ELSEVIER

14 September 1995

Physics Letters B 351(1995) 624-629

PHYSICS LETTERS B

Color-singlet technipions at the Tevatron Kenneth Lane ’

Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA

Received 23 July 1995 Editor: H. Georgi

Abstract

I discuss production and detection at the Tevatron pp collider of pairs of light (M, = lOO-200GeV) color-singlet technipions that are expected in all nonminimal models of technicolor. Gluon fusion production rates can be as large as 0 ( 1 pb) . Topcolor-assisted technicolor is required to prevent top quarks from decaying as t -+ ?r: b. An intriguing

consequence of this is that the decays rr: + r+v,, CS and a-! -+ b6 may also be suppressed so that a-: -+ W+y and r$ -+ yy are significant. These modes have spectactular signatures at the Tevatron.

The focus of dynamical electroweak symmetry breaking has sharpened lately. The emerging picture is based on topcolor-assisted technicolor [ 1,2]. In this picture, technicolor dynamics are largely responsible for electroweak symmetry breaking [3]. Extended technicolor interactions (ETC) still give rise to the hard masses of quarks and leptons [ 41. The unbro- ken technicolor interaction still must have a slowly running coupling in order that fermion masses in the GeV range are produced while large flavor-changing neutral current interactions are suppressed [ 561. However, it has been very difficult to generate a top quark mass as large as that measured in the Tevatron collider experiments [7], even with “strong” ex- tended technicolor [ 81. Thus, “topcolor” interactions for the third generation quarks seem to be required at an energy scale of about 1 TeV [ 9,10,1]. As noted in Ref. [ 21, the main challenge facing topcolor-assisted technicolor (TC2) is to provide a mechanism that generates large enough mixing between the quarks of the third generation and those of the first two.

’ E-mail address: lane@buphyc.bu.edu.

Elsevier Science B.V. SSDI 0370-2693(95)00960-4

The outline of this picture is sufficiently clear that it is worthwhile to begin thinking about its phenomenol- ogy. In this Letter, I point out that nonminimal models may have charged and neutral color-singlet pseudo- Goldstone bosons - technipions, rTf and QT$, light enough to be pair-produced at the Tevatron jjp col-

lider and that, in TC2 models, these technipions may have unconventional decay modes that make their de- tection easier. Until now, hadroproduction studies of these technipions have concentrated on single pro- duction of weak-isosinglet IT$’ through gluon fusion and production of isovector pairs, ?TT+rF and ;r,f@, via Drell-Yan processes [ 111. Single-production of z-p is invisible above backgrounds since the decay modes $’ -+ b6 and (independent of model) gg are dominant. The Drell-Yan rate for W~V? is model- independent and ranges from 30fb down to 1 fb for M, = 100-200 GeV. However, if there are colored techniquarks, we shall see that color-singlet technipi- ons are pair-produced via gluon fusion with rates that can be much larger than Drell-Yan. At the Tevatron, a(Pp --f QTTTT) N 1 fb-1 pb, depending on details of

K. Lane/ Physics Letters B 357 (1995) 624-629 625

the underlying model. The upper end of this range is well within the Tevatron’s reach.

In standard technicolor models, z-g lighter than about 150 GeV would be ruled out because the decay t -+ n-gb would dominate. However, the t + s-; b coupling is proportional to the ETC-generated por- tion of the top (and/or bottom) quark’s mass and, in TC2 models, this is at most a few GeV. Thus, there is no danger of a large branching ratio for this mode. 2

Likewise, constraints on technipions from the pro- cess b -+ sy are much less stringent in TC2 models [ 121. Normally, fermionic final states would be ex- pected to dominate VT decays. However, because third-generation fermion masses (including, possi- bly, the r-lepton) are generated only in part by ETC interactions, this naive expectation for the decays of a r/rT lighter than the top quark may be wrong. An especially interesting possibility is that the anoma- lous modes 7~: + W*Y and S-F + YY (but not Z”Y for the isovector r$) are significant [ 131. This can lead to striking signatures in j?p collisions, especially

e+!-YY + $T and YYYY. In the remainder of this Letter, I discuss gluon-

fusion of rrmr, estimate the production rates in two types of model, and discuss the possibilities for %-r decays. The scenarios considered are (1) the one- family model [ 14,l l] and (2) a multiscale model [ 15,161. Bear in mind that these models have not yet been discussed in the context of topcolor. In partic- ular, the technifermions in these models do not yet carry topcolor, as they must [ 1,2]. This will alter the technifermion-content factors in the technipion states in Eqs. (3) and (6) below and these, in turn, affect the production and anomalous decay rates. Therefore, our estimates of these should be understood to be rep- resentative of TC2 models.

There are two complementary mechanisms for gluon fusion of ?rr pairs: techniquark loops and col- ored technipion loops. 3 The perturbative techniquark loop calculation ought to be reliable when the typical momentum flowing through the loop is large com- pared to the techniquark mass (and large enough

2 Throughout this paper, I assume that there is no significant mix-

ing between ~-f and the top-pion rt associated with spontaneous breaking of f, b chiial symmetries.

3 This is implicit in Ref. [ 171, where gg + Z”Zo is calculated.

Also see Ref. [ 181.

Table 1

The factors CR and DR in Q. (1) for gg -+ 7r~r~ for the one-

family and multiscale technicolor models.

Model C3 c8 03 D8

to be in the asymptotically-free regime of the walk- ing technicolor model). However, this regime is far above the rrrr threshold region where the largest

production rates are expected. The other extreme is the chiral limit in which the

gg -+ rrrr amplitude is dominated by loops involv- ing massless colored technipions. Indeed, these mass- less particles produce a singularity that promotes the amplitude from one involving gradiently-coupled ex- ternal rrrr to one of effectively scalar-coupled ~TITT [ 191. As the mass of the internal technipions is in- creased, they start to decouple - as do heavy internal techniquarks. Consequently, the technipion loop cal- culation should provide a reasonable approximation to the amplitude in the threshold region, even in the case of broken chiral symmetry.

The amplitude for gluon fusion of longitudinal Z bosons, gg + .Z~.Z~, with massive intermediate color-triplet and octet technipions, has been calculated in Ref. [ 201. Modifying the group-theoretic factors there for the case of interest to us, the amplitude for both rgrr? and &r$! final states is given by

Mka(ql)gdq2) + STAT) = $& T

x @(a)E’(qZ) ( q2pcLq1v - 41 * 42&w a&

41 .42 >

x CT(R) [G(s-~(M2,+M~T))+DR] I R=3,8

x (1+2z(M2,,s)) . 1

Here, FT is the technipion decay constant; s = (41 +

q2)2; T(R) = 3 for R = 3 and 3 for R = 8; the factors CR and DR are listed in Table 1 for the one-family and multiscale models; and

626 K. Lane /Physics Letters B 357 (1995) 624-629

1

Z(kP,s) EE J

dxdy M2

xys-M2+k e(1 -x-y)

0

-M2/2s [n- - 2 arctan dq 2 for s < 4M2

= M2/2s In [ (m) -in-l2

(2)

s for s > 4M2.

The one-family technicolor model [ 141 con- tains one doublet each of color-triplet techniquarks

QL,R = (U, D) L,R and color-singlet technileptons

LL,R = (N, E) L,R. These have the same electroweak charge assignments as a quark-lepton generation. 4 All technifermions transform according to the same complex irreducible representation of the technicolor gauge group SU( Nrc) . To ensure that the technicolor gauge coupling “walks”, this representation may need to be larger than the fundamental.

The technipions of interest to us in the one-family technicolor model are (the color index cr = 1,2,3 is summed over) :

IWL’) = $J,B, + NE),

IZ,) = #v,v, - D,D, + NN - EE) ,

In-;) = &lU,o, - 3N@,

In-;) = -@I& - D,& - 3(Nb? - El?)).

(3)

The decay constant of these technipions is FT =

120GeV (assuming that for the topcolor pions Ft =

50 GeV; see [ 11) . The r; and r! masses arise mainly from ETC interactions. In the one-family model, the ETC masses of technifermions are comparable to those of the lighter quarks and leptons. Thus, follow- ing the M, calculations in Refs. [ 151 and [ 161,

M& = %(FT) N 87iVI~F~ 5 (125 GeV)2 FT2

(4)

for a technifermion hard mass mr 5 5 GeV. Technip- ion masses in the range 100-200 GeV are considered in this paper. Note that color-triplet and octet technip- ions receive a further contribution to their mass from

4 I as.wme throughout that isospin breaking in the technifermion

sector may be neglected.

QCD interactions and will be heavier. Typical octet and triplet states are (a = 1,. . . ,8)

I++) = &&3 IQ&?),

I$‘> = &4dap I&& -Da&), \7&) = pJT>. (5)

Multiscale technicolor was invented [ 151 as a way to implement a walking technicolor gauge cou- pling [ 51. The model considered here is a simplified version of the one studied in Ref. [ 161. One doublet of color-singlet technifermions, r,&, belonging to a higher dimensional representation of SU( NTC) is re- sponsible for most of electroweak symmetry breaking. The decay constant of the $$ technipions typically is F$ = 220-235 GeV (allowing for Fl N 5OGeV). I assume here that the light-scale technifermions consist of one doublet each of techniquarks Q and technileptons L, transforming according to the funda- mental representation of SU( NTC) . These condense at a much lower energy with typical technipion de- cay constants FT 3 FQ N FL = 30-50GeV. The color-singlet isovector technipions in this model are’

I&‘“) = C YiFI~~~) (i=qQ,L). (6)

F=$,Q,L

Here, e.g., I+$‘) = I W,“,“) and the mixing factors for these states are yw* = F$/Fv 2 0.9, yWQ =

&Fe/F,, and yw.~, = FL/F,, where F, = 246GeV. As discussed in [ 161, the diagonal mixing factors YQQ 2: YLL 2 0.9 and off-diagonal ones are small. In other words, the technipions are nearly ideally-mixed. This will simplify the discussion below of their pro- duction and decays. The colored technipions are still given by Eq. (5). In the multiscale model, Q and L get their ETC mass from the heavy 1c, while 4, ! get theirs from Q, L. Then, the current masses of Q, L will be much larger than 5 GeV and, despite the smaller QQ and EL condensates, M, can easily be in the range 100-200 GeV.

The total cross sections for pp --+ mgrr in the one- family and multiscale models (using the factors CR and DR in Table 1) are shown in Fig. 1. For the multi- scale model, FQ = FL = 40 GeV was used. The colored technipion masses were taken to be Ms = 200GeV and Ms = 250GeV. The EHLQ Set 1 parton distri-

K. Lane/ Physics Letters B 357 (1995) 624-629 627

o.8 e 0.6 b--l 1

2 0.4

b ---------- I : ------ -..--...-- --._

--.._____ ‘.

-. 0.2 -.-..._____ . ---.._._

..-...____

-.-....._

0.0 ~ 100 120 140 160 180 200

Mn(GeV)

Fig. 1. The pp + T;T, production rates at fi = 1.8 TeV as a

function of MWr. The curves are n-&g& (solid) and ?rlLpiL

(dashed) for the multiscale model; z-grr; times 100 (dotted) for

the one-family model.

bution functions [ 111 were used and the lowest or-

der cross sections multiplied by 1.5 as an estimate of radiative corrections to the gluon fusion process. For equal mass @ and ?rg, production rates for &i-F are half as large as those shown in Fig. 1.

At the Tevatron, the production rates for the techni- pions of the one-family model are only a few femto- barns and it is unlikely that they will ever be observable there, even with high-luminosity upgrades. I believe that this sets the lower bound on rrrr production by gluon fusion. On the other hand, rates for the multi- scale technipions with the parameters used here range from 0.2 to 0.7pb. Depending on VT decay modes, these could be large enough to observe with data from the current run. 5 It is important to remember that pro- duction rates vary as FF4 and increase fairly rapidly

with decreasing Ms and Ms. For example, lowering Ms to 175 GeV and Ms to 200 GeV increases the rates by a factor of 2-3, depending on M,.

An interesting feature of gg + vrrr is shown in Fig. 2 where the invariant mass distribution dc/dM is plotted for M, = 110 GeV and the cases Ms = Ms = 0 and Ms = 200, Ms = 250GeV. The distribution in the case of massless colored technipions is typical of most pair-production processes in hadron colliders: it peaks a few 10s of GeV above threshold and then falls

5 The integrated luminosity accumulated by the CDF and D0

detectors at the end of Tevatron collider run 1 should be near

125 pb-‘.

-. I

10-Z /

;_

‘, \ ‘\

\ 1 \ T

\ \

P 10-Z \ s \ \ \ 3 P

10-4 II \ \ \ \ \

‘\ \

\

‘\

10-S ““I’$ ““““““““‘I”” 200 300 400 500 600 700 BOO

M (GeV)

Fig. 2. The ?r&?r& invariant mass distribution for MWr =

1OOGeV in pp collisions at fi = 1.8TeV. The solid curve is

determined with intermediate colored technipion masses Ms =

200 GeV and Ms = 250 GeV; the dashed curve uses M3 = Ms = 0.

off rapidly. In the massive case, the distribution has sharp maxima at M = 2M3 and 2Ms, corresponding to on-shell production of colored rrrr. Thus, for any reasonable choice of masses, the color-singlet technip- ion invariant mass distribution peaks considerably far- ther above threshold than would be expected for most QCD processes. Observing this effect is tantamount to discovering the colored technipions.

Let us turn now to the ?rr decay modes. Technipi-

ons are expected to couple to quarks and leptons with stength m,,e( M,) /FT, where m,,e( M,) is the ETC- generated part of the fermion’s mass, renormalized

at M,. Assuming that mixing factors suppress inter-

generational decay amplitudes, the dominant ?i-r de- cay rates are expected to be 6

r<?r; -+ CS) N - 3 m:(M,)M

16~ F; =T

N 0.3KT h’kv ,

= 4KT Mev ,

N 25KT Mev , (7)

61 used m,(lOOGeV) = 0.3GeV and mb(lOOGeV) = 2.5GeV.

628 K. Lane/Physics Letters B 357 (199.5) 624-629

where KT = (40 GeV/Fr)* (M,,/lOO GeV) . The hadronic decay channels in rrrr production

would be difficult to detect. Without heavy flavor tag-

ging, they are impossible to see above the four-jet background. At least two heavy quarks must be tagged to bring the 7&-F signal close to the bb + 2 2jets background and this will entail a heavy acceptance loss. The r + dijet + $r signature has a large back- ground from W( --+ TV) +dijet production. The r+r-+ #r signal is impossible to reconstruct and is swamped, e.g., by ordinary Drell-Yan (Z” -+ r+r-) produc- tion. Fortunately, this unpromising scenario is not the only possibility.

Technipions have another decay mode, namely, to two electroweak gauge bosons. The amplitude for this decay is given by the triangle anomaly and the rates

are [13]

(8)

The anomaly factor is

C7-Tm2) = $mTr<Q, {Q~,~Q~,)) 1 (9)

where gi is the Bi gauge coupling and QB; is its (vec- tor or axial-vector) charge. For the isovector rr, the anomalous decay modes are g$ + Wrt y, P$ -+ Z” y and $ --f yy, with the factors given in the one-family model by

(10)

The factors for the multiscale model are related to these by S(rgQBy) = ---&S(re,By) = $S(vTBy).

These formulas assume that techniquarks and leptons belong to the fundamental representation of SU( Nrc) . As noted earlier, technifermions of the one-family model may need to belong to a higher representation to ensure a walking technicolor coupling. This would enhance their anomalous decay rates.

It is clear why these decay modes generally have been considered unimp0rtant.l For Nrc = 4, FT =

40 GeV and M, = 100 GeV, the anomalous rates are 3 keV for Wy, 2 eV for Z” y and 400 keV for yy, much smaller than the rates in Eq. (7). However, there is reason to be cautious about this conclusion: Eq. (7) may overestimate l?(z-: --+ r+FT) and r($ + b6). The fermion masses in these formulas are the ETC-

generated parts only. In TC2, the b-quark mass is due in part to ETC interactions and topcolor instan- tons [ 11. This b-mass, as well as the ETC mass of the 7, is then magnified to some extent by the topcolor and strong U( 1) interactions [ 231. Thus, the ETC masses of both the b and 7, like that of the t, may be much less than their pole masses. Whether this is sufficient to suppress the technipions’ fermionic decay rates to the level of their anomalous ones - ETC masses less than about 50 MeV are required - and yet not run afoul of phenomenological b and r constraints are model- dependent issues that cannot be settled in this paper.

Spectacular signatures are associated with the anomalous decays of technipions. For rrgr; + W+W-yy, the cleanest signals are e+e-yy + $r, where e = e or p and all invariant mass combinations tend to be large. These modes occur l/81 of the time

for eeyy and ,upyy and twice this often for epyy. For u N 1 pb, it is hard to think of backgrounds to these signals. Unfortunately, these clean modes cannot be unambiguously reconstructed. For that, one must re- sort (as in top-pair production, Ref. [ 71) to events in which one W decays hadronically, giving the signal C*yy + 2jets + ,!?r. These occur 24/81 of the time. However, there will be losses due to isolation and other cuts. It is important that the experimentalists carefully simulate their acceptance for these events. The %+i$ -+ yyyy mode is clear and unambigu- ous, though also subject to losses. In any case, it is possible now to set meaningful limits on the charged and neutral color-singlet n;rrr cross section-times- branching ratio with existing data from the Tevatron collider. We hope this will become part of the current search for new phenomena at the Tevatron.

7 Two counterexamples are: Randall and Simmons, who made up

for the small anomalous rates by considering qvr production at the LHC [ 211; Lubicz and Santorelli, who considered multiscale

v$ production in eie- annihilation and assumed an ad hoc

suppression of the fermionic decay modes 1221.

K. Lane/Physics Letters B 357 (1995) 624-629 629

This research was inspired by conversations with Estia Eichten. I thank Sekhar Chivukula, Andy Cohen, Chris Hill and Dimitris Kominis for valuable discus- sions and the Fermilab Theory Group for its hospital-

ity during the early stages of this work. This research is supported in part by the Department of Energy un- der Grant No. DE-FG02-91ER40676.

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