Technicolor at the Tevatron
FFERMILAB-Pub-11-165-T
Technicolor Explanation for the CDF
W jj
Excess
Estia J. Eichten, ∗ Kenneth Lane, † and Adam Martin ‡ Theoretical Physics Department, Fermi National Accelerator LaboratoryP.O. Box 500, Batavia, Illinois 60510 Department of Physics, Boston University590 Commonwealth Avenue, Boston, Massachusetts 02215
We propose that the 3 . σ excess at ∼
150 GeV in the dijet mass spectrum of W + jets reportedby CDF is the technipion π T of low-scale technicolor. Its relatively large cross section is due toproduction of a narrow W jj resonance, the technirho, which decays to
W π T . We discuss ways toenhance and strengthen the technicolor hypothesis and suggest companion searches at the Tevatronand LHC. PACS numbers:
1. Introduction
The CDF Collaboration has re-ported a surprising excess at M jj (cid:39)
150 GeV in thedijet mass distribution of W + jets events. Fittingthe excess to a Gaussian, CDF estimated its produc-tion rate to be ∼ σ (¯ pp → W H ) B ( H → ¯ bb ).The Gaussian fit is consistent with a zero-width res-onance. Its significance, for a search window of 120–200 GeV and including systematic uncertainties, is3 . σ [1].In our view the most plausible new-physics ex-planation of this excess is resonant production anddecay of bound states of technicolor (TC), a newstrong interaction at Λ T C ∼ several 100 GeV ofmassless technifermions [2–5]. These technifermionsare assumed to belong to complex representationsof the TC gauge group and transform as quarksand leptons do under electroweak (EW) SU (2) ⊗ U (1). Then, the spontaneous breaking of theirchiral symmetry breaks EW symmetry down toelectromagnetic U (1) with a massless photon and M W /M Z cos θ W = 1+ O ( α ). We propose that the di-jet resonance is the lightest pseudo-Goldstone isovec-tor technipion ( π T ) of the low-scale technicolor sce-nario. The immediate consequence of this hypoth-esis is a narrow I = 1 technirho ( ρ T ) resonance inthe W jj channel. This accounts for the large
W π T production rate.In this Letter we show that a ρ T of mass (cid:39)
290 GeV decaying into W plus π T of 160 GeV ac-counts for the CDF dijet excess. The ρ T signal sitsnear the peak of the M W jj distribution and willbe less obvious than π T → jj . We suggest waysto enhance this signal and tests of the ρ T ’s pres-ence: (1) The ρ T ’s narrowness will be reflected in Q = M W jj − M jj − M W [6, 7]. The M jj binsnear M π T will exhibit a sharp increase over back-ground for Q (cid:39) Q ∗ = M ρ T − M π T − M W . (2) The ρ T → W π T angular distribution in the ρ T framewill be approximately sin θ , indicative of the sig-nal’s technicolor origin. We propose further testsof the technicolor hypothesis, including other reso-nantly produced states which can be discovered atthe Tevatron and LHC.Low-scale technicolor (LSTC) is a phenomenol-ogy based on walking technicolor [8–11]. The TCgauge coupling must run very slowly for 100s ofTeV above Λ T C so that extended technicolor (ETC)can generate sizable quark and lepton masses [30]while suppressing flavor-changing neutral currentinteractions [12]. This may be achieved if tech-nifermions belong to higher-dimensional representa-tions of the TC gauge group. Then, the constraintsof Ref. [12] on the number of ETC-fermion repre-sentations imply technifermions in the fundamen-tal representation as well. Thus, there are tech-nifermions whose technipions’ decay constant F (cid:28) F π = (246 GeV) [13]. Bound states of these tech-nifermions will have masses well below a TeV —greater than the limit M ρ T > ∼
250 GeV [7, 14] andprobably less than the 600–700 GeV at which “low-scale” TC ceases to make sense. Technifermions incomplex TC representations imply a quarkonium-like spectrum of mesons. The most accessible are thelightest technivectors, V T = ρ T ( I G J P C = 1 + −− ), ω T (0 − −− ) and a T (1 − ++ ); these are produced as s -channel resonances in the Drell-Yan process inhadron colliders. Technipions π T (1 − − + ) are ac-cessed in V T decays. A central assumption of LSTCis that these technihadrons may be treated in iso- a r X i v : . [ h e p - ph ] J u l lation, without significant mixing or other interfer-ence from higher-mass states. Also, we expect that(1) the lightest technifermions are SU (3)-color sin-glets, (2) isospin violation is small for V T and π T ,(3) M ω T ∼ = M ρ T , and (4) M a T is not far above M ρ T . An extensive discussion of LSTC, includingthese points and precision electroweak constraints,is given in Ref. [15].Walking technicolor has another important conse-quence: it enhances M π T relative to M ρ T so that theall- π T decay channels of the V T likely are closed [13].Principal V T -decay modes are W π T , Zπ T , γπ T , apair of EW bosons (including one photon), andfermion-antifermion pairs [15–17]. If allowed byisospin, parity and angular momentum, V T decaysto one or more weak bosons involve longitudinally-polarized W L /Z L , the technipions absorbed via theHiggs mechanism. These nominally strong decaysare suppressed by powers of sin χ = F /F π (cid:28) γ, W ⊥ , Z ⊥ are sup-pressed by g, g (cid:48) . Thus, the V T are very narrow,Γ( V T ) < ∼
2. The new dijet resonance at the Tevatron
Pre-vious ρ T → W π T searches at the Tevatron focusedon final states with W → (cid:96)ν (cid:96) and π T → ¯ qq whereone or both quarks was a tagged b . This was advo-cated in Ref. [6] because π T couplings to standard-model fermions are induced by ETC interactions andare, naively, expected to be largest for the heavi-est fermions. Thus, π + T → ¯ bc , ¯ bu and π T → ¯ bb has been assumed, at least for M π T < ∼ m t . Whilereasonable for π T decays, it is questionable for π ± T because CKM-like angles may suppress ¯ bq . This isimportant because the inclusive σ (¯ uu, ¯ dd → ρ T ) (cid:39) . × σ ( ¯ du, ¯ ud → ρ ± T ) at the Tevatron. If π + T → ¯ bq is turned off in the default model of π T decays usedhere [16], up to 40% of the ρ T → W π T → W jj sig-nal is vetoed by a b -tag . It is notable, therefore,that the CDF observation did not require b -taggedjets [1].At first, it seems unlikely that ρ T → W π T couldbe found in untagged dijets because of the large W + jets background. However, Ref. [20] stud-ied ρ T → W π T without flavor-tagging and showedthat a π T → jj signal could be extracted. Re-cently, strong W/Z → jj signals have been observed in W W/W Z production at the Tevatron [21, 22].So, heavier dijet states resonantly produced with
W/Z/γ may indeed be discoverable at the Tevatron.The CDF dijet excess was enhanced by requiring p T ( jj ) >
40 GeV [1]. Such a cut was proposed inRef. [6]. There it was emphasized that the small Q -value in ρ T → W π T and the fact that the ρ T is approximately at rest in the Tevatron lab framecause the π T to be emitted with limited p T and itsdecay jets to be roughly back-to-back in φ .
3. Simulating ρ T → W π T Pythia ρ T → W π T signal [23].It employs the default π T -decay model of Ref. [16]in which π + T → ¯ bq is unhindered. The inputmasses are ( M ρ T , M π T ) = (290 , M π T gives a peak in the simulated M jj distributionnear 150 GeV [31]. This parameter choice is close toCase 2b of Contribution 8 in Ref. [19].The signal cross sections ( including B ( π T → ¯ qq ) (cid:39) . B ( π ± T → ¯ qq (cid:48) ) (cid:39) .
95, and B ( W → (cid:96) ± ν (cid:96) ) =0 .
21) are σ ( W ± π ∓ T ) = 310 fb and σ ( W ± π T ) =175 fb [32]. Only 20-30% of these cross sections comefrom the 320 GeV a T → W ⊥ π T . If M a T = 293 GeV,they increase slightly to 335 fb and 205 fb. If π + T → ¯ bq is suppressed, then σ ( W ± π ∓ T ) = 110 fb, a decreaseof 2/3, for a total W jj signal of 285 fb.Backgrounds come from standard model
W/Z +jets, including b, c -jets,
W W/W Z , t ¯ t , and multi-jet QCD. The last two amount to ∼
10% at theTevatron and we neglect them. The others are gen-erated at parton level with ALPGENv13 [24] andfed into
Pythia for showering and hadronization.The
Pythia particle-level output is distributed intocalorimeter cells of size ∆ η × ∆ φ = 0 . × .
1. Af-ter isolated leptons (and photons) are removed, allremaining cells with E T > R = 0 .
4. For simplicity, we didnot smear calorimeter energies; this does not sig-nificantly broaden our M jj resolution near M π T .In extracting the π T and ρ T signals, we firstadopted the cuts used by CDF [1],[33]. Our re-sults are in Fig. 1. The data correspond to (cid:82) L dt =4 . − . They reproduce the shape and normaliza-tion of CDF’s M jj [1] and M W jj [25] distributions(except that not smearing calorimeter energies doesmake our W → jj signal a narrow spike). We ob-tain S/B = 250 / jj M
40 60 80 100 120 140 160 180 200 N u m b e r o f E ve n t s / G e V jj M
40 60 80 100 120 140 160 180 200 N u m b e r o f E ve n t s / G e V W + jetsWW/WZsignal
Wjj M
150 200 250 300 350 400 450 N u m b e r o f E ve n t s / G e V Wjj M
150 200 250 300 350 400 450 N u m b e r o f E ve n t s / G e V W + jetsWW/WZsignal
FIG. 1: The M jj and M Wjj distributions in ¯ pp col-lisions at 1 .
96 TeV for LSTC with M ρ T = 290 GeV, M π T = 160 GeV and (cid:82) L dt = 4 . − . Only the CDFcuts described in the text are used. with CDF’s measurement remarkable. Our modelinputs are standard defaults, chosen only to matchthe dijet resonance position and the small Q -valueof ρ T → W π T . The ρ T resonance is near the peakof the M W jj distribution [34]. For the six bins in240–300 GeV, we obtain
S/B = 235 / R = 1 . π T and, especially, the ρ T signals by imposing topolog-ical cuts taking advantage of the ρ T → W π T kine-matics [6]: (1) ∆ φ ( j j ) > .
75 and (2) p T ( W ) = | p T ( (cid:96) ) + p T ( ν (cid:96) ) | >
60 GeV. The improvements seenin Fig. 2 are significant. We obtain
S/B = 200 / π T → jj and S/B = 215 / ρ T → W jj .Extracting the ρ T signal will require confidence inthe background shape.In addition to the jj and W jj resonances, the jj M
40 60 80 100 120 140 160 180 200 N u m b e r o f E ve n t s / G e V jj M
40 60 80 100 120 140 160 180 200 N u m b e r o f E ve n t s / G e V W + jetsWW/WZsignal
Wjj M
150 200 250 300 350 400 450 N u m b e r o f E ve n t s / G e V Wjj M
150 200 250 300 350 400 450 N u m b e r o f E ve n t s / G e V W + jetsWW/WZsignal
FIG. 2: The M jj and M Wjj distributions in ¯ pp collisionsat 1 .
96 TeV for LSTC with M ρ T = 290 GeV, M π T =160 GeV and (cid:82) L dt = 4 . − . CDF cuts augmentedwith ours described in the text are used. Q -value and the ρ T -decay angular distribution areindicative of resonant production of W π T . The res-olution in Q = M W jj − M jj − M W is better than in M jj and M W jj alone because jet measurement er-rors partially cancel. This is seen in Fig. 3 where weplot ∆ N ( M jj ) = N observed ( M jj ) − N expected ( M jj ) = N S + B ( M jj ) − N B ( M jj ) for Q ≤ Q max vs. Q max forsix 16-GeV M jj bins between 86 and 182 GeV. Thesudden increase at Q max (cid:39)
50 GeV in the three sig-nal bins is clear.The decay ρ T → W π T is dominated by W L π T .Therefore, the angular distribution of q ¯ q → ρ T → W π T is approximately sin θ , where θ is the anglebetween the incoming quark and the outgoing W inthe ρ T frame [17]. The backgrounds are forward-backward peaked. We required p T ( W ) >
40 GeV,fit the background in 250 < M
W jj <
300 GeV witha quartic in cos θ , and subtracted it from the total.(In reality, of course, one would use sidebands.) Theprediction in Fig. 3 matches the normalized sin θ well. Verification of this would strongly support the max Q E ve n t s
86 GeV - 102 GeV (1)102 GeV - 118 GeV (2)118 GeV - 134 GeV (3)134 GeV - 150 GeV (4)150 GeV - 166 GeV (5)166 GeV - 182 GeV (6) window jj M (1)(6)(2)(3)(4)(5) ) * (cid:101) cos( N u m b e r o f E ve n t s / . FIG. 3: Top: ∆ N ( M jj ) vs. Q max as described in the textfor the indicated M jj bins. Bottom: The background-subtracted W -dijet angular distribution, compared tosin θ (red). TC origin of the signal.
4. Other LSTC tests at the Tevatron and LHC
1) It is important to find the ω T and a T states,expected to be close to ρ T , near 300 GeV. Atthe Tevatron, the largest production rates involve ω T → γπ T and a ± T → γπ ± T . For our input parame-ters, these are 80 fb and 185 fb, respectively. Theirexistence, masses and production rates critically testthe technifermions’ TC representation structure andthe strength of the dimension-five operators induc-ing these decays. In addition, recent papers fromDØ [26] and CDF [27] suggest that the e + e − chan-nel is promising. The excess (signal) cross sectionsfor our parameters are σ ( ω T , ρ T → e + e − ) = 12 fband σ ( a T → e + e − ) = 7 fb.2) Finding these LSTC signatures at the LHC iscomplicated by ¯ tt and other multijet backgrounds.The likely discovery and study channels at the LHCare the nonhadronic final states of ρ ± T → W ± Z ; ρ ± T , a ± T → γW ± , and ρ T , ω T , a T → (cid:96) + (cid:96) − [18, 19]. The dilepton channel may well be the earliest targetof opportunity.3) The b and τ -fractions of π T decays should be de-termined as well as possible. They probe the ETCcouplings of quarks and leptons to technifermions,a key part of the flavor physics of dynamical elec-troweak symmetry breaking [12].If experiments at the Tevatron and LHC reveala spectrum resembling these predictions, it couldwell be that low-scale technicolor is the “RosettaStone” of electroweak symmetry breaking. For itwill then be possible to know its dynamical originand discern the character of its basic constituents,the technifermions. The masses and quantum num-bers of their bound states will provide stringent ex-perimental benchmarks for the theoretical studies ofthe strong dynamics of walking technicolor just nowgetting started, see e.g. [28]. Acknowledgments
We are grateful to K. Black,T. Bose, J. Butler, J. Campbell, K. Ellis, W. Giele,C. T. Hill, E. Pilon and J. Womersley for valuableconversations and advice. This work was supportedby Fermilab operated by Fermi Research Alliance,LLC, U.S. Department of Energy Contract DE-AC02-07CH11359 (EE and AM) and in part bythe U.S. Department of Energy under Grant DE-FG02-91ER40676 (KL). KL’s research was also sup-ported in part by Laboratoire d’Annecy-le-Vieuxde Physique Theorique (LAPTH) and he thanksLAPTH for its hospitality.
Note added in proof – An important corrobora-tion of the ρ T → W ± π T → (cid:96) ± ν (cid:96) jj signal isits isospin partner (suppressed by phase space andbranching ratios) ρ T → Z π ± T → (cid:96) + (cid:96) − jj . We pre-dict cross sections of 38 fb at the Tevatron and 155 fbat the 7-TeV LHC for (cid:96) = e and µ . ∗ E-mail:[email protected] † E-mail:[email protected] ‡ E-mail:[email protected][1]
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B345 (1995) 483–489.[30] Except for the top quark mass, which requiresadditional dynamics such as topcolor [29].[31] Other relevant LSTC masses are M ω T = M ρ T ; M a T = 1 . M ρ T = 320 GeV; and M V i ,A i whichappear in dimension-five operators for V T decaysto transverse EW boson [16, 17]; we take themequal to M ρ T . Other LSTC parameters aresin χ = 1 / Q U = Q D + 1 = 1, and N TC = 4.[32] No K -factor has been used in any of our signal andbackground calculations.[33] The CDF cuts are: exactly one lepton, (cid:96) = e, µ ,with p T >
20 GeV and | η | < .
0; exactly two jetswith p T >
30 GeV and | η | < .
4; ∆ R ( (cid:96), j ) > . p T ( j j ) >
40 GeV; /E T >
25 GeV; M T ( W ) >
30 GeV; | ∆ η ( j j ) | < . | ∆ φ ( /E T , j ) | > . W reconstructionwas resolved by choosing the solution with thesmaller p z ( νν