Nuclear Physics B (Proc. Suppl.) 13 (1999) 189-;94 189 North-Holland

SEARCH FOR THE FOURTh" GENERATION: PRESENT AND FUTURE PROSPECTS

Vernon BARGER

Physics Department, University of Wisconsin, Madison, WI 53706 USA

A survey is given of searches for fourth generation fermions at e+e - and pi6 colliders. The most stringent current constraints are obtained from neutrino counting, determinations of the r z / r w ratio and se~ches at p~ colliders for W --* L ~ and heavy quark pair production. Techniques for future searches are discussed.

1. INTRODUCTION

An outstanding puzzle in particle physics is the rep-

lication of fermion generations. This issue provides mo-

tivation to search for new fermions that may belong to

a fourth generation. For notation we use (uL, L) to

der.~t¢ tl::c we~k eige~state~ of fourth generation lep-

tons and u], v2, us, v4 to denote the four neutral lep- ton mass eigens~ates. For the fourth generation up and

down quark mass eigenstates we use the notation (a~ v), ~1,. -:,:....1.. 1~1.~1~a (,l b t) in the literature, in the

present d~,ccussion we assume the standard model with

one Higgs do,,blet.

2. THEORY CONSTRAINTS ON MASSES

For perturbative calculations to satisfy partial wave

unitarity the fourth gc:neration masses must satisfy ]

m e ; m r ~ 500 GeV, mL ~ 1000 GeV.

The consistency of radiative corrections 1,2 give further

constraints on the fermion masses. Fits to electroweak

data in terms of standard model parameters depend

on mL, m,,4, mr, ms, my, and on the Higgs mass m/~.

With three generations the constraint mt < 200 GeV is

found s for mH ~ 1 TeV. For four generations the cor-

respor~ding constraint is given to a good approximation by ~-.--., 2., IV@ql~(m~ . . . . mq) ~ "b I(mL -- mu4) 2 <~ (200 G e V ) ~ •

For a nearly diagonal quark mixing matrix this gives

(ran - r a , ) 2 < (200 GeV) ~ - ra~ , which bounds only the

a, v mass difference. However, for a substantial mixing

between the third and fourth generation quarks, con-

straints on the absolute a and v masses are obtained

that can be considerably more restrictive than that of

perturbative unitarity. Figure I shows the allowed re-

gions of ms, m~ for various values of this mixing angle

500 I ! L , , f ~ I

m t = 6 0 GoV ~ - - / ~ . . _ . ~ p.~ 400 z~'./ _...,-." x .~'-_,,,,--" I

/ .,2"- ~'.,~

200 90" / / - ~ ' / "I

,oo i o o IOO 200 ZOO 400 500

m a (BEY)

FIGURE 1 Allowed regions of ms and my for various values of the mixing angle 8 between third and fourth generation quarks, assuming m t = 60 GcV. The allowed regions lie between the curves (from Ref. 4).

e. A more general Monte Carlo analysis using the full

4 x 4 mixing matrix and constraints from CP viola-

tion in the kaon system and from 0 -0 B d-B d mixing gives

similar results. 4

3. FOURTH NEUTRAL LEPTON The simplest possibility would be a light v4. Neu-

trino counting experiments could then detect whether

it exists. From cosmology the bound Nv ~ 4.0 is ob- tained 5 from the observed 4He abundanc- wh~re Nv

is the number of equivalent left-handed ne ~,rinos with

rn~, ~ 100 eV. F[om e+e - ~ 7vP searches by the

ASP, CELLO, MAC, MARK J, and VENUS experi-

ments a 90% C.L. upper bound N , < 4.1 Las beer

obtained from the combined data. 6 Future searc-~-~-~ f~-

0920-5632/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

190 V. Barger / Search for the fourth generation

this process at LEP I and SLC can determine the num- T

ber of neutrinos to an accuracy 6N~ ~ 4-0.2. The

total Z width depends on Nv,mt , and mL. Each light

neutrino gives a contribution A F z ---- 0.17 GeV. Fu-

ture LEP i and SLC measurements will determine the

Z-width to an accuracy T of 6Fz - 4-0.03GeV, which

corresponds to 6N,, - 4-6.2.

The ratio F z / F w of the total widths can be deter-

mined from p/5 collider measurements of R -- er(p/5 --,

W --* eu)/a(p~ --* Z --* ee) and calculations of Ra =

a(p~ --+ W)/a(pp -~ Z) using the relation s

rz/r = ( R / R . ) r ( z

With three-generations contributing to F z / F w , the

UA1/UA2 measured values of R suggest that mt

60GeV. With four generations, a heavy lepton with

mL = 42 GeV could just compensate the extra neutrino

contributions. A scenario with my4 "" 10-10 s KeV and

mc ~ M w , proposed to explain the distortion of the

cosmic background spectrum, 9 has a problem with the

F z / F w ratio. Also the additional contribution from a

v-quark of mass ~ 28 GeV would be impossible to rec-

oncile with rz/rw. Figure2 illustrates F z / F w pre-

dictions for these scenarios.

| '4 i I I I |

t.3| Nv"4, mv=28 GSV, ~wGeV

Lo I, I I 50 60 70 BO 9 0

m t (eev) FIGURE 2

Predicted F z / F w ratio versus mt for a) N~ = 3, b) N~ = 4, mc = 42GeV, and rn~,~ > M w , c) N~ = 4 and m~,~.~, >_ M w , d) N~ = 4 , m~ = 2 8 G e V , mc = 4 2 G e V , and ma >_ Mw.

The large W, Z event rates at CERN and Fermilab

will reduce the uncertainty on the measured R. Mea-

surements of the W ± charge asymmet ry can be used to

resolve uncertainties regarding the d(x, Q 2 ) / u ( x , Q2)

distribution rat io which affect the prediction of Ra; a

7% change in Ra i~ equivalent ~b a~hange ~ A N ~ = 1 in

Fz. F z / F w studies at the Tevatron require knowledge

of the charm quark contributions to W-production.

At p/5 colliders the number of neutrinos can also

be determined 1°'11 f rom high p r measurements of the

ratios a( Z --* L,~ + n-jets ) / a( Z -+ e e + n-jets) and a( Z --*

uP Jr n- je ts ) /a(W -* eP -F n-jets). (Note however that

the latter rat io could be also affected by contributions

from heavy top pair production with t--* bW decays.)

Figure 3 shows the prediction for Nv -- 3 of the first

ratio at V ~ = 1.8 TeV.

I I a / p ~ =" Z + n je ts

12 - Lei,v

.vr "= I.B TeV

RD B ............... .-. - !

4 - -

i

v o ,oo zoo p.r(Z) (GeV) FIGURE 3

Predicted rat io R D = [da / dpT( Z -~ vP ) ] / [ da / dpT( Z --* e~)] at high PT that can be measured at the Tevatron. (From Ref. 11.)

By the end of this year we should know whether

there is a light fourth generation neutrino. However,

even if it is excluded, there is still the possibility of a

heavy v4. Searches at TRISTAN for stable or unsta-

ble charged heavy leptons exclude 12 a heavy neutrino

my 4 ~ 29.5 GeV for mL ~ 29.5 GeV, except f~r a win-

dow mL--mv4 ~ 10 GeV. A heavy neutrino co, dd decay

via neutrino mixing, v4 --* g + W*. The dec~y width

is proportional to [V4t[ 2 and ~4 may be observed if it

decays within the detector. At e+e - colliders the signa-

tures are e+e - -+ Z -+//4P4 "-~ 2g-I-X, 3~-I-X-{-~, 4~+~, where £ is a charged lepton (e, p, v), ~ denotes miss-

V. Barger / Search for the fourth generation 191

ing energy and X denotes hadrons. Stringent limits on

IV4tl 2 have been placed for m~ 4 ~ 2 5 G e V , with the re-

gion IV4el 2 ~ 10 - s typically excluded. 12 At LEP I and

SLC these searches may be extended 13 to find a heavy

unstable neutrino with mass m4 ~ 40 GeV and mixing

1¼tl2;~10 -~°. 4. FOURTH CHARGED LEP TON

At e+e - colliders the signatures of a charged heavy

lepton are e+e - ~ 7", Z ~ L+L - ~ ~l~ + ~, ~ + X +

/~, X + ~ . The TRISTAN limit 12 is mL ~ 29.5GeV.

At LEP I and SLC the search can be extended to mL

½Mz.

At an e+e - supercollider the LL signal from heavy

L ~ VL 4- W gives W-bosons at large angles, unlike

the electroweak background in which the W boson dis-

tribution is peaked at ~he forward and backward di-

rections. It would be possible to detect LL with mass

mL ~ 0.9 (½,Z) . At pt5 colliders heavy leptons are principally pro-

duced through real or virtual W-bosons: p~ --+ W + --* • . 1 4

L+VL. If m~ 4 ~ 0 the most promising s~gnal is ~T + jets resulting from the L -+ vL~d and/JL~'8 decays• The

principal background is W --* r(--~ v~ + hadrons) + v~-;

however, the narrow jet from r-hadronic decays can be

experimentally identified. From a search for gT + jets

events the UA1 collaboration ~ set a lower bound of

mL > 41 GeV. Future data should allow its detection

up to mL ": 65 GeV. However, if v4 is heavy the UA1

bound, disappears for the following reasons: 16 a) if

m , , 4 + m L > M w the cross section via virtual W is sup-

pressed; b) if m ~ >mr . and mv4+rnL < M w the gT is

degraded in the chain W--* vLL--* v~.~,rW*W*W*; c) if rn~ < mL and VL decays within the detector there is

little gT and erie must instead search for VL decays. At the LHC and SSC pp supercolliders the signals

from the decay L --4 VL + W for mL ~ 100 GeV and

m ~ ~ 0 axe W* -* LVL --* W ~ T and Z* --* LL

WWI~T. Substantial event rates are predicted, but

unfortunately large backgrounds from real W, Z pro-

duction, singly and in pairs, submerge the L signals. ~

Moreover heavy top covtributions tt--* (W+b) (W-b)

would further obliterate the L signals.

5. FOURTH GENERATION QUARKS

The phenomenology of fourth generation quarks de-

pends on the mass hierarchy and on the quark mixing

matrix. Charge current data plus unitarity constraints

allow the following ranges of the magnitudes tVijl of

the matrix elements: is /0.9734-0.9T54 0.218-0.222 0-0.012 ~ 0.012

[ 0.183-0.231 0.80-1.00 0.035-0.049 " 0.556 ]

I ~ ] ~ / 0-0.1378 0-0.544 0"0.999 < 0.999

\ < 0.1378 0.544 0-0.999 < 0.999]

Thus large mixing of a, v with other quarks is allowed.

We ~uppose that my < ma, following the mass order-

ing in the second and third generations. The charged

current decays of the v-quark are then v--*tW*, cW*,

and uW*, with partial widths proportional to ]Vtsl 2,

[Vcv] 2, and IV~[ 2, respectively. If mv < m t then v--*

cW* is likely to be the principal decay cbannel. 19 There

is then a close similarity in v~ searches with v --* c£v

and t t searches with t --* bey, except that the v --*

spectrum is slightly harder than t--~ ~.

The implications of the apparent rise in R = a(e + e - --* hadrons)/apt, observed by all four TRISTAN detec-

tors 6'12 at V ~ = 56 to 62 GeV, are unclear at present.

Pair production of v-quarks with mass ms around 28

GeV could account for the observed effect and this in-

terpretation is not excluded by searches for isolated lep-

tons and spherical events. At LEP I and SLC the decay 1 Z --+ v0 would be detected if m~ < ~Mz. At LEP II

and e+e - supercolliders v~ and a~ searches can be con-

tinued up to rnQ ,-~ lV~. At p/5 colliders a search for t t production with t --*

bey decays is equally a search for v~ production with

v --* c£v decays. (Note that p/~ ~ W --* tb produc-

tion has no counterpart since W ~ e~ is suppressed

by mixing.) Iu £ + ~ T + j e t s events the vO signal for

ms < M w appears as a distortion of the Jacobian peak . . . . . 20,21

in the "W" -* ev transverse mass dls tnbutmn, as

illustrated in Fig. 4. The absence of such distortion in

recent CDF data leads to a preliminary lower bound 22

of m~ > 60GeV. If m~ > Mw, v-decays to on-shell

W-bosons gives the same Jacobian peak as the W-

background, but with an enhanced event rate.

Dilepton events resulting from semileptonic decays

of v and ~ provide an exceptionally clean signal at

p/~ colliders, 2° modulo a confusion between a v~ or t t

origin. After acceptance cuts of pT(g) > 15 GeV and

#T > 20 GeV, the bb and c~ backgrounds are small com-

pared to the v{, signal for an azimuthal angular dif-

ference between the two leptons in the range 30 ° <

102 V. Barger / Search for ~he fo~zrth generation

0.6

>= (=9

0.4

! -

E

" 0

0 0

_ rnv=~..uGeV-- n>:~ _

;

. 70///~.~ ~ , ~

--:-':..- .......... X %, -t 50 1 0 0

rnTle, ~T) (GeV)

FIGURE 4 Transverse mass distributions in • + ~T + 3 jet events at V/~ = 1.8 TeV. The solid curves shows contributions from direct W plus small bb, c~ contributions surviv- ing lepton isolation cuts. The other curves include v~ contributions for various m,, values (or equivalently t t contributions for mt values). (From Ref. 20.)

A~b(~,~') < 150 °, as shown in Fig. 5. Lepton isola- tion kills the remaining bb and c~ backgrounds leav- ing "gold-plated" v~ events. For a 70 GeV (90 GeV) v-quark the expected dilepton cross section at the Teva- tron summed over e#, ee, and ## is 7pb (3.5pb); with

the present 4.5pb -1 and a~ efficiency of 0.3, the ex- pected number of events is 10 (5). In future Tewtron

runs an integrated luminosity of 100pb -1 will allow a search for the v-quark up to rnu-~200 GeV.

At the SSC the single isolated lepton signal from v0 production is of order 106 events/year for high jet

multiplicity (nj > 5) after selective cuts that reduce

the W-background 2s (e.g., PT(0 > 100GeV and ~T :> 50 GeV); see Fig. 6 which gives the v -+ f ly signal for

mt = 100 GeV. The invariant mass of the jets in the

hemisphere opposite to ~ has a peak at mr. In dilepton events with n I > 4 there is a clean v~ signal with no sig- nificant background if we require 2sa4 PT(~)> 40 GeV,

~T > 100 GeV, A¢(el, ~2) < 90 °, and A~(t] +g2, ~T) <~ 90 °. These A~ conditions make it likely that both lep-

tons originate from the same v-quark. The mass mr

can be reconstructed from the invariant mass of the

/J

,o - z / ,

.o-ol- ....... ........ ........ ; - " ............ .i=

I ' "" " ' 0 • .,o+o - - "

FIGURE 5 Distributions at ~ = 1.8 TeV in azimuthal angle A¢(g,~') in_ee, e#, and ## dilepton events of v~ (mr -- 90 GeV), bb, W W , and r~ origin. (From Ref. 20.)

. a

b

103 I ' I ~ I '

n j ~ S

to 2

IO w + tT hods.

1

• .-. 0 .04

0,0;8

~ o .o2

~O.Ol " o

I I , I C

I I i I t

v ( 5 O O ) - - t ( l O 0 ) "

I I 1 1 1 ,.00 ' 3 0 0 4 o 0 ' 50o 2 o o 4 o 0 6 o 0 c o o

m v (GeV) mopp. (GeV) FIGURE 6

Single isolated lepton+n > 5jet signal and W-back- ground from vv production at v ~ = 4 0 TeV. (Ref. 23.)

jets. For rhv = 500 GeV, Ba ,~ 1 pb. Events with 3, 4,

and 5 muons also offer good possibilities for detecting very heavy quarks through their cascade decays. We

conclude that the SSC could discover a v-quark with

mass r~r ~ 500 GeV via ~, g~, or multiple muon events.

6. B°-/} ° MIXING AND RARE K, B DECAYS

The effects of fourth generation fermions on the pro- cesses K--*Tru~, b--,ST, b--,s£+£ - , and o -o Bs-B s mix- ing have recently been investigated by Hewett. 25 Low-

est order diagrams for these processes are illustrated

in Fig. 7. Monte Carlo methods were used in sam- pling the general 4 x 4 quark mixing matrix subject to

the following constraints: (i) mixing matrix elements

V. Barter/Search for the fourth generation 193

d .

K ÷

s

W

W

W

s

U,C,t,a

b : ___W__ : d , s

:I ...... 1 ° - - . ~ . : [3 0 S°,, J ,.s d,s ' - -~ " [ . . . . . . ;I ~ b

W

F IGUR E ?

Diagrams for K ~ "ruP, b --* sT, and o -o Ba-B ̀ mixing.

from charged current measurements and unitarity, (ii)

measured kaon CP violating parameters e and e', (iii)

combined ARGUS and CLEO measurements of B~- /~

mixing, and (iv) vacuum saturation and decay constant I.

values of ~ < BK <_ 1.5 and 0.1 _< f s B ~ <_ 0.2 GeV. The

masses are stepped over the ranges mt = 40-180 GeV,

m~ = 100-400 GeV, and m L =40-300 GeV.

The predicted range of B F ( K + --* ~r+v9) are (1-

8)x10 -1° for three generations 2s and (0.2-20) × 10 -1°

for four generations. 2s'27 The current experimental up-

per limi~ is 1.4 × 10 -7. The BNL E-787 experiment

anticipates a sensitivity of about 2 × 10 -1°.

Tt.e radiative b--* s7 decay proceeds through loop

diagrar~s, and QCD corrections give a factor of ten

or so enhancement. The predicted branching fraction

is BF(b --* ST) "~ 10 - s for three generations 2s with

mt :~ 80 GeV and 10-s-10 -5 for four generations. 29 A

rece~rt est imate ~° of the exclusive B--* K* 7 mode give~,

F(B ~ K*7) ~- 0.06 r ( b - . sT) and thus BF(B ~ K7*) 0.6 > 10 -4. The current experimental limit 3t BF(B--*

K*'¢) < 2.4 x 10 -4 is not far above these expectations.

In B°-/~ ° mixing the t-exchange contributions domi-

nate in the three generation case and the ratio xs/xd of

the B ° to B~ ° mixing parameters x = A M / I " is X,/xd "~

[Vt, lz/[Vtal 2 >> 1. Hence Bs ° mixing is maximal. How- ever, for four generations the range 10 -3 < Zs/Zd ~ 10 a

is allowed. 25s2 The z s /xa < 1 possibility is unique to

the fourth generation; supersymmetry, charged Higgs

bosons and left-right symmetric models all give

z , / z~ > 1.

7. FLAVOR CHANGING NEUTRAL CURRENT

DECAYS OF v

The v --~ b(7, g, Z °, H °) flavor changing neutral cur- rent (FCNC) decays ss-s'~ may be a significant fraction

of the v ~ (u, c)W* charged current decays if mr < m t

and IVcrl/IV~W,,I ~ 10-~; see the diagrams in Fig.8.

If m t - m r ~ O(10GeV) and mr > Mz, then v --* bZ ° may even be the dominant v-decay mode. s4 The de-

cay v ~ b°H to a neutral Higgs boson is the dominant

FCNC mode 35 if mr > m b + m H and m ~ < Mz. The

branching fraction for v--* bH ° can be as large as 20%.

Searches can be made at e+e - and pi~ eolliders for these

two body decay modes of v.

v b

v-- r.g.z o, V

H o

FIGURE 8

~W use

Diagrams of neutral and charge current v-decays.

8. SUPERHEAVY QUARKONIA Suppose that the single quark decay mode v ~ t W

is suppressed by mixing angles (e.g., [Vtv[ ~ 10 -4) or

that the mass difference ma - my is small (e.g.,

5 GeV) and the a ~ bW single quark decay mode is

suppressed by small mixing. Then fourth generation

quarkonia can exist at high mass (unlike toponium)

and interesting decay modes may dominate s6 such as

¢(v~) ~ Z H and ¢(v~) ~ W+W -.

9. CONCLUDING REMARKS AND COMMENTS

Which space should we watch for the appearance

of the fourth generation? The r z / F w ratio suggests

that the fourth generation is already in trouble. How-

ever we may momentarily get around this with m~ 4

0, ~'~L '~" 42 GeV (which gives the same F z / F w as three

generations) or take a really heavy m~ 4. The F z / F w

194 V. Batger/Search :or ¢he fourth generation

ratio is also in conflict with an m y " 28 GeV explana- tion of the rise in R observed at TRISTAN. The lim- its from ~ searches at pp colliders apply equally to vO if v-charged current decays are dominunt over neutral current decays. Consequently it seems fairly likely that m~ ~ 60 GeV. The Z total "~ldth measurernent ~t SLC and LEP I will test the three generation prediction. If it agrees, then we can pull down the shutters on a fourth generation unless v4 is heavy. Searches for un- stable heavy neutrino decays at these e+e - machines can probe the range my4 ~ 40 GeV. Finally, a non- maximal value for B°-/} ° mixing is a unique possibility of the fourth generation scenario.

ACKNOWLEDGEMENTS I thank H. Baer, T. Han, J. L. Hewett, and R. J. N.

Phillips for helpful information.

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