC-PUB-3001 (1982). [18] B.F.L. Ward, SLAC-PUB-2845 (1981). [19] P. Fayet, Phys. Lett. l17B (1982) 460;
J. Ellis and J.S. Hagelin, Phys. Lett. 122B (1982) 303.
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