Searching for New Strongly Interacting Fermions with Future Colliders

Richard Vidal Fermi National Accelerator Laboratory, Batavia, IL 60510-0500

I. INTRODUCTION If the new fermion pair had an electro-weak interaction similar to the Standard Model, then they might form an SU(2) electro- The Standard Model accommodates much without explana- weak doublet. If the ªpionº mass is larger the the ªW-bosonº tion. It contains many elements that are dif®cult to motivate mass, then the ªpionº bound state of the two fermions would de-

theoretically, although they are accommodated easily. The ex-

+ cay predominantly via the ªtriangle anomalyº to W ,andwe istence of two extra generations of fermions is one good exam- might get decays very different from the familiar QCD pions [3]. ple. Since the next generation of colliders should be capable Since the new fermions are colorless, hadron colliders could of discovering other new pieces of ªnon-essentialº, low-energy not produce these new fermions copiously, but rather, they phenomenology, it is important that simple, obvious, and easily- would be produced, like the leptons, via U(1) gauge bosons, accomodated extensions of the Standard Model be considered. or possibly, via spin-1 ªrhoº resonances (as we ®nd in QCD). This kind of new physics may not resolve any of the current Here, of course, the spin-1 states would have masses greater than

problems with the Standard Model, but in the future, could pro-

1000 GeV 200 . Since the new fermions are con®ned and exist

vide the needed pieces that reveal a more comprehensive and GeV

only in bound states with masses above 100 , they cannot

complete picture. +

e e p be produced at any existing e or machines, despite One important motivation of the original idea for GUT's was their relatively small masses, but might be seen in the next gen- the uni®cation of quarks and leptons. This was ®rst attempted eration of linear colliders. To illustratehow such fermions might in an SU(4) model [1] where lepton number was considered as appear, we can examine a particular model. the fourth ªcolorº, (the other three colors coming from QCD). Later, SU(5) models [2] incorporated the leptons and quarks in II. EXPANDING THE STANDARD MODEL various SU(5) representations. However, to achieve full uni®cation at some large energy, we must be sure we have all the pieces The basic idea then is that we might have much larger gauge at lower energy. Is a signi®cant piece missing? group than the Standard Model. The group would be:

By examining the differences as well as the similarities

SU (3) SU (2) U (1) U (1) SU (2) SU (3)

L L R R c between fermions, we may be able to understand their common c origin, and get a hint about any other missing particles. Since it

is the SU(3) QCD interaction which distinguishes leptons from SU(3)

The group c is just QCD of the Standard Model, and

quarks, this observation might suggest by analogy the existence

SU(2) U(1) L the group L , just the Weinberg-Salam sector.

of another SU(3) interaction that would distinguish a new, third

0 SU(3)

There are two new non-Abelian groups: an c represent-

type of strongly interacting fermions from the other two types, SU(2)

ing a new strong-interaction, and an R corresponding to

quarks and leptons, with which we are already familiar: a new ªright-handedº weak interaction, and one new Abelian

U(1) SU(3) c

group R . The new has eight gauge bosons ± glu- SU(2)

leptons ons ± just likeQCD, and the new R has three gauge bosons

like the Weinberg-Salam model.

How do the fermions transform in this expanded model? Let

@ us limit the discussion to only a single generation of fermions.

U(1)

@ All fermions have both kinds of hypercharges, but vary-

quarks ??? ing strong and weak charges. The u-quark and d-quark are still

SU(3) SU(3) c triplets under c , but are singlets under the new ,

i.e. they do not interact via this new strong force. They trans- SU(2)

This new SU(3) strong interaction could be similar to QCD, form as the usual left-handed doublet under L , but again, SU(2) but have a scale which is at least 1000 times larger (or greater are singlets under the new R (so they ignore this force

than 100 GeV). Because of this new interaction, pairs of these too). The electron and neutrino, however, do interact via the

SU(2) SU(2) L new fermions might bind together and be con®ned into pseudo- R ,aswellasvia , but are singlets under both scalar pions, as in QCD. The masses of the new particles typ- SU(3) groups (they have no strong interactions). We will dis-

cuss the consequences of these assignments shortly.

10 GeV 1 ically might be greater than 1 , rather than the

The model also contains a pair of new fermions (called here MeV 10 for the light quarks, and they might form ªpion-likeº

v and r) that are not found in the original Standard Model.

200 GeV

bound states with masses greater than 100 , similar

0 SU(3)

They transform as triplets under c , but are singlets un-

200 MeV

to the quark bound-states at 100 . SU(3)

der c , so they are like ªmirror-imagesº of the u and d-

email address [email protected] quark. The fermions v and r (speci®cally, their right-handedpro-

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SU(2) SU(2) L jections) transform as an R doublet, but are sin- III. FERMION COUPLINGS TO THE WEAK glets ± again opposite to the two quarks. BOSONS Of course, not all the symmetries represented in this extended gauge group are apparent in low-energy interactions. They are The fermions couple to the neutral bosons via vector and hidden by the presence of Higgs bosons, just as in the Standard axial-vector currents. For a generic fermion f, the Lagrangian

Model. Here, however, there are two pairs of Higgs particles ± contains the terms: SU(2)

one transforming as a doublet under L (and a singlet un-

SU(2)

der R ), and the other pair, transforming as a doublet un-

Q q f fP +Q f (V A )fZ

f e Z L L 5

SU(2) SU(2) L

der R (and a singlet under ). The left doublet has

Y Y L

no R hypercharge, while the right, no hypercharge, which

+f (V A )fZ + f (V A )fZ

1 1 5 2 2 5 1

keeps the sectors separate and unmixed. There is also a third 2

SU(2) Y

Higgs which is a singlet under both groups, and has no L Y hypercharge (but does have R hypercharge). All three of these where:

Higgses develop vacuum expectation values, effectively hiding

f f f

L L R

SU(2) SU(2) U(1)

L R R Q T + Y Y

the , ,and symmetries at low energies. =

3L L L

v v R

If we de®ne the vacuum expectation values to be L and 1

for the neutral components of the two Higgs doublets, de®ne 1

f f

L L

T T A V Q sin

L L f L

3L 3L

SU(2) SU(2) g g

L R 2L 2R 2

the and coupling constants to be and 2

respectively, de®ne the expectation value of the singlet to be q

2 2

v U(1) U(1) g

g + g q g cos Q

S L R 1L

1L L Z ,andthe and coupling constants to be and e

2L 1L

g R

1 respectively, then the masses (at tree-level) for the gauge

1 1

f f f

bosons are: f

L R L R

V (T + T ) g sin + (Y + Y ) g cos

1 2R R 1R R

3R 3R R R

2 2

1 1

M = g v M = g v

W 2L L W 2R R

L R

1 1

f f f f

L R L R

2 2

(T T ) g sin + (Y Y ) g cos A

2R R 1R R 1

3R 3R R R

2 2

1 1

f f f f

L R L R

V (T + T ) g cos (Y + Y ) g sin

2 2

2 2R R 1R R

3R 3R R R

M = g + g v M =0

Z L

L 2 2

2L 1L

1 1

f f f f

L R L R

A (T T ) g cos (Y Y ) g sin

2 2R R 1R R

3R 3R R R

2 2

2 2 2 2 2 2

M = (g cos + g sin ) v + g cos v

2R R 1R R R

Z R 1R S

Y Y T T

L L R , R , and are the hyper and weak-charges of the left or right-handed doublets or singlets.

The fermions couple to the charged bosons via vector and

2 2 2 2 2 2

(g sin g cos ) v + g sin v M =

2R R 1R R R

R 1R S Z

2 axial-vector charged currents. For a generic fermion pair u and 4 d, the Lagrangian contains the terms:

where we have assumed the hypercharges and weak charges of

g g

2L 2L

the Higgs bosons are one half, the hypercharge of the Higgs

p p

u (1 )dW + d (1 )uW

5 5

L L

2 2 2

singlet is one, and: 2

g g

2R 2R

p p

u (1 + )dW + d (1 + )uW

5 5

R R

tan =

2 2 2 2

Since the quarks do not interact via the right-handed weak in-

T =0

teraction, then R , and they can be assigned a value for

1 1 K

2 the ªrightº hypercharge equal to their electric charge (the quarks

sin = +

2 K +4 2 have the same ªleftº hypercharge assignments as in the Standard

Model). This will assure that all the anomalies cancel each other

2 2 2

) = (m m ) m + m K (m

1R 2R

2R 1R s T =0

in the model. Similarly, for the new v and r fermions, L ,

g v m so they get the ªoppositeº hypercharge assignments (assuming

s 1R S 1

1 they have the same fractional electric charge as the quarks). For

m g v m g v

1R 1R R 2R 2R R

SU(2) SU(2)

2 2 R the leptons to transform under both L and ,there

must exist a right-handed neutrino.

Here the angle L is just the Weinberg angle of the Standard Since we have observed experimentally only a light, left-

W Z

Model, and we associate the massive bosons and L with handed neutrino, we can incorporate a right-handed neutrino by L

the charged and neutral resonances discovered at CERN. The assuming that the neutrinos are Majorana fermions and invoking

W L

other angle R has not been measured yet, and the ªright- the ªsee-saw mechanismº. The boson then couples mostly

W Z Z 2

handedº bosons , 1 and remain to be con®rmed. to the light, left-handed mass eigenstate, with a small coupling R

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W 140 GeV 140 MeV

to the heavy neutrino, reduced by a small mixing angle. The R , rather than for the pion of QCD, and the

boson then couples mostly to the heavy, right-handed neutrino, vectors and other pseudo-scalars made from other generations

GeV W

with a small coupling to the light neutrino, again reduced by the have masses in the hundreds of range. For a R around

W 100 GeV R

same small mixing angle. If the mass of the R is less than the , then the will decay predominantly to a photon W

mass of the heavy neutrino, then the R partial width to leptons and a lepton pair. If we assume that hadron colliders produces

is greatly reduced since it can decay then only to the light neu- only pairs, then we should observe two photon plus two

R R

trino state. The partial width is suppressed by the small mixing charged leptons plus T in the ®nal state [3].

angle. IV. MASSES OF THE NEW GAUGE BOSONS VI. COLLIDER PRODUCTION OF R PAIRS

W Since quarks do not interact via the new strong interaction

Because the u and d-quark do not couple to R at tree-level,

SU(3)

c R

W , pairs can only be produced at colliders via a Drell-

the R gauge boson cannot be produced with any signi®cant Z

rate in any existing hadron machines. However, the neutral Yan photon or a L . We can estimate the production rate by con- Z

Z sidering the rate relative to the production of lepton pairs at and 2 gauge bosons 1 and do couple to u and d-quarks, and so

can be produced at the hadron colliders. We know from Teva- above the same invariant mass of the pair. As in other electro-

Z weak production, we expect the rate for to be small ± we R

tron limits on production that their masses must be large ± R

R +

600 GeV W e

expect only about unit of e . This is similar to the case R

typically greater than about . If the mass of the is 4

e e

GeV cos 100 for an machines with a beam energy just above the pion

about ,then R must be small to get a large mass

Z v =2TeV v =1TeV

Z threshold. However, as in the QCD case, the rate can be consid-

2 R S

for 1 and . For example, for ,,

= 100 GeV g =0:1

M erably larger on the vector resonances.

W , and the coupling constants and

g =0:9 M M 900 GeV sin 0:998

1R Z Z R

,then and R 2

1 In addition to the pseudo-scalar , there should also exist a

cos 0:056

( ). Unlike the left-handed weak sector where vector particle R , similar to the of QCD, corresponding to the

W Z

L L the and masses are nearly degenerate, the right-handed bound state with spin one. The coupling strength of this R res-

sector could have a larger separation between the masses of the onance to the Drell-Yan photon is unknown, but could be quite

W Z Z

1 2

R and or , due to a much smaller coupling constant and large. If it is like QCD, then the rate of events at collid-

R R

much larger symmetry-breaking scales. ers will be dominated by resonance production as long as the R

GeV

Since the electron couples to both sets of gauge bosons, the is not too large ± a few hundred . The mass of the R is

e new gauge bosons could be produced at e machines. How- unknown and probably as dif®cult to calculate as the mass in ever, such large masses would prohibit their production at any QCD.

existing facility. The NLC or LHC would be the only machines

Production of the new fermions via a R resonance would then

0 0

in the near future to produce these bosons in suf®cient quantity exclude the productionof , since the spin-1 cannot decay

R R 0

to be directly observed. to two identical pseudo-scaler 's. The only way to produce

0 0

events is off resonance, at a greatly reduced rate. Thus,

R R

we do not expect many events with four photons, relative to two

0 SU(3)

V. C BOUND STATES OF TWO

E6 R FERMIONS photons plus two leptons plus T . If the production of pairs

at collidersproceeds via a resonance, then we would expect the

Assuming that the new strong interaction generates a con®n- momenta of the R 's to be quite large, and easily recognized. ing potential similar to QCD (i.e. the number of fermion gener-

ations is small), there should exist only bound states of v and r fermions, with relatively long lifetimes, and no ªfreeº fermions. VII. OTHER DECAYS OF R

Like the charged pions of QCD, there should exist pseudo-scaler

(v r) (vr) R

states such as and , as well as the neutral state Since the boson is assumed to have a mass less than mass

R R

v v r r R R

made from and . If we assume that these are the low- of the pseudo-scalar, then the dominant decay of the

W +

est mass states, then these states can decay only via the right- should be to R . Unlike the pion of QCD, the pure leptonic

decay of R should occur considerably less often. For R

handed weak interaction (similar to QCD where the charged pi- R

+ W

production, both W and will decay to an electron and a R ons can only decay via the left-handed weak interaction). Of R

SU(2) neutrino. If we assume ªuniversalityº between the generations

course, quarks do not interact via R , so only the lepton

W R of leptons(for this new weak interaction), then shoulddecay

channel is open to these new pions. However, if the mass of R

W +

W to muons (and taus) equally as often. Thus, in addition to events

R R is greater than the mass of R , then the will decay to

W containing two photons plus two electrons, colliders should also

via the ªtriangle anomalyº. The R will subsequently decay to 0

a charged lepton and a neutrino. The new neutral pion will observe events with two photons plus two muons, and events

+ also decay predominantly via the ªtriangle anomalyº to , with two photons, an electron, and a muon.

since the photon has zero mass. Observation of e events is a critical test of thismodel. Unless

We will assume that the ªscaleº of the the new strong interac- we are ready to discard universality for the right-handed weak

0 SU(3)

tion c is approximately 1000 times the ªscaleº of QCD. interaction, these other decays must eventually be observed or

The mass of the pseudo-scalar state R is then approximately this model should be discounted.

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0 SU(3)

VIII. C BOUND STATES OF THREE FERMIONS If the new strong interaction is similar to QCD, then there should also exist bound states of three fermions. Like the proton and neutron of QCD, there should be two fermion states,

one charged and one neutral, that are relatively stable. They

p (vvr) n (vrr)

would be spin- fermion states such as and R

2 TeV with masses near 1 . It is not clear whether the charged or neutral state would be heavier. Using QED, the calculation of the mass difference between the charged and neutral pion of QCD has the correct sign and approximately the correct magni- tude. However, the proton-neutronmass difference appears with the opposite sign from what is observed, casting considerable doubt on the calculation. Given how little we know about this new strong interaction, we can only speculate about which is the heavier of these two new baryons.

If the mass of neutral state is heavier than the charged state (as

n p R in QCD), then the R will decay into , and we may be able to form ªatomsº of electrons and very heavy ªnucleiº. There may be cosmological observations which provide limits on ªmatterº

in this form. If the mass of the charged state is heavier than the

p n R neutral state, then the R will decay into , and there will exist heavy neutral matter in the universe that we have not yet de- tected.

IX. ACKNOWLEDGMENTS Chris Hill, Bill Bardeen, and Estia Eichten from Fermilab were very helpful in exploring this model, as well as Roberto Peccei at Snowmass.

X. REFERENCES [1] J.C. Pati and A. Salam, Phys. Rev. D10 (1974) 275. [2] H. Georgi and S.L. Glashow, Phys. Rev. Lett. 32 (1974) 438.

[3] This contribution was inspired in part by CDF's recent e-gamma-e-

gamma- T event, although this event may have nothing to do with new strongly interacting fermions.

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