28 November 1996
Physics Letters B 388 (1996) 803-807
Low-scale technicolor at the Tevatron Estia Eichten a~1,Kenneth Lane b*2 a Fermi National Accelerator Laboratory, RO. Box 500, Batavia, IL 60510, USA b Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 0221.5, USA
Received 30 August 1996 Editor: H. Georgi
Abstract In multiscale models of walking technicolor, relatively light color-singlet technipions are produced in q4 annihilation in association with longitudinal W and Z bosons and with each other. The technipions decay as n-t -+ b6 and rg -+ c&. Their production rates are resonantly enhanced by isovector technirho vector mesons with mass Mw + MST 5 Md 5 2M,,. At the Tevatron, these associated production rates are l-10 picobams for MTT N 100 GeV. Such a low mass technipion production will also be rewarding. requires topcolor-assisted technicolor to suppress the decay t -+ r;b. Searches for ?i-TTTT7h Sizable rates are expected if M, 2 2M,, + 10 GeV. The isoscalar Wr is nearly degenerate with pr and is expected to be produced at roughly the same rate. The @T should have the distinctive decay modes tir -+ y~$ and Z&.
In the standard one-doublet Higgs model of electroweak symmetry breaking, the cross section for production in pp collisions at 1.8 TeV of a 100 GeV Higgs boson H in association with W* bosons is about
we review our proposal and point out that such a low mass for the technipion requires a new scenario such as topcolor-assisted technicolor [ 3-61 to accommodate the top quark’s large mass and prevent its decay to
0.15 pb. Even lower rates occur in nonminimal Higgs models, including supersymmetric ones. Such small cross sections require luminosities of l-10 fb-’ to detect the signature W* + H ---f C* +hb+& [ 11. In this note, we recall that very similar signatures occur in technicolor models at rates that are 30 or more times greater than the Higgs rate, large enough to be observed at the Tevatron now. In our 1989 paper proposing multiscale technicolor [ 21, we predicted that resonant production via isovector technirho ( PT) vector mesons of W/Z + ?TT, with n-T a technipion of mass of - 100 GeV decaying to heavy quarks, would occur at the Tevatron at the level of a few picobarns. Here,
rgb. If the custodial techni-isospin is approximately conserved, as we expect, the isoscalar partner WT of the PT is nearly degenerate with it and may be produced at a comparable rate. In addition, there may be an isoscalar technipion, S-F, close in mass to dT. The main decay modes of C+ are expected to be y/Z + dT and y/Z + +, with rg and @’ + 6b, providing
’ [email protected]
. * [email protected]
spectacular signatures at the Tevatron. Quark and lepton masses in technicolor are generated by broken extended technicolor (ETC) gauge interactions [7-91. Because of the conflict between constraints on flavor-changing neutral currents and the magnitude of ETC-generated masses, the classical version of technicolor failed and was replaced a decade ago by “walking” technicolor [ lo]. In this kind of gauge theory, the strong technicolor coupling &‘TC
0370-2693/96/$12.00 Copyright 0 1996Elsevier Science B.V. All rights reserved. PII SO370-2693(96)0 12 1 l-7
E. Eichren, K. Lane/Physics
runs very slowly for a large range of momenta, possibly all the way up to the ETC scale, which must be several 100 TeV to suppress flavor-changing effects. This slowly-running coupling permits quark and lepton masses as large as a few GeV to be generated from ETC interactions at this very high scale. Walking technicolor models require a large number of technifermions in order that aTC runs slowly. These fermions may belong to many copies of the fundamental representation of the technicolor gauge group (here taken to be SU( NTC) ) , to a few higher dimensional representations, or to both. This led us to argue in Ref. [ 21 that both large and fundamental representations participate in electroweak symmetry breaking 3 . The two types of technifermion condense at widely separated scales [ 131. The upper scale is set by the weak decay constant F, = 246 GeV. Technihadrons associated with the lower scale may be so light, we said, that they are within reach of Tevatron collider experiments. Light-scale technihadrons generally consist of color singlets (discussed in [ 21) and non-singlets (discussed in [ 141). In this note, we shall be interested in the color singlets. We consider first the lightest isotriplet of technirho vector mesons, pf”. We will discuss their iSOsCd~ counterpart, UT, later. The pT decay into pairs of isovector technipion states, II*,‘. In general, the latter are mixtures of the longi&dinal weak bosons W,f , Zz and mass-eigenstate (pseudo-Goldstone) technipions r:, rr;. In the simplest parameterization, with just one light isotriplet of TT, IIII,) = sinXJWL) +cosxI7i-~), where sinx = FTIF, < 1 and FT is the decay constant of IIT. The PT partial decay rates are given by (assuming no other open decay channels) [ 15,161
(1) where PAB is the technipion momentum and ci, = sin4 x, 2 sin’ x COS2 x, C0s4 x for r.457~ = WLWL, 3 Technicolor models with QCD-like dynamics cannot have a large number of representations because they produce an Sparameter that is too large and positive [ 111. Of course, such models are already ruled out because they have flavor-changing neutral currents that are too large [ 91, the problem that motivated walking technicolor. The arguments in [ 1 l] are based on scaling from QCD and on chiral perturbation theory. They fail or are questionable in walking technicolor models; see Ref. [ 121.
Letters B 388 (1996) 803-807 WLTT+TTWL, ITTTT, respectively. For technifermions in the fundamental representation of SU(NTc), the PT + ~TTT coupling aPT obtained by naive scaling from QCD is given by
ffpT = 2.91
In calculations, we take NTC = 4. Extended technicolor interactions couple technipions to quarks and leptons with Higgs-like couplings. Technipions are then expected to decay into heavy fermions: 7%-g +
b6 if M, I tf if M,
< 2m,, > 2m,;
cl; or cS, 7+u, if M,
< m, + mb,
> m, + mb.
Now - and this is the important feature of walking technicolor - technipion masses are enhanced by renormalizations that are SO large that the PT --f ~TTT channels may be closed or strongly suppressed. Thus, technirho production at the Tevatron can lead to all of the processes 44’ -+ w It -)$A
wFz,o; W+_O &ZO. L
qq+y,z”+po,+w,fw,-; W%TIfr. L T,
rates despite the small angle
x, To illustrate
we shall take M+
Mv~ N 1 IO GeV and vary M,+ E Mp; in our calculations. Note that, since PT has Z = 1, these resonant processes do not lead to Z”GT + !+P/vP + b6 final states. Such events must originate from WT, as we discuss later. Technirho events with a Z” and two heavy quark jets have one b-jet and one c-jet4. The Drell-Yan processes in Eq. (4) have O( a*) cross sections and are unobservably small compared to backgrounds unless the technirho resonances are not far above threshold, roughly Mw + M, 5 M,, s 4Note that 2 + rr~ events with a lost lepton can end up in the W + n-~ sample,
while W + *ITTwith a lost lepton may be counted VP) + VT.
E. Eichten, K. Lane/Physics Letters B 388 (1996) 803-807
2M,. This condition is favored by multiscale technicolor. We estimate the pr -+ ~ATB subprocess cross sections by vector meson dominance, taking the y, Z, W --+ Pr couplings from the condition that they reproduce y, Z, W -+ TATB at zero energy. We obtain
(5) where s^is the subprocess energy, z = cos 8 is the ??-A production angle, and I,,* is the energy-dependent total width. Ignoring Kobayashi-Maskawa mixing angles, the factors AZ,’ = +A*,0 are
+ [Qi Here, Qi and Tsi are the electric and third component of weak isospin for quark qiL,i. In these processes, the W + dijet and Z + dijet invariant masses exhibit a narrow peak not far above 200 GeV. This peak will be smeared by energy resolutions, but it should be narrower than expected from continuum production of W/Z t_ H. Our final observation is that, after all this, ordinary multiscale technicolor cannot accommodate the top quark. Its mass of m, N 175 GeV [ 171 is much too large to be generated by ETC coupling of the top quark to the low-scale technifermions [ 141. Furthermore, there cannot be a charged technipion as light as 100 GeV for, then, the top quark would tend to decay into it. Taking the coupling of rg to &bR to be fin$rCI FT, where n$rc is the ETC contribution to the top-quark mass, the top decay rate to n-$b is
For m.FTC 21 mt and FT = 40 GeV, a typical value in multiscale models, I( t -+ ‘ITT+b)cx 25 GeV N
15I( t -+ W+b); this is ruled out [ 181. Topcolorassisted technicolor (TC2) resolves these problems. In TC2 [ 51, as in top-condensate models of electroweak symmetry breaking [ 3,4], the large top quark mass is generated by strong “topcolor” gauge interactions. Thus, there can be low-scale technifermions and the ETC scale can be 0 ( 100 TeV) for all fermions. Then, mFTc is only a few GeV, so that the branching fraction B( t -+ n-,fb) is small 5 . Preliminary models of topcolor-assisted technicolor were developed in Ref. [ 61. They differ from multiscale technicolor models in that they do not contain technifermions in higher representations and the associated widely separated scales. However, there are many copies of the fundamental representation (some of which also transform under color or topcolor SU( 3)). Thus, the net effect is the same; ignoring SlJ(3) effects, FT 1: F,/fi, where No is the number of technifermion weak isodoublets. In the model of the second paper in , No = 9, so that FT = 82 GeV (or somewhat less because of color effects) for the lightest color-singlet technipions. We have used Eq. (5) with sin x = 3 to compute the PT production cross sections for M, = 110 GeV and M,, = 195-250 GeV. The individual decay channel cross sections are shown for pp collisions at 4 = 1.8 TeV in Fig. 1 (multiplied by a K-factor of 1.5, appropriate for Drell-Yan processes at the Tevatron) . No cuts were put on the technipion directions. These plots illustrate several features we expect to be general: - Except near W,, threshold, the increase in WZ and WW production is smaI1. - The inclusive W,, rate is 5-10 pb and the Zrr rate is l-3 pb for M, + Mw 5 M,, 5 2M,. The ratio g( WLGTT)/a( ZLTT) = 2-3 is about the same as expected for g( WH) /CT
5 Top-pions riot arising from top-quark condensation do couple to vzt. Their mass arises from the ETC contribution: rn& N m~x(Ft)/Ff, where fi N_ 70 GeV 151. This is sufficient to make MT, 2 mr. Mixing of top-pions with technipions is expected to be small, of order (it)/(LfT)En: N AT,-/AETC5 lo-’ [ 191.
E. Eichten, K. Lane/Physics
Fig. 1. Total Ww, WTT and ~TTT cross sections in pp collisions at 1.8 TeV, as a function of M, for MET = 110 GeV. The model described above I$. ( 1) is used with sinx = 5. The curves are W* Z” (upper dotted) and Wf Wsolid),
W* GT? (lower solid),
; W*n$ (upper ; z-Tf7~:
(upper short dashed) and z-:r, (lower short dashed). EHLQ set 1 distribution functions [ 161 were used and cross sections were multiplied by a K-factor of 1.5, as appropriate for Drell-Yan processes.
+ t4i”(?j) where fi;*
is the qi distribution
Q2 = M&. At the Tevatron, these distributions
pTf production over p$ by a factor of 2-3 over the range of Mp7. considered. - For M,, > 2M, + 10 GeV, the dominant process is r$vF production. The crossover point depends to some extent on the suppression factor tan x, but we don’t expect it to be much different from this. A search for the z-g$? channel will be rewarding. Finally, we turn to the WT. The walking technicolor enhancement of technipion masses almost certainly closes off the isospin-conserving decay tiT -+ II$II,II$. Even the triply-suppressed mode W,‘WFZL has little or no phase space for the M,,-
Letters B 388 (1996) 803-807
range we are considering. Thus, we expect the decays UT + r@, ZII:, and Sign,. When written in terms of mass eigenstates, these models are WT --+ ytiT, ~ZL, ZrF, ZZL; y@‘, Z$‘; and Wt W;, ?rg Wz, - 6 . It is not possible to estimate the relative +T magnitudes of the decay amplitudes without an explicit model of the UT’s constituent technifermions. Judging from the decays of the ordinary w, we expect UT -+ y7r$!(z-p), Zn-$( GT’) to be dominant, with the former mode favored by phase space. The WT is produced in hadron collisions just as the p!, via its vector-meson-dominance coupling to y and Z”. For M,, N M,, the WT production cross section should be approximately IQu + Qo12 times the p; rate, where QU,D are the electric charges of the @‘s constituent technifermions. The principal signatures for WT production, then, are y + 6b and f?? (or vV) + b6, with Mh6 = M,. The model of color-singlet technihadron production we have discussed here is an oversimplification, but one that captures some of the essence of modern models of technicolor. As we did in Ref. , we urge a search for W/Z + %-T --+ isolated high-pT leptons+heavy quark yets. If such events are found, the W/Z + jj mass spectrum should exhibit a narrow pT peak consistent with resolution. Sidebands Mwjj with Mjj outside the “M,” bins - should not exhibit the peak unless it turns out to be kinematic in nature. Because of the quadratic ambiguity in reconstructing the W in its &J decay, it seems best to plot the low-mass solution versus the high-mass one. We also urge a search for ~TVT production. This may not be possible now, but a search with the high-luminosity data of Tevatron Run II should be conclusive. If a 5i-T candidate is found, it will be important to determine whether c-quarks as well as b-quarks occur in its decay. Higher luminosity and more robust heavy-flavor tagging can make this possible. Finally, there should be an isoscalar @T nearly degenerate with p& generically produced with a comparable cross section, and with spectacular y&b and Z6b decay signatures. If these technihadrons are found, they will be just the first of a very large family. 6 The modes OT + ~ZL, ZZL were considered for a one-doublet technicolor model in Ref. [ZO] We have estimated the rates for the isospin-violating decays PT -f y$!, Z$ and find them to be negligible unless the mixing angle x is very small.
E. Eichten, K. Lane/Physics
E.E.‘s research is supported by the Fermi National Accelerator Laboratory, which is operated by Universities Research Association, Inc., under Contract No. DE-AC02-76CH03000. K.L.‘s research is supported in part by the Department of Energy under Grant No. DE-FG02-91ER40676. We gratefully acknowledge the hospitality of the Aspen Center for Physics where this work was completed.
References [ I] Report on the tev-2000 Study Group on Future Electroweak
  
Physics at the Tevatron, eds. D. Amidei and R. Brock, D0Note 2589 and CDF Note 3177 (1995). K. Lane and E. Eichten, Phys. Lett. B 222 (1989) 274. Y. Nambu, in: New Theories in Physics, Proc. of the XI International Symposium on Elementary Particle Physics, Kazimierz, Poland, 1988, eds. 2. Adjuk, S. Pokorski and A. Trautmann (World Scientific, Singapore, 1989); Enrico Fermi Institute Report EFI 89-08 (unpublished); VA. Miransky, M. Tanabashi and K. Yamawaki, Phys. Left. 221 B (1989) 177; Mod. Phys. Lett. A 4 (1989) 1043; W.A. Bardeen, CT. Hill and M. Lindner, Phys. Rev. D 41 (1990) 1647. C.T. Hill, Phys. Lea. 266 B (1991) 419; S.P. Martin, Phys. Rev. D 45 (1992) 4283; D 46 (1992) 2197; Nucl. Phys. B 398 (1993) 359; M. Lindner and D. Ross, Nucl. Phys. B 370 (1992) 30; R. Bon&h, Phys. Lctt. 268 B (1991) 394; CT. Hill, D. Kennedy, T. Onogi and H.L. Yu, Phys. Rev. D 47 (1993) 2940. C.T. Hill, Phys. Lett. 345 B (1995) 483. K. Lane and E. Eichten, Phys. Lett. B 352 (1995) 382; K. Lane, Boston University Preprint BUHEP-96-2, hepph/9602221, submitted to Physical Review D. S. Weinberg, Phys. Rev. D 19 (1979) 1277; L. Susskmd, Phys. Rev. D 20 (1979) 2619. S. Dimopoulos and L. Susskind, Nucl. Phys. B 155 (1979) 237. E. Eichten and K. Lane, Phys. I&. 90 B (1980) 125.
Letters B 388 (1996) 803-807
[ 101 B. Holdom, Phys. Rev. D 24 (1981) 1441; Phys. Lett. 150 B (1985) 301; T. Appelquist, D. Karabali and L.C.R. Wijewardhana, Phys. Rev. Lett. 57 (1986) 957; T. Appelquist and L.C.R. Wijewardhana, Phys. Rev. D 36 (1987) 568; K. Yamawaki, M. Bando and K. Matnmoto, Phys. Rev. L&t. 56 (1986) 1335; T. Akiba and T. Yanagida, Phys. Lett. 169 B (1986) 432. [ 111 A. Longhitano, Phys. Rev. D 22 (1980) 1166; Nucl. Phys. B 188 (1981) 118; R. Renken and M. Peskin, Nucl. Phys. B 211 (1983) 93; B.W. Lynn, M.E. Peskin and R.G. Stuart, in: Trieste Electroweak 1985, p. 213; M. Golden and L. Randall, Nucl. Phys. B 361 (1990) 3; B. Holdom and J. Teming, Phys. Lett. B 247 (1990) 88; M.E. Peskin and T. Takeuchi, Phys. Rev. Lett. 65 (1990) 964; A. Dobado, D. Espriu and M.J. Herrero, Phys. Lett. B 255 (1990) 405; H. Georgi, Nucl. Phys. B 363 (1991) 301. [ 121 K. Lane, Proceedings of the 27th International Conference on High Energy Physics, eds. PJ. Bussey and LG. Knowles, Vol. II, p. 543, Glasgow, June 20-27, 1994. [ 131 S. Raby, S. Dimopoulos and L. Susskind, Nucl. Phys. B 169 (1980) 373. [ 141 K. Lane and M.V. Ramana, Phys. Rev. D 44 (1991) 2678.  S. Dimopoulos, S. Raby and G. Kane, Nucl. Phys. B 182 (1981) 77. [ 16] E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 579; Phys. Rev. D 34 (1986) 1547. [ 171 E Abe et al., The CDF Collaboration, Phys. Rev. Lett. 73 ( 1994) 225; 74 ( 1995) 2626; Phys. Rev. D 50 (1994) 2966; S. Abachi et al., The D0 Collaboration, Phys. Rev. Lett. 74 (1995) 2632. [IS] J. Incandela, Proceedings of the 10th Topical Workshop on Proton-Antiproton Collider Physics, Fermilab, eds. R. Raja and J. Yoh, p. 256 (1995). [ 191 B. Balaji, Top-Pion-Technipion Mixing in Natural TopcolorAssisted TechnicoIor, Boston University preprint in preparation.  R.S. Chivukula and M. Golden, Phys. Rev. D 41 ( 1990) 2795.