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®ca- tion 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 0 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 0 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 0 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- 961 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 L L 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. = f 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 2 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 L 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 q 1 1 f f f f L R L R 1 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 2 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 1 2 2 2 2 2 2 M = (g cos + g sin ) v + g cos v 2R R 1R R R Z R 1R S 1 4 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 1 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 + g 1L p p u (1 + )dW + d (1 + )uW 5 5 R R tan = L 2 2 2 2 g 2L Since the quarks do not interact via the right-handed weak in- r T =0 teraction, then R , and they can be assigned a value for 2 1 1 K 2 the ªrightº hypercharge equal to their electric charge (the quarks sin = + R 2 2 K +4 2 have the same ªleftº hypercharge assignments as in the Standard Model).