Physics Letters B 281 ( 1992 ) 369-373 North-Holland PHYSICS LETTERS B

Pseudo-Goldstone boson production in ep collisions

Antonio Bueno and Fernando Corne t Departamento de l"isica Te6rica y del Cosmos, Universidad de Granada, 1:,'-18071 Granada, Spain

Received 17 January 1992

We study the production of pseudo-Goldstone bosons, as predicted in technicolor models, in ep collisions. Their production mechanism is via their coupling to two gauge bosons originated by the anomaly. Their signature is compared to the expected standard model backgrounds and some estimations of the expected sensitivity at HERA and LEP/LHC are shown.

The S U ( 2 ) X U ( 1 ) symmetry breaking mecha- nism remains an open question in spite of the great success of the standard model when compared to ex- perimental data. Indeed, there is no experimental evidence for the Higgs boson. In addition, the Higgs sector contains most of the free parameters of the theory. It is, thus, interesting to study alternative models to the Higgs mechanism and search for pos- sible experimental signals of these models. Techni- color was proposed some time ago [ 1 ] as a way to give mass to the gauge bosons W e and Z, naturally accounting for the isospin symmetry relation M w = M z cos0w and avoiding the presence of ele- mentary scalar particles. Extended technicolor models [2] offer, in addition, the possibility of generating masses for quarks and leptons. The original extendcd technicolor modcls suffered from the problem ofprc- dicting too large flavor changing neutral currents. It has been shown, however, that this problem can be solved with the walking technicolor models [ 3 ].

Technicolor models predict a largc number of res- onances with masses of the order of the technicolor symmetry breaking scale (a few TeV). But they also predict the existence of some pseudo-Goldstone bo- sons which should be light compared to that scale. They appear as a result of the spontaneous chiral symmetry breaking originated by the technifermion condensate ( ~ ) . Three of the Goldstone bosons disappear, giving masses to the W -+ and Z bosons, while the rest remain as physical particles. Let us re- call here that the basic technicolor model [4] with only one family of technifermions has an

SU(8)eXSU(8)R chiral symmetry broken into SU(8 )v lcading to 64 massless Goldstone bosons (in the limit where the strong, electroweak and extended technicolor interactions are turned off) . One of these Goldstone bosons acquires a large mass due to the technigluon anomaly and three give masses to the W -+ and Z. The remaining 60 become physical particles that receive their masses when all the interactions are turned on. Naturally, models with more technifer- mion families lead to a larger number of pseudo- Goldstone bosons.

In this letter we are going to study the possibility of producing and detecting neutral pseudo-Goldstone bosons as predicted in technicolor models in ep col- liders. In particular, we are going to discuss the cases of HERA and LEP/LHC. The energies and luminos- ities assumed in our numerical evaluations are x/.s=314 GeV, L = 10 32 c m - 2 S - l for HERA and xfs= 1.4 TeV, L = 1033 cm-2 s - ' for LEP/LHC.

The production mechanism of the pseudo-Gold- stone bosons in ep collisions is via their coupling to two gauge bosons. This coupling is originated by the chiral anomaly in the same way as the n°Tq , coupling in QCD. The tensorial form of the amplitude is com- pletely fixed by the anomaly and can be written as

lvv,v2 = Cvv,v2 Eu~,,pk"~k~e'(c a2 , ( 1 )

where k; (el) is the momentum (polarization vector) of the corresponding gauge boson and Cpv,v2 is given by

Cvv,v2 gig2 .~&\%c (2) -- 27t2fv

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Volume 281, number 3,4 PHYSICS LETTERS B 14 May 1992

withft, being the pseudo-Goldstone boson decay con- stant and Nrc the number of technicolors, g~ and g2 are the coupling constants of the two gauge bosons with generators T ~ and T 2, respectively. The anom- aly factor .~¢ is

4sC=tr{ T~( TIT2 + T 2T~ )L}

+tr{T~(T~T2+ T2T')R} , (3)

where L, R denote the gauge generators for the left and right technifermions and 1 "~ is the gcnerator as- sociated to the Goldstone boson W. Thus, .~¢ depends on the quantum numbers of the technifermions that enter in the composition of the pseudo-Goldstone boson W. It is clear from cqs. ( 1 ) - (3) that all the model dcpendence is contained in the constants Cpv,v~. We will leave thcse constants as free parameters.

In all the cases we arc going to discuss in this letter, the main production mechanism is via "[-7 or 7-g fu- sion. Other contributions, like Z-y, Z - Z or Z-g can safely be neglected due to the large Z mass. We have used thc Weisz~iker-Williams [ 5 ] approximation that relates the ep cross-section to the one for 7P collisions via

I

Go(s )= J aw(ys)f(y ' Q2) dy , (4) ymin

whcre Ymin =Stain/S, with x/s (ni l ) the center of mass energy for the ep (TP) collisions and f (y , Q2) is thc photon flux obtained from the incident electron of mass me:

n y ~ . (5 )

We first study the case of a colorless, isospin triplet pseudoscalar boson. Being an isospin triplet, it can- not couple to gluons. So, its main production mech- anism is via Y-7 fusion. The deep inelastic contribu- tion to the 7P production cross-section of a pseudo- Goldstone boson po with mass Mp? is given by

I ~ - ,~4 lz~ I

o ' (Tp- ,P°X)= f dx f dQ2~ (F/)(x' Q2) Xmm Q~ q,4

da X ~ (7~?:/)_,po (r/); ~ = x g ) , (6)

where Xmin=(M~,?+Q~))/g and c?7)(x, Q2) is the quark (antiquark) distribution function. The inte- gral ovcr Q2 has to be cutted at Q2=Q~ because in the region where Q2 < Q~ thc parton model is not re- liable anymore. For the quark distribution functions we have used set I of Eichtcn et al. [6], taking Q2 = 5 GeV 2.

Since the production mechanism involves a t- channel exchange of a photon, the region of low Q2 is important. In particular, the case of elastic scattering off the proton has been shown to be important in similar processes [ 7 ]. In this case the cross-section

Q2m~

1 f ~ [ TI2dQ2 (7) a(YP-* P(~P) - 16rr~2 Q~t,

where the integration limits are

max

+\[[.f~(Mp?+mp)2][g-(.kle?-mp)2]}, (8)

with rnp being the proton mass and

C~°~e2 [F~(Q2)A+F~(QZ)B] (9) ~'/_. I T [ 2 = 2Q 4

contains the electric and magnetic form factors of the proton:

0 2 GE(Q 2) =F~ ( 0 2 ) +F2(Q 2 ) 4m~

~GM(Q2)/2.79~ ( 1 + Q2/0.71 GcV2) -2 ,

GM(Q2)=F~(Q2)+Fz(O2)~2.79GE(Q 2) (10)

and A and B are defined by

4 2 2 2~ 2 2 ~ 2 2 4 A=2moQ + 2mpMct Q -4mpsQ + 2moQ 4 2 2 ~ 2 2 4 + M,IQ - 2Mp?sQ + 2My? Q

+ 2.f2Q2- 2gQ4 + Q 6 , '.

B= (1/2rn~) ( m4 On- M~?Qa + g2a4- gQ 6

2 2 0 4 9 - 4 2 6 +rnpMe, Q -2mpsQ +mpQ ). (11)

The contribution of the elastic scattering amounts to roughly one third of the total production cross-sec- tion, e.g. the total cross-section at HERA is atot= 1.4× 10-3 pb for Mi~ = 60 GeV and Cp?.rr= 1X 10 -4 GeV- ~ (this value corresponds to a model where the

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Volume 281, number 3,4 PHYSICS LETTERS B 14 May 1992

left-handed technifermions are weak isotriplets and their right-handed partners are isosinglets, with N'rc = 4 [ 8 ] ) while the elastic contribution amounts to a ~ = 0.5 × 10 -~ pb. The dominant decay modes will be 77 and TZ (when kinematically allowed). In both cases the expected background from the standard model is very small, allowing for a very clear signa- ture of the pseudo-Goldstone boson. In fig. 1 (dashed line) we show the bounds in the plane (Cp0.rv, Mpo) obtained requiting 10 events per year. For the region where MpV> 180 GeV a constant Ceor~> 1 × 1 0 -2 G e V - ' is required. However, it seems difficult to ob- tain such a large value for Cp,0 w in models that do not involve a very large number of technicolor or techn- ifermion families.

For a fixed value of Cvovy one can reach much larger values of Mp,~ at LEP /LHC. This, however, causes some uncertainties. For large enough values of Me?, the decay P~ --,tt becomes kinematically allowed. But the Yukawa coupling P° t t is unknown and strongly model dependent. On the other hand, tt pairs will be copiously produced at L E P / L H C via photon-gluon fusion [9]. Therefore, if F(P~)-- ,77)+F(P~>-,TZ ) < < F ( P ° - , t t ) an unrealistically large value of Cp?w will be needed to produce an observable signal for ,~/p? > 2m~. We show in fig. 2 (dashed line) the more optimistic case, where the tt branching ratio can be completely neglected in front of the two gauge boson

2 0 0 . . . . i . . . . i . . . . I . . . . i . . . .

150

I / / I / / / I 0 0 X. --

,,,l .... I .... I . . . .

0 20 40 60 8 0 100

C~rt (tO -(OeV-')

Fig. I. Bounds in the plane (Cv~, Mr) that can be obtained at HERA for a color singlet, isotriplet (dashed line), color octet, isosinglet (dot-dashed line) and color octet, isotriplet (solid line) pseudo-Goldstone boson.

~t

. . . . [ . . . . [ . . . . I ' ' ' - ' - [ . . . .

800

f

600 - - ,, " "

ll,

, I / 4 0 0 l "~

- / ",

200 --I "-'" . . . . . . . . . . . . -- I I

0 I 0 0 2 0 0 300 4 0 0 500

Cp.~ (10-6GeV -I )

Fig. 2. Thc same as fig. l for LEP/LHC.

branching ratio. I f this is not the case, the corre- sponding values of Cp0w can be obtained dividing the ones shown in fig. 2 by the square root o f the branch- ing ratio B R ( P ° - , 7 7 + y Z ) .

A possible colorless isospin singlet would also be produced via 77 fusion, but the main decay mode will be into two gluons. Since, the two jet background in ep collisions is extremely large, very large values of Cps~ will be required to obtain an observable signal, and we will not further discuss this case.

We now turn our attention to the case of color octet pseudo-Goldstone bosons, distinguishing again the case ofisospin singlet and isospin triplet. In both cases the production mechanism is via photon-gluon fu- sion but, while the isospin singlet pseudo-Goldstone boson will mainly decay into two gluons, the main decay product of the isospin triplet one will be pho- ton-gluon. The signatures are, thus, very. different, requiting separate studies of the standard model backgrounds.

The two gluon decay of the isospin singlet, color octet pseudo-Goldstone boson will give rise to two jets. The lowest order background to this signal will be due to the following processes:

~'q~qg, Ygl--'(lg, 7g~q(l, (12)

and its p~ distribution is shown in fig. 3 (upper, dashed line) for HERA and fig. 4 (upper, dashed line) for LEP/LHC. It has been shown, however, that "higher order" terms cannot be neglected, especially at low values ofPt [ 10]. These terms are due to the quark

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Volume 281, n u m b e r 3,4 PHYSICS L E T T E R S B 14 May 1992

&"

an

, , , , ,~ J , , , , , i i , , I i02

i01

100

l O - I

1 0 - 2

1 0 - 3

1 0 - 4

20 40 60 80 100 120

Pt (GeV)

Fig. 3. Transverse momentum distribution for inclusive jet pho- toproduction (upper lines ) and for the photon in ep--, cTX ( lower lines) at HERA. The first case is the standard model background for the production of a color octet, isospin singlet pseudo-Gold- stone boson, while the second one is the background for a color octet, isosinglet pseudo-Goldstone boson. The dashed lines cor- respond to the results obtained when only the lowest order terms are taken into account.

.o

xy

b

103

102

101

100

1 0 - 1

1 0 - 2

1 0 - 3

1 0 - 4

< ' ' 1 . . . . I . . . . I'' t

100 200 300

Pt (GeV)

Fig. 4. The same as fig. 3 for LEP/LHC.

and gluon dis t r ibut ion functions in the photon. The par ton processes contr ibut ing to them are

q iq i~q~q i , CtiCli----~(~i(:li,

q iq j - ' q iq l , OiOj--q'qiOj,

qi(:l,--a'qiqi, (:tiqi----~'(:liqi ,

q/=b ---*q/lj, (:bqi - -~(- l jqy ,

q,Qj~qi(lj, Qiqj ~bqy,

q ig~q ig , dl ,g~Q,g,

qi(:l~ - ' g g , ( ] iq i ---" g g ,

gg- '~qi (]~ ,

gg-~gg,

gq, -~gqi,

g o i --~ g q i • (13)

We have calculated them using the parametr iza t ion o f Drees and Grassie [ 11 ] for the photon structure function and the results, added to the lowest order contr ibut ion, are shown in figs. 3 and 4 (upper , solid l ine) .

The pseudo-Golds tone bosons are very narrow, with typical decay widths of the order of 10 -5 GeV. They, thus, would originate an extremely narrow ja- cobian peak at p , = ~Mp~. When taking into account the binning due to the exper imental resolution, the signal would be an excess of events in one single bin. In fig. 1 we have plot ted the bounds in the plane (Mp~,Cr,~.{~) for HERA (dot-dashed l ine) . These bounds have been obta ined with two requirements. First , we have required an excess of events in a bin (Apt= 1 GeV) larger than one s tandard deviat ion from the s tandard modcl expectat ion in the corre- sponding bin. Second, we have required a m i n i m u m of 10 events. Indeed, the second requi rement is re- sponsible for the upper part o f the curve, where the m i n i m u m value of C~,~g that can be obta ined at HERA increases when increasing the value of MpS. In the lower mass region, where the first requirement is responsible for the bounds, one observes that the min imum obtainable value of Cp~s decreases when increasing the mass of the pseudo-Golds tone bosom This is due to the fast fall with Pt of the background predic t ion (fig. 3). The ma x imum sensit ivi ty is ob- ta ined for Mro~ ~ 130 GeV, when the curves deduced

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from each requirement cross. It is interesting to note that since all the excess o f events is expected in one single bin, the obta ined bounds are insensi t ive to the value of Cess s entering in the decay o f the pseudo- Golds tone boson.

In the case of L E P / L H C we run into the same un- certainty as the onc we found for the color singlct, pseudo-Golds tone boson. Assuming that the domi- nant decay mode is into two gluons, we obtain the same general behavior as in the case of HERA (fig. 2, dot -dashed l ine) . The max imum sensit ivi ty is now reached for Me8 ~ 420 GeV and the m i n i m u m valucs o f Cp~g arc, in general, lower than the ones obta ined at HERA. However, it is interesting to note that for low pseudo-Golds tone boson masses, i.e. Mi,8 < 130 GeV, HERA turns out to be more sensitive than LEP/ LHC. Since the pseudo-Golds tone boson p s is pro- duccd in the s-channel, these bounds roughly scale with the two gauge boson branching ratio if the t i de- cay is not suppressed.

Let us, finally, turn our a t tent ion to the case o f a color octet, isospin triplet. The product ion mecha- nism is the same as before (i.e. pho ton-g luon fu- s ion) , with the only difference that the main decay mode is now into photon-gluon. The background will now be ep--, yX in the s tandard model. This process has been recently calculatcd by Bawa et al. [ 12 ]. Wc have part ial ly redone their calculation using Eichten et al. d is t r ibut ion functions. The lowest order par- tonic processes contr ibut ing to ep--,TX are

Tq~Tq, T q ~ T q . (14)

The Pt d is t r ibut ion obta ined from these processes is shown in fig. 3 (lower, dashed l ine) for HERA and fig. 4 (lower, dashed l ine) for L E P / L H C . At higher order the processes

gq~Tq, gq-)Tq, qq~Tg (15)

also give a significant contr ibut ion, especially at low p, at L E P / L H C (figs. 3 and 4, lower, solid l ine) . Re- peating the same analysis as in the previous case we obta ined the bounds shown in figs. 1 and 2 (solid l ines) , respectively. The fact that the background is much smaller now allows to probe regions where the coupling constant Cp~.t~ is much smaller, while the general behavior o f bounds is very similar. The main

difference is that the l imit o f t e n events is reached at much lower values ofMe~ (Mp~ ~ 50 GeV for HERA and Mp~ ~ 180 GeV for L E P / L H C ) .

In summary, we have studied the possible signals o f pseudo-Golds tone bosons at ep colliders ( H E R A and L E P / L H C ) . Since the cross-section for each pseudo-Golds lone boson depends only on two pa- rameters: M~, and Cpv~v2 (where all the model de- pendence is inc luded) , wc have taken them as free parameters and we have studied the bounds in the (Cpv,v~, Me) plane that can be obta ined i f no signal is found. In particular, we have considered three dif- ferent possibil i t ies for the color and isospin quan tum numbers of the pseudoGolds tone boson: color sin- glct, isospin triplet and color octet, isospin singlet and triplet. A fourth possibili ty, i.e. color singlet, isospin singlet has not been considered because the back- ground is too large to allow for interesting bounds.

The authors thank R.D. Peccei for discussions and F. del Aguila for a careful reading of the manuscript .

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