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Low-scale technicolor at the Tevatron and LHC
Physics Letters B 669 (2008) 235–238
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Physics Letters B www.elsevier.com/locate/physletb
Low-scale technicolor at the Tevatron and LHC Estia Eichten a,∗ , Kenneth Lane b a b
Fermi National Accelerator Laboratory, PO Box 500, Batavia, IL 60510, USA Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA
a r t i c l e
i n f o
Article history: Received 27 June 2007 Received in revised form 20 September 2008 Accepted 20 September 2008 Available online 27 September 2008 Editor: B. Grinstein
a b s t r a c t The Tevatron experiments CDF and DØ are close to making definitive statements about the technicolor discovery mode ρ T → W π T for M ρT 250 GeV and M πT 150 GeV. We propose new incisive tests for this mode and searches for others that may be feasible at the Tevatron and certainly are at the LHC. The other searches include two long discussed, namely, ω T → γ π T and + − , and a new one—for the I G J P C = 1− 1++ partner, a T , of the ρ T . Adopting the argument that the technicolor contribution to S is reduced if M a T M ρT , we enumerate important a T decays and estimate production rates at the colliders. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Long ago we pointed out that technicolor’s (TC) walking gauge coupling [1–4] strongly indicates that the energy scale of its bound states is much lower than the roughly 1 TeV expected from the earliest TC studies [5]. Thus, the lightest technihadrons may well be within reach of the Tevatron collider, with production rates of several picobarns; they certainly are accessible at the LHC. Furthermore, they should have striking decay signatures. To review the arguments [6–8]: (1) The walking TC gauge coupling probably requires either a large √ number N D of technifermion doublets so that ΛTC 250 GeV/ N D 100 GeV, or two TC scales, one much lower than 250 GeV. (2) Walking enhances the masses of pseudo-Goldstone technipions, π T , more than those of their vector partners, ρ T and ω T . This probably closes the vectors’ all-π T decay channels, leaving only those involving at least one electroweak ±,0 (EW) gauge boson (especially longitudinally-polarized W L ) and perhaps a π T . Another striking final state is + − . Technipions are expected to decay via extended technicolor (ETC) interactions [9] to the heaviest flavors possible, putting a premium on b-tagging. Thus, those accessible at the Tevatron will appear in vector-mesondominated Drell–Yan processes such as q¯ q → γ , Z , W → ρ T → W π T → ± ν bq¯ and ω T → γ π T0 → γ bb. At the LHC, large backgrounds tend to force one into looking at all-EW boson final states ending up in e and μ-generation leptons. The phenomenology of the lightest π T , ρ T and ω T of lowscale technicolor—bound states of the lightest technifermion colorsinglet EW doublet, ( T U , T D )—is embodied in the “Technicolor Straw-Man Model” (TCSM) [10,11]. The TCSM’s most important assumptions are: (1) These technihadrons may be treated in isola-
*
Corresponding author. E-mail addresses: [email protected] (E. Eichten), [email protected] (K. Lane).
0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.09.047
tion, without significant mixing or other interference from highermass technihadrons. (2) The T¯ T technipions Π T are not mass eigenstates, but they may be treated as simple two-state mixtures ±,0 ±,0 of W L and mass-eigenstate π T :
|Π T = sin χ | W L + cos χ |πT .
(1)
Here, sin χ = F T /246 GeV, where √ F T is the πT decay constant. In a model with N D 1, sin χ ∼ = 1/ N D ; in a two-scale model, F T
246 GeV [6]. This implies that the technivectors are very narrow, with decay rates suppressed by some combination of phase space and powers of sin χ and/or EW gauge couplings. (3) Techni-isospin is a good symmetry. (4) Finally, something like topcolor-assisted technicolor [12] is needed to keep the top quark from decaying copiously into π T+ b when M πT 160 GeV. Thus, if π T+ is heavier
¯ than the top, it does not decay exclusively to t b. Notwithstanding the isolation assumption above, many highermass states are reasonably expected. In Refs. [13,14] it was argued that walking TC invalidates the standard QCD-based calculations of the precision-electroweak S-parameter [15–18] because the spectral functions in the integral for S cannot be saturated by just the lightest ρ T and its axial partner, a T . Something more must make the spectral integrals converge much slower than they do in QCD; the obvious possibility is a tower of vector and axial-vector isovector mesons. The main message of this Letter is that the lightest a T is within reach of the Tevatron and LHC if the ρ T and ω T are, and that a T decays also produce unusual signatures to aid their discovery. In fact, it has long been recognized that the S-parameter may be significantly reduced or even made negative if ρ T and a T pairs in the tower are close in mass and have comparable couplings to their respective currents; see, e.g., Refs. [19–21]. More recently, a number of attempts have been made to model walking TC and calculate S using the AdS/CFT connection; see, e.g., Ref. [22,23]. We adopt these papers’ suggestion that M a T M ρT and explore its
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phenomenological consequences.1 For M a T M ρT = 200–250 GeV, its discovery should be possible at the Tevatron. We expect there would be little trouble discovering and studying a T at the LHC. Preliminary studies for all these technihadrons at the LHC appear in Refs. [24–27]. Our second motivation is the appearance of interesting anomalies in searches for ρ T → W ± π T → ± / E T b jet by the DØ and CDF Collaborations. In 2006 the DØ Collaboration presented two analyses of a 388 pb−1 data set, one cut-based, the other using a neural net (NN) [28]. While it was expected that the NN analysis would exclude a greater region in the (M W bj , M bj )-plane than the cutbased one, in fact neither excluded beyond M ρT 215 GeV and M πT 120 GeV for the default TCSM parameters used; see Fig. 3 in Ref. [28]. Presumably, the NN analysis was limited by an excess near that endpoint. There are two recent CDF analyses, one in late 2006 based on 955 pb−1 [29], and a new one using 1.9 fb−1 [30,31]. The TCSM parameters used were the same as DØ’s as far as the ρ T → W π T search is concerned. The 2008 analysis improves on the 2006 one, e.g., excluding M πT < 110 GeV, M ρT < 210 GeV at the 95% C.L. However, as with DØ, the CDF exclusion plot (Fig. 4 in [31]) falls well short of the expected level at and above M πT = 125 GeV and M ρT = 210 GeV.2 An interesting variable used in the CDF analyses is Q = M W bj − M bj − M W . The resolution in Q is a few GeV, much better than in M bj and M W bj alone, because jet energy uncertainties largely cancel in the difference. If there is a narrow ρ T decaying to W π T , histograms of M bj or M W bj with Q less than fixed values—say 5, 10, 15, . . . , 50 GeV—will exhibit a sudden increase in one of the invariant mass bins when, and only when, Q has its resonant value. In the 2008 analysis CDF presents color-coded two-dimensional plots of M bj vs. Q -value. The colors in these plots are hard to distinguish; we urge CDF to show histograms, with error bars, of M bj or M W bj for a range of cuts on Q . In the remainder of this Letter, we describe other studies and searches for low-scale TC that may be possible at the Tevatron with larger data sets and some that certainly can be carried out at the LHC. For our Tevatron calculations, we use M ρT = M ωT = 225 GeV, M a T = 225–250 GeV and M πT = 125 GeV. The isoscalar technipion π T0 in the TCSM is assumed heavy, 300 GeV, so that none of the lightest technivectors decay into it. The other TCSM parameters used here are sin χ = 13 , Q U = Q D + 1 = 1, N TC = 4 and M V 1,2,3 = M A 1,2,3 = M ρT = 225 GeV. The latter are defined in Eqs. (3) below.3 Typical cross sections for these parameters are
σ p¯ p → ρT0 → W ± πT∓ 2.5 pb;
σ p¯ p → ωT → γ πT0 0.3 pb, σ p¯ p → ωT → γ Z 0 0.07 pb;
σ p¯ p → ωT → + − 0.2 pb, σ p¯ p → ωT → ± ν 0.3 pb.
2. The ρ T and the ω T The angular distribution in qq¯ → ρ T → W π T is approximately sin2 θ , where θ is the angle in the subprocess c.m. frame between the incoming quark and the outgoing W [11]. The reason is that 80–90% of this process is qq¯ annihilation to W L π T , effectively a pair of pseudoscalars. Verification of this angular distribution would be strong confirmation of its underlying TC origin. Requiring Q M ρT − M πT − M W will greatly enrich the signal-to-background for this analysis, and the background angular distribution can be subtracted by measuring it in sidebands. A second interesting study is the ratio of two-b-tag to one-btag events in ρ T → W π T . The ratio of ρ T0 to ρ T± production is fairly well known because the relevant parton distribution functions are. The ETC coupling of π T to quarks and leptons suggest ¯ bc ¯ and that π T ’s less massive than the top quark decay to bb, ¯ The two-b to one-b ratio tests this common but not theoretibu. cally well-established assumption. For example, Ref. [33] considers a search for ρ T± → γ π T± → γ τ ντ based on the supposition that
¯ are suppressed by CKM-like mixing angles. πT± → bq
We hope that 4–5 fb−1 at the Tevatron are sufficient to carry these studies out. Careful simulations of their signal and backgrounds are needed to determine that. The signal processes may be generated with Pythia [34]. The new release and its description may be found at http://www.hepforge.org. At the LHC, the ρ T → W π T → ν bj signals are swamped by backgrounds from t t¯ and W plus heavy flavor production. The t t¯ cross section is two orders of magnitude larger there than at the Tevatron! The best channel for a quick discovery and then observing the sin2 θ distribution is ρ T± → W ± Z 0 → ± ν + − [24, 26]. For e and/or μ final states, the cross section times branching ratio ranges from about 100 fb for M ρT = 300 GeV to 15 fb for
M ρT = 500 GeV. Integrated luminosities of 2.5–15 fb−1 are needed √ for S / S + B = 5σ . The studies in Ref. [26] indicate that the sin2 θ distribution can be seen with (10, 40, 80) fb−1 for M ρT = (300, 400, 500) GeV. The 3π T decay channel of the ω T is closed, while techni-isospin conservation greatly suppresses ω T → W π T . Therefore, for M ωT M ρT and Q U + Q D 1, its major detectable decays at the Tevatron ¯ and + − . For Q U + Q D = 0, ρ T and ω T are ω T → γ π T0 → γ bb
σ p¯ p → ρT± → W ± πT0 1.5 pb,
The studies we propose include the angular distribution in ρ T → W π T and W Z ; the decays ω T → γ π T , γ Z , + − and their an±,0 and their decay disgular distributions; and the search for a T tributions. With even modest luminosity, the LHC should be able to discover the ρ T and a T up to masses exceeding 500 GeV and over a wide range of TCSM parameters [24,26]. Discovering the ω T at the LHC may require 10–100 fb−1 , depending on its mass and decay mode. We stress again that the studies carried out so far to determine the LHC’s reach for technicolor are preliminary and more careful ones are needed. The LHC studies in Refs. [26,27] used M ρT = M√ ωT = 300–500 GeV, M a T = 1.1M ρT and M πT = 200–350 GeV (and s = 14 TeV).
(2)
1 The I = 0 partner h T of a T presumably is nearly degenerate with it, but it cannot be produced via the VMD process at hadron and lepton colliders. 2 Of course, if both experiments are seeing a signal, either DØ fluctuated up or CDF down. 3 The ALEPH Collaboration at LEP searched for a ρ T enhancement in e + e − →
W L+ W L− and claimed a limit of M ρT > 600 GeV [32]. The ALEPH analysis does not apply to the TCSM because it has a ρ T0 → W L+ W L− coupling that is proportional
to sin2 χ 1. We have re-examined the ALEPH data and concluded that it sets no meaningful limit on the TCSM for the masses and other parameters assumed here. We shall present our analysis in a forthcoming paper.
decays to γ π T0 are greatly suppressed and ω T → ¯f f decays are forbidden altogether. It is very important that these final states are sought in the new high-luminosity data sets at the Tevatron. There is much to be done for the ω T at the LHC. Its discovery may well be the first thing, and γ Z 0 may be the channel to focus on. The cross sections times branching ratios of Z → e + e − , μ+ μ− are (20, 6, 3) fb for M ωT = (300, 400, 500) GeV. The angular distributions for q¯ q → ω T → γ π T and γ Z L0 are proportional to 1 + cos2 θ . The superb energy resolution achievable in the γ Z → γ + − final states compensates somewhat for the lower signal rates [26], and should help distinguish the signal’s cos θ dependence from the background’s. We also urge that ω T → + −
E. Eichten, K. Lane / Physics Letters B 669 (2008) 235–238
237
studies be carried out. These depend on TCSM parameters and may help determine them. 3. The a T If a T and ρ T are close enough in mass to reduce the S-parameter to an acceptable level, the channels a T → 3π T and ρ T π T certainly are closed. The two-body decay modes consistent with techni-isospin symmetry (for “strong” decays) and CP conservation are then a T → G π T and G W L , G V T , and W L V T where V T = ρ T or ωT , G = γ or a transversely polarized W or Z . Following Refs. [10, 11], the decay amplitudes are:
M a T ( p 1 ) → G ( p 2 )πT ( p 3 ) =
eV a T G A πT 2M V 2
F˜ 1 F 2∗λμ + λμ
e A a T G V πT
M aT ( p1 ) → G ( p2 )V T ( p3 ) =
eV a T G V V T 2M 2V 3
2M A 2
F˜ 1 F 2∗μν F 3∗λν + λμ
ga T ρ T π T 2M a T
λμ
e AaT G A V T
M a T i ( p 1 ) → ρ T j ( p 2 ) W Lk ( p 3 ) =
F 1 F 2∗λμ ;
2M 2A
(3)
F 1 F 2∗μν F 3∗λν ; λμ
(4)
(a)
3
i jk sin χ F 1λμ F 2∗λμ .
(5)
Phase-space limitations imply that only G π T and G W L are important. The a T also decays to fermion pairs via the W and Z ; these modes become dominant (but do not lead to large cross sections at the Tevatron) when the M V , A are large. In Eqs. (3)–(5), νρ F nλμ = nλ pnμ − nμ pnλ and F˜ nλμ = 12 λμνρ F n ; (i , j , k) are isospin indices. The TCSM mass parameters M V 2,3 , M A 2,3 are similar to M V , A ≡ M V 1 , A 1 in Ref. [11] and are expected to †
†
be O ( M ρT ). The factors V a T G A πT = 2 Tr( Q a T { Q G A , Q πT }) and †
†
A a T G V πT = 2 Tr( Q a T [ Q G V , Q πT ]) are given in Ref. [11] by using Q a T = Q ρT and the other charges as defined there. The couplings of a T to the axial part of the weak bosons G A = ( W A , Z A ) are † f Ga T = 2 α /αa T Tr( Q a T Q G A ) = (− α /αa T /(2 sin θ W ), − α /αa T sin(2θ W )). These enter the bosons’ propagator matrices. Here, αaT = ga2T /4π is analogous to αρT of the TCSM and is defined by
Ω| 12 T¯ γμ γ5 τi T |a T j ( p ) = M a2T μ ( p )δi j / ga T . If we scale g ρT from the ρππ coupling g ρ determined from the decay τ → ρντ , and set ga T = g ρT to make S small, then αa T = 2.16(3/ N TC ) in the
(b) Fig. 1. a T decay rates for parameters given in the text. Total width (black). (a) a0T → W ± π T∓ (red dotted),
i
¯f i f i (blue dashed), W + W − (blue dot-dashed) and + − ¯f f i (red dashed), W ± π 0 (blue dotted), γ π ±
TCSM. Sample decay rates are shown in Fig. 1 for 225 < M a T < 250 GeV and the other TCSM parameters we used in our Tevatron calculations. The most important decay modes are a0T → W ± π T∓ , + + 0 0 + + 0 W + W − , and + − ; a+ T → W π T , γ π T , Z π T , and W Z and, + perhaps, γ W . These decays yield prominent signatures involving leptons, missing transverse energy, photons and b-jets. As for ρ T and ω T , the a T are very narrow. In Fig. 2 we display the signal production rates at the Tevatron ∓,0 ±,0 for W ± π T , γ π T (summed over all charges), W ± Z 0 , Z 0 π T± , γ W ± , γ Z 0 , + − and ± ν .4 These include contributions from ρT , ωT and a T intermediate states. The cross sections without the a T present are 3.9, 0.45, 0.68, 0.67, 0.04, 0.07, 0.13 and 0.20 pb, ±,0 respectively. So, e.g., there is about 1 pb of a T → W π T and ± ± 0.3 pb of a T → γ π T . As M V i , A i is increased, the rates for processes involving a transverse EW boson decrease while + − and ± ν rates increase. In hadron colliders, all the production comes from these narrow resonances, not their tails, so that the invariant masses of the final states are sharply defined. If M a T
M ρT ,ωT + 20 GeV, it should be possible to discern the separate vector and axial vector contributions. The more precisely measured Q -value will be helpful.5 Also, determination of the final state angular distribution may clarify what is happening. Similar rates as in Fig. 2 occur at the LHC for technihadron masses that are 1.5–2 times as large. As already mentioned, ρ T± → W ± Z and ω T → γ Z (and possibly γ π T ) have the most man± ageable backgrounds. The a± T is best sought in its γ W L mode. The cross section times branching ratio to e and μ final states is (170, 65, 30) fb for M a T = (330, 440, 550) GeV. As for ω T → γ Z L , this mode has a 1 + cos2 θ angular distributions. The best hope for discovering a0T at the LHC appears to be the + − channel. In conclusion, the time is ripe for dedicated searches for lowscale technicolor at the Tevatron. There is, or soon will be, enough
4 No K-factor has been applied to these cross section estimates. Standard-model contributions to W Z , γ W and γ Z rates are not included. For narrow resonances at a hadron collider, they may be added incoherently to the signal rates.
couraging results, for
(magenta short-long dashed). (b)
i
i
T
T
(green dot-long dashed), W ± Z 0 (blue dot-dashed), Z 0 π T± (black long dashed), γ W ± (green dot-dot-dashed) and ± ν (magenta short-long dashed). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
5
Just such a study was carried out for the ATLAS detector at the LHC, with en0 ± + − ¯ ρT± , a± T → Z π T → bq in Ref. [27].
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E. Eichten, K. Lane / Physics Letters B 669 (2008) 235–238
Mrenna for including the new a T processes in Pythia. We thank Adam Martin and Veronica Sanz for many valuable conversations. We also thank Michael Barnett, Ken Hayes, and Colin Morningstar for helpful input on a technical point. K.L. also thanks Laboratoire d’Annecy-le-Vieux de Physique Theorique for its hospitality and support. FNAL is operated by Fermi Research Alliance, LLC, under contract DE-AC02-07CH11359 with the US Department of Energy. K.L.’s research is supported by the Department of Energy under Grant No. DE-FG02-91ER40676.
References
Fig. 2. Production rates for W π T (black solid), Z π T (red dotted), W Z (black dotdashed), γ π T (green dashed), γ W (blue short dashed), γ Z (blue dot-short dashed), ± ¯ + − (magenta dot-long √ dashed) and ν (magenta long dashed) in p p collisions at the Tevatron with s = 1.96 TeV. The rates Z π T , W Z and γ π T are nearly identical over the whole range; except at low a T mass where the γ π T rate is lower. All charge modes are summed. M ρT = M ωT = 225 GeV and M πT = 125 GeV, and other parameters are given in the text. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
data to discover, or rule out, ρ T and π T with masses below about 250 GeV and 150 GeV. If ρ T → W π T is found, its decay angular distribution is approximately sin2 θ , an important confirmation of the underlying technicolor dynamics. It will also be profoundly ¯ There is good theoretimportant to search for ω T → γ π T → γ bb. ical reason to expect that the spectrum of low-scale technicolor is richer than heretofore thought, with the axial vector state a T approximately degenerate with its ρ T partner. The axial states also decay into EW gauge bosons plus a technipion. At the LHC, the most promising modes appear to be ρ T± → W L± Z L0 , ω T → γ Z L0 and
± 2 a± T → γ W L . The first has a sin θ decay distribution while the 2 other two are 1 + cos θ . Luminosities of a few to a few 10s of fb−1 are sufficient to discover ρ T and a T up to about 500 GeV; the ω T may require 10–100 fb−1 . Finally, ω T , a0T → + − are likely to be the most promising ways to study these states at the LHC. Detailed simulations are needed. We urge the detector collaborations to carry them out.
Acknowledgements We are especially grateful to Meenakshi Narain and Weiming Yao for discussions about the search for technihadrons and to Steve
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Contents lists available at ScienceDirect
Physics Letters B www.elsevier.com/locate/physletb
Low-scale technicolor at the Tevatron and LHC Estia Eichten a,∗ , Kenneth Lane b a b
Fermi National Accelerator Laboratory, PO Box 500, Batavia, IL 60510, USA Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA
a r t i c l e
i n f o
Article history: Received 27 June 2007 Received in revised form 20 September 2008 Accepted 20 September 2008 Available online 27 September 2008 Editor: B. Grinstein
a b s t r a c t The Tevatron experiments CDF and DØ are close to making definitive statements about the technicolor discovery mode ρ T → W π T for M ρT 250 GeV and M πT 150 GeV. We propose new incisive tests for this mode and searches for others that may be feasible at the Tevatron and certainly are at the LHC. The other searches include two long discussed, namely, ω T → γ π T and + − , and a new one—for the I G J P C = 1− 1++ partner, a T , of the ρ T . Adopting the argument that the technicolor contribution to S is reduced if M a T M ρT , we enumerate important a T decays and estimate production rates at the colliders. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Long ago we pointed out that technicolor’s (TC) walking gauge coupling [1–4] strongly indicates that the energy scale of its bound states is much lower than the roughly 1 TeV expected from the earliest TC studies [5]. Thus, the lightest technihadrons may well be within reach of the Tevatron collider, with production rates of several picobarns; they certainly are accessible at the LHC. Furthermore, they should have striking decay signatures. To review the arguments [6–8]: (1) The walking TC gauge coupling probably requires either a large √ number N D of technifermion doublets so that ΛTC 250 GeV/ N D 100 GeV, or two TC scales, one much lower than 250 GeV. (2) Walking enhances the masses of pseudo-Goldstone technipions, π T , more than those of their vector partners, ρ T and ω T . This probably closes the vectors’ all-π T decay channels, leaving only those involving at least one electroweak ±,0 (EW) gauge boson (especially longitudinally-polarized W L ) and perhaps a π T . Another striking final state is + − . Technipions are expected to decay via extended technicolor (ETC) interactions [9] to the heaviest flavors possible, putting a premium on b-tagging. Thus, those accessible at the Tevatron will appear in vector-mesondominated Drell–Yan processes such as q¯ q → γ , Z , W → ρ T → W π T → ± ν bq¯ and ω T → γ π T0 → γ bb. At the LHC, large backgrounds tend to force one into looking at all-EW boson final states ending up in e and μ-generation leptons. The phenomenology of the lightest π T , ρ T and ω T of lowscale technicolor—bound states of the lightest technifermion colorsinglet EW doublet, ( T U , T D )—is embodied in the “Technicolor Straw-Man Model” (TCSM) [10,11]. The TCSM’s most important assumptions are: (1) These technihadrons may be treated in isola-
*
Corresponding author. E-mail addresses: [email protected] (E. Eichten), [email protected] (K. Lane).
0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.09.047
tion, without significant mixing or other interference from highermass technihadrons. (2) The T¯ T technipions Π T are not mass eigenstates, but they may be treated as simple two-state mixtures ±,0 ±,0 of W L and mass-eigenstate π T :
|Π T = sin χ | W L + cos χ |πT .
(1)
Here, sin χ = F T /246 GeV, where √ F T is the πT decay constant. In a model with N D 1, sin χ ∼ = 1/ N D ; in a two-scale model, F T
246 GeV [6]. This implies that the technivectors are very narrow, with decay rates suppressed by some combination of phase space and powers of sin χ and/or EW gauge couplings. (3) Techni-isospin is a good symmetry. (4) Finally, something like topcolor-assisted technicolor [12] is needed to keep the top quark from decaying copiously into π T+ b when M πT 160 GeV. Thus, if π T+ is heavier
¯ than the top, it does not decay exclusively to t b. Notwithstanding the isolation assumption above, many highermass states are reasonably expected. In Refs. [13,14] it was argued that walking TC invalidates the standard QCD-based calculations of the precision-electroweak S-parameter [15–18] because the spectral functions in the integral for S cannot be saturated by just the lightest ρ T and its axial partner, a T . Something more must make the spectral integrals converge much slower than they do in QCD; the obvious possibility is a tower of vector and axial-vector isovector mesons. The main message of this Letter is that the lightest a T is within reach of the Tevatron and LHC if the ρ T and ω T are, and that a T decays also produce unusual signatures to aid their discovery. In fact, it has long been recognized that the S-parameter may be significantly reduced or even made negative if ρ T and a T pairs in the tower are close in mass and have comparable couplings to their respective currents; see, e.g., Refs. [19–21]. More recently, a number of attempts have been made to model walking TC and calculate S using the AdS/CFT connection; see, e.g., Ref. [22,23]. We adopt these papers’ suggestion that M a T M ρT and explore its
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phenomenological consequences.1 For M a T M ρT = 200–250 GeV, its discovery should be possible at the Tevatron. We expect there would be little trouble discovering and studying a T at the LHC. Preliminary studies for all these technihadrons at the LHC appear in Refs. [24–27]. Our second motivation is the appearance of interesting anomalies in searches for ρ T → W ± π T → ± / E T b jet by the DØ and CDF Collaborations. In 2006 the DØ Collaboration presented two analyses of a 388 pb−1 data set, one cut-based, the other using a neural net (NN) [28]. While it was expected that the NN analysis would exclude a greater region in the (M W bj , M bj )-plane than the cutbased one, in fact neither excluded beyond M ρT 215 GeV and M πT 120 GeV for the default TCSM parameters used; see Fig. 3 in Ref. [28]. Presumably, the NN analysis was limited by an excess near that endpoint. There are two recent CDF analyses, one in late 2006 based on 955 pb−1 [29], and a new one using 1.9 fb−1 [30,31]. The TCSM parameters used were the same as DØ’s as far as the ρ T → W π T search is concerned. The 2008 analysis improves on the 2006 one, e.g., excluding M πT < 110 GeV, M ρT < 210 GeV at the 95% C.L. However, as with DØ, the CDF exclusion plot (Fig. 4 in [31]) falls well short of the expected level at and above M πT = 125 GeV and M ρT = 210 GeV.2 An interesting variable used in the CDF analyses is Q = M W bj − M bj − M W . The resolution in Q is a few GeV, much better than in M bj and M W bj alone, because jet energy uncertainties largely cancel in the difference. If there is a narrow ρ T decaying to W π T , histograms of M bj or M W bj with Q less than fixed values—say 5, 10, 15, . . . , 50 GeV—will exhibit a sudden increase in one of the invariant mass bins when, and only when, Q has its resonant value. In the 2008 analysis CDF presents color-coded two-dimensional plots of M bj vs. Q -value. The colors in these plots are hard to distinguish; we urge CDF to show histograms, with error bars, of M bj or M W bj for a range of cuts on Q . In the remainder of this Letter, we describe other studies and searches for low-scale TC that may be possible at the Tevatron with larger data sets and some that certainly can be carried out at the LHC. For our Tevatron calculations, we use M ρT = M ωT = 225 GeV, M a T = 225–250 GeV and M πT = 125 GeV. The isoscalar technipion π T0 in the TCSM is assumed heavy, 300 GeV, so that none of the lightest technivectors decay into it. The other TCSM parameters used here are sin χ = 13 , Q U = Q D + 1 = 1, N TC = 4 and M V 1,2,3 = M A 1,2,3 = M ρT = 225 GeV. The latter are defined in Eqs. (3) below.3 Typical cross sections for these parameters are
σ p¯ p → ρT0 → W ± πT∓ 2.5 pb;
σ p¯ p → ωT → γ πT0 0.3 pb, σ p¯ p → ωT → γ Z 0 0.07 pb;
σ p¯ p → ωT → + − 0.2 pb, σ p¯ p → ωT → ± ν 0.3 pb.
2. The ρ T and the ω T The angular distribution in qq¯ → ρ T → W π T is approximately sin2 θ , where θ is the angle in the subprocess c.m. frame between the incoming quark and the outgoing W [11]. The reason is that 80–90% of this process is qq¯ annihilation to W L π T , effectively a pair of pseudoscalars. Verification of this angular distribution would be strong confirmation of its underlying TC origin. Requiring Q M ρT − M πT − M W will greatly enrich the signal-to-background for this analysis, and the background angular distribution can be subtracted by measuring it in sidebands. A second interesting study is the ratio of two-b-tag to one-btag events in ρ T → W π T . The ratio of ρ T0 to ρ T± production is fairly well known because the relevant parton distribution functions are. The ETC coupling of π T to quarks and leptons suggest ¯ bc ¯ and that π T ’s less massive than the top quark decay to bb, ¯ The two-b to one-b ratio tests this common but not theoretibu. cally well-established assumption. For example, Ref. [33] considers a search for ρ T± → γ π T± → γ τ ντ based on the supposition that
¯ are suppressed by CKM-like mixing angles. πT± → bq
We hope that 4–5 fb−1 at the Tevatron are sufficient to carry these studies out. Careful simulations of their signal and backgrounds are needed to determine that. The signal processes may be generated with Pythia [34]. The new release and its description may be found at http://www.hepforge.org. At the LHC, the ρ T → W π T → ν bj signals are swamped by backgrounds from t t¯ and W plus heavy flavor production. The t t¯ cross section is two orders of magnitude larger there than at the Tevatron! The best channel for a quick discovery and then observing the sin2 θ distribution is ρ T± → W ± Z 0 → ± ν + − [24, 26]. For e and/or μ final states, the cross section times branching ratio ranges from about 100 fb for M ρT = 300 GeV to 15 fb for
M ρT = 500 GeV. Integrated luminosities of 2.5–15 fb−1 are needed √ for S / S + B = 5σ . The studies in Ref. [26] indicate that the sin2 θ distribution can be seen with (10, 40, 80) fb−1 for M ρT = (300, 400, 500) GeV. The 3π T decay channel of the ω T is closed, while techni-isospin conservation greatly suppresses ω T → W π T . Therefore, for M ωT M ρT and Q U + Q D 1, its major detectable decays at the Tevatron ¯ and + − . For Q U + Q D = 0, ρ T and ω T are ω T → γ π T0 → γ bb
σ p¯ p → ρT± → W ± πT0 1.5 pb,
The studies we propose include the angular distribution in ρ T → W π T and W Z ; the decays ω T → γ π T , γ Z , + − and their an±,0 and their decay disgular distributions; and the search for a T tributions. With even modest luminosity, the LHC should be able to discover the ρ T and a T up to masses exceeding 500 GeV and over a wide range of TCSM parameters [24,26]. Discovering the ω T at the LHC may require 10–100 fb−1 , depending on its mass and decay mode. We stress again that the studies carried out so far to determine the LHC’s reach for technicolor are preliminary and more careful ones are needed. The LHC studies in Refs. [26,27] used M ρT = M√ ωT = 300–500 GeV, M a T = 1.1M ρT and M πT = 200–350 GeV (and s = 14 TeV).
(2)
1 The I = 0 partner h T of a T presumably is nearly degenerate with it, but it cannot be produced via the VMD process at hadron and lepton colliders. 2 Of course, if both experiments are seeing a signal, either DØ fluctuated up or CDF down. 3 The ALEPH Collaboration at LEP searched for a ρ T enhancement in e + e − →
W L+ W L− and claimed a limit of M ρT > 600 GeV [32]. The ALEPH analysis does not apply to the TCSM because it has a ρ T0 → W L+ W L− coupling that is proportional
to sin2 χ 1. We have re-examined the ALEPH data and concluded that it sets no meaningful limit on the TCSM for the masses and other parameters assumed here. We shall present our analysis in a forthcoming paper.
decays to γ π T0 are greatly suppressed and ω T → ¯f f decays are forbidden altogether. It is very important that these final states are sought in the new high-luminosity data sets at the Tevatron. There is much to be done for the ω T at the LHC. Its discovery may well be the first thing, and γ Z 0 may be the channel to focus on. The cross sections times branching ratios of Z → e + e − , μ+ μ− are (20, 6, 3) fb for M ωT = (300, 400, 500) GeV. The angular distributions for q¯ q → ω T → γ π T and γ Z L0 are proportional to 1 + cos2 θ . The superb energy resolution achievable in the γ Z → γ + − final states compensates somewhat for the lower signal rates [26], and should help distinguish the signal’s cos θ dependence from the background’s. We also urge that ω T → + −
E. Eichten, K. Lane / Physics Letters B 669 (2008) 235–238
237
studies be carried out. These depend on TCSM parameters and may help determine them. 3. The a T If a T and ρ T are close enough in mass to reduce the S-parameter to an acceptable level, the channels a T → 3π T and ρ T π T certainly are closed. The two-body decay modes consistent with techni-isospin symmetry (for “strong” decays) and CP conservation are then a T → G π T and G W L , G V T , and W L V T where V T = ρ T or ωT , G = γ or a transversely polarized W or Z . Following Refs. [10, 11], the decay amplitudes are:
M a T ( p 1 ) → G ( p 2 )πT ( p 3 ) =
eV a T G A πT 2M V 2
F˜ 1 F 2∗λμ + λμ
e A a T G V πT
M aT ( p1 ) → G ( p2 )V T ( p3 ) =
eV a T G V V T 2M 2V 3
2M A 2
F˜ 1 F 2∗μν F 3∗λν + λμ
ga T ρ T π T 2M a T
λμ
e AaT G A V T
M a T i ( p 1 ) → ρ T j ( p 2 ) W Lk ( p 3 ) =
F 1 F 2∗λμ ;
2M 2A
(3)
F 1 F 2∗μν F 3∗λν ; λμ
(4)
(a)
3
i jk sin χ F 1λμ F 2∗λμ .
(5)
Phase-space limitations imply that only G π T and G W L are important. The a T also decays to fermion pairs via the W and Z ; these modes become dominant (but do not lead to large cross sections at the Tevatron) when the M V , A are large. In Eqs. (3)–(5), νρ F nλμ = nλ pnμ − nμ pnλ and F˜ nλμ = 12 λμνρ F n ; (i , j , k) are isospin indices. The TCSM mass parameters M V 2,3 , M A 2,3 are similar to M V , A ≡ M V 1 , A 1 in Ref. [11] and are expected to †
†
be O ( M ρT ). The factors V a T G A πT = 2 Tr( Q a T { Q G A , Q πT }) and †
†
A a T G V πT = 2 Tr( Q a T [ Q G V , Q πT ]) are given in Ref. [11] by using Q a T = Q ρT and the other charges as defined there. The couplings of a T to the axial part of the weak bosons G A = ( W A , Z A ) are † f Ga T = 2 α /αa T Tr( Q a T Q G A ) = (− α /αa T /(2 sin θ W ), − α /αa T sin(2θ W )). These enter the bosons’ propagator matrices. Here, αaT = ga2T /4π is analogous to αρT of the TCSM and is defined by
Ω| 12 T¯ γμ γ5 τi T |a T j ( p ) = M a2T μ ( p )δi j / ga T . If we scale g ρT from the ρππ coupling g ρ determined from the decay τ → ρντ , and set ga T = g ρT to make S small, then αa T = 2.16(3/ N TC ) in the
(b) Fig. 1. a T decay rates for parameters given in the text. Total width (black). (a) a0T → W ± π T∓ (red dotted),
i
¯f i f i (blue dashed), W + W − (blue dot-dashed) and + − ¯f f i (red dashed), W ± π 0 (blue dotted), γ π ±
TCSM. Sample decay rates are shown in Fig. 1 for 225 < M a T < 250 GeV and the other TCSM parameters we used in our Tevatron calculations. The most important decay modes are a0T → W ± π T∓ , + + 0 0 + + 0 W + W − , and + − ; a+ T → W π T , γ π T , Z π T , and W Z and, + perhaps, γ W . These decays yield prominent signatures involving leptons, missing transverse energy, photons and b-jets. As for ρ T and ω T , the a T are very narrow. In Fig. 2 we display the signal production rates at the Tevatron ∓,0 ±,0 for W ± π T , γ π T (summed over all charges), W ± Z 0 , Z 0 π T± , γ W ± , γ Z 0 , + − and ± ν .4 These include contributions from ρT , ωT and a T intermediate states. The cross sections without the a T present are 3.9, 0.45, 0.68, 0.67, 0.04, 0.07, 0.13 and 0.20 pb, ±,0 respectively. So, e.g., there is about 1 pb of a T → W π T and ± ± 0.3 pb of a T → γ π T . As M V i , A i is increased, the rates for processes involving a transverse EW boson decrease while + − and ± ν rates increase. In hadron colliders, all the production comes from these narrow resonances, not their tails, so that the invariant masses of the final states are sharply defined. If M a T
M ρT ,ωT + 20 GeV, it should be possible to discern the separate vector and axial vector contributions. The more precisely measured Q -value will be helpful.5 Also, determination of the final state angular distribution may clarify what is happening. Similar rates as in Fig. 2 occur at the LHC for technihadron masses that are 1.5–2 times as large. As already mentioned, ρ T± → W ± Z and ω T → γ Z (and possibly γ π T ) have the most man± ageable backgrounds. The a± T is best sought in its γ W L mode. The cross section times branching ratio to e and μ final states is (170, 65, 30) fb for M a T = (330, 440, 550) GeV. As for ω T → γ Z L , this mode has a 1 + cos2 θ angular distributions. The best hope for discovering a0T at the LHC appears to be the + − channel. In conclusion, the time is ripe for dedicated searches for lowscale technicolor at the Tevatron. There is, or soon will be, enough
4 No K-factor has been applied to these cross section estimates. Standard-model contributions to W Z , γ W and γ Z rates are not included. For narrow resonances at a hadron collider, they may be added incoherently to the signal rates.
couraging results, for
(magenta short-long dashed). (b)
i
i
T
T
(green dot-long dashed), W ± Z 0 (blue dot-dashed), Z 0 π T± (black long dashed), γ W ± (green dot-dot-dashed) and ± ν (magenta short-long dashed). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
5
Just such a study was carried out for the ATLAS detector at the LHC, with en0 ± + − ¯ ρT± , a± T → Z π T → bq in Ref. [27].
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Mrenna for including the new a T processes in Pythia. We thank Adam Martin and Veronica Sanz for many valuable conversations. We also thank Michael Barnett, Ken Hayes, and Colin Morningstar for helpful input on a technical point. K.L. also thanks Laboratoire d’Annecy-le-Vieux de Physique Theorique for its hospitality and support. FNAL is operated by Fermi Research Alliance, LLC, under contract DE-AC02-07CH11359 with the US Department of Energy. K.L.’s research is supported by the Department of Energy under Grant No. DE-FG02-91ER40676.
References
Fig. 2. Production rates for W π T (black solid), Z π T (red dotted), W Z (black dotdashed), γ π T (green dashed), γ W (blue short dashed), γ Z (blue dot-short dashed), ± ¯ + − (magenta dot-long √ dashed) and ν (magenta long dashed) in p p collisions at the Tevatron with s = 1.96 TeV. The rates Z π T , W Z and γ π T are nearly identical over the whole range; except at low a T mass where the γ π T rate is lower. All charge modes are summed. M ρT = M ωT = 225 GeV and M πT = 125 GeV, and other parameters are given in the text. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
data to discover, or rule out, ρ T and π T with masses below about 250 GeV and 150 GeV. If ρ T → W π T is found, its decay angular distribution is approximately sin2 θ , an important confirmation of the underlying technicolor dynamics. It will also be profoundly ¯ There is good theoretimportant to search for ω T → γ π T → γ bb. ical reason to expect that the spectrum of low-scale technicolor is richer than heretofore thought, with the axial vector state a T approximately degenerate with its ρ T partner. The axial states also decay into EW gauge bosons plus a technipion. At the LHC, the most promising modes appear to be ρ T± → W L± Z L0 , ω T → γ Z L0 and
± 2 a± T → γ W L . The first has a sin θ decay distribution while the 2 other two are 1 + cos θ . Luminosities of a few to a few 10s of fb−1 are sufficient to discover ρ T and a T up to about 500 GeV; the ω T may require 10–100 fb−1 . Finally, ω T , a0T → + − are likely to be the most promising ways to study these states at the LHC. Detailed simulations are needed. We urge the detector collaborations to carry them out.
Acknowledgements We are especially grateful to Meenakshi Narain and Weiming Yao for discussions about the search for technihadrons and to Steve
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