Orchids to The Standard Model

C. Jarlskog CERN, Geneva, Switzerland

and Department of Physics

University of Stockholm Stockholm, Sweden

ABSTRACT

I briefly review the following aspects of the Standard Electroweak Model: the number of families and neutrino physics; beauty-top physics and the Higgs sector, I also present the results of a survey on what professional physicists and students consider to be the most urgent current question in physics.

Preface

This "Silver Rochester Conference" is indeed a tribute to the Standard Model. In fact all the plenary talks, with one exception, deal with the Standard Model. The exception being the talk on two-dimensional quantum gravity, by Dr. Brezin. Consequently, in order not to overlap too much with other speakers, I shall not deal at all with QCD. By Standard Model, in the following, I mean the Standard Electroweak Model. Espe­cially after the encyclopaedic talk by Dydak, on the physics of the Z-peak and radiative correc­tions, I feel that I should not say much about that. The scope of my talk will be limited to the following topics:

Contents

1 The rich heritage of the Standard Model

2 Orchids to the Standard Model

3 The number of families, N f a m

4 W h y three families?

5 W h a t if there are massive neutrinos?

5.1 The simplest scheme with massive neu­trinos

6 Results on neutrino physics

7 The top quark

7.1 W h y is the top quark needed?

7.2 The physics of Z -+ bb

7.3 Limits on the top mass

7.4 The top mass from radiative correc­tions

7.5 The top mass from weak decays

7.6 Evading limits on the top mass

8 The Higgs boson

8.1 No fundamental Higgs?

9 A survey of current urgent questions in physics

9.1 Answers from professional theorists

9.2 Answers from professional experimen­talists

9.3 Answers from students

10 Acknowledgements

11 References

1 The rich heritage of the Standard Model

Often the Standard Model is presented in the books as if it came in a beautifully wrapped pack­age from "heaven", a gift to the mankind. The package neatly contained the symmetry group, the left-handed doublets and the right-handed singlets and the interactions. All one had to do was to add the Higgs sector and use it. In real-

61

ity the situation has been very different. In fact no such package was delivered. The Standard Model slowly grew out of a large number of ex­perimental findings and theoretical concepts. Of course, it is founded on relativity and quantum mechanics. Some of the by now old findings and concepts which go into its formulation are the following.

* The Dirac equation (Dirac 1927 [1]) *Discovery of continuous /3-spectrum (Chad-

wick, 1914 [2]) and the concept of neutrino (Pau-li, 1930 [3]).

* The concept of isospin (Heisenberg, 1932 [4]), inspired by the discovery of the neutron [5]

* The Fermi theory of weak interactions (Fermi, 1934 [6]).

* The idea that massive particles mediate forces (Yukawa, 1935 [7]).

* The Klein Model, with the concepts of what we call lepton-hadron universality and unifi­cation of weak and electromagnetic forces (Klein, 1938 [8]). Unfortunately, this Model did not get the attention it deserved and does not seem to have had much influence on the development of the modern gauge theories.

* The idea of local isospin symmetry (Yang and Mills, 1954 [10]).

* The theta-tau puzzle [9] and the idea of parity violation (Lee and Yang, 1956 [11]).

The above list only gives some of the essen­tial ingredients of the Standard Model. There are many more, such as the concepts of quarks, the GIM-cancellation, etc. The greatness of the Standard Model lies in the fact it has been able to synthesize so many experimental findings and beautiful theoretical concepts within a rather sim­ple framework.

The modern model building started with a mo­del, by Schwinger (Schwinger [12]), in which there is an isotriplet of gauge bosons, W*,j, W~, ex­actly as in the Klein Model of 1938. Just because one sometimes refers to the Standard Model as the Glashow-Weinberg-Salam Model [13] by no means means that it was created from ashes by these authors. The moral is, perhaps, that some­times it is better to be the last than to be the first, if you wish to have your name immortally attached to a finding.

The Standard SU(2)xU(l) Model

2 Orchids to the Standard Model

The Standard Model, with its symmetry group 5(7(2) x [ / ( l ) , has three sectors (see the figure). First there is the gauge sector, denoted by G, including G — W,B. This sector, especially the part involving the W, is the most beautiful one in the Model. It is characterized by just one coupling constant, the g of the SU(2). The W-bosons have beautiful self-interactions.

Here in Singapore, an appropriate measure of the goodness of a theory is given by how many Orchids it gets. On a scale spanning from zero (poor) to three (excellent), I would give two and a half Orchids to the gauge sector of the Model. Had the symmetry group been a simple non-abelian one I would have given it three Orchids.

Next there is the fermion sector, denoted by / . There, the fermions (quarks and leptons) are introduced in left-handed doublets and right-handed singlets. Thus, parity and C-conjugation asymmetries are introduced into the Standard Model by hand; they are not "explained". The fermions interact with the gauge sector via the link L ( / , G ) . Here a new coupling constant, g', enters as well as a number of hidden parameters,

62

the weak hyper charges Y. These are chosen to

satisfy the relations Q = I3 + Y. It is true that

there are relations among the Y ? s if one requires

that the anomalies cancel [14]. But such relations

should come out by themselves. Also, there re­

mains some arbitrariness. Therefore, I give one

and a half orchids to the fermionic sector of the

Standard Model.

If we had only these first two sectors of the

Standard Model all fermions and gauge bosons

would be massless. The Higgs sector, denoted

by if, is introduced to solve the mass problem.

This gives rise to a Higgs potential, V(H), as

well as the links L(G, H) and L(f, H). Once the

isospins and the hypercharges of the Higgs mul­

tiplets) are specified there are no new parame­

ters in the link L(G, H). The number of parame­

ters in the Higgs potential V(H) depends on how

the Higgs multiplets are chosen. In the Minimal

Standard Model the Higgs is a doublet and there

are only two free parameters in the Higgs poten­

tial. The link L(f,H) is the "ugliest" feature

of the Standard Model. First of all it involves

solely non-gauge interactions. In fact every term

in £ ( / , H) is invariant by itself, under the action

of the symmetry group, and, therefore, its coeffi­

cient is not constrained by other terms in the La-

grangian. In the Minimal Standard Model (with

three families and massless neutrinos) there are

fifteen free parameters in L(f, H), Thus from the

seventeen free parameters of the Minimal Stan­

dard Model fifteen of them are due to the Higgs.

Does the Higgs sector deserve to get any Or­

chids? I am not sure. First I thought that it

certainly shouldn't get any. But do we have a

better alternative? The answer is no. After all,

the Standard Model, with its Higgs sector, con­

stitutes a consistent framework and it has led

to an enormous progress in our understanding of

Nature. Therefore, I will happily give the Higgs

sector one Orchid.

3 The number of families, N f a m

The most impressive new result since the last

Rochester Conference [15] which took place in

Munich is the recent accurate determination of

the number of families

In mathematics there are families of curves,

families of functions and so on. These refer to

objects which share some common properties.

Also in physics, à la Standard Model, we have

families of quarks and leptons. Each family con­

tains a set of {up — like, down — like, electron —

like, neutrino — like} objects, which form the

well-known left-handed doublets and right-han­

ded singlets. The Minimal Standard Model is of­

ten defined to be the version with only one Higgs

doublet and no right-handed neutrinos (i.e., ob­

jects with vanishing weak isospin and hy per char­

ge, / = Y = 0).

In the Minimal Standard Model the number

of families is given by the number of the (left-

handed) neutrinos. This number is computed

from the "invisible" width of the Z, viz.,

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where Tz denotes the total width, the subscript h

refers to hadrons and is the theoretical width

(166 MeV) for one massless neutrino.

In fact, some years ago, it was generally be­

lieved that in order to determine the number of

families one would have to look for e + e ~ —* Z —•

vvy, by measuring the single photon in the final

state. It was expected that such a measurement

would take some time. But it turned out that

the hadronic peak cross-section was an excellent

probe of the number of families. The method was

first used at SLC by the MARKII Collaboration,

which last summer quoted [16] N„ = 3.8 ± 1.4

and concluded that Nv < 5.5 at 90% C.L.

The number of families, as reported at this

Conference [17], is shown in Table 1. For the sake

of comparison, I have also included the results

of the so-called "two-parameter fit" which were

presented at the Rencontre de Moriond earlier

this year ([18], [19])

If I take the liberty of computing the weighted

averages of the above results, I find

Dydak [20], who knows about the correlations

among the above experimental results better than

I do, quoted the value NFam - 2.89 ± 0.10. The

above results show that there are only three fam­

ilies, if one assumes the validity of the Minimal

Standard Model.

Table 1: The number of families (Minimal Model)

4 W h y three families?

The answer to the above question, in all hon­esty, is that we don't know why.

Some years ago, I remember that the number of families was supposed to be four. It was said that the number should be even and that it was hard to get the answer three. The number of families was computed from the geometry of the " compactified space" which we were supposed to live in. Later on, it turned out that many pos­sible solutions were found and the subject faded out of fashion. However, that does not exclude the (attractive) possibility of having a connec­tion between the geometry of space-time and the number of families.

At this Conference, there was a contribution by Frampton [21] who addressed the above ques­tion. Within the framework of an extended gauge model and by assuming that there be asymptotic freedom and no anomalies, he and his collabora­tors find that the number of families is at most three. The model can be tested, which is nice, and most probably will be ruled out by future data. That seems to be the usual fate of almost all testable models. I wish to emphasize that the question "why three families" is still very much open and certainly deserves our attention. Na­ture has presented us with a clue which we don't understand.

As far as I am concerned [22], the number three is wonderful. At our present stage of un­derstanding, it looks "great" that Nature seems to be content with only three standard families. Why? Because of the following. Going from one to two families entails new subtle phenomena: family-mixing and GIM-cancellation [23]. The transition from two to three families is again ac­companied by a beautiful subtlety: the entrance of CP violation [24] on the scene. However, there is no known fundamentally new phenomenon as­

64

sociated with the transition from three to four families. The quark mixing matrix, for the case of four families, looks horrible with six rotation angles and three phases. Just writing it down takes a whole page. And all this complication for nothing in return? Therefore, it seems nice that we are not bothered with such " trivial-looking" complications. Surely there is new physics. How could the 3-family Standard Model, with its 17 free parameters be the ultimate theory? How­ever, the "new Physics" is hopefully of a more subtle kind, something which we can learn from.

It is also important to notice that the CP struc­ture of the three-family model is quite elegant. The same can not be said about the four-family model. In fact, in order to have CP violation in the three-family model 14 conditions have to satisfied, viz.,

where the angles are those of the Kobayashi-Maskawa parametrization [25] of the quark mix­ing matrix. These conditions are unified [26] in a single relation detC^O where C is the commu­tator of the (square of the) quark mass matrices, VI7,

For a review see [27]. J is the CP-invariant, here given by J = sf$2S3CiC2C3sin£, In fact there is an infinite number of such commutators of func­tions of mass matrices, the one in Eq.(5) being the simplest among them. They are very help­ful for a better understanding of the structure of

where again Tu is the theoretical width for just one massless neutrino.

It turns out that, in principle, you don't have to extend the Minimal Standard Model very much to get a number less than say three. All one needs to do is to extend the Minimal Standard Model just a "tiny bit", by allowing right-handed neu­trinos. In fact there is no known reason why we should not have such objects. All other fermions have right-handed partners, why then not the neutrino? It is true that right-handed neutrinos introduce, in general, a large number of new pa­rameters into the theory but we get something in return. Massive neutrinos can oscillate [28]. They can, in some cases, take part in double-beta decay. They can have magnetic moments, etc.

Let us call the extensions of the Minimal Stan­dard Model through addition of an arbitrary num­ber of right-handed neutrinos the "Slightly Non-Minimal Standard Model(s)" . In fact, in the lit­erature, a large number of such models have been considered, some within the framework of the so-called see-saw mechanism. I also had a look ([29], [30]) at such models because I was asked to write an article for a Festschrift dedicated to Tor l e i f Er icson , on the occasion of his 60-th birthday. I thought there was only one appropriate topic for the occasion, the neutrino. Torleif and the neutrino hypothesis were born in the same year,

Torleif being about one month older than the neutrino. However before writing the article it was necessary to take a closer look at the neu­trinos. I found ([29], [30]), to my great surprise, that adding right-handed neutrinos can only de­crease the invisible width of the Z, This result, which was overlooked by other authors who had worked on such neutrinos, at the first sight looks strange. After all, if you add new particles into your theory you expect to get more decay chan­nels and larger widths. Just for fun, I asked some of my colleagues if they could guess what would happen if one would add right-handed neutrinos and everybody guessed that the width would in­crease. The reason it does not increase but in fact can only decrease is very simple. The right-handed neutrinos have vanishing isospins and hy-percharges, Therefore, they do not couple to the gauge bosons. However, they can mix with the left-handed neutrinos and weaken their couplings to the Z. Such mixings can only decrease the in­visible width - never increase it. There is a the­orem which summarizes this result, as follows.

Take the Minimal Standard Model with Nfam

families. Add to it an arbitrary number of right-handed neutrinos. Then, the effective number of families can only be smaller than (or equal to) the true number of families [29]

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CP violation in the three-family case. Note that none of the elements of the quark mixing matrix is allowed to be zero, if CP is to be violated.

5 W h a t if there are massive neutrinos?

The last result, in section 3, is quite intriguing. The central value, of the number of families has gone down since the Rencontre de Moriond, last March, and now lies below three. Of course, the result is consistent with three. Nevertheless, it is interesting to ask the following question: is it possible to get a "number of families" which is less than three?

Of course, in an extended model the quantity defined in Eq.(2) need not have anything to do with the true number of families. It need not even be an integer! In such cases, what we have is an "effective number of families", Nj^, defined by

The upshot of the theorem is that LEP alone cannot measure the number of families, unless one assumes that the Minimal Standard Model is correct. It is important to keep this fact in mind. One needs to make a general analysis, which takes into account all constraints, such as coming from lepton universality, neutrino masses and oscillations, double-beta decay, etc.

If LEP were definitely to establish that the number of families is even slightly larger than three, say 3 + e, e > 0, then we know that all models with three families, à la Minimal Stan­dard Model, and an arbitrary number of right-handed neutrinos are excluded. That I think is a very nice feature of a potential precision mea­surement of the number of families.

What if LEP were to find a number slightly less than three, say

(8)

Here s = sm0, c = cosO, 9 being the mixing angle, which in this simplest scheme is related to the masses, viz., s2 = Mp/(Mp+MF). The term Xpp originates from the decay Z —• vpvF\ the next term refers to the channels with two Fermi neutrinos and the last term keeps track of the channel Z —• v F v F . Moreover À = À ( M § , M p ,

Mp) is the triangular function [33], which always appears in two-body kinematics.

The above relations convey a very simple mes­sage. They are saying that, for example, if the mass of the Pauli neutrino is larger than Mz/2 then the Z can not decay into two Paulis ( 0 ( M z — 2Mp) = 0). In such a case the first term, Xpp vanishes. If the decay to two Paulis is allowed, then there is the appropriate suppression factor, coming from the matrix element and the phase-space, i.e., the factor (1 - 4 M | / M f ) 3 / 2 . Simi­lar arguments apply to the remaining terms in Eq.(10).

From Eq.(10) it follows that if any of the masses Mp or Mp vanishes then e = 0. Also, if both the Pauli and the Fermi neutrinos were much lighter than the Z , so that we can neglect their masses as compared to M z , we would get from Eq.(10)

In other words, as far as the Z-physics is con­cerned, this model and the Minimal Standard Model are indistinguishable if Mp.Mp « Mz as well as when either of Mp or Mp vanish. Now consider the other extreme case where both the Pauli and the Fermi neutrinos are heavier than Mz/2. Then none of them is produced in Z-decays and one gets the largest possible value for e, i.e., e — 1, which corresponds to = 2 in gross disagreement with data.

How big can e be in the simplest scheme? Us­ing the constraint m{yT) < 35 MeV gives [32]

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what can we then learn? I shall now turn to this question.

5.1 The simplest scheme with massive neu­trinos

The general case (with an arbitrary number of right-handed neutrinos) being too complicated to deal with let us instead consider the "simplest scheme" ([30], [31]) which may serve as a peda­gogical toy model.

Take the Minimal Standard Model with three families and add just one right-handed neutrino. Unfortunately, this simple extension already in­troduces four additional parameters into the the­ory. Petcov and I [32] have studied the phe­nomenology of this model in some detail. It turns out that the parameters of the model are tightly constrained by data. In fact what really con­strains the model (as far as the number of fami­lies is concerned) is the knowledge that the tau-neutrino cannot be any of ^ e , ^ ) ^ ' 1 ^ together with the information that m(vT) < 35 MeV.

In this simplest scheme the four neutrinos (the three in the doublets and the right-handed sin­glet) mix. The physical neutrinos are linear com­binations of these neutrinos. One finds that the physical neutrinos are, in general, Majorana neu­trinos (i.e., each its own antiparticle). Two of them are massless and the other two are massive. We can refer to the latter as the Pauli neutrino, i/p, and the Fermi neutrino, vp) and denote their masses by Mp and Mp respectively. One finds that e, in Eq.(9), is given by [32]

This means that if LEP were to find an effec­tive number of families which is "substantially" smaller than 3 (e.g., a number like 2.9 with tiny errors) then the simplest scheme will be ruled out. Therefore, it is indeed important to measure the number of families as accurately as possible. Let us hope that it will be done.

In spite of the fact that the neutrino hy­pothesis has been with us for sixty years we are totally ignorant about the "nature" of the neu­trino. We have as yet no answer to such funda­mental questions as "is it its own antiparticle or not?". What are the neutrino masses and mag­netic moments? Do the neutrinos oscillate? In addition to questions on the nature of the neu­trino, we would like to know their role in the

(10) (12)

( H )

Roos, Pakvasa, Peccei and Verzegnassi on differ­

ent aspects of beauty-top physics.

The top quark, in spite of not having been

seen yet, is "omnipresent" because of the follow­

ing reasons. 1) The Minimal Standard Model

minus the top quark is inconsistent and in dis­

agreement with data. 2) The top quark, by being

heavy, affects the phenomenology, especially that

of the Z —» 66 vertex. 3) One can estimate the

mass of the top quark from the radiative correc­

tions involving virtual top quarks. Here below, I

give a short review of the above aspects of "top

physics".

7.1 W h y is the top quark needed?

The top quark is needed in the Standard Model

for several reasons: Suppose that there were no

top quark and we try to get away with a 5-

quark version of the Standard Model, with two

left-handed doublets and one left-handed (Q =

—1/3) singlet as well as the usual right-handed

singlets for all the five quarks. Then the the­

ory will not be consistent because of anomalies.

Another problem with such a model is that it has

no CP violation. Suppose that you say that

I don't worry about anomalies and CP. Maybe

there is some "beyond physics" which takes care

of these problems. Is there anything wrong phe-

nomenologically? The answer, as it has been

known for a long time, is that you get into trou­

ble with flavour-changing neutral currents.

The rate and the topology of Z —• 66 are also

highly affected as follows. The coupling of the

Z to the quarks (i and j) may be written in the

form

67

Universe. Are they partially responsible for the

dark matter of the universe? Are we getting too

few neutrinos from the sun? At this Conference,

these questions are addressed [34] by Okun and

by Nakamura. Below, I will briefly discuss only

a few points.

6 Results on neutrino physics

At this Conference a new limit on the mass of

the electron-neutrino was presented by Bowles,

from Los Alamos. From the study of the decay 3H —*3He+e + i7e the new improved result reads

[35]

It is interesting to note that the limit on the mass

of the electron-neutrino has improved by a factor

of 10 4 in half a century. In 1936 [36] the limit

used to be 0.1 MeV'.

The C H A R M II Collaboration, from CERN,

presented their latest results on and

v^e —• j /^e, based on about 1500 events of each

type. In the Born approximation the ratio of

these two cross sections is given by

where x = sin29. The (preliminary) result, pre­

sented by Santacesaria [37], reads

where sin29o is to a good approximation just the

corresponding quantity appearing in the above

ratio. For details and earlier results from the

CHARM Collaboration see [38].

Santacesaria also presented [37] results on v^N

—> vN/j,p,} where N is a nucléon (inside their glass

target). She reported that 58 ± 19 such events

have been seen, a result [39] which is compatible

with the expected rate from the Standard Model.

7 The top quark

There are two missing ingredients in the Min­

imal Standard Model, the top quark and the

Higgs boson. The top topic is a hot one and was

much discussed at this Conference. See the pre­

sentations/submitted papers by Albright, Barger,

Ganguli and Gurtu, Kûhn, Ma, Maalampi and

where I3 and Q denote respectively the third

component of the isospin and the electric charge

of the quark i. In the five-quark model the neu­

tral current coupling of the up-type quarks are as

given in Eq.(16), i.e., they are diagonal. But for

the down-type quarks only the charge term is as

before. The isospin term is now a non-diagonal

matrix with entries

In the six-quark model the neutral currents are

diagonal, viz.,

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Here the factor —1/2 is the remnant of the third component of the isospin for down-type quarks and Vaj is the element aj of the quark mix­ing matrix a = u,c and j = d!, s, 6. Thus, be­cause of the absence of the top quark, the GIM-cancellation does not operate (the term VuVtj is missing in Eq. 17). Since the empirical magni­tudes of Vub and Vcb are small (\Vub\ < < V& « 0.05) the couplings in Eq.(15) for the b-quark are numerically very different from those in the six-quark model. Consequently, the phenomenol­ogy of the five-quark case is indeed very differ­ent from that of the standard six-quark scenario. Let us now consider some of the consequences for LEP physics.

7.2 The physics of Z -+ 66

In the five-quark model, from Eqs.(15)-(17), we have that Ihh = (-l/2){(Vub)2 + (Vcb)2} « 0. Therefore, the coupling of the b-quark to the Z is almost purely vector. The forward-backward asymmetry, being proportional to 2gv9A/(\gv\2+ \$A\2) is, therefore, expected to be very small. The expected rate of the process Z —» 66 as com­pared to that of the six-quark model is given by

The above ratio is approximately equal to 0.08, for sin26 ~ 0.25. LEP has measured the rate and has found it to be in agreement with the predic­tion of the six-quark model (r(66) « 378 MeV [40]) and, therefore, in gross disagreement with the five-quark model. The results, as presented at this Conference, are shown in Table 2.

Note that when there are three items in the quoted errors they denote, respectively, the sta­tistical, systematical and the uncertainty due to the leptonic branching ratio. Otherwise, the lat­ter uncertainty is included in the systematical errors and, in fact, gives the bulk of that error. I shall not go into the details of these determina­tions and refer the interested reader to the arti­cles quoted in the references ([41] - [44]).

Recently, at LEP, the b-lifetime and the forward backward asymmetry in e + e ~ —* (7, Z) —» 66 have been measured. One finds ([41], [45])

(18)

The results are again in agreement with the pre­dictions of the Standard Model (Abb & 0.09 [40]). The b-lifetime has also been measured at LEP and is found to be [46]

to be compared with the previous world average [47]

The B — 5-mixing has also been seen at LEP ([45]. Indeed the future of b-physics, at LEP, looks very good.

The special role of the top quark in the phe­nomenology of the vertex Zbb was emphasized in several contributions to this Conference. The point is that beauty couples predominantly to top and, in the Standard Model, there is the strange phenomenon that a very heavy quark does not necessarily decouple from the low en­ergy world. In the six-quark model, the quantum corrections involving virtual top quarks are ex­pected to be important. For a heavy top quark the predicted branching ratio of Z —• 66 de­creases (6(br) « - f ( m f / M ^ ) 2 ) . The effect is about 2% for mt — 250 GeV. For a discussion of this point see, for example, [48].

7.3 Limits on the top mass

If there is a top quark (as we believe we know there is) what is its mass? If you had asked the theorists that question some ten years ago the answer, most probably, would have been "about 15 GeV". After all, why should the top be much heavier than the other quarks? However, the pre­ferred theoretical value of the top mass has be­come larger with time. The first indication that mt is probably large came from the observation of large B - B mixing [49]. I remember that already in 1984 some of us [50] were quite ex­cited about this large mixing as the data from the UA1 Collaboration were showing a substan­tial number of "same sign dimuon events". We are now used to the idea of a heavy top. There is, a priori, nothing wrong with it. Nevertheless, it is puzzling that the ratio mu/mt seems to be (see below) less than 6 x 10~~6. How does a single Higgs generate such a disparity?

The direct experimental limits on the top mass from the proton-antiproton colliders are shown in

Table 2: Beauty width of the Z

Table 3. I refer you to the talk by Pondrom [51] for a thorough discussion of how these limits have been obtained. Note that the lower limit on the top mass from LEP experiments is much lower. It is essentially determined by the kinematical limit for Z —+tt and reads mt > 44 GeV,

Table 3: Direct 95% C.L. lower limits on mt (GeV)

Any measurable (for example My/) of the Stan­dard Model may be expressed as a function of the set in Eq.(21). Inserting the experimental values of the first three parameters, one com­putes the measurable in question as a function of mt and MH and compares the result with data. Thus, measured observables impose limits in the mt-mH plane. The measurables are the neutral current data (v — quark, v — electron, electron-quark) as well as the widths and the masses of the gauge bosons. Recently such analyses have be­come very popular. I am afraid that I will not be able to refer to all the relevant papers on the sub­ject. However, in Table 4, I have listed some ex­amples of such determinations (especially those submitted to this Conference), together with the result quoted by Dydak. The central value of the Higgs mass, in [57], is taken to be 250 GeV and the quoted ±16 GeV error is from varying the Higgs mass in the specified interval. In addition to the determinations quoted in Table 4, the in­terested reader may also consult a paper, submit­ted to this Conference, by Barger et al. [58]. It is interesting to note that if the top mass indeed lies in the predicted range the hadron colliders should discover it before the end of this century.

7.5 The top mass from weak decays

As mentioned before, historically, the very first indication that the top quark is heavy came from weak decays, i.e., from the observation of a large 5 - 5 - m i x i n g [49].

At this Conference, in contributions by Al­bright [59] and Maalampi and Roos [60], the in­formation on mt coming from weak decays was discussed. The inputs are the empirical values of the elements of the quark mixing matrix as ob­tained from decays, B — 5-mixing, CP-violation, etc. A consistent picture emerges if the top quark mass is heavy (100 to 200 GeV) . Albright quoted mt = 122^37 GeV and the best fit obtained by Maalampi and Roos [60] reads mt — 14524-

69

7.4 The top mass from radiative correc­tions

Consider now the theoretical situation. Al­though the top quark has not yet been "born" in any experiment, it manifests itself in loops (quantum corrections), and thus contributes to measurable quantities. The quantity which is most sensitive to the top quark is the self-energy (mass) of the W. The mass of W in turn in­fluences the strength of the charged current in­teractions. That influences the ratio of neutral currents and charged currents, etc.

The Standard Electroweak Model has five es­sential parameters. Nowadays, since the Z mass is accurately determined, the natural choice for these parameters is the set

where a and are respectively the fine struc­ture and the muon decay coupling constants. The other 12 parameters of the Electroweak Model (quark masses and mixings, lepton masses) are less important for what follows, the most impor­tant among them being the charm mass. The first three quantities in the above set are accu­rately measured and the last two are unknowns.

Table 4: The top mass in GeV

7.6 Evading limits on the top mass

You may ask how sacred are the top mass de­terminations discussed above. The answer is that they are not entirely sacred. If you change the inputs the outputs also change. An example is the "no fundamental Higgs" scenario which is discussed in section 3. Another example is the "two Higgs-doublets" extension of the Minimal Standard Model. At this Conference the conse­quences of adding a second Higgs doublet were discussed by Barger [61] and by Kiihn [62]. One finds that all limits on rat can easily be evaded in a general two-doublets model. It is interest­ing to note that the mass spectrum of the Higgs particles which gives such an evasion, can not be of the kind that one has in the the minimal su-persymmetric extension of the Standard Model.

Peccei et al. [63] have studied the consequences of allowing non-standard couplings for the top quark. Such couplings may arise if the top quark is the origin of a dynamical breaking of the SU(2) xJ7(l) symmetry of the Standard Model (see sec­tion ) . First of all, from comparison with data, they obtain restrictions on the additional cou­plings. In addition, they show that in such a scenario it is possible for the top quark to be quite heavy (for example mt = 500 GeV).

8 The Higgs boson

Most theorists believe that if the Standard Higgs particle exists, most probably there is "more", i.e. there are also other particles never seen by (wo)man before. We should keep in mind the essential features of the Standard Higgs:

Good Features : It provides the simplest known scheme for generating masses, for the W and Z as well as for the quarks and leptons. Therefore, the Standard Higgs, even if it did not exist, has been excellent as a "working hypothesis". In ad­dition it gives p = 1, which is in agreement with

data.

Bad Features: From the seventeen free param­eters of the Standard Electroweak Model fifteen are due to the Higgs. These parameters cannot be predicted within the Standard Model. The problem is that the Higgs interactions with the fermions are not gauge interactions and, there­fore, their strengths are arbitrary.

Disastrous Feature: The energy scale asso­ciated with the electroweak symmetry breaking caused by the Higgs is v « 250 GeV. This gives a cosmological constant A = S^G/v^ 4 (GW is the gravitational constant). This cosmological constant is 54 orders of magnitude larger than the observed upper limit. If the Standard Model with its Standard Higgs were the whole story we would have a very hard time in understanding why our Universe is so well behaved [64]. There is probably more than just the Higgs, that is if there is a Higgs.

Irrespectively of whether we like the Higgs or not we must take it very seriously simply be­cause we have no viable alternatives. There are, of course, several scenarios for what an alterna­tive theory may look like. None of them is as simple and most of them have problems with ex­periments.

At this Conference, several searches for the Standard Higgs were presented all of which have given negative results. The results, as presented at the Conference, are listed in Table 5. Since then the lower limit has slightly gone up [65] and at the time of writing of this article (Nov. 1990) reads MH > 44 GeV 95%C.L.. These limits have been obtained by considering the production and decay chain

70

Here Zv stands for a virtual Z and / j , j = 1,2 denote two arbitrary fermions, quarks or leptons. The Higgs decays predominantly to the heavi-

Table 5: Excluded region for M J J (GeV)

est fermion pair into which energy-momentum

conservation permits it to decay. For the upper

range of the excluded domain f\ = 6, whereas,

for example, the OPAL lower range concerns f\ —

ix. The most spectacular result is that the lower

limit now goes to zero Higgs mass. A very light

Higgs, with a mass smaller than twice the muon

mass, would decay to e + e ~ . One looks for such

vertices appearing together with the decay prod­

ucts of the virtual Z . If the mass of the Higgs is

still smaller one can look for the apparent miss­

ing energy-momentum in the event. LEP has

now taught us, in a clean way, that there is no

such object with a mass below 25 GeV.

Many previous experiments had looked for the

Standard Higgs, in a variety of " low energy" pro­

cesses, such as 7T —• euH, K —* 7riï, T —> Hy.

Many theorists have spent days and nights in

trying to understand the matrix elements, Q C D

corrections, etc, which go into these processes.

The subject has been much debated and all along

there was no such objectl This is, of course, sad

but I suppose it is the price one has to pay for

having the privilege of working at the boundary

of "Terra Incognita".

What does the theory tell us about the Higgs

mass, provided that the Higgs particle exists?

There is no really water-tight limit from the­

ory. Nevertheless, there is a general consensus

(though not yet any proof) that the Higgs mass

is most likely no larger than about 700 GeV. This

bound, called the triviality bound, comes from

the fact that the Higgs sector of the Standard

Model is not asymptotically free. The effective

self-coupling of the Higgs boson becomes " too

large" at high energies and the perturbation the­

ory breaks down. This is the same problem which

one encounters in Q E D (the Landau pole) . But

in QED, involving only the electron-photon in­

teractions, you never worry about that because

the energy at which the theory goes out of con­

trol is so huge (larger than the visible mass of

the universe) that you know you will never get

there. However, in the case of the Higgs interac­

tions the dangerous region could lie just around

the corner if the mass of the Higgs is large. So

you can think of the Higgs sector as an effective

theory which is valid up to some energy scale,

say A. For the theory to make sense, the Higgs

mass had better be smaller than A. This gives a

constraint on the Higgs mass, M H < 700 GeV,

There is also a limit on the Higgs mass coming

from "vacuum stability". There is a quantum

correction to the Higgs potential coming from

virtual top quarks. With increasing top mass the

potential well tends to become more and more

shallow until at some point there is no longer any

vacuum state! This scary situation may be coun­

teracted by having a larger Higgs mass, which

makes the well deeper. The present lower limit

on the Higgs mass, from vacuum stability, is un­

fortunately not so interesting as it below the ex­

perimental lower limit. Graphs showing the M H

vs. mt vacuum stability bound may be found,

for example, in articles listed in Ref. [70].

8.1 N o fundamental Higgs?

Is it possible that there is no fundamental Higgs

and that the Higgs particle is simply a bound

state (a condensate) of top-antitop quarks? The

point is that the top is heavy, so it is sort of

different from the other quarks. Maybe there is

"new physics" at very high energies, say above an

energy scale A, which is responsible for the for­

mation of the bound state. At low energies the

bound state could behave as a point-like struc­

ture, just like a nucléon looks point-like at very

low energies. Such ideas have recently been put

forward by Nambu [71] and have been studied

by a number of authors ([72], [73]). At this Con­

ference the subject was discussed by Hill and by

Nambu.

In such frameworks, once the t-quark has been

discovered, a huge "desert" sets in, in the sense

that there are no new fundamental particles to

be found until one reaches the scale A. It turns

out that there is a "see-saw" behaviour in mt

versus A. In other words, a larger value of A

(the energy scale of the new physics) is needed

in order to have a small value of the top mass. If

one assumes that A be smaller than the " Planck

mass" one gets [73] mt = 218 GeV and MH -

7 1

246 GeV, Lowering the scale of the new physics to A = 1 0 1 5 GeV gives mt = 230 GeV and MH = 260 GeV, See also [63] for further discussions of the condensate picture.

In conclusion, the top mass in the conden­sate approach tends to be quite a bit larger than the value found from radiative corrections in the standard picture (section 7) . That is good as it makes the condensate picture testable and in a few years we should know how it fares. Of course, the major question to be answered, in the con­densate scenario, is where does the new physics come from and what does it look like?

9 A survey of current urgent questions in physics

The Proceedings of Rochester Conferences are invaluable documents for those who care to know about how ideas in particle physics are born and either develop or die out. The aim of the physics of our time (a better understanding of the laws of nature) is, of course, no different from what it was at earlier Rochester Conferences. But our specific questions, emphases and outlooks are indeed very different from those of the early Rochester gatherings. In this section, I would like to present the results of a (low statistics) experiment which I have done to find out what are the urgent questions of today. The study was triggered by a series of lectures to CERN summer students in July 1990. I thought it might inter­est those youngsters to know what the profes­sional physicists consider to be the most urgent questions in physics (not just particle physics). I was especially curious to know what the stu­dents considered to be their urgent questions, in physics, so I also asked them the same question. The question I asked was the following:

Suppose that you could ask and get the answer to one single question in physics. What would be your question? Please restrict yourself to such questions which you believe may possibly be answered in less than 30 to 40 years.

First of all, I should explain my "cuts" x = corridors of the CERN Theory Divi­

sion and the CERN Cafeteria close by t = the first three weeks of July 1990.

The collected number of events consisted of

answers from 130 professional theorists,

70 professional experimentalists, 37 students.

First of all I should mention that in the corri­dors of the Theory Division I asked anyone who happened to be around and who looked like a physicist. These people were mostly theorists. My sample of experimentalists (mostly at the Cafeteria) was somewhat biased because I would approach people I knew but sometimes they were together with some physicists whom I did not know. All the theorists, except one person, an­swered the question which I asked them verbally, I was a bit surprised by how quickly their answers came. A couple of people did say "let me think" but in less than one minute their thinking pro­cess was over and they supplied me with their answers. The "exceptional theorist" gave me a lecture on why one can't ask such questions but I know that his theoretical reasoning must have been wrong as the other 130 people did answer.

All the experimentalists, whom I questioned (again verbally), with the exception of three peo­ple, answered the question. But in general they were not as quick as the theorists. Some of them would think a little while and then answer. The three people who did not answer said that they would like "to think it over", went away and never answered.

My sample of students is much smaller than I had hoped for. Since there were many students they got a written version of the questionnaire to fill in and return to me. They could also fill in their names, institutions and ages, if they wanted to.

9.1 Answers from professional theorists

The answers from theorists are shown in Ta­ble 6. From Table 6 one sees that the most ur­gent question of the theorists is "the origin of masses". Some people phrased it "the origin of symmetry breaking" and when I asked what they meant by it they said that they meant the mechanism of mass generation. Furthermore (5 people) said that they would be content just to know whether the Higgs is the origin of sym­metry breaking/masses. Perhaps closely related questions were the ones on the origin of families and CP violation which are shown on the fol­lowing lines. Thus altogether the mass and the

72

Table 6: The theorists urgent questions

fami ly p r o b l e m is "the question" for 47/130' = 36% of the theorists.

The next most urgent question was related to QCD. Here, there was some more dispersion in the way the answers were phrased. Ten peo­ple wanted to understand confinement, four peo­ple were interested in computations in Q C D . A "quantitative test", "understanding the AI = 1/2-rule", "possibility of seeing the confined quarks" were the remaining phrasings. However, they did say that their question had to do with QCD. So, for 19/130 = 15% Q C D is the ques­tion.

The next entry which may need some explana­tion is quantum mechanics. Here the questions were phrased as "understanding non-locality"(the late John Bell's question), "interpretation of quan­tum mechanics" and "measurements".

As is seen from Table 6 there were 21 peo­ple whose questions I could not combine under a natural common heading. Let me quote some of the singlet answers;

*Why is data in condensed matter so precise? *Has field theory (except QED) anything to

do with nature? *What is a gauge theory (crucial properties of

the family of local observables which identify a gauge theory)?

*Can one solve the n-dimensional Ising Model on the back of an envelope?

*Can we understand renormalization without perturbation theory?

*Is there a new mathematical language that is useful for physics?

*Will our notions of space-time radically chan­ge?

*Can one think of cosmology in a scientific way?

*Is there anything beyond quantum physics? *What is consciousness, theory of mind, be­

yond physics?

9.2 Answers from professional experimen­talists

The answers from experimentalists are listed in Table 7.

Again, the most urgent question was related to the mass and family problem which was the main concern of 43/70 = 61%. This is quite re­markable! The only entry in Table 7 which needs some explanation is the one on the nature of our universe. There the five questions were phrased as follows; "is the universe closed?", "was there a Big Bang and will the universe have an end?", "what was there before the Big Bang?", "what is the origin of the arrow of time?" and " can we understand the black holes?".

Now I turn to the "singlets". They were: *Are the electroweak and strong interactions

unified?

73

Table 7: The experimentalists urgent questions

*What is the true theory of gravity? *Can one experimentally discover the gravi-

ton? * What is the role of neutrinos in the universe? *Does the top-quark exist? *What is the explanation of the uncertainty

principle? It was interesting to note that usually the the­

orist and the experimentalist asked "the same question" in different ways. Theorists who wanted to know about the theory of all interactions said that they believed or were convinced that such a thing existed. All the experimentalists, in­terested in the same question, phrased it much more humbly as "is there a theory of all forces?". This "modesty" was often explicitly expressed. The experimentalist would tell me that he or she would like to know the origin of all masses but thought that was asking too much. That is why there were many answers on, for example, the neutrino mass or the muon mass. Some of the experimentalists also gave the motive for their questions (I did not ask why) which usually was because they would like to do experiments and look for, for example dark matter or quark de­grees of freedom in nuclei, etc.

We see that the theorists and the experimen­

talists, in 1990, agree on what is the "most ur­gent question". However, beyond that the opin­ions diverge. Confinement and the cosmological constant seem to be "theoretical problems".

9.3 Answers from students

Unfortunately, only 37 summer students an­swered the question; 30 in the age group 19-23 years and 4 in the age group 24-27 years. The re­maining three students did not specify their ages. The answers are shown in Table 8.

A few comments on the contents of the Table 8 are now in order. The "how to compute" ques­tions had to do with how should one i) " calculate the interference of two waves" and ii) "find an­alytic solutions in non-abelian gauge theories". There were also two students who wanted to know how to do the " Lorentz contraction of a relativis­t s spinning wheel". The authors of these "how to calculate" questions came three from univer­sities in the United Kingdom and one from the United States.

The questions on quantum mechanics were "who or what can be an observer in quantum me­chanics?" and "is the probability interpretation of quantum mechanics going to survive?".

The 11 singlet questions were

74

Table 8: The students urgent questions

*Why does the basically simple idea of gauge invariance describe nature so pretty well - what's the real cause?

* Assuming that there is no "end of physics" -what directions will the future experiments take?

*How well can we trust in our calculations of global scale phenomena based on infinitesimal description of nature?

*Can we get rid of renormalisation in quantum field theories?

*Is space-time quantized? *What is the concept of V-A current? * Being an astronomer, I would really like to

know, what are the values of the "cosmic param­eters" etc) of the universe? I would also like to know about life ...

*What is the solution of the cosmological con­stant problem?

*Is particle physics going to be the religion of the 21st century?

* Artificial intelligence with electronics? *Are the laws of physics simpler than we be­

lieve? Again, the students agree with the professional

on what the most urgent current question in phy­sics is. To me the most remarkable difference between the answers from the students and the professional was that the students were much more conscious of the word "life" than we are. In seven of the 37 answers from the students this word was explicitly mentioned. In other words, in the little sample of 37 answers, approx­imately every fifth student cared about the con­nection life-physics. Not a single one of the 200 "grown-up physicists", theorists and experimen­talists, used that word.

Acknowledgements

This report was prepared while the author was a visitor at the CERN Theory Division. I am in­debted to a number of Colleagues for interesting discussions. Special thanks go to Amanda and Pierre for their cheerful encouragement.

This work has been supported by the Swedish Research Council NFR.

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78