CP-violating lepton-energy correlation in ee → tt

9 January 1997

PHYSICS

ELSEVIER

LETTERS B

Physics Letters B 391 ( 1997) 172- I76

CP -violating lepton-energy correlation in eZ -+ tt Bohdan Grzgdkowski a*1,ZenrO Hioki b*2 a Institute for Theoretical Physics, Warsaw University, Hoia 69, PL-00-681 Warsaw, Poland ’ Institute of Theoretical Physics, University of Tokushima. Tokushima 770, Japan

Received 16 August 1996; revised manuscript received 23 September 1996 Editor: PV. Landshoff

Abstract In order to observe a signal of possible CP violation in top-quark couplings, we have studied the energy correlation of the final leptons in e+e- + t7 -+ e+e-X / e*X at future linear colliders. Applying the recently-proposed optimal method, we have compared the statistical significances of U-violation-parameter determination using double- and single-lepton distributions. We have found that the single-lepton-distribution analysis is more advantageous.

The top quark, thanks to its huge mass, is expected to provide us a good opportunity to study beyondthe-Standard-Model physics. Indeed, as many authors pointed out [l-8], CP violation in its production and decay could be a useful signal for possible nonstandard interactions. This is because (i) CP violation in the top-quark couplings induced within the SM is far negligible and (ii) a lot of information on the top quark is to be transferred to the secondary leptons without getting obscured by the hadronization effects. In a recent paper, we have investigated CP violation in the ti-pair productions and their subsequent decays at next linear colliders (NLC) [ 81. We have focused there on the single-lepton-energy distributions. In this note, we study both the double- and single-leptonenergy distributions in the process e+e- + ti + l+f?X / L’*X, and we compare the expected precision of CP-violation-parameter determination in each case. For this purpose, we apply the recently-proposed optimal procedure [ 91. ’ E-mail address: [email protected]. * E-mail address: [email protected]. 0370-2693/97/$17.00 PII

SO370-2693(96)0

Let us briefly summarize the main points of this method first. Suppose we have a cross section

where the fi( 4) are known functions of the location in final-state phase space 4 and the ci are modeldependent coefficients. The goal would be to determine ci’s. It can be done by using appropriate weighting functions Wi( 4) such that J Wi( 4)Z (4) d4 = ci. Generally, different choices for wi(4) are possible, but there is a unique choice such that the resultant statistical error is minimized. Such functions are given by

(1) .i where Xij is the inverse matrix of h4ij which is defined as Mij G

J

Copyright 0 1997 Elsevier Science B.V. All rights reserved. 1439-6

(2)

B. Grzqdkowski,

Z. Hioki / Physics Letters B 391 (1997) 172-176

When we take these weighting functions, the statistical unce~~nty of ci becomes Aci = dmN

7

(3)

where (Tr 5 s( da/dqb)dc#J and N = Leffa~ is the total number of events, with Lee being the integrated luminosity times efficiency. In our analyses, we assume that only interactions of the third generation of quarks may be affected by beyond-the-Standard-Model physics and that all nonstandard effects in the production process (e+e- -+ tf) can be represented by the photon and Z-boson exchange in the s-channel. The effective ytT and Ztf vertices are parameterized in the following form:

173

single-lepton-energy distributions of the reduced lepton energy (2)~ 2EJ( 1 - a)/( 1 + ~)/~~, E being the energy of e* in the e+e- cm. system, and p = Jl - 4mT/s: Double distribution ‘+ rrdxdf

=

kCjfi(X,ij

(7)

3

i=l

where x and R are for P and P respectively, ci = 1,

c:! = 5,

cs = $Re(f!

- $)

,

and

flch3 = f(x>ftn) + rl’gtx)gtX) + rl[f(x)g(f) + gtx)ft~)l~ (v=yorZ),

(4)

where g is the SU(2) gauge-coupling constant. In principle, there are also four-Fermi operators which may contribute to the process of th production. However, as it has been verified in Ref. [ lo], their net effect is equivalent to a modification of A, and B,. Therefore, without loosing generality we may restrict ourself to the vertex corrections only. For the on-shell W, we will adopt the following parameterization of the tbW vertex:

.f2(X%f)

= f(x)g(5)

-

.f3(X,f)

= ~~(~)~(~)

-

+ rlWg(4gW

-

+ rl[W(x)g(X) f

-

~gtx)f(~)

-

g(x)f(@, fixby

g(xM-8

3

f(xPg(jZ)

g(xP!f(R)l.

Single d~s~ribu?ion

(8) where f corresponds to @,

(5)

+1,

c;==@,

c; =Re(ff),

CT =Re(jt)

and fl(X>

=f(x)

f3Cx)

where PER E ( 1 T qy)/2, & is the (tb) element of the Kobayashi-Maskawa matrix and k is W’s momentum. Using the above parameterization, applying the narrow-width approximation for the decaying intermediate particles, and ~su~ng that the StandardModel con~bution dominates the CP-conserving part, we get the following normalized double- and

-i-qg(x),

= W(n)

j-2(x) =g(x),

-t v &g(x).

Since all the functions and parameters in these formulas are to be found in Refs. [7,8], we only remind here the normalization of f(x), Sf(x), g(x) and &g(x):

s

f(x)dx

= 1,

(9) q, 7’ and 5 are numerically given at fi = 500 GeV as q = 0.2021,

7j’ = 1.3034,

5 = -l.O572Re(D,)

- du+,Jdx

dcr-fdx

+ d&fdx

d% dxdf

-

dxdx-

d%

- fi) - f$).

(12)

and thereby we are able to compute the statistical significance of the asy~etry observation Nso = I&j/A&t. In Fig. 1 we present lines of ~oustan~ Nso as funcand Re(ff - f$“) for tions of Re(D,) = Re(&) L = 50 fb-’ and ree = 0.5 (which mean Net =I 726). Two solid lines, dashed lines and dotted lines are determined by 10.4247Re(D,,z)

+0.3089Re(ff

- j’z”)]

for Nsb =I, 2 and 3 respectively. We can confirm Ace to be non-zero at lcr, 2rr and 3@ level when the pa-

+ O.O609Re(Dz)

= -0.3441&+0.3089Re(f~

Since ~&+_+ti= 0.60 pb for 4 = 500 GeV, the expected number of events is Nfe = 6~~~~L~~, where lppstands for the lie- tagging efficiency (= et ; et is the single-lepton-detection efficiency), L is the integrated luminosity in fb-’ unit, and Be (5 0.22) is the leptonic branching ratio for t. Consequently we obtain the following result for the error

= “so/j/G

dxd2

For our SM parameters, it becomes

-t 0.3089Re(f:

=

Au = 0.2085,

AAee = O.lSlS/~,

has been found as a useful measure of CP violation via 6 [4,7]. In Ref. [S] we have computed a(x) for the case where both 5 and Re( ft - $i) terms exist. Practically however, measuring differential asymmetries like a(x) is a challenging task since they are not integrated and therefore expected statistics cannot be high, For this reason, we shall discuss another observable here. A possible asymmetry would be for instance

Att = 0.3638Re(D,)

= -Re(f;)

- 0.1771 Re(Dz)

da-/dx

dxdf-

= Re($)

and its statistical error is estimated to be

for the SM parameters sin’ Bw = 0.2325, i%& = 80.26 GeV, MZ = 91.1884 GeV, fZ = 2.4963 GeV and mr = 180 GeV. In Eqs. (7), (81, CP is violated by non~v~ishing 5 and/or Re(ff - &!) terms. 3 First, let us discuss how to observe a combined signal of CP violation emerging via both of these parameters. The energyspectrum ~yrnrne~ a(x) defined as a(x) =

For Re(D,) = Re(&) 0.2, e.g., we have

(11)

3 In the present note, r, 7 and W* are assumed tobe 511 tbek mass shell since we are adopting tbe now-wide approxim~on for them, and the con~bution from the imaginary part of the 2 propagator is also negligible since s is much larger than M$. Therefore we do not have to consider Q-violating effects triggered by the interference of the propagators of those unstable particles with any other non-standard terms [ 111.

rameters are outside the co~es~nding lines. It can be seen that we have good chances for observing the effect at future NLC unless there is a conspiracy cancellation between those parameters. Table 1 shows the 4 dependence of Nso for the same EeeL. In order to discover the mechanism of CP violation, however, it is indispensable to separate the planter in the top-quark production (5) 4 and that in the decay (Re( f,$ - jk) ). We shall apply the optimal procedure of Ref. [ 93 to the double distribution first. Using the functions in Eq. (7), we may calculate elements of the matrix M and X defined in Eqs. ( I), (2) : 4 We use 8 instead of R~$i?,.~z) as a basic parameter when we discuss parameter measurements, since ( is directly related to the distributions (7) and (8).

Z. Hioki / Physics Letters B 391 (1997) 172-176

B. Grzqdkowski.

175

Table 1 Energy dependence of the statistical significance Nso of Ae measurement for CP-violating parameters Re( D,) = Re( Dz) = Re( ff ) = - Re( j;“) (3 P) = 0.1, 0.2, 0.3 and 0.4. The numbers below Nso (those in the parentheses) are for the asymmetry AU. 6

(GW

500

600

700

800

900

1000

gy~+tf (pb)

0.60

0.44

0.33

0.25

0.20

0.16

P =O.l

2.8 (0.1043)

2.5 (0.1097)

2.3 (0.1132)

2.0 (0.1155)

1.8 (0.1171)

1.7 (0.1183)

P = 0.2

5.7 (0.2085)

5.2 (0.2195)

4.6 (0.2263)

4.1 (0.2309)

3.7 (0.2342)

3.4 (0.2365)

P = 0.3

8.9 (0.3127)

8.0 (0.3292)

7.2 (0.3395)

6.4 (0.3464)

5.8 (0.3513)

5.3 (0.3548)

10.1 (0.4527)

9.1 (0.4619)

8.2 (0.4683)

7.5 (0.4730)

P = 0.4

12.4

11.3

(0.4170)

(0.4389)

This means the parameters are measured with errors of5

Re(f-i)

A,$ = 7.1651/a, A Re( f: - ff) (= 2dm)

= 8.3824/a. (13)

Next we shall consider what we can gain from the single distribution. We have from Eq. (8)

+. ~,,,I.,,I,..I,,“.“““‘,““““‘.‘,,-06

-0.8

-1

-0.4

-0.2

0

0.2

0.4

0.6

0.8

\\. 1

pig. I. We can confirm the asymmetry Au to be non-zero at la, 2a and 3a level when the parameters Re( D,,z) and Re( f! - fi) am outside the two solid lines, dashed lines and dotted lines respectively.

= 1,

Ml2

= Ml3

=

M22 = 0.0898,

M12 = Ml3 =0,

M23 = 0.1499,

M33 = 0.2699

and Xl, = 1,

x12 = x13 = 0,

1

Re(D)

Ml1

Ml1 = 1,

X23 =

-84.4279,

x22 =

151.9915,

X33= 50.6035.

Therefore we get A[ = 12.3285/fiand A Re( ff) = 7.1136/a from the I+ distribution, and analogous for A,$ and A Re( fi) from the !Z- distribution. Since these two distributions are statistically independent, we can combine them as

0, M22 =0.2070, A,$ = 8.7176/a,

M23 =

-0.3368, M33 = 0.6049

and XII = 1,

A Re( ft - ff) = lO.O6Ol/fi.

(14)

It is premature to conclude from Eqs. ( 13) and ( 14) that we get a better precision in the analysis with the Xl2 =

X23 = 28.5825,

x13 =

0, X22= 51.3389,

X33 = 17.5662.

5Note that r~ in IQ. (3) is unity in our case since we are using normalized distributions.

B. Crzgdkowski, 2. Hioki/Physics

176

double distribution. As it could be observed in the numerators in Eqs, ( 13), ( 14), we lose Some indoortiun when integrating the double di~t~but~onon uw variable. However, the size of&he expected uncertainty depends also on the number of events. That is, Nee is suppressed by the extra factor EeBe comparing to Ne.

This suppression is crucial even if we could achieve et = 1. For N pairs of bi and E! = I we obtain At = 32.5686fJj;i, ARe(f;

- r;)

= 3&1018/fi

from the double distribution, while

from the single distribution6 Therefore we may say that the single-lepton-dis~ibution analysis is more advantageous for measuring the parameters individually~ In suck, we have studied how to observe possible CP violation in e’e- + tf -+ C%-X and -!?*Xat NLC. For this purpose, CP-violating distributions of the final-lepton energies are very useful. Using these quantities, we introduced a new asymmetry Au in Eq. ( 1O), which was shown to be effective. Then, applying the optimal procedure 191) we computed the statistical significances of CP-violation-parameter determination in analyses with the double- and singlelepton-energy distributions. Taking into account the size of the leptonic branching ratio of the top quark and its detection efficiency3 we conclude that the use of the single-lepton dis~bution is more adv~~g~us to determine each CP-violation parameter separately. We are grateful to S. Wakaizumi for discussions and to K. Fujii for kind correspondence on the top-quark detection efficiency. This work is supported in part by the Committee for Scientific Research (Poland) under grant 2 F03B 180 09, by Maria Sklodowska-Curie Joint Found II (Poland-USA) under grant MEN/NSF96-2.52, and by the Grant-in-Aid for Scientific Research No.06640401 from the Ministry of Education, Science, Sports and Culture (Japan). 6ff we take qBa = 0.15 as a more realistic value ] 12], we ate led to the same results as in [ 8 I.

Letters B 391 (1997) 172-176

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