Physics Letters B 287 (1992) 216-224 North-Holland PHYSICS LETTERS B

The top mass and pseudo-Goldstone bosons at LHC/SSC

H. Schlereth Paul Scherrer lnstitut, CH-5232 Villigen PSI, Switzerland

Received 20 December 1991; revised manuscript received 27 April 1992

We consider models where the top mass is built up both from a top condensate and radiative contributions and mass generation in the weak boson sector is dynamical. As a consequence charged and neutral pseudo-Goldstone bosons appear. Their masses are estimated and found to be in a range accessible at LHC/SSC. Also they fall naturally in the region where the standard model requires new physics to appear. A brief qualitative discussion concerning their observability is added. Basically the search can be performed together with the search for charged and neutral Higgses. Particular important would be to discriminate them from SUSY charged Higgses. It is noted that the predicted scalar spectrum cannot be imitated by an extended Higgs sector of the standard model. Extension of the radiative mass generation to the z-sector calls for the introduction of a new heavy lepton doublet with mass in the region 1-2 TeV.

1. Introduction

If mass generation occurs via the Higgs mechanism as in the standard model (SM) [ I ] and in the Nambu-Jona-Las in io type bootstrap approach [2,3 ] no massless Goldstone bosons occur in the spectrum as long as the gauge couplings are not switched off. In the case, however, that the weak boson masses arise from a dynamical mechanism not related to sponta- neous symmetry breaking as it would happen in bound state models [4,5] there might be a problem as to the fate of the Goldstone bosons i fa top conden- sate, ( /- t) , contributes to the top mass, m , at the same time [6]. Fortunately, if a bound state structure is also assumed in the quark sector there are generic ra- diative contr ibut ions to mt (and m b the mass of the bo t tom) which break the symmetry explicitly. Since

we talk in the framework ofrefs. [4,5 ] the symmetry in question is the global SU (2)L. The ensuing Gold- stone bosons G +, G o ( _+, 0 refers to electric charge) are thus becoming pseudo-Goldstone bosons (PSGs). In the following we estimate their masses and discuss briefly their observability at LHC/SSC.

It should be noted that the question whether the weak bosons are fundamental gauge particles or ex- hibit the properties of bound states at some higher scale will be experimentally not quickly decided and

should theoretically not be judged with the help of prejudices based on QCD type bound state theories (see ref. [ 5 ] ).

In fact the Yang-Mills relations between the gauge coupling constants of the SM can be obtained with- out gauging the SU(2)L if one introduces electro- magnetism via the mixing 3 3 W i , ~ W u +2A~ ( W~, and

A u denote the third weak isospin component of the weak boson and the photon respectively and 2 = sin 0w [4 ,5]) and requires local electromagnetic gauge in- variance [ 7 ]. This notwithstanding an unexpectedly small weak boson selfcoupling can be interpreted as

a sign ofcomposi teness [8 ] ~1 Also for LEP physics massive Yang-Mills theory is

effectively one-loop renormalizable and reproduces

the experiments as well as the SM. Therefore other predictions based on mass generation mechanisms should be looked for. The PSGs to be discussed in this paper are one such possibility.

Weak boson form factors of the form 1/( 1 + Q 2 / m ~w, ) ~ with a >/1 would presumably have as mass scale the mass of the first excitation of the weak bo-

~ The point of view of ref. [ 8 ] arises when electromagnetism is not introduced as in ref. [ 7 ] but by minimal substitution. The option taken in this paper can be ruled out at LEP II.

216' 0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

Volume 287, number 1,2,3 PHYSICS LETTERS B 6 August 1992

son. With a composite scale A ~ 1.2 TeV (see below) and judging the excited level spacing from the p' in QCD (rap,= 1.6 GeV~-5AQcD with AQCD-----300 MeV) we are entitled to expect m w, ~ 5.1.2 ~ 6 TeV (see also ref. [8 ] ). It is therefore easily possible that form factors remain unnoticed at LEP II. At LHC/ SSC Q2 is in the range up to ~ 5 TeV 2, respectively

12 TeV 2. There the presence of a form factor must show up.

Before we embark to estimate the PSG masses we briefly recall in the next section the scales of new physics set by the SM.

2. The new physics scales of the SM

The largest Higgs mass, mu, for which perturba- tion theory remains valid for all energies is deter- mined from the tree level partial wave unitarity con- straint in the J=O coupled channel analysis of W + W f , ( 1/X//2)ZLZL, ZLH, ( 1 / x / ~ ) H H scatter- ing ( W~ and ZL denote the longitudinal weak boson fields and H the Higgs field). From I Re ao I < ½ [ 9 ]

2 2 m 2 and m 2 (s de- it follows for s, mH >> m w, s>> notes the CMS energy squared and mw, z the weak boson masses)

rnn <~ 700 GeV. ( 1 )

The upper bound obtained from lattice simula- tions [ 10 ] is

mH ~< 650 GeV. (2)

A natural condition for a regulator field is that it must not introduce a strong coupling constant into the theory where it acts as regulator. The forces be- tween the particles should not be drastically changed by the regulator.

The closeness of the numbers in ( 1 ) and (2) can be interpreted to express just this condition. The interpretation of the Higgs as a mere regulator field (see also ref. [ 11 ] ) is certainly not enforced by ( 1 ) and (2) but it might look surprising that Nature should have taken perturbation theory into account when trying to put the Higgs as a physical particle.

In the kinematic regions s>> m 2, m 2, s<< rn~--, oo (Higgs removed) the strongest unitarity con- straint comes from the I = 0 channel ( l / x / ~ ) X (2W~- W F +ZLZL) and puts an upper limit on the energy [ 9 ],

~ 1.2 TeV. (3)

In spontaneous symmetry breaking models one ex- pects in this energy region strongly interacting longi- tudinal weak bosons described by their equivalence to the corresponding would be Goldstone bosons ~2.

In a substructure model one would interpret the energy bound obtained after removing the regulator field as the composite scale of the weak bosons A w. In the following we take therefore

A w ~ - 1.2 TeV. (4)

The onset of new physics should therefore mani- fest itself in an energy ran~_e starting around the bound of the regulator mass, ~/s~, 600 GeV and extending up to ,v/~ ~Aw ~ 1.2 TeV.

An acceptable model for particle physics beyond the SM should put the appearance of new physics (new particles, form factors) in this range dictated by the SM without especially tuning its parameters.

3. The pseudo-Goldstone boson masses

The generic form of the quark mass generating part of the low energy effective lagrangian in models where a substructure of quarks (mediated by a gauge force that becomes strong at a scale A o, see below) is as- sumed, takes for the (t, b) sector the form

f2 /47r . . . . f2/4lC LPM= ---ST-- (2LtRtR(2L + ---7i--- QLbRb'R QL

, ~ Q 1 , 0

r a d - r a d + M r tL tR+Mb 6LbR. (5)

Q1-- (tL, bL) denotes the left-handed SUL(2) doublet and tR, bR are the right-handed singlet partners. The four Fermi terms originate as the low energy remnant of the strong gauge forces. It is reasonable to normal- ize AQ such that o n l y f 2/4n, f 2/4n>~ 1 is considered as is appropriate for a strong coupling constant. The four-fermion part of (5) is invariant under SU(2)L and for f=)ralso under SU (2) R.

The last two terms denote the contributions from the electromagnetic and color mass generating dia- grams depicted in fig. 1. We keep only the first dia- gram so that the quark mass matrix comes out to be

#2 See ref. [ 12 ] for a review and ref. [ 9 ].

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} ' , g } , ,g ~,,g

o = :-- + :-- ~ + T' T' T"

Fig. 1. The one-loop quark mass generating diagram (which generates a mass matrix of rank one) is shown, together with one two-loop diagram which raises the rank of the mass matrix. Further and higher order diagrams are indicated by dots. T' and T" denote heavy intermediate states, the wavy lines are either gluons (g) or photons (y). The external lines correspond to massless quarks marked by Q.

o f rank one giving mass only to one family in this ap- proximation which we take to be ( t, b) [ 13 ]. In these diagrams a photon respectively a QCD-gluon con- nects a t or b quark to a heavy excited state, T' , of mass mT, ~ AQ.

TO keep the gauge current conserved the vertices in fig. 1 cannot arise in the fundamental lagrangian but are effective magnetic type interactions of the low en- ergy effective lagrangian. For instance for the electro- magnetic case one would have

~ - O~( Qtru~T' )A ~ (6) / I Q

They feed down to the quark level the chirally un- protected mass o f the excited state T' to create radia- tive quark mass contributions M~;~ ad ~at,bAQ and Mgrad ~asAQ (? and g mean photon and gluon re-

t , b

spectively, rad stands for radiative, a~ is the strong coupling constant and at = 4a, orb = ~a with a de- noting the fine-structure constant) . Note at = 4aa. It is reasonable to assume the existence of such mag- netic dipole transitions in a bound state model. In fact similar vertices occur in the QCD, for instance in the NN'~, system (N' is the radial excitation of the nu- cleon N).

Recall that chiral protection is an unavoidable in- gredient o f composite models of quarks based on confining gauge forces which is expressed by the anomaly constraints [14]. In these constraints the excited states do not enter since only the global fla- your quantum numbers of the groundstate particles count. Recall also that the mass o f the radial excita- tion of the pion is m~, ~ 1 GeV and therefore does not participate in the chiral protection o f the pion mass.

Clearly the radiative terms in (5) break the SU (2)L symmetry explicitely. Also SU (2) R is explicitely bro- ken by these terms if M[ ad # M~, ad. In fact the first or- der electromagnetic diagram gives ~,traa _ , I ~r~d z v J t - - . . T l v J b "

In models where the bound state structure is such

that QCD-color is carried only by one (chirally pro- tected) fermionic constituent [15], q/C(x), the gluonic contribution in fig. 1 can be suppressed. Namely at high loop momenta (the cut-off in evalu- ating the diagrams in fig. 1 should be placed above AQ) the non-color part o f the intermediate bound state T' may act essentially as spectator (electric charge on the contrary is distributed to all constitu- ents [15] ) . Since out of ~uC(x) alone a mass term cannot be formed the gluonic mass contribution may become suppressed.

We do not know to what extent this will happen in the unsolved strong bound state dynamics. But we will occassionally consider the limit M~'b rad-,0. Note that the lowest electromagnetic diagram for fig. 1 gives for the b-quark mass (assumed to be purely radiative, see below) as an order of magnitude estimate

l a rnb~ ~nAQ~--4-5 G e V , (7)

where (12) was used. The corresponding estimate with the gluon diagram would give mb ~ 500 GeV!

We consider now a situation where condensate for- mation is such that

<h>#0, <b-b)=0. (8)

We do not dwell here about the origin of this charge asymmetric condensate built-up since we will ex- plore only its consequences for the top mass (see however ref. [ 6 ] ).

From (5) we obtain then (to lowest order in at,b and a~)

f 2 / 4 n < h> ..1- /IA-7,rad 4- /1Arg, rad m,- A~

mb = M ~ 'rad + A/-~' tad . ( 9 )

We consider these mass relations at a QCD scale Q2 ~ 10 GeV e say. Since we are interested only in (9)

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in the following this justifies the neglect of higher di- mensional four-Fermi operators in (5). In fact we find below QE/A2 e << 1.

In the full starting lagrangian which contains the constituent preon fields (in some model which to specify is not needed here) there is no t or b mass term. Therefore when the mass generating terms are collected into ~M at low energy the external legs of the diagrams in fig. 1 correspond to massless t and b quarks. We have then the relations

Mt~,rad = 4M~,rad, M g, rad = M~'rad. ( 1 0 )

Next we want to estimate the effective scale of top condensate formation A~ - ~ (which need not coincide with AQ [ 6 ] ). We calculate AQ from a for- mula given in ref. [ 16 ] which in our language reads

AQ~ (40 -50)Aw. (11 )

The idea is that the coupling of a W to a pair of quarks is proportional to the overlap of their bound state wave functions whose extension is roughly A ~v ~ respectively AO ~. Then ( 11 ) expresses the condition that this is the known weak coupling.

We find then from (4)

AQ _~ 50-60 TeV. (12)

In the subsequent calculations we take AQ = 60 TeV for the quark composite scale. The sensitivity of the PSG masses to changes in AQ is considered at the end of this section.

The value in ( 12 ) is not large enough to suppress flavour changing neutral current effects (FCNC) by itself sufficiently [ 17 ]. However, models of the type considered in refs. [15,6] do not have tree level FCNC dangerous operators [ 18 ].

Adopting for the quark masses mt= 140 GeV [ 19 ] and mb= 5 GeV one derives from (9), (10) and (12) the two inequalities

3 1 3N/f 2 T 4 7.5 ~<A~ ~< 3N/f 2 ~ 7.8 TeV. (13)

In the limit M~'~ ~d--, 0 one obtains equality at the LHS of ( 13 ). A force acting on this distance scale can be viewed as a Van der Waals type force [ 6 ].

Next we note that the following global SU (2) gen- erators are spontaneously broken by the condensates (8) ,

T -+L-R, T3L--R (14a) +

TO+R, (14b)

U( 1 )L--R, (14C)

where T ± = T 1 + iT 2. Consequently the following spectrum of Goldstone

bosons, which are to be viewed as bound states of the (t, b) system arising from the attractive force acting

13) at the distance ~3 f2x/ fS~ (8 TeV)- 1 by ( is obtained,

G-~{ysb, G+,~6~st,

1 G°~ ~ (i-yst-675b) , (15a)

A-~t-b, A+~6t, (15b)

and the pseudoscalar singlet

1 H ° ~ ~ (/-75t+b-75b) • (15c)

Upper indices refer electric charge. Note that in (15a), (15c) there appear pseudoscalars whereas (15b) contains scalars.

Because QL---- (t, b)L and tR, bR carry QCD color there is also a number of color octet Goldstone bo- sons. For example the spontaneous breakdown SUE(6) XSUR(6)~SU(6)L+R generates 24 octet Goldstone bosons which are pseudoscalar.

Now all mentioned Goldstone bosons are lifted to massive pseudo-Goldstone bosons (PSGs) due to the property of the radiative quark masses (9) to break the relevant global symmetries explicitely.

An estimate of the PSG masses can be obtained from Dashen's formula. For the PSGs (15a) it takes the form

m2*- =~ ~-.-/"/IArT'radt --'"t"l- '~4rg'rad --+mb)Ac,

rn~0 ~ 2 ( M t ~,rad + Mtg'rad)Ac, (16)

where in the brackets one finds the contributions to the quark masses (see (5), (9) ) which explicitely break the global SU(2)L. It is assumed that M~,;g ,tad << Ac ~3. Otherwise corrections to (16) become im- portant. It is then straightforward by use of (9), ( 10 )

~3 This is a safe assumption at least for Mtg, gad--*0 since then M~ 'tad = 4M~ 'rad = 4mb ~ 20 GeV,

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and having mb = 5 GeV to obtain the inequalities

lx//~c <~mGo <~ 4X/4~e ,

lxf~¢<~ma+_ ~ 2 x / ~ . (17)

In the limit Mg~ ~d ~ 0 one gets equality at the RHS o f (17 ) .

With (13) one then finds f o r f 2 /4n= 1

274~< m60 ~< 544 GeV,

274 ~< mG_+ ~< 430 GeV, ( 18 )

and varying the strong coupling constant up to f 2/47~ = 8 gives

194~< mGo ~< 381 GeV,

194~<m~+ ~<301 GeV. (19)

IfMtgb ~d would be chirally suppressed as discussed above then for M,g,g "d--,0 one obtains a t f 2 /4n= 1

mco=548 GeV, m~_+ =452 GeV, (20)

and f o r f 2/47t= 8

m~o=388GeV, m 6 ± = 3 2 0 G e V . (21)

These values are consistent with the onset of new physics appearing in an energy range below 600 GeV but still considerably higher than the weak boson masses. They are therefore clearly consistent with the expectations based on the SM itself. An uncertainty i n f 2 / 4 n in the range 1 to - 10 which is realistic for a strong coupling constant ~4 changes the PSG masses by 130-160 GeV, but the common lower bound only by _~ 80 GeV. A potential error in estimating the PSG masses occurs when takingAQ from (12) and putting it numerically equal to AQ appearing in (9). There- fore, to see the dependence on changes in AQ, let us neglect momentarily ( 12 ) and raise AQ dramatically up to 500-1000 TeV (these values are FCNC safe [ 17 ] ). As is easily seen this amounts to multiplying m~+_.o by a factor ~ 2, respectively ~ 2.5. Looking at the relations ( 17 ) - ( 21 ) one notices that in the worst case the lightest PSG is still not heavier than

mG_+ g0.9-1.1 TeV, (22)

and

~4 For ins tance for the nNN coupl ing (g,v~--mN/f~) one has g~/4n~ 10. For a theory based on an S U ( 2 ) [ 15,6] ins tead of an SU (3 ) gauge group one expects even a smal ler value.

m~o - 1.1-1.4 TeV. (23)

So even with a very large AQ the scale where new physics becomes definitely visible which we identify with the mass of the lightest PSG, just touches upon the upper end of the range expected from the SM. We think, however, that the masses based on (12) and f2/4rc_~ 1-10 are more realistic than (22) and (23) so that the PSGs are well separated from the other bound states with mass ~ O (A w). Altogether the PSG masses come in a range which will be scanned at LHC/SSC during the search for charged and neutral Higgses. We consider therefore in the next section some of the eventual signatures of the PSGs.

F o r f = f i n (5) the mass of the charged scalars A -+ (15b) is estimated as

[ I arrad I arrad "lA (24) m ~ _+ ~ w,', t -~ , ' , b )-Xc,

m,_+ ~ 350 GeV, (25)

f o r f 2 / 4 n ~ 1 and M~{ "d =0. The mass of the singlet ( 15c ), H °, is discussed below. Finally, the color octet PSGs acquire masses once as is switched on. If we apply a formula used in technicolor [ 20 ] for this case,

2 2 mGco~or Ac 3as(At) (26)

mL+ -m~o - A~cD C~om

(aem denotes the electromagnetic finestructur con- stant; otherwise the notation is obvious), we find

mGco,or ~ 0.15 Ac ~0.6-1.2 TeV (27)

( f 2 / 4 7 ~ = 8, respectivelyf 2/47r= 1 and AQ= 60 TeV). The colored PSGs do not appear when ( / - t ) = 0 for as---, 0 [6].

4 . P r o d u c t i o n a n d s i g n a t u r e o f t h e P S G s

We may try to describe the PSG-system and its in- teraction with the weak bosons by a chiral lagrangian approach. This will be studied in detail elsewhere [21 ]. Here we consider only two tree-level vertices that arise in the chiral lagrangian, namely

i ~ W ~ ( G ~ O u G ° - G ° OuG :~ ) ,

g2fAAV + (28) W ~ Z u ,

where g is the weak coupling constant, W u and Z u

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denote the charged and neutral weak boson respec- tively and fa~A¢. The mixing argument between W 3 and the photon described in the introduction gives ~=g. Analogous couplings as in the first line of (2 8 ) given for W ~ exist for Z u and the photon [ 21 ].

Notably there exists a tree level coupling for the process A -+ --, W -+ Z. Such tree-level coupling does not exist in models with extended standard Higgs struc- ture [22,23] (that is when only singlet and/or dou- blet Higgses are added to the SM). It does exist when nonstandard Higgses, such as triplets, appear in the extended Higgs sector.

Unfortunately in our case this tree level process gives an enormous width to the A_+ scalars:

FA~wz=~4~( g2fA~2(m'-'A-A~zmA'mw] \ m w ]

FAowz ~- (50--70)mA. (29)

Therefore the scalars (15b) would not qualify as particles or observable resonances. For the pseudo- scalar PSGs a rough order of magnitude estimate of their width is F 6 ~ O ( ( g Z / 4 n ) m c ) , taking ~=g. In this case the tree-level coupling is absent. A more de- tailed width analysis will be performed elsewhere.

However, the chiral lagrangian approach to the in- teraction vertices with the weak bosons is not well justified (as it is in the n, p, A~ system) because the symmetry breaking scale is far away from the weak boson mass f~ >> mw. In fact this causes a problem in the weak boson sector of this approach [ 21 ]. If we try instead to guess the interaction vertices from the assumption that the weak bosons interact directly with the top and bottom content of the PSGs the tree level coupling ~g2fA A :~ W u Z u cannot be con- structed. This will be discussed in detail in ref. [21 ]. For the moment we note that the large width (29) following from the chiral lagrangian approach may not reflect the correct physics.

Note that this PSG scalar spectrum cannot be imi- tated by extended Higgs sectors of the SM, such as more doublet models, SUSY-extensions, E6 based models or nonstandard Higgses.

Therefore experimentally there exists the principal possibility of distinguish the case for PSGs from any Higgs sector by identification of the complete scalar particle spectrum in the mass region ~ 200-400 GeV.

This topic will be worked out in future considera-

tions. In this paper we discuss only a few points on a qualitative level and confine us essentially to G -+'° and n ° .

By the couplings in the first line of (28) PSG-pairs are produced in DreU-Yan type processes at LHC/ SSC. Also production by fusion (see below) may be possible and more enhanced than Drell-Yan. Fur- ther appropriate t-channel processes which do not share the Drell-Yan propagator suppression should be considered.

To avoid QCD background from W*~ t-b--,2 jet ( * denotes virtual) or the charged Higgs mode [ 24 ] H - --, {b--,2 jet, rare leptonic events must be considered.

However, semileptonic modes like G - =/-75b~ W-(675b)--, W - 2 jet may be distinguishable from H--- . W - (~b) --, W - 2 jet by appropriate kinematic cuts. Tagging the charged lepton l ( l= e, #), from the W decay will reduce other QCD background.

Note that the spatial extension of a PSG bound state is roughly A~- i ~ 4-8 TeV- ~. So QCD is truly pertur- bative and the weak decay t--, Wb happens before fragmentation.

However, due to the Goldstone type Yukawa inter- actions (fG ~Ac)

f fft fyuysbOuG + ~ ~ G+ f75b, (30)

direct decays G-- , t -b can happen, although sup- pressed by a factor mG/fG ~ ~ - ~ . Because of the large energy release into the ~ b system fragmenta- tion will now precede the weak decay (the QCD string between/-and b is stretched out on a shorter time scale as the weak interaction time).

If the invariant mass of the jets from t-b--,2 jet can be approximately determined it is possible to iden- tify the presence of the Goldstone Yukawa interac- tion (30) above QCD background. Less background occurs in the rare leptonic modes like

G - _~ ( i-~'sb )s--, W - ( 6ysb )s ~l#y7 ,

G°_~ ( i-75t )s--,l~lG + ~l~t l ' vl, 77

( l , l '=e , l~) . (31)

The idea is that in the s-wave bound state (denoted by the subscript s as a reminder) annihilation into 77 and 2g via the triangle anomaly [ 25-27 ] is much en- hanced over the case when (6b) / (Ft ) are produced

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with just long range QCD interactions acting be- tween them (A6~D >>Av ~ ) as would be the case for H - - , t-b-~ W - (5b) followed by b-b-, 2 jets. Below we discuss that also in this system binding can occur if m,> 400 GeV.

A signature like this one could also show up in neu- tral Higgs (H °) searches namely [28] ~p~H° i - tX followed by H ° ~ y 7 and tagging the l from t - , W b - . (l~)b.

In this case the two photons arise not due to the triangle anomaly but as a one-loop effect in the Higgs system. This causes a difference in their angular dis- tribution [25,26 ]. Also one might investigate whether by appropriate cuts the signal from the spectator top in the H ° process can be distinguished from the one in (/-b L.

The possibility to have heavy quark bound states due to strong Higgs exchanges arises in principal also in two doublet models and the minimal supersym- metric SM (MSSM) depending on the free parame- ter tg fl which occurs in these models [ 29,30,24 ]. For large enough tg r, for instance, the coupling in the 6b) channel due to H ° exchange becomes strong. Ex- isting upper bounds on this parameter [31,30] to- gether with the small mass of the bottom indicate, however, that this coupling remains effectively per- turbative for m, up to ~ 200 GeV. The dependence on the top mass becomes particularly visible if, as suggested [ 24,29-31 ] tg f l~ m J m b in which case mb drops out from the coupling and in both channels, i-t and b-b, the coupling becomes strong for mr> 400 GeV. So with mt presently unknown ~5 this possibil- ity cannot be ruled out, although it appears unlikely that m,>400 GeV [19].

Further for the neutral Higgs there exists the chan- nel H °--, W + W - while for the neutral PSG only GO--+ W + W - (&sb) is possible.

Fusion processes i - b ~ H - , gb- - , tH- were studied in refs. [24,26]. Because of the Goldstone Yukawa interaction (30) fusion like i -b~G- which would bring up the PSGs as resonances can in principle oc- cur. However, to produce (/-bL the two fermions must be brought together as close as A ~-~ (A~ ~ 4-8 TeV) to feel the strong binding force (and to over- come the factor A~ -t in the interaction). These con- ditions are more stringent than i-b---,H- fusion im-

~5 O f c o u r s e a t L H C / S S C m , wi l l be k n o w n .

poses [24,26 ]. A quantitative analysis will be tried elsewhere.

A clear signal would be the absence of the decay G - - , r~ . This decay is a clear signal for a charged Higgs [24,26]. A PSG could not decay to only z~. Unfortunately the prospects of observing H - - , z~, are not bright especially if m M + > m t + m b so that H---,i-b can occur. One needs BR ( H + - , ~ v , ) ~- 50%, a value hardly obtainable in MSSM [ 24,26 ]. So the absence of the zp, decay can in practice not be used to distinguish a charged PSG from a H-+. Note also that G--- , W - G O is kinematically not allowed because m a - < mao. On the other hand H + --, W +H ° might occur [24 ].

A class of tree-level forbidden rare decays offers the possibility to distinguish between scalar charged Higgses and PSGs. These are the one loop allowed decays H -+--, W-+y and H+-~ W+-Z [22,23,32].

In gauge models with a doublet and/or singlet sca- lar Higgs structure [22,23 ] they proceed via the ef- fective interactions [ 32 ]

ge +_ :~ gg' +_ :~ M z W u~Fu~H ' ~ M z W u ~ Z ~ H ' (32)

respectively Mz denotes the Z mass, g' the hyper- charge coupling constant and Wu~- 0 u W~- 0, W u etc. F~,~ is the photon field strength and Z,,~ the analogous expression for the Z field. On the other hand the cor- responding PSG decays G + ~ W+y and G ±- , W+-Z proceed because of the pseudoscalar nature of the PSGs via the following effective interactions:

~ + :g ~_+ :g h2/4n W ~ F , , ~ G , hZ/4n ~ Ac ~ Ac Wu~Zu~G '

(33)

respectively where h2/4n is an unknown dimension- less effective coupling and ff'u~-ej,~poW v,. In the W +Z channel one can trigger on the three charged leptons arising in the chain W - Z - - , ( l - ~ t ) ( [ + [ - ) where l, [=e, ~. With enough statistics this would allow one to distinguish between the scalar Higgs case (32) and the PSG case (33). G°---,ZZ - , (l + l - ) (l + l - ) can be discussed in analogous fash- ion. The suppression factor p/A~ (p a characteristic momentum) in (33 ) can become of order one at the SSC (Ac ~ 4-8 TeV, p g 6 TeV) eventually also at LHC (p~2.5 TeV). Cuts and background in the We?, channel are discussed in refs. [24,33]. In principle

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weak boson fusion based on (32), (33) can also be studied.

Finally, in models with nonstandard scalar Higgs sector the W-+Z mode can arise at tree level

+ :g M w W ; Z u H [23 ]. Again this case is distinguised from (32) and (33).

5. Conclusion

Without the mixing argument based on W3~ --, W 3 +2A, as discussed in the introduction ~ in (28) is a free parameter. In particular it could be a stronger coupling constant than given by ~ = g (g denotes the weak coupling constant). Clearly a noticeable devia- tion from ~ = g would tell us that we are not dealing with Higgs scalars out of a gauge model.

The leptonic modes G---.I~yy, G°-- . l~rVrY7 where the two photons come by the triangle anomaly are indicative for originating from a pseudoscalar fermion-antifermion bound state.

The tree-level forbidden processes G ~ WZ, G ~ Wy

differentiate between pseudoscalars and scalars. There are, however, also j e = O- Higgses (in models where CP but not C and P separately are conserved [29,30,24].

In addition the PSGs of technicolor [20] are also pseudoscalar. However, if the full spectrum of scalar particles G-+, G O and H ° in the 200-400 GeV mass region can be identified these latter cases can be eventually excluded (see the discussion o f H ° below. )

Hadronic modes like G - --* tb can test the presence of the Goldstone Yukawa interaction (30) if the in- variant jet mass can be approximately determined. Semileptonic modes may also be useful.

Finally if the forces that form the condensate (Ft) SO are effective Van der Waals forces, as sug- gested in ref. [6 ], no triangle anomaly is related to them. That implies for the mass of the pseudoscalar singlet H ° in (15c)

mE0 ~ \~'~( )lAfT, r ad t --~..'4- AAfg. r a d t "~- mb)A¢,

mh, o = ma • • (34)

This mass relation is a prediction of the Van der Waals hypothesis of ref. [6] (electromagnetic corrections are neglected in (34)) . It deviates from the relation expected in technicolor models were the chiral

anomaly contributes to the mass of the pseudoscalar singlet H°c , namely

m , % >> me+- • (35)

(P-+ denotes a charged PSG of technicolor. Compare the relation in QCD rn,, >> ms.) The aspects men- tioned above will be worked out more quantitatively in future work [21 ]. We will also comment on the meaning of radiative corrections in the present framework [34]. If we extend the radiative mass generation considered for the b-quark to the z-lepton then the intermediate state in the corresponding dia- gram of fig. 1 must be a heavy charged lepton T with mass m r ~ 1-2 TeV. This is to get the ratio m b / m t ~ 3

(at a typical QCD scale) right. The fact that this mass is in the region of A w as

given in (4) can be incorporated in a bound state model [ 6 ] such that it does not appear as an accident [6,35]. The T lepton appears then in a full SU (2)L doublet (Nr~)L. N O is a heavy "neutrino", mNo ~ m r

[6]. Since there are also off-diagonal radiative dia-

grams connecting z- and T-legs there is a z - T mixing. If we denote the off-diagonal mass by rh the mixing angle is given by sin fl,~ rh/Mr.

Thus there arises naturally the possibility to under- stand a possible excess of the z lifetime over the ex- pectation from lepton universality [36] because a factor 1/cos2fl appears in the z lifetime formula [35]. Further it turns out that the T lepton could be sur- prisingly narrow because the decay T--. W ~ happens via presumably small mixing angels [ 35 ]. Finally no radiative Dirac neutrino masses appear in the pres- ent scheme unless the neutrino in question has a small magnetic moment.

Acknowledgement

The author is grateful to F. Jegerlehner and M. Locher for the possibility to perform this work at the Paul Scherrer Institute. For discussions the author thanks F. Jegerlehner, P. Minkowski, H.B. Nielsen, M. Locher, C. Verzegnassi and D. Wyler. F. Jegerleh- ner is also thanked for reading the manuscript.

223

Volume 287, number 1,2,3 PHYSICS LETTERS B 6 August 1992

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