641

HIGGS

John ELLIS CERN - GENEVA Switzerland

ABSTRACT The theoretical motivations for the existence of Higgs bosons are reviewed, and their properties in simple models are described. The Higgs mass is very uncertain, but there may be a prefe­ rence for it to be about IO GeV. Experiments to look for Higgs bosons are discussed.

RESUME On passe en revue les motivations theoriques pour l'existence des bosons de Higgs, et on decrit leurs proprietes dans des modeles simples. La masse du boson de Higgs est tres indeterminee, mais pourrait bien etre de l'ordre de IO GeV. On discute des experiences pour chercher des bosons de Higgs. 642

I. INTRODUCTION Why should Higgs bosons exist ? What are thfermions blow up at high energies,which means that higher order corrections to theit low energy predictions are infinite and uncalculable1). Sensible renormalizab le gauge theories which make finite predictions, such as the 2) Weinberg-Salam model ,must3) use spontaneous symmetry breaking to give masses, and as far as we know this entails the existence of Higgs Bosons. These considerations are discussed in more detail in section 2. The Higgs bosons are scalars with an almost totally indeterminate mass, probably between about 7 GeV and TeV in the simplest version of the Weinberg-Salam model, and perhaps with a slight preference for a mass around I 0 GeV4) , The Higgs couplings are very precisely fixed in the simplest model. Those to fermions are proportional to their masses, and therefore the Higgs likes to decay into pairs of the heaviest fermions kiner1atically accessible, e.g. - H -+ T+ T , bb , t't, . . . . These properties are reviE�wed in section 3. Because of their uncertain mass, the best experiments to search for the are less well-defined than those designed to look for the w± and Present experiments only constrain m to be 15 MeV. Promising Z0 • H � ways to look for heavier Higgs bosons include heavy onium + H + QQ y (for mH 2 , 0 decays (for mH m 2 , e+e- + z" + H (for mH up to < mq) Z ) -S z / ) "' 100 GeV with LEP)S . If the Higgs weighs more than 1 00 GeV, which certainly seems theoretically to be a possibility, then only its i�ndirect effects may be visible for the foreseeable future. Experiments to seareh for Higgs bosons are discussed in section 4.

2. MOTIVATIONS Clearly we would like our physical theories to make finite predic­ tions . This means that higher order diagram corrections to the lowest order diagrams should be calculable, as is the case in QED . However, weak interaction theories have always been beset with infinities. For example, the old 4-fermi theory had many incalculable divergences which arose from the circumstance that its lowest order cross-section (cf. fig. I) rose (the centre-of-mass a energy) 2 at large s , which meant that higher order diagrams (see fig. 2) were infinite. It was known for a long time that one way of reducing these divergence 643

problems was to introduce intermediate vector bosons w± and into the current­ Z0 current lagrangian. This made the cross·-sections for -fermion scattering more manageable, but now the cross-sections for ff + w+w- rose too fast at large s , and higher order diagrams like that in fig. 3 were still infinite. It was realized that one way to minimize these residual problems was to give the vector bosons couplings among themselves which were of the gauge theoretical form as in fig. 4. This step removed many infinities, but there were still some + - + - left. That from e e + w w was very small, being proportional to me , but 2 that in w+w- w+w- was very large, being proportional to rn The only w • 2) + known recipe to remove these remaining divergences which occured with massive vector bosons was to introduce exchanges as well, as in fig. 5. These Higgs bosons would be responsible for the other ' masses, and would have couplings linked to mf or respectively. 3) m; It has in fact been shown that the only theories with cross-sec­ tions that are sufficiently well-behaved at high energies l/s) that their (0 a higher order diagrams are calculable are in fact gauge theories with mass gene­ rated by spontaneous symmetry breaking using Higgs fields. Furthermore, in these mode�s at least one - and possibly many more - of the Higgs fields actually appear as physical, detectable particles. So, if Higgs bosons exist and are so important, what are their properties ?

3. PROPERTIES To discuss the properties of Higgs bosons we will start by looking l)2)6) at the simplest gauge theory, the Weinberg-Salam , , model with a simple + complex weak isospin doublet of Higgs fields � = (� , �0 ). The Higgs self­ couplings take the form of a potential

( I) where must be 0 and µ2 is genErally taken to be 0 . > > As seen in fig. 6, the potential II) then has a minimum at a non-zero value of

v2 (2) 2 The lagrangian must also contain gauge-covariant kinetic terms for the Higgs bosons

µ ' i wi � (3) 1. 2 1 2 644

When the value of [¢[ goes to the value (2) minimizing the potential these (I), kinetic terms give terms that are masses for the vector bosons . When a this happens , Higgs fields Wtwt get "eaten" to become longitudinal polarization 3 states of the and Z0 w± + ¢ its complex conjugate + - ¢ and (4) , ¢

But 'the fourth field become$ a physieal Higgs boson H

¢0 + � H + v (5)

We said before that the couplings of this Higgs boson were connected with parti­ cle masses . When ¢ takes the value v (2) a coupling of the type g ff ¢ + fH + gfH ff(H v) which means that (6)

Correspondingly, the kinetic term contains a piece (3)

which tells us immediately that 4m2 2 w v (7)

and that 2m 2 w (8) v

wh ich again exhibits the connectiJn with mass that we "xpected from section 2.

The couplings (6) and are totally fixed by the theory, unfortu­ (8) nately the Higgs mass is totally arbitrary. From we find that (I) 2 2/ 2 (9) = � >w2 µ2 We saw above in equation that v 2 is. directly connected to the known (7) = );""' quantity GF , but the individual values of µ2 and are totally unknown at th is point . 4) An attractive possibility is that actually µ 0 . This is (a) = for economy (b) because µ is theoretically a divergent quantity if it is non-zero (c) because is in some sense already constrained to be small. The µ meaning of this last point is that modern grand unification theories contemplate mass scales of the order of 1015 to 1019 GeV . But in order for perturbation 7) theory to be valid for the weak interactions , mus t be 0 which < (I), gives via (2) a limi t on µ

0(103) GeV m TeV 0) µ < � H < I (I

Since is in th is sense absolutely microscopic, it is nstural to suppose that for some as yet unknown reason it is in fact zero .

But then how does spontaneous symmetry breaking work The answer is ? 8) provided by radiative corrections (fig. 7) to the Higgs potential which (I) have the form

(I I)

When added to V(¢) gives a minimum at 1¢1 # 0,which would mean that (I I) , m and m would be determined purely the ma sses of all the particles , mf w H dynamically, and none would be put in by hand . In fact

2 (12) �

which can be seen as a radiative correction to the naive formula (9) for 0. µ = Taking sin2e 0.20 in equation (12) gives w =

10.4 GeV (13)

2 For various reasons such as the uncertainty in sin 8w and the possible exis­ tence of heavy fermions , the value (13) should be given a sizeable error (0(± 2) GeV but it at least indicates an interesting ball-park to search for ?) a Higgs boson.

The value (12) is not actually a strict lower limit on . With � o ons it is possible that the potential have a minimum the radiative c rrecti (II) at /¢1 # 0 even if µ2 is slightly O. The requirement that the absolute < ) minimum of the potential be at 1¢/ # 0 in fact constrains9

7.3 GeV ( 14) >

O) 0.20 . One could be even more radical l , and suppose that the world is not in fact sitting at an ab solute minimum of the potential , but merely at a local minimum. This will be unstable, but its lifetime will exceed the age 646

of the universe years) if (101 0

26 MeV (15) > 0

This is probably the absolute lower limit on , but more reasonable limits (JO) � would be those of equations and (14) , with perhaps a slight preference for the neighbourhood of JO GeV (12).

couplings (6) and tell us that Higgs bosons will like to The (8) decay into pairs of the heaviest particles kinematically available - which may be a very distinctive signature Table indicates the dominant decay modes ! I and branching ratios for different values of m . Different branching ratios H 4) and production rates for a Higgs boson with mass around JO �eV are shown in more detail in fig. . We see that in this range decays into T+T- and cc 8 are to be preferred . The decay widthof the Higgs is small unless it is heavier than a or Z0Z0 pair. This is shown in Table 2. The fact that r w+w- H � � around TeV reflects the breakdown of perturbation theory which led to the I bound (JO).

The discussion so far has all been in the context of the simplest Weinberg-Salam model 1) with just one complex Higgs doublet and just one neutral physical Higgs boson. All other weak interaction models have more Higgs bosons , generally including charged ones as well as neutrals. Many of the quali­ tative features discussed above are likely to appear in these models as well - couplings correlated with particle masses, Higgs mase:es in the range JO GeV to TeV - but their phenomenology is rather more uncertain. For a recent dis­ I cussion and references , please look at ref . 5, as there' is not enough time to discuss these other possibilities here .

4. EXPERIMENTS So far the best experimental restrictions on Higgs bosons come from various considerations 1) which all suggest that m 15 MeV . H � These include the absence of certain decays of excited nuclei : z* + Z + H , the absence of anomalies in Xrays from muonic which would have signalled a Higgs exchange potential , and the absence of an anomalous long-range scalar po­ tential in -nucleus scattering . As yet, high energy physics does not rule out any mass range for the Higgs . Even the experimental upper limit on + + ) K + n + H is insufficient] to rule out - mn . Good places to look � < � for Higgs bosons seem to be : 647

JO GeV T + H + � < y This decay! Z) is relatively large because of the large bbH coupling (6) in fig. 9 and rival decay modes are suppressed by the Zweig rule. We expect that for m GeV H < 8 + H y) f(y + ( 16) + +µ- f (y µ ) - Putting in the expected branching ratio for T + µ+µ of about 3 7. , we guess B(T + H "'10-4, and this ball-park probably also applies to + y) 8 GeV m JO GeV (see fig Trigger signals could be the y recoiling < H < 8) . against the H , and its decays into T+T- which should 2S of the �-;; � 7. decays of a Higgs with m 4 GeV . H >

30 GeV ( ?) Topsilon + H + y � < Here we gain from the increased mass of the as well as its charge 2/3. We therefore expect B(T + H "' few x 10-3 . When (if the + y) ?) topsilon is found, this should be one of the first decay modes to look for.

SO GeV � < This decay13) would proceed through the diagram of fig. 10.. It has been calculated that the branching ratio

for SO GeV (17) � <

for JO GeV . The rate (17) should be � "' accessible to LEP, which should permit experiments with up to J06 or 107 Z0 decays .

JOO GeV � < This reaction1) proceeds via the diagram in fig. at a rate II, comparable with that for e+e- + µ+µ- at centre-of-mass energies up to 200 GeV for - m "' JOO GeV . Leptonic decays Z0 + e+e- ou µ+µ- would be � < I; z useful signatures for this reaction. LEPS DO IT ! 648

> 100 GeV indirect effects � Heavy Higgs could no t be produced directly at LEP , but they could 14) - + - have relatively strong indirect effects , e.g. on the reaction e+e + w w .

The above processes seem to be the best candidates for Higgs searches. What are the chances in other reactions which can be studied Unfor­ ? ) tunately, the cross-section in collisions is e;qJectedljlS to be rather l l sma : µ-HX) a(vN + (18) µ-x) a(vN + when the Higgs mass is negligible compared with the centre-of-mass energy 12 Evm Thus we expect that even for a light Higgs at the CERN, SPS or /; °' N • FNAL a(H) /a J0-5 . However , the Higgs may not be totally undetectable total � this way by looking for H r+1- decays . + The cross-sect,on for H production in -hadron collisions is 16) 4 generally expected to be small, but may be enhanced ) for 0 GeV by � '" I mixing between the Higgs and a scalar P-wave bb P , in which case b fig. 12 could become important . It could lead to a cross-section

+ - 10-3 7 to 10- 35 cm2 + H X) B(H µ µ ) ( 19) o(pp + + - 2 (MeV) [� �l wh ich might be detectable if [m - mp is .(. a few tens of MeV . One cannot H [ yet even exclude logically the ludicou� possibility that the is in fact T" the with its cross-section enhanced by being <; 1 0 MeV away from a P !I , b state !

CONCLUSIONS 5. The Higgs boson : - is essential to gauge theories, - may (or may no t) have a mass 0(10) GeV, - has characteristic coupling properties, - is not impossible to find , (?) - is interesting. 649

ACKNOWLEDGEMENTS would like to thank my collaborators MARY GAILLARD, DEMETRE NANOPOULOS and CHRIS SACHRAJDA, and members of the ECFA/LEP exotic particles working group . Also it is a pleasure to thank TRAN THANH VANH for the delightful atmos­ phere at this meeting, and FERNAND HAYDT and RENE TURLAY for inviting me to come .

TABLE I

MASS OF HIGGS BOSON DECAY MODES

2 m 2 m e+e-, e mH µ yy 2 + - 2 mµ < mH < m1T µ µ 2 m1T 4 GeV ordinary hadrons to 1 0 7. < < ; ll µ+µ-) '\, I 12 I 3 ( + - 10- 3 4 GeV < m GeV cC: B(µ µ ) < �H < T+T- : rv : ; '\, 12 GeV m 30 GeV bb cc- 0 H < (?) : '\,I : I 30 GeV 200 (?) < < GeV tt 200 GeV m w+w-, o < �H < z o z <

TABLE 2

MASS OF HIGGS BOSON LIFETIME / DECAY WIDTH

100 MeV 10- ll sec. GeV 7 sec. I I o-1 10 GeV "' 100 keV 100 GeV 100 MeV -v I TeV TeV '\, I 650

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FIGURE CAPTIONS

Lowest order 4-fermi interaction which gives as I. cr • 2. Divergent loop diagram. 3. Divergent loop with intermediate state. w+w- 4. Gauge self-couplings of intermediate vector bosons. 5. Scalar Higgs exchange in e+e- + w+w-. 6. The Higgs potential (1) with absolute minimum at l�I O. # 7. A typical radiative correction to the Higgs potential (1). 8. Branching fractions for the production and decay of a Higgs boson with mass � 10 GeV, taken from ref . 4. 9. Diagram12) for H decay. T + + y 10. Diagram13) for Z0 + H 1+1- decay. 11. Diagram for e+e- + Z0 + H. 4) 12. Diagram for hadron + hadron + H + X via Pb - H mixing. Higgs mass (Gev )

Fig. 8

' H ' ::.IH

Fig. 9 Fi g. 10

11 Fig. Fig. 12