UTPT-94-26





New strong sector, odd-parity processes,
and the Tevatron



B. H 1
OLDOM


Department of Physics
University of Toronto
Toronto, Ontario
CANADA M5S 1A7





 1 Nov 1994 ABSTRACT


The color-octet isosinglet "rho" of a new strong- interaction sector is
readily produced in pp collisions. Its odd-parity decay to an "eta" and a
gluon may exceed its decay rate to dijets. At center of mass energies
sufficiently greater than the colored "rho" mass, the odd-parity
production of ("omega" + colored "eta") or ("rho" + colored "pion")
may be comparable to tt production. Considering that the "omega" has
a dominant odd-parity decay mode, we end up with (Z, W, or ) + 4 jet
events with two of the jets containing b or b .




1 holdom@utcc.utoronto.ca


In this paper we will consider the existence of a new strongly interacting sector
characterized by a mass scale on the order of 200-400 GeV. New physics in this mass
range is accessible to the Tevatron, and we would like to explore the relevant signatures.
Such a sector of new physics may be associated with the generation of quark and lepton
masses. The scale of this physics is somewhat below that required for electroweak
symmetry breaking, but it is well known that a new strong gauge sector at 1 TeV
(technicolor) is not by itself sufficient for generating quark and lepton masses. Additional
dynamics is required, and it may exist on scales greater than 1 TeV (extended technicolor)
and/or less than 1 TeV. Recent examples of the latter possibility are found in [1][2][3].
In particular, the phenomenological implications of "multiscale-technicolor" models have
been studied in some detail [4].
The low-lying sector is distinguished from a conventional technicolor sector by its
relative lack of participation in electroweak symmetry breaking. To emphasize this we will
use the prefix "meta" rather than "techni".2 The important point is that the strong
production of metacolor resonances does not imply the strong production of the
longitudinal components of the W and the Z. In a multiscale technicolor model (here
metacolor is technicolor) the light sector fields have small overlap with the Goldstone boson
fields. Decays into longitudinal components of the W and Z are suppressed by powers of
F1/F2, where F1 and F2 are the technipion decay constants of the light and heavy sector
respectively [1]. In [3] the gauge interaction involved in electroweak symmetry breaking
itself breaks at 1 TeV, and the unbroken subgroup is metacolor. Here the metacolor
sector does not participate in electroweak symmetry breaking at all, and the Goldstone
bosons due to electroweak breaking would couple to metafermions only through loops
involving heavy fields. This would yield even weaker couplings of Goldstone bosons to
metacolor resonances.
A requirement for our study is that the metafermions include at least one doublet
which carries the same SU(3)CSU(2)LU(1) quantum numbers as a doublet of quarks.
We shall consider the mesonic resonances composed of these colored fermions, and we
initially assume isospin symmetry in their description. The main difference between the
spectrum of states in this sector and the QCD mass spectrum is that the ground-state
pseudoscalar states may be relatively heavier (but still lighter than the vector mesons). M
and PM will denote the vector and pseudoscalar states, with a prime added for isosinglet
states and a subscript "8" added for color octet states.
Also, we will be interested in processes in pp collisions with high partonic center-of-
mass energy, such that at Tevatron energies the dominant production source will be qq
annihilation and not gg fusion. This is the situation for tt production.
Consider first the color-octet, isosinglet metarho, 0
M8 . This is the resonance
produced most copiously in pp collisions, since it is produced in qq annihilations via a



2 We use the term metacolor in a more general sense than in [3].
1


virtual gluon. 0
M8 decays strongly to two colored metapions, if allowed, which in turn
would most often produce 4 jets. If the 0
M8 mass is below twice the lightest colored
metapion mass then the standard expectation is that its width is dominated by decay into
two jets via gg or qq . But consider the "odd-parity" decay 0 0 0
M8 ( PM g or PM8 g) where
P 0 0
M ( PM8) is the color-singlet (color-octet) metaeta. This width can be estimated by scaling
up ( 0 ), while the competing width to gg or qq can be estimated by scaling up
( e+e-). We find, ignoring the phase space suppression factor,

( 0 0 0
M 8 PM g or PM8 g ) 1 + 5/2 9( 0 )
8.9 . (1)
( 0M 8 q q or g g ) 5/2 + 3/2 s ( e + e -)

The 5/2 in the numerator is the color factor for the P 0
M8 g mode, the 5/2+3/2 includes
flavor and color factors for the qq and gg modes, the 9 compensates for the isosinglet
photon coupling,3 and we use s = 0.1 for the value of the QCD coupling at the scale of
the 0
M8 mass. The leading dependence on the unknown number of metacolors will cancel
in the ratio.
Thus we find that the 0 0 0
M8decay into PM g or PM8 g can easily compete with the
modes which produce dijets.4 If P 0 0
M and PM8 are below the tt threshold then their
dominant decays is to two gluons, and the result is a source of 3-jet events with total
invariant mass peaked at the 0 0 0
M8 mass. Of course if the PM and PM8 masses are too large
then the resulting phase space suppression can imply that the 2-jet modes will dominate.
The conclusion is that the production of the 0
M8will yield 2, 3, and/or 4 jet events with a
relative frequency determined by the mass spectrum. These are interesting signals, but
they must compete against a large QCD background.
[The other case, when the P 0 0
M and/or PM8 is above the tt threshold, may be an
interesting top quark production mechanism. This is similar to the tt production
mechanism in [5] which also involves an intermediate P 0
M8 . One difference is that the
mechanism in [5] relies on gg fusion, while the mechanism here can proceed via qq
annihilations. We will consider these issues in more detail elsewhere [6].]
Do signatures more striking than multijet production occur? One such signal is Z,
W, or production in association with four jets, with some jets containing a b or b . We
will find new physics contributions to this signal when we consider the production of
metacolor resonances for center of mass energies greater than the 0
M8 mass. To get some
idea of what to expect we turn to the low energy data for e+e- collisions, as shown in Fig.
1. (This figure is extracted from Ref. [7]). At s 1.1 GeV 1.4m, the production of 3
or more pions starts to exceed the production of 2 pions. At this s the ratio

[e +e - (3 pions)]
R 1 (2)
[e +e -  + -)]


3 We could have used (0) in place of 9(0), but then there is a complication with - mixing.
4 We have reached a conclusion different from the one appearing in a footnote in [4].
2


is roughly 1/2.

Figure 1: R [e+e- hadrons]/[e+e- +-]

4


R

2




0 1 2
s (GeV)

R1 rises rapidly until it peaks at s 1.6 GeV, at which point it exceeds 2. The main
source of data [8] between these two scales includes 4 but not 3 production, thus
providing only a lower bound on R1. In this region and even higher, the production of
multipion states is dominated by quasi-two-body processes [9].

e+e- m1 +m2 n (3)

The dominant contribution to the 4 data occurs via + , as evidenced by the rapid
increase in 4 production occurring at the + threshold [8][9]. The production of +
is well modeled by vector meson dominance via an intermediate off-shell 0, which
involves the odd-parity coupling g [10].
In the metacolor case we may assume a similar occurrence; we may have the cross
section for q q g (0 0 ,0 ,0
M P M8 or M PM8 ) starting to compete with the cross section for
the production of a pair of colored metapions for sufficiently large partonic c.m. energy
s . The required s is probably higher than 1.4 m( 0
M8) since the pseudoscalars here are
relatively heavier. q q 0 0
MPM8 is the exact analog of e+e- with isospin space
exchanged for color space, and thus we consider

qq 0 P 0
R M M8 (4)
2 [qq bb]

in lowest order QCD. The cross section for any one of the three other final states ,0 ,0
M PM8




3


should be similar, and all these processes could again be modeled by vector meson
dominance via an intermediate off-shell 0
M8 . If we take R1 defined in (2) to be dominated
by the production of + , and if we take the s in R1 and the s in R2 to be above the
respective thresholds by the equivalent amounts, then we estimate

R 2 6N
R M . (5)
1 5

This accounts for various charge, color and flavor factors, and NM is the number of
metacolors. There are of course other modes where the final meta-vector-meson is colored
instead of the meta-pseudoscalar, and other modes where both metamesons are colored.
If the meta-vector-meson is colored then its dominant decays are such that the result is a
multijet event.
We now consider the ratio of physically relevant quantities


pp 0 0
M PM8 , (6)
[pp tt]

where each cross section involves an integral over s . Remembering that qq is the
dominant production source at Tevatron energies, we may thus deduce from (5) that this
ratio is of order unity if the 0 0
M + PM8 threshold is in the 400 GeV range, i.e. not too
much higher than the tt threshold.
Perhaps most interesting is that we have a mechanism for the production of the
color-singlet, isosinglet metaomega 0
M . We will assume that the metaomega is below
threshold for decay to three metapions. The odd-parity decays involving longitudinal W's
and Z's, 0 + -
M ( WL WL ZL , Z L , ZLZ , WLW) were considered in [11] for conventional
technicolor, but here these modes are suppressed. Instead, the odd-parity decay involving
the color-singlet metapion PM rather than the Goldstone boson is likely the dominant
mode. We therefore have the processes


0

qq g 0M + PM8
| 0 (7)
P + (Z or )
M
|

PM + W

which involve the vector coupling of the (transverse) W and Z.
In the first branch, the P 0 0
M8 and PM decay predominantly to gg and bb
respectively.5 This provides us with a source of (Z or ) + 4-jet events, with two of the
jets originating in a b or b . The second branch produces W + 4-jet events, but the
nature of these events will depend on the mass of the P +
M . If high enough it decays to t b ,
and if not the c s mode should dominate. The ratio of the : Z : W rates is, ignoring


5 The P 0
M8 may also have a nontrivial branching ratio to bb .

4


phase space suppression, 1 : (1 - 2 s2) 2/(2cs)2 : 2/(2cs)2 = 1 : 0.4 : 2.8 where s sinW.
If m (P 0
M) approaches m (M) - mZ , the photon mode can come to dominate. We note
that there is no resonance peak in the total invariant mass of these events, but there will
be resonant peaks in various of the other invariant mass combinations.
As noted above we also have the production of the color- singlet, isotriplet metarho
0,
M . The metarho will decay predominantly into 2 PM if allowed. More interesting [1] is
when it is below this threshold, in which case it can decay into PM + WL (or ZL in the case
of 
M ). But here again, decays involving longitudinal W or Z are suppressed in some
model dependent manner. Two other processes are then worth checking. One is the
decay into PM plus a transverse W or Z. The transverse component can substitute for
the longitudinal component because of the axial couplings of the W and Z, and this will
give a lower bound on the total production of PM + (Z or W). We compare this to the
2PM mode, ignoring for the moment the PM mass, and estimate

( 2
M PMWT ) 12 f
0.017 . (8)
( 2
M PMPM) s 2m

Another mode for the 0
M is the odd-parity decay. But here we find

( 0 0
M PM ) 9( 0 )
0.007 . (9)
(M PMPM) ( )

We therefore expect that regardless of the suppression of decay modes involving
longitudinal W's or Z's, the dominant process involving the metarho 0,
M is the following.

q
q g M + PM8
|
PM + (W or Z) (10)

In the W mode one of PM or PM8 is neutral and the other is charged (both are isotriplet).
The nature of these events again depends on whether the charged metapion is above the tb
threshold. In any case the W + 4-jet events have at least two of the four jets as b-jets
from the decay (P 0 0
M or PM8 ) bb . This produces a signal which is similar in most respects
to the W + 4-jet events with b-tags used as a signature of tt production at the Tevatron.
In the Z mode both P 
M and PM8 are charged. If PM8 is below the tb threshold then the
result is Z + 4-jets with none of the jets having b's, unlike (7). If P 
M8 is above the tb
threshold then we have Z + ( 4 jets) with b-tags. The ratio of the W : Z rates is 2 : 1,
and the total rate for the sum of modes in (10) is approximately 3 times that in (7).
Our analysis has relied on isospin symmetry in the new sector. An example of how
this may occur concurrently with a large top mass is described in [3]. If there is
substantial explicit isospin breaking then our results would change. In particular the 0
M
and 0
M states could mix such that the mass eigenstates become UU and DD .[4] Both of



5


these states would have decays resembling those of the 0
M , and our source of + 4-jet
events with b-tags would be lost.
In summary we have described how a new strong sector below the electroweak
symmetry breaking scale can give rise to (W, Z, or ) plus 4-jet events with b-tags in pp
collisions at a rate similar to tt production. Such events could occur with a total invariant
mass in the 400-600 GeV range, of interest to the Tevatron. The various metamesons
appearing in these processes are relatively narrow and should provide clear invariant mass
resonant peaks. We encourage in particular a search for single photon plus multijet
events to complement the study of W or Z plus multijet events.



Acknowledgements
I thank M. Bando for a collaboration which led into this work, and I thank M.V.
Ramana for his comments and his interest. I also thank P. Sinervo for correspondence
and J. Terning and G. Triantaphyllou for discussions. This work was supported in part
by the Natural Sciences and Engineering Research Council of Canada.





6


References

[1] K. Lane and E. Eichten Phys. Lett. B222 (1989) 274.


[2] S. F. King, Phys. Lett. B314 (1993) 364.


[3] B. Holdom, Phys. Lett. B314 (1993) 89, University of Toronto preprints UTPT-
94-18, hep-ph/940744 and UTPT-94-20,  both to appear in
Physics Letters B.


[4] K. Lane and M.V. Ramana, Phys. Rev. D44 (1991) 2678.


[5] E. Eichten and K. Lane, Phys. Lett. B327 (1994) 129.


[6] B. Holdom and M.V. Ramana, work in progress.


[7] A. C. Mattingly and P. M. Stevenson, Rice University preprint DE-FG05-
92ER40717-7,  (1993).


[8] V. A. Sidorov, in: Proc. of the XVIIIth Intern. Conf. on High energy physics
(Tbilisi, 1976).


[9] J. P. Perez-Y-Jorba and F. M. Renard, Physics Reports, 31 (1977) 1.


[10] F.M. Renard, Nuovo Cimento, 64A, 1969, 979.


[11] R.S. Chivukula and M. Golden, Phys. Rev. D41 (1990) 2795.





7



