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%From: DJOUADI@LPS.UMONTREAL.CA
%Date: Thu, 15 Jul 1993 19:07:23 -0400 (EDT)


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\nn \hspace*{11cm} UdeM-LPN-TH-93-159 \\

\vspace*{0.3cm}

\centerline{\large{\bf SIGNALS OF NEW LEPTONS}}

\vspace*{5mm}

\centerline{\sc G.~Azuelos$^{1,2}$ and A.~Djouadi$^1$}

\vspace*{8mm}

\centerline{$^1$ Laboratoire de Physique Nucl\'eaire, Universit\'e de
Montr\'eal, Canada.}
\centerline{$^2$ TRIUMF, Vancouver, Canada.}

\vspace*{0.1cm}

\begin{small}
\begin{center}
\parbox{14cm}
{\begin{center} ABSTRACT \end{center}

\nn We discuss the production of heavy leptons at a future high--energy
e$^+$e$^-$ linear collider with a center of mass energy of 500 GeV. Signals and
backgrounds are analyzed for their single production in association with
ordinary leptons.}
\end{center}
\end{small}

\vspace*{1cm}

\nn {\bf 1.~Introduction} \\

\vspace*{-2mm}

\nn Many theories beyond the Standard Model (SM) lead to the existence of new
fermions. In most of the cases these new fermions have non--canonical SU(2)$
\times$ U(1) quantum numbers, e.g. the left--handed (LH) components are in
weak isosinglets and/or the right--handed (RH) ones in weak isodoublets.
Examples of such fermions [besides a fourth generation with a heavy neutrino]
are the following [1,2]:  \\
$i)$  In the unifying group SO(10), which is one of the simplest
and most economic extensions of	the SM,	the smallest anomaly--free
fermion	representation has dimension 16.  It contains a	right--handed
neutrino in addition to	the 15 Weyl fermions in	one lepton--quark
generation.  These heavy neutrinos are of the Majorana type. \\
$ii)$ In the	exceptional group E$_6$, which is suggested as
low energy limit of superstring	theories, each generation of fermions
lies in	the 27 dimensional representation.  Thus, in addition to the
usual chiral fields, twelve new	fields are needed to complete the
representation. Among	these, there will be two weak
isodoublets of heavy leptons, a	RH and a LH doublet, and two
isosinglets of neutrinos which can be either of	Dirac or Majorana
type. \\
$iii)$ Mirror fermions, whose chiral properties are opposite to those
of ordinary fermions [i.e. the RH components in isodoublets
and the	LH ones	in isosinglets] appear in many extensions of the
SM. They provide a way to restore left--right
symmetry at the	scale of the electroweak symmetry breaking, and	they
naturally occur	in lattice gauge theories. \s

\nn These new fermions will mix with the ordinary fermions of the SM, and this
mixing will give rise to new currents which determine to a large extent their
decay properties and allow for new production mechanisms [2,3]. In this report,
we briefly discuss the signals and backgrounds for the production of the new
leptons at a high--energy $\ee$ linear collider with a c.m. energy of
500 GeV [4]. A more complete discussion can be found in [3]. \\

\nn {\bf 2.~Production and Decay} \\

\vspace*{-2mm}

\nn If the new particles have non--zero electromagnetic and weak charges, they
can be pair produced if their masses are smaller than the beam energy.
In general the reactions are built--up by a superposition of photon and $Z$
boson exchanges [additional contributions could come from extra
gauge bosons if their masses are not much larger than the c.m.~energy of the
collider]. The cross sections are large and, up to phase space suppression
factors, of the order of the point-like QED cross section for muon
pair production. At a 500 GeV $\ee$ collider this gives cross sections
$\sigma \sim 400$ fb which, with the expected integrated luminosity
of $\sim$ 20 fb$^{-1}$ [4], lead to several thousand events. This large
number of
events allows to probe masses up to the kinematical limit of 250 GeV and, due
to the clean environment of $\ee$ colliders, to investigate in detail the
properties of these fermions. \s

\nn The mixing allows an additional production mechanism for the new
fermions: single production in association with their light partners. In the
case of quarks [and for second and third generation new leptons if
inter--generational mixing is neglected] the production process is mediated by
$s$--channel gauge boson exchange; since the mixing angles are restricted to
values smaller than ${\cal O} (10^{-1})$ by present experimental data [1], the
cross sections are rather small. But in the case of [the first generation]
heavy leptons, additional $t$--channel exchanges, $W$ exchange for neutral
leptons and $Z$ exchange for charged leptons are present, increasing the cross
sections by several orders of magnitude. This results in large production rates
which allow to probe lepton masses close to the total c.m. energy if
the mixing angles are not prohibitively tiny. For instance, for a heavy
neutrino with a LH mixing to the electron, the production cross section
is of ${\cal O}(1~{\rm pb})$ at a 500 GeV collider if the neutrino mass is
around 300 GeV and its mixing angle close to the bound $\theta_{\rm mix} \simeq
0.1$. \s

\nn Present experimental data imply that the masses of the new states are
larger than $M_Z/2$ and for not too small mixing angles, larger than $M_W$; the
mass range up to $m_F \sim M_Z$ can be probed at LEP200. The heavy fermions
decay through mixing into massive gauge bosons plus their ordinary light
partners; for masses larger than $M_W/M_Z$  the vector bosons will be on--shell
and will decay into light quarks and leptons. Because the decay is suppressed
by
small mixing angles, the new fermions have very narrow widths: for $\theta_{\rm
mix} \sim 0.1$ and masses around 100 GeV the partial decay widths are less
than 10 MeV. The charged current decay mode is always dominant and
asymptotically the branching ratios are 1/3 and 2/3 for the neutral and charged
current decays, respectively.  To fully reconstruct the fermions from their
final decay products, one needs the branching ratio of their decay into visible
particles. For the decays of $N,E$ into charged leptons and $W/Z$ bosons which
subsequently decay into two jets, the branching ratios are
approximately 0.43 and 0.23, respectively [in the case of the $Z$ boson, one
can
also include the cleaner $e$ and $\mu$ decays, but the branching ratio is
rather small: $\sim 6\%$ compared to $\sim 70\%$ for hadrons].\s

\nn In the following, we will discuss the signals and the various backgrounds
for the single production of charged and neutral heavy leptons [with a LH
mixing to electrons] at a 500 GeV collider. The analysis will be based on an
integrated luminosity of 50 fb$^{-1}$ which corresponds to $\sim 2$ years
running of a standard \ee\ collider [4]. \\

\nn {\bf 3. Signals and Backgrounds} \\

\vspace*{-2mm}

\nn The processes for the production of the charged and neutral heavy leptons
$E$ and $N$ were simulated by incorporating in the PYTHIA [5] generator the
matrix elements for the three body reactions: $e^+ e^- \ra N \nu_e (E^\pm e^\mp
) \ra \nu_e e^\pm W^\mp (e^\pm e^\mp Z)$ and forcing the gauge bosons to decay
hadronically; full hadronization was allowed to take place. All the resulting
particles were then subjected to detector resolution and acceptance effects.
The parameters for the detector were taken from the ``standard'' set of [6]
but with angular acceptance up to $|\cos\theta| < 0.98$ for the electromagnetic
and hadronic calorimeters as well as for the charged particle tracker. In the
case of the neutral heavy lepton, the missing momentum vector was calculated
and subsequently assumed to be the reconstructed neutrino momentum. The
background processes were simulated using existing parameter options in PYTHIA.
\s

\nn In the case of the charged lepton $E$, the signal consists of an \ee\ pair
and two jets. Other processes likely to produce such a configuration are:
(i) $ e^+ e^- \to e^+ e^- Z$, with the $Z$ decaying hadronically; the cross
section is 3800 fb;
(ii)  $ e^+ e^- \to Z Z$, with a cross section of 615 fb;
(iii) $ e^+ e^- \to t \bar{t} $, followed by  $ t \to b W$ and leading to two
electrons and 2 jets but with missing momentum; and
(iv) $ \gamma \gamma \to e^+ e^- q \bar{q} $  which has a large cross section
but the jets have small invariant masses and the resulting  events have the
primary electrons going mostly along the beam pipe.
In the case of the neutral lepton $N$, the signal consists of an electron, a
pair of jets and missing momentum. The backgrounds that one has to consider
are:
(i) $ \ee\  \to e \nu W$ with a cross section of 5800 fb when the $W$ decays
hadronically;
 (ii) $ \ee\ \to WW$ where one of the $W$'s decays hadronically and the
other to an $e \nu$ pair and the cross section in this case is 1140 fb;
(iii) $ \gamma \gamma \to e (e)  q \bar{q} $ where one of the electrons
escapes observation. \s

\nn The analysis proceeded by selecting among all ``reconstructed'' final state
particles the $e^-, e^+$ with a momentum greater than 30 GeV. The following
cuts were found to suppress considerably the background processes without
affecting significantly the signals. \s

\nn For the charged lepton: (1) One and only one \ee\ pair. (2) $ 85 < M_{jj}
< 105 $ GeV where the lower bound on the reconstructed $Z$ mass was set
intentionally high so as to avoid a possibility of confusing a $Z$ with a $W$.
(3) $|p_{l^+}| > (E_{\rm beam}-M_E^2/4E_{\rm beam})-40$ GeV and $|p_{l^-}| >
\frac{2}{3} M_E -133$ GeV, with $M_E$ the reconstructed mass; these kinematic
constraints ensure energy-momentum conservation, with some tolerance for
detector resolution effects. (4) A cut $|M_{ll} - M_Z| > 12$ GeV which is
effective against the $ZZ$ background. (5) Cuts $\cos\theta_Z > -(M_E+440)/720$
and $\cos\theta_Z < (2100-M_E)/2000$, which are necessary to reduce the
background from $ e^+ e^- \to e^+ e^- Z$. (6) $\cos\theta_{ll} < 0.5$ since in
the signal, the
two leptons are mostly back--to--back. Cuts (3) and (5) apply to $E^-$, similar
ones apply for $E^+$. \s

\nn In the case of neutral leptons, similar cuts where applied: (1) One and
only one $e^-$. (2) $ 70 < M_{jj} < 90 $ GeV for the reconstructed $W$ mass.
(3) $|p_{\nu} | > (E_{\rm beam} -M_N^2/4E_{\rm beam})-40$ and $|p_{l}| >
\frac{2}{3} M_N - 133$. (4) A cut $ M_{ll} > 120$ GeV, effective against the
$WW$ background. (5) $\cos\theta_W < 2.58-M_N/240$ reduces the background from
$ e^+ e^- \to e^- \bar{\nu} W$. (6) $\cos\theta_{l\nu} < 0.5$; here also the
two leptons from the signal are mostly back--to--back. \\

\nn {\bf 4. Results and Discussions} \\

\vspace*{-2mm}

\nn Fig.~1 shows the reconstructed invariant mass histograms for heavy leptons
with masses of 250, 350 and 450 GeV and with mixing angles $\theta_{\rm mix}
=0.05$ in the case of the charged lepton and $\theta_{\rm mix} = 0.025$ for
the heavy neutrino. For these values, one can see that the signal peaks stand
out clearly from the background events, especially for heavy lepton masses not
too close to the total c.m. energy of the collider. For the $\gamma \gamma$ and
$t \bar{t}$ backgrounds, no events survived [in the former case, because it was
not possible to generate a sufficient number of events, only an upper limit of
$< 15$ surviving background events/5 GeV can be given]. The backgrounds from
vector boson pair production have been suppressed to a very low level; the
backgrounds from single $W$ and $Z$ production are relatively higher. \s

\nn For smaller mixing angles, the signal cross sections have to be scaled down
correspondingly. For lepton masses of the order of 450 GeV, only slightly
smaller $\theta_{\rm mix}$ values can be probed, while for masses around 350
GeV one can go down by at least a factor of two. The situation is much more
favorable for heavy neutrinos than for charged leptons, the cross section
being one order of magnitude larger. For instance, assuming a mass of 350 GeV
and requiring that the ratio of the signal events to the square root of the
background events be larger than unity, one can probe mixing angles down to
$\theta_{\rm mix} \sim 0.005$ for neutral leptons and $\theta_{\rm mix} \sim
0.03=2$ for charged leptons. \s

\nn In conclusion. Because the cross sections are large and the environment in
\ee\ colliders is very clean, pair produced new leptons can be unambiguously
detected up to masses close to the beam energy. For new leptons of the first
generation, one can reach masses close to the total center of mass energy of
the machine in the process of single production in association with ordinary
electrons and neutrinos, provided that the mixing angles are not prohibitively
tiny. \\

\nn {\bf Acknowledgment:} One of us (A.D.) would like to thank the organizers
of this workshop for creating a nice and very stimulating atmosphere. \\

\nn {\bf References}. \\

\vspace*{-2mm}

\nn [1] See e.g. the talks given by J. Hewett and E. Nardi, these proceedings.
\s

\nn [2] See A.~Djouadi, D.~Schaile and C. Verzegnassi [conv.] et al., Report
of the Working \\ \hspace*{5mm} Group ``Extended Gauge Models", Proceedings of
the Workshop ``\ee\ Collisions \\ \hspace*{5mm} at 500 GeV: The Physics
Potential", Report DESY 92-123B, P.~Zerwas, ed. \s

\nn [3] For details and for a complete set of references, see A.~Djouadi, Prep.
UdeM--LPN--TH \\ \hspace*{5mm} --93--157, and G.~Azuelos and A. Djouadi, Prep.
UdeM--LPN--TH--93--158. \s

\nn [4] See e.g. the talk given by B. Wiik, these proceedings. \s

\nn [5] T. Sj\"ostrand, PYTHIA 5.6 and JETSET 7.3, Report CERN-TH.6488/92. \s

\nn [6] P. Grosse-Wiesmann, D. Haidt and J. Schreiber, in the same proceedings
as in Ref.~[2].

\end {document}

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 1898 1718 m 1898 1684 l s
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 /xs 0 def
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l
 1278 91 l 1275 91 l s 1282 126 m 1282 97 l 1280 92 l 1277 90 l 1274 90 l s
1284
 128 m 1284 99 l 1283 94 l 1279 92 l 1276 92 l s 1299 139 m 1300 138 l 1302 139
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127
 m 1300 98 l 1299 93 l 1295 91 l 1292 91 l s 1299 126 m 1299 97 l 1298 92 l
1294
 90 l 1291 90 l s 1301 128 m 1301 99 l 1300 94 l 1296 92 l 1293 92 l s 1312 146
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 143 l 1764 138 l 1761 131 l 1759 122 l 1759 115 l 1761 107 l 1764 100 l 1767
95
 l 1771 91 l s 1770 145 m 1766 142 l 1763 136 l 1760 130 l 1758 121 l 1758 114
l
 1760 106 l 1763 99 l 1766 94 l 1770 90 l s 1772 147 m 1769 144 l 1765 139 l
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l
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133
 915 l s 149 892 m 149 905 l s 148 891 m 148 904 l s 151 893 m 151 906 l s 168
 892 m 168 914 l s 167 891 m 167 913 l s 169 893 m 169 915 l s 144 921 m 168
931
 l s 143 920 m 167 930 l s 145 922 m 169 932 l s 144 941 m 168 931 l s 143 940
m
 167 930 l s 145 942 m 169 932 l s 155 950 m 155 970 l 151 970 l 148 969 l 146
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167
 955 l 168 958 l 168 964 l 167 967 l 163 970 l s 154 949 m 154 969 l 150 969 l
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l
 162 950 l 166 954 l 167 957 l 167 962 l 166 966 l 162 969 l s 156 951 m 156
971
 l 152 971 l 149 970 l 147 968 l 145 965 l 145 959 l 147 956 l 151 953 l 156
951
 l 159 951 l 164 953 l 168 956 l 169 959 l 169 965 l 168 968 l 164 971 l s 144
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987
 l 144 991 l 144 996 l 146 999 l 151 1001 l 168 1001 l s 150 981 m 145 986 l
143
 990 l 143 995 l 145 998 l 150 1000 l 167 1000 l s 152 983 m 147 989 l 145 992
l
 145 997 l 147 1001 l 152 1002 l 169 1002 l s 132 1017 m 161 1017 l 167 1018 l
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cl
 s 131 1330 m 133 1325 l 138 1322 l 147 1320 l 152 1320 l 160 1322 l 166 1325 l
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1322
 l 154 1322 l 163 1324 l 168 1327 l 169 1332 l 169 1336 l 168 1341 l 163 1344 l
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1384
 m 132 1381 l 134 1378 l 139 1376 l 168 1376 l s 131 1383 m 131 1380 l 133 1377
 l 138 1375 l 167 1375 l s 133 1386 m 133 1382 l 135 1379 l 140 1377 l 169 1377
 l s 144 1371 m 144 1383 l s 143 1370 m 143 1382 l s 145 1372 m 145 1384 l s
132
 1395 m 168 1395 l s 131 1394 m 167 1394 l s 133 1396 m 169 1396 l s 149 1395 m
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 128 1449 m 127 1451 l 124 1453 l 142 1453 l s [4 8] 0 sd 3 lw 326 225 m 326
426
 l 352 426 l 352 561 l 378 561 l 404 561 l 430 561 l 430 493 l 457 493 l 457
594
 l 483 594 l 483 695 l 509 695 l 535 695 l 535 729 l 561 729 l 561 561 l 588
561
 l 588 493 l 614 493 l 614 359 l 640 359 l 640 460 l 666 460 l 666 561 l 692
561
 l 692 493 l 719 493 l 719 359 l 745 359 l 745 493 l 771 493 l 771 393 l 797
393
 l 797 493 l 823 493 l 823 661 l 850 661 l 850 393 l 876 393 l 902 393 l 902
325
 l 928 325 l 928 628 l 954 628 l 954 460 l 981 460 l 981 359 l 1007 359 l 1007
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797
 2770 l 796 2772 l 792 2773 l 787 2773 l 784 2772 l 781 2769 l 779 2764 l 779
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1031
 2750 l s 1033 2786 m 1033 2752 l s 1032 2785 m 1053 2785 l s 1031 2784 m 1052
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 l 1084 2772 l 1081 2771 l 1078 2768 l 1076 2763 l 1076 2760 l 1078 2755 l 1081
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 l 1097 2768 l 1096 2771 l 1094 2773 l 1091 2774 l 1086 2774 l 1083 2773 l 1080
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s
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 cl s 1062 2592 m 1063 2591 l 1064 2592 l 1063 2593 l 1062 2592 l cl s 1062
2585
 m 1062 2574 l s 1061 2584 m 1061 2573 l s 1063 2586 m 1063 2575 l s 1067 2585
m
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l
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l
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1324
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m
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cl
 s 1192 1125 m 1190 1123 l 1192 1122 l 1193 1123 l 1192 1125 l cl s 1194 1127 m
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 cl s 1216 1158 m 1211 1156 l 1208 1151 l 1206 1143 l 1206 1138 l 1208 1130 l
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 1143 l 1227 1151 l 1224 1156 l 1219 1158 l 1216 1158 l cl s 1239 1149 m 1239
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 1148 m 1238 1149 l 1240 1152 l 1241 1154 l 1244 1156 l 1251 1156 l 1254 1154 l
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 1145 l 1279 1146 l 1283 1146 l 1288 1145 l 1291 1142 l 1293 1137 l 1293 1133 l
 1291 1129 l 1288 1125 l 1283 1124 l 1279 1124 l 1274 1125 l 1272 1127 l 1271
 1130 l s [12 12] 0 sd 3 lw 1224 1011 m 1448 1011 l s [] 0 sd 1 lw 1508 1044 m
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 1516 1011 l s 1523 1043 m 1515 1010 l s 1525 1045 m 1517 1012 l s 1524 1044 m
 1532 1011 l s 1523 1043 m 1531 1010 l s 1525 1045 m 1533 1012 l s 1540 1044 m
 1532 1011 l s 1539 1043 m 1531 1010 l s 1541 1045 m 1533 1012 l s 1562 1044 m
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 1586 1011 l s 1577 1043 m 1585 1010 l s 1579 1045 m 1587 1012 l s 1594 1044 m
 1586 1011 l s 1593 1043 m 1585 1010 l s 1595 1045 m 1587 1012 l s [4 8] 0 sd 3
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