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TECHNICOLOR ENHANCEMENT OF t¯t

arXiv:hep-ph/9207226v1 9 Jul 1992TECHNICOLOR ENHANCEMENT OF t¯tPRODUCTION AT TeV-COLLIDERSThomas Appelquist and George TriantaphyllouDepartment of Physics, Yale University, New Haven, Ct. 06520January 8, 2018AbstractIt is shown that a technicolor theory containing a color-octet technipion,usually denoted by P 0′8 , will give rise to an enhancement of t¯t production atthe Tevatron, LHC and SSC, via the process gg →P 0′8→t¯t. The relevantcross-sections are computed taking into account the large lower bound on thetop mass coming from the ”top search” experiments at LEP and CDF.

At theLHC and SSC, the signal is found to be comparable to the QCD background,making the process quite accesible.0

Technicolor theories typically contain pseudo-Goldstone bosons (technipi-ons), which arise from the breakdown of global chiral symmetries. Here, the pro-duction and subsequent decay of a color-octet technipion at the Tevatron, LHCand SSC is studied.

The sub-process considered isgluon −gluon →P 0′8→t¯t,where P 0′8 is the technipion. The subscript ”8” denotes that it is a QCD octet, thesuperscript ”0” that it is neutral, and the prime that it is a singlet under the weakSU(2)L. This particle is expected to be light compared to most technihadrons, andtherefore more accessible to the TeV-colliders.

However, it is assumed throughoutthis paper that its mass is above the t¯t production threshold.The effective ETC couplings of the technipions to the quarks are proportionalto mq/Fπ. Therefore, q¯q fusion as a production mechanism is not considered, noris the decay of the technipions into quarks lighter than the top or the bottom.

Thedecay of the technipions to two bottom quarks or to two gluons is not consideredeither, even though it gives non-negligible cross-sections, since the background tothese processes makes them difficult to observe. Moreover, we consider only thecolor-octet P 0′8 as the intermediate technipion, because color counting factors makeits cross-section approximately eight times larger than the color-singlet one.

Also,because the color-singlet technipion mass does not receive a QCD contribution, itcould lie below the t¯t production threshold. The results of this paper could, however,also be applied to a color-singlet technipion, if corrected by the relevant countingfactors.Color-octet technipions exist only in models with at least one colored doubletof technifermions.A one family model will be employed here.It has a globalSU(8)L × SU(8)R chiral symmetry that breaks down to an SU(8)L+R and thus1

produces 63 Goldstone bosons, 3 of which are ”eaten” by the W’s and the Z0, and60 of which acquire masses depending on their quantum numbers. Even thoughpresent experimental constraints on the S parameter do not favor a large technicolorsector [1], a theory with a complete techni-family is viable if the technicolor groupis not too large [2].

In the following, the technicolor gauge group SU(NTC) withNTC = 2 will be used.The process in question attracted the interest of several authors some yearsago [4-7]. However, the top mass used in those computations never exceeded 70GeV [5].

Given the dependance of the technicolor signal and the QCD backgroundon the quark and technipion masses, the current lower bound on mt ( mt > 91 GeV[7]) and the emergence of new classes of technicolor theories (the so-called walkingtheories [8]) that lead to larger technipion masses make it important to recomputethe relevant cross-sections.The mass of the color-octet technipion is estimated first. It receives contri-butions mainly from QCD and ETC interactions.

The QCD contribution, accordingto a previous estimate [9], givesM2P ≈9 ln 22π αs(M2P ) M2V ,(1)where MV is the mass of the lightest technivector resonance.To find MV , thefollowing scaling relation is used:MV = (3/NTC)1/2(Fπ/fπ) mρ ,(2)where fπ is the pion decay constant, and Fπ = 246 GeV√ND , with ND the number oftechnidoublets. For the one family model, ND = 4, so Fπ = 123 GeV.

Inserting theexpression for MV into Eq.1 gives MP ≈400 GeV .2

There is also an ETC contribution to the P 0′8mass. A previous estimategives roughly [10]M2P ≈g2ETC< ψ ¯ψ >2M2ETCF 2π,(3)where METC can range from 10 to 1000 TeV, and g2ETC/4π2 is expected to be O(1).In conventional technicolor theories, the chiral condensate < ψ ¯ψ >≈Λ3TC/4π2 ,where ΛTC ≈MVmρ ΛQCD denotes the technicolor confinement scale.

In these theories,therefore, the ETC contribution to the technipion mass can be at most about 100GeV. Walking technicolor models, however, can give larger masses to the technipionsvia high-momentum enhancement [8].

The upper limit of the technicolor condensate< ψ ¯ψ > in these models is of order METCΛ2TC , so the ETC contribution couldeven approach 1 TeV. The SU(NTC = 2) technicolor model with ND = 4 givesa somewhat enhanced condensate, but well below the upper limit.

Masses in therange 350 −550 GeV will be considered here.Next, in order to determine the cross-section for the sub-process gg →P 0′8 →t¯t, the partial decay widths of the P 0′8 to two gluons and to a quark pair are needed.They are [3]Γ(P 0′8 →gg)=5N 2TC384π3 α2s(M2P ) M3PF 2πandΓ(P 0′8 →t¯t)≈m2tMP4πF 2π 1 −4 m2tM2P!1/2,(4)where MP is the technipion mass, and α2s(M2P ) is the QCD coupling evaluatedat M2P . The width for t¯t decay depends on the specific assumption made for theETC-induced coupling of the technipion to t¯t.

Here, a CP-conserving coupling ofstrength 2mt/Fπ is used. A typical choice for the top mass, mt = 120 GeV, and3

the technipion mass, MP = 350 GeV, gives 0.05 GeV and roughly 20 GeV for thedecay widths of the techipion to gg and t¯t respectively. The latter could be smallerif the technipion mass is closer to the t¯t production threshold.To estimate the total decay width of the technipion, denoted here by Γtot,we note that it decays predominantly into a t¯t pair.

This is the case as long asmt >∼2 × 10−2MP . Thus, Γtot ≈Γ(P 0′8→t¯t) .

This estimate is valid as long asthe technipion mass does not become very close the t¯t production threshold, i.e. aslong as 1 −4m2t /M2P>∼10−6.Using the relativistic Breit-Wigner formula, the sub-process cross-section, forN TC = 2, then readsˆσ TC(gg →P 0′8 →t¯t)=π2Γ(P 0′8 →gg) Γ(P 0′8 →t¯t)(ˆs −M2P )2 + M2P Γ2tot=103(8π)3α2s(M2P ) M4P m2t (1 −4m2t /M2P )1/2F 4π ( (ˆs −M2P )2 + M2P Γ2tot ).

(5)The QCD final-state corrections are neglected in this expression. The decay widthsof Eq.4 should actually be corrected before being inserted in the cross-section forgg →P 0′8→t¯t since the relevant quantity entering these widths is not the massof the technipion, but the invariant mass√ˆs of the process.These correctionsare not taken into account, partly because the use of strict invariant mass cutsmakes their effects negligible, and partly because the uncertainty introduced by thetechnipion and top-quark masses, which are still experimentally unknown, makessuch an analysis too detailed.

It should be noted in particular that Eq.5 cannot beapplied for technipion masses, or√ˆs values too close to the t¯t production threshold.The result of Eq.5 can be carried one step further, in order to compute the4

differential cross-section with respect to the scattering angle. Since the technipionhas zero spin,dˆσ T Cdcosθ = ˆσ TC/2, where θ is the scattering angle measured in thegluon-gluon center-of-mass frame.The ingredients are now in hand to compute the integrated cross-section forthe process pp →P 0′8 →t¯t .

Denoting by s the total C.M. energy of the pp beams,we have ˆs = sxaxb = sτ, where τ ≡xaxb , and xa and xb are the momentumfractions of the two interacting partons a and b, considered to be massless.

In ourcase, they are gluons. The parton distribution functions for gluons, denoted byfg(xi, ˆs), i = a, b, can now be used, to writeσ TC(pp →P 0′8 →t¯t) ==Z τ+τ−dτZ Y−Ydy1Z y+y−dy2fg(xa, ˆs)fg(xb, ˆs)2q1 −4m2t /ˆs cosh2(y1−y22)dˆσ TCdcosθ (gg →P 0′8 →t¯t) ,(6)where the q¯q contribution to the process has been neglected.Here y1,2 are therapidities of the two top quarks measured in the laboratory frame and τ is defined asabove.

According to the above definitions, x ab = √τ exp(± y1+y22) . The quantitiesy± are defined as y± =minmax(±Y, ∓ln τ −y1).

The integration limits τ±, Y , andy± correspond to experimental cuts, and will be discussed shortly. The integratedcross-section σ TC is then computed for various top and technipion masses.

For thegluon distribution functions fg, the HMRS(B) functions are used, as described inRef.[11]. The integrals in Eq.6 are done numerically by a Monte-Carlo algorithm[12].

The program is stopped as soon as 104 Monte-Carlo-generated events havepassed all the cuts. This gives sufficiently small statistical errors.The form of Eq.5 implies that, while the cross-section can increase quadrat-ically with mt, this only happens for mt small enough so that the total width is5

dominated by decays other than the decay P 0′8 →t¯t. For the allowed mt range, how-ever, Γ(P 0′8→t¯t) dominates, making the integrated cross-section (Eq.6) roughlyindependant of the top mass, when the√ˆs integration range is larger than thelargest technipion width considered.If, however, the integration is done over afixed invariant mass range smaller than, or comparable to, the width to the lightestt¯t pair considered, the integrated cross-section decreases with the top mass, sincethe portion of the width falling inside the integration bin decreases.It is essential to estimate the background for this process, in order to seehow clear the signal will be experimentally.

The quantities ˆσ QCD(gg →t¯t) andˆσ QCD(q¯q →t¯t) are considered here, as they are expected to give the main con-tribution to the background. It should be noted that the technicolor process hasa substantial interference with the QCD process gg →t¯t.

This interference is ne-glected here, however, since the cuts applied on the invariant mass (see discussion oncuts below) reduce its effects to less than 10%. The QCD cross-sections for q¯q andgg fusion are taken from Ref.

[13], and they are then inserted into the numerical al-gorithm, in order to compute the cross-section σ bgd(pp →t¯t). For the q¯q processes,the up, down, and sea-quark distribution functions are used, again according to theanalysis of Ref.[11].

The computation for the Tevatron takes into account that itis a p¯p collider, unlike the SSC and LHC, which will be pp colliders. Finally, thereis an ambiguity as to which scale µ should be used for the calculation of the QCDcoupling for the background processes, having s-channel amplitudes on one hand,and t- and u-channel on the other, but this does not affect our results by more than10%.

The value µ =√ˆs is used here.A convenient choice of cuts, τ± for τ, ±Y for y1, and y± for y2 is needed6

in order to reduce the background as much as possible.The minimum possibleτ (= ˆs/s) cut will be determined by the experimental resolution δ√ˆs for the invariantmass. We will assume that a resolution of roughly 20 GeV - approximately 5% of the√ˆs values studied here and comparable to the natural line width of the technipion- is possible.

This of course depends on the details of detection of the hadronicjets and charged leptons after both t’s undergo the decay t →Wb. In Tables 1-3,numerical results are presented for integrated cross sections for both the technicolorprocess and the background.

The results are for a 20-GeV√ˆs bin centered aroundthe mass of the technipion. Thus, for this bin,τ± = (MP (GeV) ± 10 GeV)2s (GeV2).

(7)This choice has also the advantage of reducing the interference effects of the tech-nicolor and QCD processes to less than 10%, which is satisfactory for our purposes.Rapidity cuts are also placed, constraining the longitudinal momenta of tand ¯t to lie between the two wings of a momentum-space hyperboloid around thebeam axis. This reduces the QCD background, which is larger along the beam axis,and it also removes from the integration region of Eq.6 part of the phase spacethat is experimentally inaccessible, due to its proximity to the beam axis.Therapidities y1 and y2, measured in the laboratory frame, are constrained by Y andy± respectively.

A specific value for Y , for a given τ, automatically determines y±.The cut Y = 2.5 is chosen for the results presented in Tables 1-3. This is not veryrestrictive, since, even for p⊥= 0, it allows p ∥to be roughly as large as 6mt.

Thesignal-to-background ratio does not vary substantially with the choice of Y. Thisis due to the heaviness of the top quark, which makes the QCD background lessanisotropic than it is for lighter quarks.7

MP = 350 GeV√s = 1.8 TeV√s = 16 TeV√s = 40 TeVmt (GeV)σ TC (pb)σ bgd (pb)σ TC (pb)σ bgd (pb)σ TC (pb)σ bgd (pb)900.242.821080087032001200.192.216048067019001500.171.6140210580840Table 1:Numerical results for the different cross-sections in picobarns, for MP =350 GeV. The numbers given are rounded up to contain only two significant figures.The invariant mass bin width is 20 GeV.

The results are for NTC = 2; the technicolorcross-section increases quadratically with NTC = 2. Various choices for the top massare made.

The three different choices for the total C. M. energy correspond to theenergies of the Tevatron, LHC, and SSC respectively. The Monte-Carlo relativestatistical errors are typically on the order of 1 %.From the tables, it is apparent that colliders with larger center-of-mass ener-gies lead to larger production cross-sections.

This is because, for a given invariantmass√ˆs, they probe regions of smaller τ’s, where the parton, and especially thegluon, distribution functions f(√τ, ˆs) are larger. Another manifestation of the de-crease of f(√τ, ˆs) with increasing τ is the fact that, for a given √s, larger technipionmasses, corresponding to larger√ˆs values, give smaller cross-sections.For the range of technipion and top masses chosen, the background gg-fusionprocess has a cross-section that decreases with increasing top mass, unlike the q¯qprocess.Therefore, since the total C.M.

energies considered here correspond tosmall τ values, where the gluon distribution functions dominate over the quarkones, the total background decreases with increasing top mass.The technicolorcross-sections also decrease with increasing top-mass, a behavior in agreement withthe rough theoretical expectations based on Eq.5.The Tevatron cross-sections are quite small, and no more than a few signal8

MP = 450 GeV√s = 1.8 TeV√s = 16 TeV√s = 40 TeVmt (GeV)σ TC (pb)σ bgd (pb)σ TC (pb)σ bgd (pb)σ TC (pb)σ bgd (pb)900.0410.5710030049013001200.0280.52732103509601500.0220.46541402606401800.0190.394480210370Table 2:Results of the same computation as in Table 1, but with MP = 450 GeV.The increased technipion mass allows larger top masses to be considered. However,results for a top quark heavier than 180 GeV are not given, since present constraintson the ρ parameter [2] indicate that it is unlikely to be heavier than that.events per year should be expected.

The signal-to-background ratio is also worsefor the Tevatron than for the LHC and SSC. This is due to the fact that the q¯qcontribution to the background is larger at the Tevatron, where the ˆs/s valuesconsidered correspond to larger quark distribution functions.

Another reason whythe contribution of q¯q fusion to the background is larger is that the Tevatron is a p¯pcollider. At the LHC and SSC, the technicolor and background cross-sections arecomparable to each other, indicating that a substantial signal could be observed infuture experiments for the range of top masses studied here, if the P 0′8 exists.It is also useful to plot the corresponding differential cross-sections in theinvariant mass.

The computation of dσ T Cd√ˆsand dσ bgdd√ˆscan be done by a Monte-Carlo algorithm similar to the one used for Eq.6. A plot of the differential cross-sections dσ T Cdp⊥and dσ bgddp⊥could be even more useful, as p⊥may be easier to determineexperimentally than√ˆs [14].

Both of these plots will appear in a future publication.It is worth pointing out that the signal coming from a technipion P 0′8 can be9

MP = 550 GeV√s = 1.8 TeV√s = 16 TeV√s = 40 TeVmt (GeV)σ TC (pb)σ bgd (pb)σ TC (pb)σ bgd (pb)σ TC (pb)σ bgd (pb)900.78 ×10−20.14641203106201200.52 ×10−20.1341962004801500.37 ×10−20.1229721403601800.29 ×10−20.122252110260Table 3:Results for MP = 550 GeV.distinguished from a Higgs particle H0, since the latter has a much smaller cross-section for the same detection channel. Indeed, the fact that the technipion is acolor octet, and that its decay width Γ(P 0′8→gg) depends quadratically on thenumber of technicolors, makes the technipion production rate roughly 8N 2TC timeslarger than the corresponding Higgs process [3].To conclude, our results show that presently allowed values for the top massare such that a considerable enhancement of t¯t pairs at LHC and SSC energiescan be expected from color-octet technipion production and decay.

A similar, butsomewhat smaller, enhancement can be expected from the color-singlet technipion,if it lies above the t¯t threshold. Therefore, the process considered here can be usedas a direct test of a large class of technicolor models.

Finally, it is worth noting thatthe enhancement of b¯b production from technipion decay could also be interesting,especially if the technipion masses are below the t¯t production threshold.AcknowledgementsWe thank Charles Baltay, Ken Lane, Steven Manly and Torbjorn Sjostrand for veryhelpful discussions.10

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