γZ0 production and new physics in the TeV region

Nuclear Physics B289 (1987) 301-318 North-Holland, Amsterdam

y Z ° P R O D U C T I O N AND NEW PHYSICS IN THE TeV REGION* Zbigniew RYZAKt Center for Theoretical Physics, Laborato~. for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Received 8 December 1986 We discuss the experimental limits on compositeness that may come from a study of the yZ ° final state at the future e+e - and p~ accelerators. In the framework of the strongly coupled standard model, we present the effective interactions up to dimension six which contribute to the f + f---, yZ ° process. We calculate the relevant cross sections and analyze the production rates at the LEP II and Tevatron I and II colliders. We give the values of the compositeness scale A which lead to the observable effects at those machines.

1. Introduction I n the near future, a n u m b e r of new accelerators will become operational. They will allow experimenters to test the detailed structure of interquark and interlepton interactions up to several hundred GeV in the c.m. energy. With this perspective in mind, it becomes important to look for particular interactions and particular channels, where deviations from the standard model will be easiest to detect. A theoretical discussion of such a problem m a y lead to different results, depending on w h a t model one adopts as an alternative to the Glashow-Salam-Weinberg (GSW) model. In this paper, we study a possible experimental signature of compositeness. It has been realized for a long time that one of the most sensitive tests of the G S W m o d e l is a test of the gauge boson interactions. In view of this, various authors have proposed the study of the production of W + W -, W -+Z °, Z ° Z °, W -+7 a n d Z ° y pairs in the p~ or e+e - annihilation experiments as the best way of checking the high energy predictions of the G S W model. It seems to us (compare ref. [1]) that a study of the Z ° 7 reactions is a particularly promising one. On one hand, this channel allows for a high experimental precision with a clean and easy-to-analyze final state. On the other hand, the existence of substructures will give rise to additional mechanisms to produce Z ° y pairs, hopefully at a rate observable above the " s t a n d a r d model background". The aim of our paper is to give a quantitative analysis of the last statement. We introduce and study non-standard * This work is supported by funds provided by the US Department of Energy (DOE) under contrac! # DE-AC02-76ER03069. t On leave of absence from Warsaw University, Warsaw, Poland. 0550-3213/87/$03.50©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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interactions which may arise in composite models. We measure the strength of those interactions in terms of some dimensionless couplings and one parameter A. A has a dimension of energy and probably characterizes the scale of compositeness. At the end, we arrive at discovery limits, i.e. we map out regions of the parameter space which yield observable changes in the 7Z ° production rates at the LEP II and Tevatron I and II machines. Although most of our discussion is applicable to any composite model, our analysis proceeds in the framework of the strongly coupled standard model (SCSM) [2, 31. The lagrangian of the SCSM is the same as the GSW lagrangian with parameters adjusted in such a way that the SU(2)L gauge interactions become confining at the weak interaction scale. As a result, the left-handed physical fermions, intermediate vector bosons, and the Higgs particle become composite. The experimentally observed weak interactions at energies below G~ 1/2 are best described by an effective lagrangian, £P~n, which involves only physical fields. The construction of ~eff is facilitated by an assumption that it possess an approximate SU(2)w global symmetry, which is the symmetry of the SCSM in the limit when the U(1) unbroken gauge interaction is turned off, and the Yukawa couplings are sent to zero. The symmetry breaking effects can be treated perturbatively except for a direct W 3 U(1) gauge boson mixing. The mixing is unusually large (the mixing parameter k ~- 0.45) but its effects can be easily summed to all orders leading to a redefinition of the physical fields. The strength of the interactions involving only a rearrangement of preon lines is of the order gwf( ~ 0.66 (much different from a typical in the strong interactions), and the U(1) coupling constant is the QED coupling e. Given those assumptions, &off containing operators of dimension four and lower is in fact the standard model in the unitary gauge [3]. In our analysis, we go one step further and include operators of dimension six which involve the Z ° and y fields. In the next section, we explicitly list all the operators up to dimension six which lead to the 7Z ° final state in the e+e - and p~ annihilations. We calculate relevant cross-sections and parametrize the non-standard contribution in terms of three constants, one being the compositeness scale A. In sect. 3 we analyze the discovery limits at the LEP II collider, where the parameters describing the machine are taken from ref. [4]. In sect. 4 we analyze the discovery limits at Tevatron I and II, where the parameters of the machines come from refs. [5, 6]. In sect. 5 we conclude and discuss the existing literature that deals with the issue of the non-standard 7Z ° interactions.

2. Interaction iagrangian in the SCSM We will construct the interaction part of the £~°eff in terms of fields whose quanta can exist "on-shell" at the energies - G F 1/2. At the beginning, we use in our analysis the U(1) field a t and the SU(2)w isotriplet of the intermediate vector

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bosons W~ ( - W ~ 1, W~, W~3). Later, we take into account the a~W~3 mixing by introducing fields, creating mass eigenstates Z ° and 3'. The form of the dimension six operators is fixed by the assumed CP-invariance of the theory, U(1) gauge invariance, and the global SU(2)w symmetry. First, there exists a contact interaction [7, 8] where two composite fermions can annihilate into a 3', W 3 pair. The only operator one can write is:

-s°c

f

_

'r

=

•

w%,

(1)

where the sum is over all 12 left-handed SU(2)w fermion doublets, FL,, • are the Pauli matrices and f,~ = O,a~- O~a,. We assume the approximate SU(12) flavor symmetry because the breaking effects are small at the energy scale considered (they are O(m2/s) where m is a typical fermion mass). As mentioned before, SU(2)w is broken by direct W33' interactions so we may allow for W 3 W 3 3 ' and W33'3' vertices. Most generally, one could write three independent W 3W 33, operators, out of which one (W~ if: 3/~(Opf~o)) vanishes for the on-shell gamma. This leaves us with [7, 9]: --*°~'WWv= ~----~P~(gl 0aW~3 0vW3a + g2 0a 0 ~W~3W~3),

(2)

where j ~ = !~ roo" There are two W33,V interactions that may contribute to the 2 ~tsvO a J y Z ° production [7,101: 1

K'(h' 0q.% + h2P"0%)

(3)

Note that the operators we consider can receive contributions from exchanges of some exotic states. What we mean is that in the dispersion analysis of those operators in appropriate channels, one could find poles at the masses of the exotic states. Here, we assume that the masses of those states are of the order of, or bigger than, A. Most generally then, A corresponds to a scale where compositeness becomes apparent; either by a discovery of some new structure or by a discovery of a spectrum of new composite states. One can use the underlying preon picture to establish the relative normalization of the operators i.e. to express the f, g and h coupling constants in terms of powers of e, gwf~ = g and some overlap constants x which probably are of the order of one. The best method of doing so is graphic: by drawing preon lines. Looking at fig. 1, we see that: f= O(ge),

g = O(e),

h = O(e2).

(4)

To write the final form of the L~°int,we shall explicitly take into account the aW 3

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Composite Vertex

Operator

Preen Vertex

e

Lc

.

Lwwy

Lwyy

Fig. 1. Graphi_.ccrepresentations of dimension six vertices, where different lines have the following designations:/~_~s a composite fermion; [ ] is a preon fermion; E~]is a composite vector bosom . . . . . . is a preon scalar and [ ~ is the U(1) gauge field.

mixing by making a linear transformation [3]: = cos Ow

A~,=a.+

3 ,

sine w W3 ,

(5)

where Z., A~ create the physical Z ° and ./ particles, respectively. The full interaction lagrangian with operators through dimension six is: e

ffc

*'~°int------- 2 sin ewcos e w z~,j~

l

e

A2 cos2Ow + O

e2

- eA~j~ - --~ sin ewcos Owj~Z~F~'~

(e2sinOw)][xllO.Z~,O~Z,~+KlaO,~O,,Z.Z~]ff~,~ cos2Ow

1 e2 A2 c o s e w [K21 ePFlaVFvp -.I.-K22_ff'P'voqPFvp]ap.,

(6)

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305

where

j~= E~:v"(g:v + gb:) 4':, f s~ =

Eo%:~.:, F

:L =

E ~,:3"/:.~:L. f

g:v= r:- 20:sin~Ow.

g:,..= -:r:. the summation goes over all the physical fermion fields, q:f, and charge (third isospin component) of the f t h field. We also use

Qf(T~) is

sin 0 w = e

the

(7)

and at the end of this section we comment on the validity of this assumption. Born diagrams that correspond to the process f+/--*Z°+7 are shown in fig. 2. Fig. 2a describes the standard model contribution, fig. 2b the contact term contribution, fig. 2c the ZZ3, contribution and fig. 2d the ZT"~ contribution. After including all the relevant couplings, the last diagram (fig. 2d) has one more power of e than the others. Therefore, we will ignore the contribution of the Zyy vertex.

(a)

(b)

(c)

(d)

f

-

Zo

T

),

g 0

f

..Z 0

Fig. 2. Born graphs contributing to f + f ~ yZ°: (a) the standard model contribution; (b) the contact term contribution; (c) the ZZy vertex contribution; and (d) the Z~"t vertex contribution.

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The resulting cross section can be written as: do

do TM - - + dz

dz

do I ~

do N +-dz '

(8)

where z = cos 8cm. The standard model cross section is:

f2. s - M 2 [ 2 ( _ s 2 + M ~ ) l ] dz = 2 X 2 ~ : X 2 ) ( g 4 2 + g A ) ~ [ ( s _ M ~ ) 2 1---z 2 - 1 '

do

rra 2

TM

(9a)

where x 2 = sin20w and the fermion mass m F << M z < ~-. The interference term between the standard model and the new effective interaction is:

7rO~2

do I

S2 _ M 4

0--7 = 2 x E ( 1 - x 2)

[~cTa/(g/v--gfA)--gfvg/AKZ] sEA2 '

(9b)

where

gll "}-2~12 [1 + O(e sinew)]. COS20w

KZ

Finally, the part that comes solely from the new interactions is: ~Ot2

do N

.,)

l ,: :, +

+ lr/(g:v_g:,),,:c+

g 2)]

dz

X

A4s2

2 + -M2 +z

2(S )] Mz

S5--/.2 - 2

.

(9c)

It has been claimed by some authors that radiative corrections to diagrams in fig. 2a may become sizable [11] at 0 - - 0 and 0--~r. Fortunately, we are mostly interested in a region of 0 where the chance of seeing the additional interactions is the best, and this obviously corresponds to 0 = :r.1 In this region of 0, the radiative corrections are 1%-2% of the standard model cross section [12], and they are too small to affect our results. We shall not include them. F r o m the formulas (9b) and (9c) one can see that for each A the additional contribution is parametrized in terms of two couplings x c and Xz- As follows from their definition and from our discussion above, the "natural" values of these couplings are r c -- 0(1) and x z -- 0(5). In our calculations, we shall adopt sin20w = 0.2 [13] and a = 11 [14] which corresponds to the values of those parameters at

vrs- GEl~ 2

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307

U p to now we have overlooked one more possible effect that may change the cross section for f + ( ~ Z 0 + 3'. We have assumed that in the photon channel, only the 3'W 3 mixing occurs. In general, one can expect that there are other isospin one j e c = 1 - - states that mix with photon. Both physical 3' and Z ° fields have to be linear combinations of all those fields. If by analogy with eq. (5) one defines the probability of a , turning into Z~ as tg 0w, then eq. (7) receives corrections of the order O(~2M2 / M *2) where M* is the mass and ?~ is the mixing parameter of some weak-isospin one vector boson. The reason we have not included those corrections in our formulas (9) is that it is hard to say what are the "natural" values of (compare ref. [15]). Some authors [16] advocate ~2 0c ( M Z / M * 2)sin20w. This makes the correction to the cross section O(sinZOw M~v/M .4) and hopefully smaller than the one we consider. In a general case, one can put limits on O(~2M2/M .2) but does not know how to divide them between ~ and M*. We believe that generically ?~ << 1 [17], and the whole problem does not arise.

3. 3' Z 0 production at LEP II Naturally, to discover the interactions that testify to some new "layer" of physics, one has to reach to the highest energies and luminosities possible. Here we shall discuss the information one can gain by studying the process e + e - ~ 3'Z ° at L E P II. Following ref. [4], we assume v~---200 GeV and the yearly integrated luminosity So= 500 p b - 1 as the parameters that describe the machine. The obvious trigger for observing a 3'Z ° event is a hard gamma with energy E v = (s - MZ)/2f~, balanced by the products of the Z ° decay (or not balanced in the case of the Z ° ~ v~). The type of background* this process can receive is described by the diagrams of fig. 3. Fig. 3a shows one of the bremstrahlung diagrams, and fig. 3b shows a e+e - ~ 3'f( production. Both of those diagrams describe events that are totally different kinematically from a typical 3 ' Z0~ / / e v e n t . Also, they occur at a rate smaller than the standard model e + e - ~ 7 Z ° production rate by a factor O(sinZ0w a/47r). We are convinced that experimenters should be able to measure the cross section d o ( e + e 3'Z °) to a high degree of accuracy. (A way of checking the selection criteria is to compare the Z ° decay rates as seen in the e+e - ~ 7Z ° to the ones measured at the Z ° factories: LEP I and LSC.) In fig. 4 we plot the standard model cross section ((1 - z 2 ) d o S M / d z ) alongside the new interactions ((1 - z 2) doX/dz + (1 - z 2) doN/dz) **.We have used x c = 1, x z = 5 and A -- 0.7 TeV to calculate the additional cross section. Obviously, the best

* Here we assume the energy resolution of the EM calorimeter to be not worse than 1% for a photon o! energy - 80 GeV. This means that the 3,Z° and "rW events will be clearly distinguishable [18]. * * Both cross sections are scaled by (1 - z 2) for a better comparison.

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308

(a)

(b) e-

e tFig. 3. Bremsstrahlung diagrams for the process e + e - ~

yff: (a) the final state bremsstrahlung; and (b) the initial state bremsstrahlung.

4.C

4.0

"~E 3.0

3.0

o v b~

2"0

2.0

1.0

1.0

COM I

i

i

-I.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 COSOcm

i

0.6 0.8

.0

Fig. 4. ( d o / d c o s 0cm)(1 - COS20cm) for e + e - ~ y Z ° where the upper curve is the standard model term (SM) and the lower curve is the additional "composite" contribution (COM) for A = 0.7 TeV, ~¢c = 1, ~;Z = 5.

way to observe any deviations from the standard model is to measure d o t ° t / d z around z -~ 0. Let's assume that the experiment consists of measuring the e+e 7 Z ° events at intervals Az = 0.2 over a period of one year. A discovery of the non-standard interactions at a 68% CL would correspond to measuring in some interval a number of events that is off by one standard deviation from the number predicted by the standard model. In fig. 5 we show a "one-sigma envelope" (scaled by ( 1 - z2)) where for each interval we plot + N ~ s ~ , and NSM is the standard model prediction for a year of running at LEP II. In the same figure we show

Z. Ryzak / New physics in the TeV region

309

300

200 N

8 w

i

I00

~m

-I00 -0.9-0.7-0.5-0.3-0.1

0.1

0,3

0.5

0.7

0.9

Fig. 5. d (-# of e v e n t s ) / d cos 0cm(1 - c o s 2 0 e m ) in a year of running at LEP II. The shaded region is the standard model l a envelope and the continuous curve is the additional contribution predicted by our model (A = 0.7 TeV, t¢c = 1, •z = 5).

z2), i.e. the number of events per unit z coming from the new interactions (again rc = 1, r z = 5, A = 0.7 TeV). A clear conclusion is that for the given set of parameters one should measure an excess of the ~,Z ° events above the one-sigma limits. In fact, for rc = 1, and ~¢z = 5 all A up to A a = 0.925 TeV yield the production rate above the "one-sigma envelope" in at least one Az interval. Similarly, for each pair 0¢z, Jcc) we define a discovery limit to be the value of A -- A d such that for all A > A a the number of the ~,Z ° events agrees with the standard model prediction to within the lo limit. For A < A d, this number may differ by more than one standard deviation. (Since in general s << A 2 and the interference term do z is a dominant one in the non-standard contribution, we expect that for r z and Kc negative the observed number of events is lower than the standard model prediction.) In fig. 6 we show the values of A d as a function of ~c and r z . Kz is scaled by ~, because a change of one in the original overlap constants ~11 and K12 changes r z by 5. An interesting feature of the function Ad(KZ, Kc) shown in fig. 6 is its discontinuity along two lines emerging from the origin. To explain this strange behavior, let us look at a n u m b e r of the additional y Z ° events as a function of A for Kz and Kc negative. In both figs. 7a and 7b we have shown lo limits, and depicted the point

~(doI/dz + doN/dz)(1

-

310

Z. Ryzak / New physics in the TeV region

Kz 5 -4

-3

-2

-I

t

(

I

2

3

4 4

:3

- 3

2

2

I

I

0

0

-I

-I

-2

-2

-3

-3

-4

.K

c

-4 ,

-4

-3

-2

-I

0

I

2

3

4

Fig. 6. The discovery reach A d as a function of x z and ~c. All values of A d are in TeV.

(a)

co

(b)

m--m

[or

~

l(r

W

"6

A

.Q

E Z -I(3

-I cr

K c < O , Kzl < 0

K c < O , Kz 2
I
Z. Ryzak / Newphysics in the TeV region

311

A a where the number of events leaves the lo band. An increase in the [Xz[ or IKcl changes the situation from fig. 7a to 7b and obviously the change in A a is discontinuous. Note that fig. 7b shows that there may be a region of A where a conspiracy occurs, i.e. A < A d but still one stays within the lo limit. In general, all of those characteristics can be read off from fig. 6. 4. ~, Z 0 production at Tevatron I and II

The study of the ,/Z ° final state is particularly advantageous at the p~ machines. We will specialize the case to the experiments at Tevatron I and II. We assume that in the both phases of the Tevatron operation the c.m. energy is v~-= 2 TeV. The yearly integrated luminosity is projected to be .T I = 10 pb -a [5], and ~ n = 500 pb-1 [6], for Tevatron I and II, respectively. Again, the obvious trigger for observing a y Z ° reaction is a high-pT hard photon balanced by the Z ° decay products. In fact, in p~ collisions direct photons come mostly from high-pT~r ° and ~ mesons, decaying into photon pairs, where the two photons are not resolved in the detector. Fortunately, those apparent "photons" are 0 final generally accompanied by other jet fragments. In contrast, in a typical TZ~q~ state, for the values of PT we will be interested in, T is very well-isolated with one or two hadron jets measured at the opposite side of the detector. In fact, a simple kinematical calculation shows that a probability that y will be inside one of the jets coming from the Z~q~ decay is at most a couple of percent. Moreover, in such a case, the energy of the whole jet is much smaller than the energy of the y, and this is very unlikely if the "photon" comes from the ~r° or ~ decay. The experience from studying the hard photon events at ISR and SpaS [19] shows that the suppression of the or°, ~ background can be very efficient. The only important background comes from the high-pT direct photons produced in the processes" (a)

q+g--->q+~,,

(b)

q+Ct---'g+~'.

(10)

We analyze this signal alongside our main discussion and show that it poses no problem with respect to our study. We calculate do(p + ~ ---,Z ° + -/+ X) in terms of the fundamental quark interactions given in sect. 2 and the quark distribution functions that come from ref. [20]. We use AQCD = 0.2 GeV as suggested by the experimental data [21]. The cross section we need to study is

do

dydpr=2pT

fl

SXaX b 1

dx~-E [ f i P ( x ~ , Q 2 ) f i P ( x b , Q2 ) x~ sx a + u 3 i +f~P(x~'Q2)f~r'(Xb'Q2)]

d6i~-*~,z° dt" , (11)

312

Z.

R y z a k / N e w physics in the T e V region

where p T and y are the transverse momentum and rapidity of the photon coming from the p + ~ ---, Z ° + Y + X reaction, respectively. - x~t + M 2 Xb =

SXa+

U

= Xat,

t=

-vrse-Y pT,

M~ - u ,

Xm

-

S+

t

,

U = XbU,

u = --v~eY pT,

(12)

ff

(fi ~) are the structure functions of the ith quark in a proton (antiproton). comes from colors and d S / d ~ is the invariant cross section of a fundamental interaction i + i ~ 7 + Z°- Later, we shall separately discuss the standard model cross-section where d8 is essentially given by (9a) and the additional "composite" cross-section where d8 is given by (9b) and (9c). Analogously, we calculate the direct photon production cross section where the fundamental processes are given in (10). We use the gluon distribution functions from ref. [20]. The cross sections for (10) can be easily calculated [22] and we just quote: d°qvl 2 8¢raas ~'2 ..{_/~2 d/" = eq 9~ 2 /.fi ,

(13a)

dSqg 27raas ~2 + ~2 d f = eq ~ _s.a ,

(13b)

where eq is the fractional quark charge and a s = as(Q 2) is the QCD coupling constant. In fact, (13b) corresponds to the case when the gluon comes from the proton. In the other case, one has to substitute ~ ~. Hereafter, we use Q2 = £. A different choice affects the ~/Z ° production rate only very little. It does change the QCD prediction for a hard gamma production, but we may bury all the uncertainties in a k-factor. The value of k is of the order one (0.5 + 2) [22] and whichever we choose does not change the final conclusion. In fig. 8 we plot three cross sections d o / d y d p x l y = o for observing a hard photon which comes from either the QCD processes (QCD), or the y Z ° production as predicted by the standard model (SM), or the additional ,/Z ° production as predicted by the composite model (A). We have chosen x z = 5, xo = 1 and A = 0.75 TeV to calculate the additional "composite cross section" A. One may see from fig. 8 that the QCD and SM cross sections fall off exponentially with p T whereas A stays approximately flat over a large region of PT. This suggests that a really striking signature of compositeness is a significant increase in the number of photons with PT of the order of, and bigger than, 100 GeV. In fig. 9 we show

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I 0 -I ~ - ~

I ....

I ....

I ....

313

I ....

\X\

\

",,,

,.,Q

%.~

-- -

.........'...

I 0 -6

i i i i I i i i ~I , i i , I , ~, , ! ~ IO0 200 :500 400

0

I , ,'~.l i 500 600

Fig. 8. d o / d p T d y l v = o cross section for: a direct g a m m a Q C D p r o d u c t i o n (the Q C D curve), "FZ ° p r o d u c t i o n as p r e d i c t e d b y the s t a n d a r d m o d e l (the S M curve), y Z ° a d d i t i o n a l p r o d u c t i o n as p r e d i c t e d b y o u r m o d e l for A = 0.75 TeV, and Joe = 1, ~z = 5 (the A curve).

I 0 z>

,

102 i ,--.-..,

i0 I

x'\'l .... \ k\ X

i :

r~

I ....

"%

I ....

I ....

I ....

%,,~

'~-o I 0 °

.........

~Z. .............

"-.Oco

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!

J

10 -2 I

0 -5

, ,

0

, P ....

50

I ....

IO0

i ....

150

1,,,

200

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,1

250

300

Fig. 9. do/dyie=o(Px ) cross section for observing p h o t o n s with PT bigger t h a n the given value of PT. The m e a n i n g of the Q C D , SM a n d A curves is the same as in fig. 8. A g a i n , A = 0.75 TeV, Xc = 1, ~z = 5.

d o / d y l y = o for measuring a photon with PT bigger than a value given on the horizontal axis, (i.e. d o / d y = fp~dp'Tdo/dp'Tdy ). Again, all three cases are depicted. N o w let us discuss the counting rate that follows from fig. 9. We assume that photons are best measured and identified in the central region of the detectors. At the Tevatron detectors the central EM calorimeters cover at least [y[ ~< 1 [24]. On

Z. Ryzak / Newphysics in the TeV region

314

the other hand, d o / d y d P x changes up to no more than 50% in this region of y. We can conclude that the number of events observed within the [y[ ~< 1 region of the central detector in a year of running is 2 d o / d y l y = O . ~ (within at most 10%-20%), where £~o is the relevant integrated luminosity. In particular, for Tevatron I ~q~i= 10 pb -1, and it means that a level of d o / d y = 0.05 pb in fig. 9 corresponds to one event per year. We believe that a statistically significant rate is nine events per year (3o above 0) which corresponds to a d o / d y = 0.45 pb level. Fig. 9 shows us that the A curve crosses this level at PT = 175 GeV. Moreover, it is an order of magnitude bigger than the SM value and about equal to the Q C D value there. One concludes that in a year of running at Tevatron I there could be around 18 photons observed with PT bigger than 175 GeV and [y[ ~< 1. Nine of those events should be identifiable as the y Z ° events. We clearly see that the QCD production is not a significant background even if the measured PT is SO high that the Z~qc~ decays into one hadron jet. As discussed in refs. [20, 23], the invariant mass distribution of a single Q C D jet is strongly peaked at 0, with the average value of 30-40 GeV. We believe that the shape of this distribution suggests that the Q C D ,{ + jet events will be separable from the "yZ~q~ events. Reversing our argument, we see that a measurement of the number of the high-p T g a m m a events consistent with the Q C D prediction for PT > 175 GeV and ]Yl ~< 1 excludes all A ~< 0.75 TeV at a 30 level. Relaxing the requirement of the statistical significance to the l a level (i.e. we look for only 2 new events) moves the whole argument to p T > 225 GeV and A < 1 TeV. The same discussion applies to Tevatron II except that the one e v e n t / p e r one y e a r / w i t h i n ]y[ ~< 1 level is now 10 -3 pb. As shown in fig. 10 the measurement of

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,

I

300

heV]

,

,

,

,

I

,

'1-00

,

,

,

500

Fig. 10. do/dy[y=o(pT ) cross section as in fig. 9. Here, A = 1.6 TeV, ~z = 5, ~c = 1.

Z. Ryzak / Newphysics in the TeV region

315

the hJgh-pT photons with PT > 325 GeV allows one to probe compositeness down to A = 1.6 TeV at the 3o level. The measurements at pT > 375 GeV probes compositeness down to A = 2 TeV at the l o level. All of those results apply to xc=land xz=5. In table 1 we give the 3a discovery limits A d for several xc and r z. The upper value in each box corresponds to the Tevatron I case, and the lower one corresponds to the Tevatron II case. The signature of compositeness for all of the (rz, xc) pairs is the increase in the production of the high-p T gammas. Naturally, for r z and x c negative and P'r small enough (PT <-100 GeV), the production rate of the 7Z ° is lower than the standard model prediction because dor~/dydpT+doI/dydPT < O. Yet, due to the high QCD background, those effects could be observed only in the leptonic modes, and the relative significance of the new interactions there is lower than in the high-px region. On the other hand, for pT>_. 175 GeV, do N dominates over [daI[ and the net effect is indeed the increase in the -/Z ° production rate. For a moment d o N > [doI[ looks like a breakdown of our effective lagrangian method. After all, I d o l [ - 1 / A 2 whereas da N - s/A 4. Note however that the production of the longitudinally polarized Z ° 's due to the new interactions goes like (s/A4)(s/M 2) (cf. eq. (8c)). We see that da N - [daI[ as soon a s 1/A 2 - (s/A4)(s/M2), i.e. when s / A 2 - Mz/A. In most cases, the 7Z ° states we are considering are produced in the kinematical region where s/A 2 << 1. This proves that our method of discussing the effects of compositeness is reasonable.

TABLE 1 The discovery limits A d for given values of x c and ] r z ~Xz\Xc

2.0 1.0 0.5 0.0 -0.5 - 1.0 - 2.0

-2.0

-1.0

-0.5

0.0

0.5

1.0

2.0

0.89 1.91 0.75 1.59 0.72 1.52 0.74 1.56 0.80 1.67 0.87 1.83 1.03 2.18

0.83 1.85 0.63 1.35 0.52 1.13 0.50 1.10 0.62 1.31 0.73 1.54 0.94 2.00

0.87 1.87 0.60 1.31 0.45 0.95 0.37 0.79 0.52 1.09 0.66 1.41 0.90 1.92

0.89 1.91 0.63 1.36 0.45 0.95 0.00 0.00 0.43 0.93 0.61 1.31 0.86 1.86

0.92 1.98 0.68 1.46 0.53 1.14 0.38 0.82 0.44 0.94 0.59 1.28 0.85 1.82

0.96 2.07 0.75 1.60 0.64 1.34 0.54 1.13 0.53 1.13 0.62 1.34 0.86 1.81

1.06 2.26 0.90 1.90 0.82 1.73 0.76 1.61 0.73 1.54 0.75 1.60 0.89 1.90

The upper value in each box corresponds to Tevatron I. The lower value in each box corresponds to Tevatron II. All A d are in TeV.

316

Z. Ryzak / New physics in the TeV region

Up to now we have avoided a discussion of the most important source of o + confusion in identifying a 7Z~.qC a state, that is a 7Wlyq~ state. In fact, taking into account the projected energy resolution of the hadron calorimeters [24], it seems impossible to distinguish between the two on the event-to-event basis. But it is not a problem. The 7W ± state is not a background, it is a signal of the same physics. The standard model cross-section for the qCl ---, W +-7 reaction is of the same order as the one for qCq---,Z°7, with some peculiar cancellations at cos 0cm = - 1 [25]. Those cancellations make the standard model production rate for p + ~ ~ y + W +-+ X smaller than for p + P ~ 7 + Z ° + X. Obviously, in the composite model some non-standard interactions will change the 7W ÷ production rate, in a way very similar to the one we discussed for the 7Z ° production. Since 7Z ° and 7W -+ are two different states, the increase in the production of the high-p a- photons is a sum of the two effects. The conclusion is that the efficiency of the Tevatron high-pT3, study in probing compositeness is even better than suggested by table 1. Only should one indeed discover the compositeness in this way (i.e. should one see, above the " G S W background", high-pa- photons balanced by jets of the invariant mass - M w - M z ) will it matter whether it is a 7W -+ or a 7Z ° signal. In any case the problem would be quickly settled by observing leptonic modes.

5. Summary and discussion

The composite structure of the intermediate vector bosons may reveal itself in the non-standard y Z ° interactions. One may use the effective lagrangian method in the strongly coupled standard model to discuss the discovery limits of the future e +e and p~ accelerators. It turns out that the study of the high-pr photons at the Tevatron machine is a particularly sensitive test for the existence of substructures. The additional non-standard 7Z ° production, alongside the comparable 7W +production, will allow one to study compositeness down to 1-2 TeV region. LEP II will have a chance to study the 7Z ° production in detail, and may put the limits on compositeness somewhere around 1 TeV. At LEP II though some other process, like e ÷ e - - - , W ÷ W -, may be even more sensitive to the existence of substructures [26]. In our discussion we adopt certain values of the integrated luminosity £,o for each machine we discuss. A change in ~ has its bearing on the discovery limits Ad, and one may show that the relationship is A d -&ol/4. This, and the lower value of fs-, suggests that the experiments at SpaS at CERN can put limits on A a no better than a couple hundred GeV in their studies of the high-p a" photon production. Most of the existing literature concerning the non-standard 7Z ° interactions deals with the issue of the radiative Z ° decays. For example, some of the vertices we study in sect. 2 have been introduced in this context in a variety of papers [7-10]. Note, however, that the region of the parameter space we have chosen to explore yields the additional operators of dimension six greatly suppressed at s = Mz2. For

317

Z. Ryzak / New physics in the TeV region

.......

zO

y ,~.~..~,_~~

.......

Z0

Z0..... ~ 7" Fig. 11. Triangle graphs contributing to the 7ZZ and yTZ interactions.

example, their contribution to the F(Z ° ~ e + e - y ) is negligible (Fnew(Z ° ~ e + e - 7 )
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