The τ polarization measurement at LEP and the nature of the τ-W-ντ coupling

Physics Letters B 288 (1992) 227-231 North-Holland

PHYSICS LETTERS B

The z polarization measurement at LEP and the nature of the z - W - v T coupling Paolo Privitera

1

Institut fur Experimentelle Kernphysik, Universitiit Karlsruhe, W-7500 Karlsruhe, FRG Received 5 June 1992

The recent measurement of the z polarization at LEP is explicitly analyzed in terms of the z - W - v , coupling. When the validity of the neutral current prediction for PT and lepton universality in the neutral current sector is assumed, the analysis of the leptonic r decays excludes the possibility o f a ( V + A ) - ( V + A ) interaction, which is not constrained by the existing p measurement, at 3a level. From the semileptonic z decays, a value of the chirality parameter is obtained, h~, = --2gvgA/(g2v + gg2 ) = 1.22+0.33, which is consistent with h~ = 1 expected for pure V-A coupling and favours a negative helicity of the yr.

1. I n t r o d u c t i o n

T h e w e a k decays o f charged h e a v y leptons represent a s u p e r i o r p r o b e o f a universal weak interaction. T h e e x h a u s t i v e a n d precise m e a s u r e m e n t s o f t h e / z -~ e v g decay give an i m p r e s s i v e c o n f i r m a t i o n o f the V - A structure o f the i n t e r a c t i o n [ 1,2]. T h e situation is not as satisfactory for the z lepton. So far, only m e a s u r e m e n t s o f the p p a r a m e t e r in z --* e v ~ and z ~ I~V-ff decays were available [ 3 ]:

current z decay, but no d a t a are available for the moment. In this context, it is interesting to interpret the r polarization m e a s u r e m e n t recently p e r f o r m e d at L E P not only in t e r m s o f the electroweak m i x i n g p a r a m e t e r sin 2 0w but also as a test o f the structure o f the r - W vr coupling.

2. T h e ~r p o l a r i z a t i o n m e a s u r e m e n t

p = 0.70 -4- 0.06.

A m o r e recent m e a s u r e m e n t o f the A R G U S Collaboration [4] gave p = 0.742 + 0.035 + 0.020.

(2)

T h e A R G U S C o l l a b o r a t i o n has also m e a s u r e d the z n e u t r i n o helicity [ 5 ] f r o m a parity v i o l a t i o n a s y m m e try in the z - - a i r decay into three charged pions, obtaining a v a l u e o f the chirality p a r a m e t e r : (hvr)z-alv -

2gvgA

_ 1.14 + (l aA +0.34 ,, . . . . 0.17g- Z v- + g ~

(3)

T h e m e a s u r e m e n t o f r + z - spin c o r r e l a t i o n observables [ 6 ] with a high statistics sample c o u l d drastically i m p r o v e the present knowledge o f the w e a k charged l

at LEP

( 1) T h e e l e c t r o n - p o s i t r o n collisions at the L E P accelerator p r o v i d e a copious p r o d u c t i o n o f z + z - pairs. T h e difference in the coupling o f the Z ° to right-handed and left-handed z ± produces an average longitudinal p o l a r i z a t i o n P~ : nc

Pr =

nc

2gv g~ (g~C)2 + (g~C)2,

(4)

where g~C and g~C are respectively the neutral current v e c t o r and axial v e c t o r coupling constants. N o t e that P~+ = - P , - . In the s t a n d a r d model, P, is related to the electroweak m i x i n g p a r a m e t e r through p~ =

2(1 - 4 s i n 2 0w)

~ - 2 ( 1 - 4 s i n 2 0w).

1 + ( 1 - 4 sin 2 0w) 2

Partly supported by CERN.

0370-2693/92/$ 05.00 @ 1992-Elsevier Science Publishers B.V. All rights reserved

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Also the other final fermions produced through Z ° exchange present a net polarization, but the z offers the unique possibility of measuring it using the sensitivity of the decay process [7]. The measurements of the r polarization performed by LEP experiments [8] are reported in table 1. Combining all LEP results, the mean value obtained is P~ = - 0 . 1 4 5 + 0.035,

(6)

indicating a parity violation in the process e+e - --* Z ° ~ z + z - . Using eq. (5), this result corresponds to a value of the electroweak mixing parameter sin 2 0w = 0.2319 + 0.0044.

3. The weak decay of a polarized The decay characteristics o f the z lepton were already established in 1971 by Tsai [9], even before the z lepton was actually discovered. In particular, it was clear that since z + and z - decay via weak interactions where parity is not conserved, the angular distribution of decay products in the z rest frame depends strongly on the spin orientation of the z and the characteristics of the t - W - v ~ vertex. 3.1. z---~ gv-Y

The leptonic decay o f a polarized z can be described in the most general way by a local, derivative-free leptonic four fermion interaction [2 ]: M=

Table 1 The Pr measurement at LEP: the first error quoted on P~ is statistical, the second is systematic. The value obtained combining all the experiments for each decay mode is also reported, adding the statistical and systematical error in quadrature. Decay mode

Pr

Experiment

z --*/tv~

-0.19 + 0.13 + 0.06 -0.05 +0.19 +0.08 -0.17 +0.16 4-0.10

ALEPH DELPHI OPAL

average

-0.15

"t ---+ e / / ~

-0.36 + 0.17 + 0.06 -0.12 + 0.22 + 0.08 +0.20 -4- 0.13 + 0.08

±0.10

average

-0.05 4- 0.10

~" ---+ 7~/-'

-0.130 4- 0.065 ± 0.044 -0.35 +0.11 +0.07 -0.08 4- 0.10 4- 0.07

average

-0.17

z--~ pv

-0.124 4- 0.047 4- 0.051 -0.24 4- 0.09 -4- 0.07

average

-0.16

z ~ al u

-0.15 -4-0.15 4-0.07

228

ALEPH DELPHI OPAL

20 August 1992

4GF

v~

x ~_. gg~<-g~lV~l(ue).)((-~),~lFyfT~>,

(7)

7=S,V,T e.u=R,L

(n,m)

where y labels the type of interaction ( F s scalarpseudoscalar, F v vector-axial vector, F T tensor), the indices e a n d / l indicate the chiral projections (lefthanded, right-handed) o f the spinors of the observed particles (e the lepton,/L the tau), n indicates the helicity of the lepton antineutrino and rn that of the z neutrino, n and m are uniquely determined for given y, e , / l . The normalized lepton energy distribution is dF d---~ cx 2 - 6x 2 + 4x 3 + 4 p ( - 1 + 9x z - 8x 3) _~p~ [_ 2 + 4x - 6x 2 + 8x3

ALEPH DELPHI OPAL

+0.06 ALEPH DELPHI

+0.06 ALEPH

+4c~(1 - 12x + 27x 2 - 16x3)],

(8)

where x = E e / E ~ ax in the laboratory, p, ~ and ~ are 2 2 functions of g{u, and all the terms rn~/rn~ have been neglected, A term in ~lrne/rn~ has also been dropped in eq. (8) since only a vector interaction will be considered in the following (that is g S = g~u = 0 which implies q = 0). The predictions for different combinations of the interaction at the t - V t and z-v~ vertices are reported in table 2. The existing measurement of p is already precise enough to exclude all the possible

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Volume 288, number 1,2

Table 2 The predictions for different combinations of a vector interaction at the g-~e and z - u r vertices. A normalization IgvLL2 q- [gLRlV2 + gVRL2 q_ igVRi2 = 1 as in ref. [2] is used. g--ue

r-u¢

p

~

6

tl

V- A V A V+ A v - A V-A V-A

V- A V A V+ A V A V+A

3/4 3/8 3/8 3/4 3/8 3/8 0

1 0 0 -1 2 2 3

3/4 0 0 3/4 3/6 3/16 0

0 0 0 0 0 0 0

3.2. r ~ h a d r o n

u

The r semileptonic decay is determined by the decay amplitude [ 10 ] M oc - ~ ( u ¢ ) y u ( g v + gAyS)U(Z - ) • JU,

where JU is the matrix element of the hadronic current. The normalized energy distribution for r ~ hu is dF

d----~ ¢x 1 + h , ¢ P ¢ S h ( 2 X - 1),

combinations different from (V - A ) - ( V - A), apart from the (V + A ) - ( V + A) which has the same predictions p = 6 = 3. The determination of ~ distinguishes between these two possibilities. One can, more generally, consider a mixture of ( V A ) - ( V - A) and (V + A ) - ( V + A), which implies

p=a=

3,

IgVRI2 --IgVLI2 Ig~RI2 + I g L v l 2 '

~=

(9)

Another possibility is to fix (V - A) at the g - F t vertex and allow a mixture of (V - A) and (V + A) at the z-u¢ vertex. The matrix element is M ~ ~(g)yu (1 - yS)u(~e) •~ ( u ¢ ) y u ( g v

+ gAY5)U(r-),

g v = g VL + g~R ,

gA = g VR -- g VL .

(10)

(11)

In this case the decay parameters are p = 3(l+hv¢), = 2 - hv,,

hv~ -

2gvgA g2 + gA2"

a-

(14)

3 1 + h,~ 16 1 - l h . ¢ ' (12)

(13)

Notice that the fact of having constrained the g-F~ vertex changes the meaning of the observables. In particular, p, 6 and ~ are determined once one of them is measured.

(15)

where x = E h / E ~ ax in the laboratory and hv¢ is the chirality parameter defined in eq. (13). In the case z ---, n u the z polarization sensitivity S~ is simply equal to unity, while for r ~ p u , a t u the spin-one hadron presents both longitudinal and transverse spin states, that give Sp ~ 0.46 and Sat ~ 0.12. The correspondent reduced sensitivity to PC can be recuperated by measuring the helicity of the spin-one hadron through the decay distribution of the hadronic system [11].

4. The P~ measurement and the T-W-v~ coupling

The measurement of P~, discussed in section 2, is performed by the LEP experiments fitting the experimental distributions to the theoretical expectations. In this procedure, the V - A form for the weak charged current z decay is explicitly assumed (p = 6 = 3 and ~ = h , , = 1). As a matter of fact, the measurement of Pc is a measurement of~P¢ and h,¢P¢ [cf. eqs. ( 8 ) - ( 1 5 ) ] , and thus contains interesting information about the nature of the z - W - u ¢ coupling. In order to extract quantitative results one can turn around the usual argument of accepting the charged current prediction of the standard model and "testing" the neutral current sector. The latter being extensively tested now, one may assume the validity of the standard model prediction for Pc and lepton universality in the neutral current sector to test the charged current structure of the third generation lepton, the z. The precise measurement of the Z ° parameters performed by the four LEP experiments [ 12 ] sin z 0w = 0.2337 + 0.0014

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20 August 1992

Table 3 The leptonic decay parameter ~ and the chirality parameter h~ for the different z decay modes. The averages for the leptonic (~r~e~r) and hadronic [(h~)r_hv )] decay modes are also reported. The values are extracted combining the measurement of the z polarization and sin~ 0w at LEP. Leptonic decay parameter

Chirality parameter hv~

z ~ ev~

z --~/lye

z ~ £v~-

z --~ Try

z --~ pv

z --~ a i r

z - . hv

0.39=t=0.81

1.17 + 0 . 8 1

0.80+0.58

1.26 + 0.46

1.19 + 0.47

1.15+ 1 . 2 8

1.224-0.33

Table 4 The leptonic decay parameter ~ and the chirality parameter h~ for the different r decay modes. The values are extracted combining the measurement of the z polarization at LEP and the ARGUS measurement of ( h ~ ) ~ a l ~ . Leptonic decay parameter ~

Chirality parameter h,~

r - ~ ev-ff

r -~ lt~,~

z -~ g t , f f

z --, n v

r -~ p v

z -~ h v

0.39 + 0.91

1.15 + 1.54

0.79 + 1.06

1.24 + 1.49

1.18 + 1.42

1.20± 1.40

can, thus, be converted in a predicted value for the z polarization using eq. (5): ppred = - 0 . 1 3 0 + 0.011.

(17)

It is a simple matter then to extract the chirality parameters for different z decay modes using the P~ values of table 1. For example, (~P~)~r ePred

5.

-- ~r~u,r = 1.17 ± 0 . 8 1 .

-

(h~) ....

- 0.88+0.66,

(19)

and one can easily compute all the other combinations. Note that no specific assumption on the origin and the value of P~ is made to obtain these results. In particular, one can derive the ratios ~. . . . ~ r l ( h , ~ ) ~ _ , w and (hv~) . . . . p v / ( h v T ) r ~ a l v , which can then be multiplied by the A R G U S measurement of (h,~)~-al~ [eq. (3)] to determine the 230

Conclusions

(18)

For the leptonic decays, an additional 20% systematic error has been added to take into account variations o f p within its error and of~ in the interval 0 to 1. The results for each decay mode and the average values of the leptonic (~,_e,~) and of the hadronic [ (h~)~--h~ ] decay modes are summarized in table 3. Another possible approach is to derive ratios of the chirality parameters for different z decay modes, using the P~ values of table 1. For example,

(h~P~) ....

value of ~ and h~ for the various decay channels. The results are summarized in table 4. However, the present error ( ~ 100%) in the measurement of (h,~P~)~a~ at LEP (only ALEPH has analyzed this decay so far) is limiting this determination.

The measurement of the z polarization at LEP gives not only a precise measurement of the z coupling to the Z ° but also new informations about the structure of the weak charged current z decay. Assuming the validity of the neutral current prediction for P~ and lepton universality in the neutral current sector, the leptonic decay parameter ~ e , r and the chirality parameter ( h , , ) ~ h ~ for the semileptonic z decays are determined. The leptonic decay parameter value ~ev;

= 0.80 + 0.58

(20)

excludes a ( V + A ) - ( V + A ) i n t e r a c t i o n (see section 3.1 ) at 3a level, and is consistent with a pure ( V - A ) (V - A) interaction. The chirality parameter determined from the hadronic decay modes (h~T)~h. = 1.22 + 0.33

(21)

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is consistent with h,, = 1 expected for pure V - A coupling at the leptonic z-W-u~ vertex. It also indicates that the u~ is a left-handed particle with a significance of m o r e t h a n six s t a n d a r d deviations. If (V - A) is explicitly a s s u m e d for the g--fie vertex n~ , one can relate the leptonic decay p a r a m e t e r to the chirality p a r a m e t e r using eq. (12):

(22)

which is also consistent with the (V - A) hypothesis, a n d can n o w be c o m b i n e d with eq. (21) to yield hLEP

~,

= 1.22+0.28.

(23)

P r e l i m i n a r y updates [ 13 ] of the P~ m e a s u r e m e n t at LEP, which include an increased statistics a n d the L3 experiment, have b e e n recently presented. P e r f o r m i n g the same analysis previously described, a m o r e precise value is obtained: "~urhLEa= 1.05 ± 0.20. A n o t h e r m e t h o d to d e t e r m i n e ( a n d h,~, which uses the A R G U S m e a s u r e m e n t of ( h , , ) ~ a ~ , a n d makes no a s s u m p t i o n o n the m o d e l s t a n d a r d m o d e l n a t u r e o f P~, has also been discussed, b u t it is currently l i m i t e d by the error o n the LEP d e t e r m i n a tion of ( h ~ P ~ ) ~ a ~ , . A more precise m e a s u r e m e n t of A R G U S [14] is also available: ( h , ~, rARGUs ~alu = 1.25 + n 9a+ 0.15 ....

-0.08

Acknowledgement

The a u t h o r thanks W. De Boer, M. Feindt, P. G r o s s e - W i e s m a n n a n d K.R. Schubert for m a n y useful discussions a n d c o m m e n t s .

References

2gvgA = 1.20 ± 0.58,

20 August 1992

'

The increasing statistics collected at LEP will certainly i m p r o v e the errors on the h~ d e t e r m i n a t i o n for both methods, a n d a n error ~< 10% should be easily achieved.

Notice that in this case, as discussed in section 3.1, the measurement of the p parameter is enough to constraint h,~ [see eq. (12)]. The present error of ~ 0.03 on the p parameter corresponds to ~ 0.08 error on h,~.

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