Composite-technicolor standard model

Volume 188, number 1

COMPOSITE-TECHNICOLOR

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2 April 1987

STANDARD MODEL

B. Sekhar C H I V U K U L A and H o w a r d G E O R G I Department of Physics, Boston University, Boston, MA 02215, USA and Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA

Received 16 January 1986 We characterize a class of composite models in which the quarks and leptons and techniferrnions are built from fermions (preons) bound by strong gauge interactions. We argue that if the preon dynamics has as [SU(3) x U(1)]5 flavor symmetry that is explicitly broken only by preon mass terms proportional to the quark and lepton mass matrices, then the composite-technicolor theory has a GIM mechanism that suppresses dangerous flavor changing neutral current effects. We show that the compositeness scale must be between ~1 TeV and -~ 2.5 TeV, giving rise to observable deviations from the standard electroweak interactions, and that B-B mixing and CP violation in K mesons can differ significantly from the standard model predictions. The lepton flavor symmetries may be observable in the near future in the comparison of the compositeness effects in e+e - --*~+~- with those in e+e - ~ e+e -. The so-called standard model of strong and electroweak interactions leaves m a n y questions unanswered. Two of these questions stand out because their answers can be f o u n d by experiment in the imaginable future. These two questions are: (1) W h a t physics breaks S U ( 2 ) x U(1), giving mass to the W and Z? (2) W h a t physics communicates the S U ( 2 ) x U(1) breaking to the quarks and leptons? Neither of these questions can be evaded simply by pushing the associated physics up to arbitrarily high energies. They are, therefore, the two central problems in particle physics today. In a model with a fundamental Higgs doublet, supersymmetric or not, the answer to question (1) is " t h e Higgs potential" and the answer to question (2) is " t h e Y u k a w a couplings". Such models yield no insight into the nature of flavor or the peculiar structure of the quark and lepton mass matrices. These flavor questions are answered, if at all, at some higher energy scale. On the one hand, it is disappointing that these models do not contain any clue to where to look for the physics of flavor. O n the other hand, this is precisely what saves them from flavor changing neutral current ( F C N C ) effects. The G I M [1] mechanism that suppresses F C N C effects also prevents us from meaningfully asking about the physics of flavor.

Until G I M violating effects are seen and understood, we will not know what flavor really is. " T e c h n i c o l o r " [2] is a beautiful answer to question (1). Unfortunately, technicolor research has been slowed by the lack of an attractive answer to question (2). The problem is that the conventional approach, extended technicolor, gets the physics of flavor mixed up with the mechanism by which SU(2) x U(1) breaking is c o m m u n i c a t e d to the quarks and leptons. The typical result is large F C N C effects. This has led to efforts to push up the extended technicolor scale [3], but not to any satisfactory models. Evidently, what is needed is a GIM-like mechanism for technicolor models that allows us to decouple the answer to question (2) f r o m the physics of flavor. Unfortunately, attempts to implement such a mechanism in the context of extended technicolor have been c u m b e r s o m e and inconclusive [4]. A n o t h e r answer to question (2) in technicolor models has been suggested by Bars [5] and by Preskill [6] in the context of composite models in which the quarks and leptons and technifermions are all built from fermions (which, for brevity, we will call preons), b o u n d by as yet unobserved strong gauge interactions at a compositeness scale f (we will define f more precisely below). The suggestion was that nonrenormalizable interac-

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tions induced by the physics at f could provide the couplings between ordinary fermions and technifermions needed to generate the quark and lepton masses. In this note, we characterize and discuss the composite models in which this mechanism for mass generation is consistent with the GIM mechanism. We will not discuss physics at the confinement scale, f , explicitly, but we will identify the symmetry properties of the low-energy ( E < f ) theory that are crucial to the suppression of F C N C effects. We will then note that there is an essentially unique way of realizing the required symmetry structure in the composite model. Finally, we will discuss the phenomenology of our class of composite models and show how the composite G I M mechanism works in practice, In all of this, we will be using only general properties of field theory, symmetry properties, and dimensional analysis based on the assumption that the strong preon gauge interactions have no small dimensionless parameters. We will not discuss any necessarily more speculative attempts to construct an explicit preon dynamics. We call a model in the class to be described in detail below (if, indeed, any can actually be constructed) a "composite-technicolor standard model" (CTSM). As we will see below, the phenomenology of such a model at energies of the order of the S U ( 2 ) x U(1) breaking scale ( v - 1 / G ~ - v ~ 250 GeV) and below is largely determined by the symmetry structure and independent of the details of the preon dynamics. For an app¢opriate range of parameters, the physics is very similar to that of the standard model. We will compare CTSM with its relatives, the standard model and the supersymmetric standard model. We close with a suggestion for the experimental observation of flavor symmetry in e + e - scattering. The underlying idea of the GIM mechanism that we wish to abstract from fundamental Higgs models and use in composite models is the following:

The theory has.a global [SU(3) x U(1)] 5 flavor symmetry, one S U ( 3 ) × U(1) factor each for lefthanded (LH) quarks, LH leptons, right-handed (RH) 100

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charge 2 / 3 quarks, RH charge - 1 / 3 quarks and R H leptons. But the global symmetry is broken explicitly by terms proportional to the three mass matrices for the charge 2 / 3 quarks, the charge - 1 / 3 quarks and the leptons. We assume, simply, that our composite model has the same property. As we will discuss, we may want to enlarge the original global symmetry to include a custodial SU(2) symmetry [7] for the right-handed technifermion fields. We will also assume that there is an additional unbroken U(1) that expresses the conservation of technifermion number. In fact, we could assume a much larger symmetry, as large as an SU(45 + 4n) [for an SU(n) technicolor], under which all the left-handed fermions transform as a 45 + 4n. This large symmetry is broken explicitly because an S U ( 3 ) x S U ( 2 ) x U(1) x SU(n) subgroup (associated with the strong, electroweak and technicolor interactions) is gauged. This leaves invariance under gauge symmetries, the [SU(3) × U(1)] 5 flavor symmetry, and U(1)'s acting on the technifermions. Some of the details of our model depend on what subgroup of SU(45 + 4n) is left unbroken by the strong preon interactions. But for the suppression of FCNC effects, the crucial fact is that whatever the global symmetry of the preon dynamics, it must contain as a subgroup the [SU(3)x U(1)] 5 flavor symmetry broken explicitly only by terms proportional to the quark and lepton mass matrices. Now that we have characterized the low-energy symmetry structure of our composite models, we must ask whether it is reasonable to assume that this structure can actually be produced in sensible preon models. It is certainly not unreasonable to assume that one can construct models with the required global flavor symmetries. The "moose" models [8] discussed by one of the authors are examples. What about the explicit symmetry breaking? For a preon model involving only fermions and strong gauge interactions, the only possibility is preon mass terms. Thus we assume that the flavor symmetries in the underlying preon theory are explicitly broken by three sets of preon mass matrices Mu, M D, and M t, proportional to quark and lepton mass matrices m U, roD, and me.

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N o n e of the preon masses can be much larger than f , or else the corresponding preons would have decoupled above the confinement scale and would not participate in the preon dynamics. We will now discuss the phenomenology of these models. Our principal tools will be symmetry and dimensional analysis. The new feature of the composite-technicolor standard model is the possibility for the explicit appearance of the flavor symmetry breaking preon mass matrices in the nonrenormalizable interactions induced by the preon dynamics. It will, therefore, be useful to organize our discussion of the nonrenormalizable interactions in terms of the number of preon mass factors they contain. We begin with terms that contain no factors of the M 's. The leading nonrenormalizable contributions are dimension-six operators involving fourfermion fields. The fermion fields are ¢L, UR, DR, LL, and l R, which are triplets of quark doublet, charge 2 / 3 quark, charge - 1 / 3 quark, lepton doublet and charge - 1 lepton fields, respectively, and

~L =

mL ,

(1)

an SU(2) doublet of technifermion fields and P R and mR, SU(2) singlets. We assume that technicolor is some SU(n) gauge interaction with p and m transforming like n ' s with electric charge + 1 / 2 for p and - 1 / 2 for m [so that the SU(2) × U(1) anomalies cancel]. We will sometimes combine the L H fields and the L H charge conjugates of the R H fields into a (45 + 4 n ) dimensional vector, ~L. All possible global symmetries of the preon dynamics that act nontrivially on the light fermions are contained in the SU(45 + 4n), under which the light L H fields transform as a 45 + 4n. If we build terms that have the SU(45 + 4n) symmetry, therefore, they are certain to be invariant under all the relevant symmetries of the preon dynamics. According to naive dimensional analysis (NDA) [9], all the dimension-six operators have coefficients of the same order of magnitude. We define our compositeness scale, f , so that all these coefficients are of order 1/f 2. Because of the flavor

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symmetries, none of these terms can produce any F C N C effects. These terms do, however, produce effects that mimic and modify the ordinary weak interactions. For example, a term like (2) is always allowed by the flavor symmetries and contributes in a variety of neutral current weak interactions. Since we know that the standard model gives a reasonable description of the neutral current weak interactions, we can derive a rough lower bound on f. A slightly stronger bound can be obtained by considering the effect of these terms in high-energy e+e - collisions [10] ,1. The precise values for these bounds will depend on the details of the symmetry assumed for the preon dynamics, and we will discuss them in another work. For now we will assume a lower bound of order f>_ 4v = 1 TeV.

(3)

If a custodial SU(2) symmetry is not imposed, these interactions contribute to the p parameter in order v2/f 2. For example, a term like

( X / f 2 )( P R"[p.P R )( P R"/'ttP R )

(4)

renormalizes the Z mass but not the W mass. Then the bound on f would be stronger, f>_ 10t;. As we will see below, this is very close to being unacceptable for other reasons, but it cannot quite be ruled out. We next consider terms with one power of M. In our estimates, we will ignore complications due to such things as the renormalization group scaling of the masses and the coefficients. Our aim is not to track down every factor of two, because N D A can give us only rough estimates anyway. We want to identify the important features of the model as simply as possible. The leading terms with one M are the dimension-six operators that give rise to the quark

,1 F o r a

discussion of the isoscalar axial vector current, see ref.

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and lepton masses,

(ZLM, eR)(mR L) + h.c. or (Z, LM, dR)%y(~?yLpg ) + h.c., (~LMvUR)(~RTL) + h.c. or

(,IMuUR)cy(LLmR)+h.c.,

(5)

( d/L MDDR)(W~RTL) + h.c. or

+ h.c.,

where x and y are SU(2) indices. The terms on the left come from terms involving two gt's and two ~ ' s , while those on the right come from terms involving four ' ~ ' s and their hermitian conjugates. N D A suggests that the coefficients of these operators are of order 1/(4~rf 3) and that the expectation values of the technifermion bilinears are of order 4~rv3. Thus the light fermion masses, rn, are related to the preon masses, M, by

M-- (f/v)3m.

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Now that we have an idea of the scale of f , we will briefly discuss the rest of the phenomenology. The main conclusion is that all of the F C N C effects induced by the preon dynamics in CTSM are suppressed by powers of the quark masses. In m a n y cases, the extra F C N C effects in CTSM are smaller than those induced by second-order electroweak interactions in the standard model. However, because the functional dependence of the effects on the quark masses is different in CTSM, the terms involving m t are relatively more important. Some of these terms, such as those contributing to CP violation in the AS = 2 sector, or Bs-B s mixing, can be fairly large. As an example, we will discuss the leading contribution in CTSM to AS = 2 processes. This comes from the four-quark operator, which has the form (with the coefficient suggested by N D A )

[1/(4~r )4f6] ( ~LY~MuMtuqJL )( ~/Ly~,MuMtuqJL). (10)

(6)

Another useful constraint on the parameters can be found by considering the t quark mass. We know that M t cannot be too large, or else it would decouple. Let us assume (perhaps conservatively) that

Such a term is allowed by the explicitly broken flavor symmetry no matter what subgroup of SU(45 + 4n) is preserved by the preon dynamics. This gives a coefficient of the AS = 2 operator, (JL'~/~SL) 2, o f order --

M t _< 4~rf.

(7)

(11)

Thus

rn t < 4,trv3/f 2.

6,

(8)

Furthermore we know from experiment that 25 GeV < m t- This implies an upper bound for f ,

where in terms of the K M matrix, V, the mixing parameter ~ is

=

VqdVqsttlq/mc.

(12)

q = t,c,u

f < 10v = 2.5 TeV.

(9)

In fact, both bounds, (3) and (9), are conservative. We might expect f somewhere near the geometric mean, 5v or 6v, = 1.5 TeV. If the t quark mass is much larger than 25 GeV, the upper bound on f is reduced by ( m t / 2 5 GeV) t/2 ,z

,2 A bound very similar to (8) but logically independent can be obtained by considering the effect of the preon mass matrices on the p parameter. A term involving four technifermion fields and four M ' s contributes to a Ap of order (mt/4"n'v)4(f/v) 6, which m u s t be less than about 0.01.

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We have arbitrarily used m c for normalization in (12) to make ~ dimensionless. The dominant contribution from the box diagram in the standard model to the CP conserving AS = 2 amplitude is of order

[~2/(41r)2]G2m2c.

(13)

where ~q = rq~ gqs.

(14)

Note that the CTSM contribution, (11), is formally a third-order weak effect, proportional to

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G~ and doubly G I M suppressed. However, the

( f / u ) 6 can be a large enhancement factor. The term in (11) proportional to m 4t is particularly interesting because m t is so much larger than m c. The ratio (11)/(13) is

¢ ¢ (/c)[GFm~/(4~r)z](f/o) 6.

(15)

To be consistent with the observed K - K mixing, the real part of (15) must be not much larger than 1. This gives a bound on a rather complicated combination of f , m t and the KM angles. The ratio ~/(c, on which (15) depends, can be large if the t quark is heavy and the mixings to the t quark are not too small. We do not yet know enough about the parameters to know for sure whether it is satisfied, but it is certainly not yet ruled out. The situation for the CP violating part of the amplitude is different. Here the dominant contribution from the box diagram is [Im(~t2 )/(4vr )2] G2m2t"

(16)

The imaginary part of (11) is of order [exp(~t2 ) G 3 m 4 / ( 4 ~ r ) 4 ] ( f / o ) 6 ,

(17)

and is very likely larger than (16). This means that CP violation in K - K mixing in CTSM is likely to be larger than in the standard model. Such an enhancement of CP violation might be welcome [12]. A similar enhancement occurs in AB = 2 processes, Bs-B ~ and B-B mixing. This could produce observable mixing effects in the B-B system, where mixing is not expected in the standard model. Before we close, we will compare the composite-technicolor standard model with the other "standard" models. The obvious weak point of CTSM is that we do not know for sure that there is any gauge field theory that gives the required preon dynamics. But if we can clear that hurdle, CTSM will have some clear strong points. As in the other standard models, which also have GIM suppressions, there is no upper bound on the scale at which flavor physics actually produces the flavor violating preon mass matrices. Unlike the standard model (and its twin, the strongly coupled standard model [13]), CTSM has no fundamental

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scalar fields to require a fine tuning when the model is embedded in a more complete theory at a higher scale. Unlike the supersymmetric standard model. C T S M does not suffer from the Hall-Kostelecky-Raby disease of sensitivity to flavor physics at arbitrarily large scale [14]. The symmetry structure of the preon theory in CTSM, like that in QCD, is an automatic consequence of form of the gauge couplings and renormalizability, with no extra assumptions needed. If CTSM is the way that nature has chosen to break the S U ( 2 ) × U(1) symmetry and give mass to the quarks and leptons, then some of its nonstandard effects will show up in the next few years, certainly at LEP, very likely at TRISTAN and perhaps at other machines. The best chance for quantitative confirmation of the ideas discussed here in the near future is probably in the comparison of the compositeness effects in e+e ---, ~t+~t- with those in e + e - ~ e+e . So long as the flavor [SU(3)X U(1)] 2 symmetries are there for the leptons, the dominant corrections to the electroweak gauge physics come from the following terms in the lagrangian:

(a/f 2)(dLY"gL )( dCYUdC ) + (b/f 2)( dcY~[c ) (c/f2)(?e,y~'dR)(?r~y, gR) =(a/fZ)[(YcT~ec)(gcy~,ec) X (?,V,d~) +

+ 2(ecT"eL)(~LV~dLL) + . . . ]

+(b/f2)[(eLY"eL)(~'RYt~eR) + (eL'Y~teL) x

+

+ '" ]

+(c/'fa)[(eRy~'eR)(eRy~,eR) + 2(~RY"eR)(~Ry,/ZR) + "'" ].

(18)

We expect the absolute values of a, b and c to be of order 1. If the symmetry of the preon dynamics is larger than the cross product of the flavor symmetry with the gauge symmetry, then the three coefficients in (18) can be related. For example, in the limit in which there is an SU(9) symmetry that acts on all the L H lepton and antilepton fields (or any larger symmetry including it, such as the SU(45 + 4n) discussed above), we find a = c = - b/2.

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T h e relations b e t w e e n e + e - ~ ~ + ~ - a n d e+e --, e+e - i n (18) directly test only the l e p t o n flavor symmetry. It is the q u a r k flavor symmetries that are crucial for the G I M m e c h a n i s m that we have described. Nevertheless, if evidence of compositeness at a scale -- 1.5 TeV appears, we will have a strong c i r c u m s t a n t i a l case, based o n the observed suppression of F C N C effects, that the s y m m e t r y structure of the p r e o n d y n a m i c s is as we have discussed i n this paper. By studying the low-energy evidence for compositeness that we expect to be f o r t h c o m i n g i n the near future, it should be possible to d e t e r m i n e which extension of [ S U ( 3 ) x U(1)] 5 is preserved b y the p r e o n dynamics. This will be a clue to the n a t u r e of the p r e o n d y n a m i c s a n d it will b e i m p o r t a n t to try to construct models that i n c o r p o r a t e the s y m m e t r y structure. But it is very unlikely that we will b e able to u n d e r s t a n d the p r e o n d y n a m i c s completely o n the basis of the low-energy i n f o r m a t i o n alone. W e will n e e d a m a c h i n e like the p r o p o s e d SSC, where it should be possible to find further clues to the n a t u r e of the physics above the compositeness scale. W e are grateful to Larry A b b o t t , Eddie Farhi, K e n Lane, Marie Machacek a n d Lisa R a n d a l l for useful comments, a n d to Estia Eichten for a message.

References [1] s. Glashow, J. Iliopoulos and L. Malani, Phys. Rev. D 2 (1970) 1285. [2] E. Farhi and L. Sussldnd, Phys. Rep. 74 (1981) 277, and references therein.

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[3] T. Appelquist, D. Karaboli and LC.R. Wijewardhana, Phys. Rev. Lett. 57 (1986) 957; T. Appelquist and L.C.R. Wijewardhana, Yale University preprint YTP-86/17 (1986); B. Holdom, Phys. Rev. D 24 (1981) 1441. [4] S. Dimopoulos, H. Georgi and S. Raby, Phys. Lett. B 127 (1983) 101; S.-C. Chao and K. Lane, Phys. Lett. B 159 (1985) 135. [5] I. Bars, Nucl. Phys. B 208 (1982) 77. [6] J. Preskill, report presented at APS/DPF meeting, (Santa Cruz, CA, September 1981) AIP Conf. Proc. No. 81 (AIP, New York) pp. 572-589. [7] P. Sikivie, L. Susskind, M. Voloshin and V. Zakharov, Nucl. Phys. B 173 (1980) 189. [8] H. Georgi, SU(2)×U(1) breaking, compositiness and flavor, in: Architecture of fundamental interactions at short distances, Les Houches XLIV, eds. P. Ramond and R. Stora (North-Holland, Amsterdam, 1987); Nucl. Phys. B 266 (1986) 274. [9] A. Manohar and H. Georgi, Nucl. Phys. B 234 (1984) 189; see also H. Georgi and L. Randall, Nucl. Phys. B 276 (1986) 241. [10] E. Eichten, K. Lane and M. Peskin, Phys. Rev. Lett. 50 (1983) 811; L. Hall and S. King, Harvard University preprint HUTP86/A060. [11] C. Korpa and Z. Ryzak, Phys. Rev. D 34 (1986) 2139; see also I. Bars, J.F. Gunion and M. Kwan, Nucl. Phys. B 269 (1986) 421; University of Southern California preprint USC-86-01; G. Brandt, Siegen University preprint SI86-12. [12] P. Ginsparg, S. Glashow and M. Wise, Phys. Rev. Lett. 50 (1983) 1416; 51 (1983) 1395; F.J. Gilman and J.S. Hagelin. Phys. Rev. Lett. B 133 (1983) 443. [13] M. Claudson, E. Farhi and R.L. Jaffe, Phys. Rev. D 34 (1986) 873, and references therein. [14] L. Hall, V.A. Kostelecky and S. Raby, Nucl. Phys. B 267 (1986) 415; see also H. Georgi, Phys. Lett. B 169 (1986) 231.