Michel Parameters Averages and Interpretation

Preprint - Server BONN-HE-98-04 (26-October-1998) h " g R;L ;V ;T = S X = "; p x- 2 (1) i tto ) ` : xima- an i ansatz b osons ) ( W-b oson ( ts leads to

erages and j the appro v j y should hold j of general ea ) j mo del ` ( h ) o curren " b etter w

most ysics. ( en ! . This is a go o d appro

ev g standard vier b osons. propagators an een the t w so-called the be the ariance and lo calit v teraction. the for tin en y kind of new ph tz in should ev er tion for new hea and imation a p oin mediating b et Neglecting for an Loren ev w o 1 w the tof ari- is based on non-trivial assumptions and I w discuss some of them,limits b efore on I the giv couplings Ho t v in of tz in ! t symmetric b er conserv- terms tro duction to rom these mea- um and F in There are excel- terpretations e eanin ys. wing Loren in harged Higgs b oson in e erages. YS results v deca and ! teraction -b oson in left-righ wing these are dedicated to the ed W e free, lepton n orld a t-in ys y the follo of DECA I will not giv deriv ativ deca are t-handed bined to w arameters in o sections follo GeV on the mass of a c terpretation w y

hel P in LEPTONIC F couplings t reviews in the literature [1]. t, lo cal, deriv In the most general case the matrix elemen G 4 ing, 4-fermion p oin len 2. the leptonic can b e describ ed b an sp eci c mo dels. Mic an the t 5 tan ys are com : mo del deca t e h if w ts as ys, ap- the and The The new with hin tw o ab out er limit of 2 erages that tations of w deca curren v er w starting and t tz struc- approac data insp ected ev non-standard In the next w its Alo risk, orld a presen data ho the on terms rst grounds. mo del at There the pure then w are there These en. hes: in e in the is the ation is quite dif- eral hel parameters in or ys. The lik assumptions limits is t miss them. mediating to sev t b ers t. t general ysics general, few standard lo ok mo del hes to this question: ph regions. um in t up dated terpretation seen there ts of Mic n exclude t as e are asking the question is tted uon deca e the The question b eing what w these e This motiv the e h In v di eren is new as driving p eople to study the w ww of migh er b oth approac of tal results on the Loren on ha limits ysik.uni-b onn.de presen indep enden these v of mak h has a guess (a mo del) ab out ho o approac can er ou o Higgs doublets can b e set and a 229 GeV limit on a righ and quite w to harged curren y arameters mo del w approac hes Institut, Nussallee 12, 53115 Bonn, German c ysics space eak from P signs mo del ODUCTION be w ph a task to what ything else. the stahl@ph excluded that ts alisc The e ysics as p ossible, lo ok at the data and see extensions y ork of sp eci c mo dels are giv terpretations. are haracter of the standard mo del curren tz structure of m hes are hel w will of t from what w giv h learn second be t. new erages preferred/excluded ysik INTR ysics, is m I will try to co There are t No The new measuremen Ph three sections I will talk ab out general limits and one guesses wrong, one migh there the will proac for parameter p oin second approac the can new ph whic there an ab out where to go. feren Loren V-A c established and no rst ph and in can it of new exp erimen ture mo dels (95 % c.l.). 1. mo dels with t framew suremen e-mail: A. Stahl a Mic Av 2

Equation 1 assumes conservation of lepton

numb ers. It has b een extented to lepton

umber non-conserving currents [2]. The n τ -

χ- e

result is a sp ectrum indistinguishable from

the one following from eq. 1, however the

meaning of the couplings g changes. Each

coupling is replaced by the original coupling

plus a sum of several lepton numb er violat-

ing new couplings. If such new physics ex-

Figure 1. A feynman diagram of the decayof a

ists, it will still show up in a deviation of

in a SUSY mo del. The dashed lines represent

the Michel parameters from their standard

SUSY particles.

mo del values, except for some pathological

cases.

The argument for assuming derivative free

and they might not even b e lighter than the

couplings is an argument of simplicity. The

case of derivatives in connection with a

Apart from these assumptions on the decay of the

vector current can be approximately sub-

's built into the Michel sp ectrum an actual mea-

stituted by a scalar current through the

surement of the parameters has to make also some

Dirac equation. Therefore such kind of new

assumptions ab out their pro duction. One would

physics would not b e missed. However the

like to treat the pro duction with the same gener-

extension to couplings involving derivatives

ality as the decay (see [4]), as new physics in the

of a tensor current create non-trivial exten-

charged current decay might go along with new

sions of the sp ectrum and are not included

physics in the neutral current pro duction. How-

in the ansatz of eq. 1. DELPHI has investi-

ever this increases the number of parameters to

gated such kind of couplings and I wantto

an unmanageable amount. Therefore all exp eri-

refer the reader to their presentation [3].

ments assume the pairs to b e pro duced purely

by spin 1 b osons. Most exp eriments re t the

The assumption of 4 fermions participating

p olarization, i.e. they allow for an arbitrary cou-

in the decay might sound obvious at rst

pling of the pairs to this vector current. The

sight, but there are p ossible extensions of

coupling of the current to the initial electrons is

the standard mo del, where the two unob-

xed to the standard mo del value and has proba-

served particles in the decay are no longer

bly little impact on the measurement. Pro duction

neutrinos. For example g. 1 shows a feyn-

of pairs through scalar or tensor b osons would

man diagram of a decaying through SUSY

however drasticly change the picture.

particles. The two unobserved particles are

Now with these restrictions in mind we can take

sneutrinos which don't have spin 1/2.

the averages. They are presented in g. 2 for

! e and g. 3 for ! [5{12]. The

Although not mentioned in the list of prep o-

average takes into account the correlations be-

sitions to the most general ansatz, there is

tween the parameters within each exp eriment ,

a serious assumption entering the calcula-

but treats the di erent exp eriments indep endent

tion of the sp ectra from eq. 1. In inte-

of each other. There is no sensitivity to the -

grating over the phase-space of the unob-

parameter in ! e decays. The measure-

served neutrinos, it is assumed that their

ments havenow reached a precision of a few p er-

masses are small compared to m . This is

certainly ful lled for the standard mo del,

For SLD I assume the correlation matrix elements not

though new physics might come with new

including to b e the same as in the t assuming lepton

universality. neutrinos (right-handed ones for example) 3

ALEPH ALEPH ALEPH 0.747+/-0.024 0.776+/-0.049 0.16+/-0.16

DELPHI DELPHI DELPHI 0.764+/-0.044 0.905+/-0.081 0.38+/-0.25

OPAL OPAL 0.779+/-0.055 0.777+/-0.047

SLD SLD SLD 0.71+/-0.15 0.54+/-0.31 -0.59+/-0.94

CLEO CLEO CLEO 0.747+/-0.013 0.750+/-0.048 0.01+/-0.23

ARGUS ARGUS 0.68+/-0.08 0.69+/-0.08

ρ 0.748+/-0.010 η ρ 0.771+/-0.018 η 0.127+/-0.066

ALEPH ALEPH ALEPH ALEPH 1.01+/-0.10 0.788+/-0.070 1.03+/-0.13 0.786+/-0.072

DELPHI DELPHI DELPHI DELPHI 0.951+/-0.091 0.727+/-0.069 1.16+/-0.14 0.721+/-0.092

OPAL OPAL OPAL OPAL 1.13+/-0.41 0.72+/-0.34 0.79+/-0.41 0.63+/-0.25

SLD SLD SLD SLD 1.16+/-0.52 0.85+/-0.44 0.75+/-0.52 0.82+/-0.33

CLEO CLEO CLEO CLEO 0.979+/-0.051 0.720+/-0.034 1.050+/-0.083 0.786+/-0.052

ARGUS ARGUS ARGUS ARGUS 1.11+/-0.22 0.56+/-0.15 1.26+/-0.30 0.73+/-0.21

ξ 0.986+/-0.039 ξδ 0.726+/-0.026 ξ 1.110+/-0.045 ξδ 0.756+/-0.035

Figure 2. New world averages of the Michel pa- Figure 3. New world averages of the Michel pa-

rameters of the decay ! e . The average is rameters of the decay ! . See g. 2 for

indicated by the number at the b ottom and the details.

shaded band. The solid line is the standard mo del

3 3

exp ectation ( ; 0; 1; ). Errors are statistical and

4 4

systematic added in quadrature [5{11]. Some old

measurements of are also included.

B ( ! ) = (17:36 0:06) %) and the life-

time [14] ( = (290:5 1:0) fsec) give

cent. There is very go o d agreement with the stan-

A = 1:000 0:005

dard mo del for ! e and a reasonable agree-

A = 0:972 0:016

ment in case of ! .

The rst step towards mo del indep endent lim-

One can now use the relations presented in a pre-

its on the couplings g is the determination of

vious talk [15] to set limits on the g . At the 90 %

the Fermi constant activein decays. From the

con dence level we get the pictures presented in

formula of the leptonic decay width

g. 4 and 5. The freedom of cho osing the overall

2 2

phase has b een used to make the standard mo del

B ! ` G m m

` `

= 1+4 + (2)

` `

coupling g real. The limits on the couplings

192 m

to a right-handed (g ) are already quite strin-

2 2

gent, whereas the whole parameter space is still one derives A = G =G , where G is

op en for scalar typ e couplings to a left-handed the Fermi constant as measured in decays.

. There is also no lower limit on the standard The up dated values for the branching ratios

mo del coupling. [13] (B ( ! e ) = (17:81 0:06) % and

e 4

S V S V

RR 0.71 RR 0.18 RR 0.79 RR 0.20 S V T S V T

LR 0.99 LR 0.13 LR 0.083 LR 1.10 LR 0.14 LR 0.090 S V T S V T

RL 2.0 RL 0.52 RL 0.51 RL 2.0 RL 0.51 RL 0.50 S V S V

LL 2.0 LL LL 2.0 LL

Figure 4. Limits on the coupling constants Figure 5. Limits on the coupling constants

g for ! e decays: The upp er let- g for ! decays: The upp er let-

ter in each box indicates the typ e of coupling ter in each box indicates the typ e of coupling

(Scalar/Vector/Tensor), the lower two letters the (Scalar/Vector/Tensor), the lower two letters the

chiralityofthe (right letter) and the daughter chiralityofthe (right letter) and the daughter

lepton (left letter). The circle de nes the allowed lepton (left letter). The circle de nes the allowed

range of the couplings (assuming A = 1) and the range of the couplings (assuming A = 1) and the

` `

shaded area is the region still consistent with the shaded area is the region still consistent with the

measurements of A and the Michel parameters measurements of A and the Michel parameters

(90 % con dence level). These limits on the cou- (90 % con dence level). These limits on the cou-

plings are also printed in the lower right corner plings are also printed in the lower right corner

of eachbox. of eachbox. 5

ν ALEPH ALEPH τ 0.752+/-0.019 0.086+/-0.078 DELPHI DELPHI 0.790+/-0.038 0.06+/-0.11 ν L3 L3 e 0.762+/-0.035 0.27+/-0.14 - FCNC OPAL OPAL τ 0.781+/-0.033 0.027+/-0.055 SLD e- 0.72+/-0.09 CLEO CLEO 0.747+/-0.012 0.015+/-0.087 ARGUS ARGUS

0.731+/-0.031 0.03+/-0.22

A feynman diagram of the decayof a

Figure 6. ρ 0.750+/-0.011 η 0.048+/-0.035

through a avor changing neutral current indi-

cated by the dashed line. ALEPH ALEPH 1.000+/-0.076 0.782+/-0.051 DELPHI DELPHI 0.974+/-0.061 0.699+/-0.028 L3 L3

0.70+/-0.16 0.70+/-0.11 UNIVERSALITY 3. OPAL OPAL 0.98+/-0.24 0.65+/-0.16

SLD SLD

precision of the measurement can be in-

The 1.05+/-0.35 0.88+/-0.27

by applying the universality constraint creased CLEO CLEO

1.010+/-0.043 0.745+/-0.028

the Michel parameters, i.e. requiring the on ARGUS ARGUS

1.03+/-0.11 0.63+/-0.09

Michel parameters for the decays ! e and

e ξ ξδ

! to b e identical. Universality is used

0.988+/-0.029 0.735+/-0.020

here in a slightly di erent meaning. In general

we sp eak of universality, if the basic couplings

Figure 7. New world averages of the Michel pa-

of the fermions to the b osons are universal, i.e.

rameters of decays under the assumption of uni-

indep endent of the fermion avor . But uni-

versalitybetween ! e and ! . See

versal couplings not necessarily imply universal

g. 2 for details.

Michel parameters. The example shown in g. 6

might illustrate that. It shows a lepton decay-

ing through a neutral current, violating lepton

g. 8 also indicates the precision achieved in de-

avor at the tree level. In such a mo del there

cays. For some of the couplings for the decayofa

might b e universal couplings and a Cabibb o typ e

right-handed lepton g we have almost reached

mixing angle at each vertex, which might di er

the precision of decays. To get go o d limits on

for ! e from ! .

the couplings g however, one needs to measure

I should also mention that when assuming uni-

more than just the shap e of the sp ectrum [16].

versal Michel parameters for ! e and

Notice that in decays there is even an upp er

! one do es not require them to b e iden-

S V

limit on g and therefore a lower limit on g

LL LL

tical to the Michel parameters of ! e ,be-

which requires some measurement involving the

cause otherwise one would not have to measure

neutrinos.

them again .

The world averages on the Michel parameters

4. HADRONIC DECAYS

under the assumption of universality are given in

g. 7 and the limits on the couplings from these

Also hadronic decays can b e investigated with

values are shown in g. 8. There is go o d agree-

resp ect to the Lorentz structure of the charged

ment with the standard mo del. For comparison

current:

I am sp eaking here ab out the tree level couplings of a

4.1. !

mo del, not the e ective couplings of the Michel ansatz.

The simplest case is the decay of a into a

With decays we do not reach the precision yet that is

single pion and a neutrino. The decay can be achieved in decays.

4.2. !

S V

The situation with the decayofa to two pions

through a pure vector current is similar to !

. There is one parameter to measure, which

is with the same meaning as b efore. However,

decaytotwo pions can also b e mediated by

RR 0.63 RR 0.16 the

ts. The extension is non-

S V T scalar and tensor curren

trivial in the sense, that the shap e of the sp ectrum

is mo di ed in a way which cannot b e simulated by

a pure vector current and new parameters app ear.

A calculation including scalar currents has b een

LR 0.11 LR 0.070 ted in [17].

LR 0.84 presen ts, though, exclude scalar and

S V T Most exp erimen

tensor currents. This might be understo o d as a

reasonable simpli cation, if one thinks of a mea-

surement with this decay channel only. But if

the same assumption is made in a measurementof

RL 0.51

RL 2.0 RL 0.52 +

correlations with one decaying to a lepton

S V

this b ecomes an inconsistency. As one searches

for scalar or tensor currents in the leptonic de-

cay one should not neglect them in the hadronic

decays.

Strong interactions participate in the decay and

LL 2.0 LL

in uence the sp ectra. There is a form factor

F Q which has to be known to extract the

Figure 8. Limits on the coupling constants g

Michel typ e parameters. The two pion decays

in decays under the assumption of universality

are however well understo o d, so that this causes

between ! e and ! . The black

no serious problems.

circles in the center indicate for comparison the

limits for decays. For details see g. 4

4.3. !

either mediated by a vector or a scalar current.

The situation with this decay is very similar

The pion cannot b e coupled to a tensor current.

to the two pion decay { the exp eriments measure

Scalar- and vector current are however indistin-

just one parameter { but with the additional com-

guishable in the sp ectrum which reads in the rest

plication, that the hadronic structure of the decay

frame of the decaying

is less understo o d. One has the choice to either

measure the form factors simultaneous with the

2 2 3 2

G f m cos d

= A (1 + h cos ) : (3)

Michel typ e parameters or to assume some mo d-

d 64

els on the decay. In the rst case the hadronic

Here cos is the Cabibb o angle, h the helicity uncertainty increases the statistical error in the

of the decaying , and cos the Gottfried Jack- second it feeds into the systematics, as the mo d-

son angle. The normalization A cannot b e disen- els havetobevaried within reasonable ranges.

tangled from the pion decay constant f without Figure 9 displays the world average on the pa-

a theoretical prediction for f . The only Michel rameter averaged over the one, two, and three

typ e parameter to measure is which is the neg- pion decays channels. The value is in agreement

ative of the neutrino helicity. with the standard mo del exp ectation of 1. 7

ALEPH ALEPH a 0.2 0.992+/-0.010 1 1.000+/-0.029 DELPHI ALEPH ρ 0.1 0.997+/-0.028 0.987+/-0.016 0 L3 ALEPH π 1.030+/-0.031 0.994+/-0.024 -0.1 SLD DELPHI 0.93+/-0.11 0.993+/-0.029 -0.2 CLEO SLD 1.03+/-0.07 0.93+/-0.11 -0.3 CLEO CLEO 0.995+/-0.010 1.03+/-0.07 -0.4 ARGUS CLEO -0.5 1.020+/-0.039 0.995+/-0.010 0246810 ξ ξ

h 1.0000+/-0.0056 h 1.0000+/-0.0057

Figure 10. Functional dep endence of the Michel

parameter on m = tan (in GeV) in mo dels

Figure 9. New world averages of the parameter

with two Higgs doublets. The three horizontal

from hadronic decays. The numb ers in the

lines indicate the currentworld average of and

left b oxwere evaluated under the assumption of

its 1 standard deviation error band.

universalitybetween ! e and !

on the recoiling . See g. 2 for details.

= (5)

5. TAU DECAYS THROUGH A

with

CHARGED HIGGS

(m +m )m tan

f f

In the framework of mo dels with the Higgs

c (f )= : (6)

sector extented to two doublets there app ears

apart from three neutral Higgs b osons a pair

Figure 10 shows the variation of as a function

of charged b osons H . These charged Higgs

of m = tan as an example. Also the branching

b osons represent a scalar current through which

ratio ! is mo di ed through . This

the lepton might decay [18]. It is helicity blind

additional information can be included through

and breaks universality as it couples prop ortional

the following two relations:

to the fermion masses. Describing the decays

() 1+4K

through eq. 1 the couplings are

(e) g 1+4K

g = 1

m m

0 e

(m + m ) tan

1+2K = ()+2K (e) (7) f f

g =

B m m

0 else (4)

It is =1:0014 0:0024 [13], K the factor cor-

recting for the restricted range of momenta used

where f and f are the in- and outgoing fermions

in the measurements of the branching ratios (in-

2 5 3

at the vertex. These additional couplings mo dify

tro duced in [13]), =(G m )=(192 ), and B

0 `

the Michel parameters to

the average of the branching ratios of ! e

and ! b oth corrected for phase-space,

radiation, etc.

I should mention that in such mo dels there

c ( f )

are typically more new particles (SUSY particles)

1+ c (f)

than just the new Higgs b osons. These could give

1 c (f)

additional contributions to decays which further

mo dify the Michel parameters. To which extend

1+c (f) H 8

40 1.1

38 1

36 0.9

34 0.8

32 0.7

30 0.6

28 0.5

0 2 4 6 8 10 0 200 400 600 800 1000

Figure 12. Functional dep endence of the Michel

Figure 11. The value of as a function of

parameter on the mass of the second W b oson

m = tan in units of GeV from the t of eq. 5

(in GeV) in left-right symmetric mo dels. The four

and 7 to the world averages.

o o

graphs corresp ond to mixing angles of 0 , 7:5 ,

o o

15 , and 22:5 degrees (top to b ottom). The three

horizontal lines indicate the currentworld average

is largely mo del dep endent. These additional con-

of and its 1 standard deviation error band.

tributions are ignored here.

Then m = tan is tted to the world averages

of the quantities in eq. 5 and 7. The result- 2

2 42

ing is shown in g. 11. The minimum is

reached at in nity, i.e. there is no sign at all of

a charged Higgs b oson. The resulting limit on

the mass dep ends on tan and is particularly in-

34 teresting for large values of tan . At the 90 %

el charged Higgs b osons with a mass

con dence lev 32

wer than 2:5 tan GeV are excluded (2:3 tan

lo 30

A similar limit (2:2 tan GeV

GeV at 95 % c.l.). 28

can b e derived from the branching at 90 % c.l.) 26

100 200 300 400 500 600

ratio of the decay B ! [19].

Figure 13. The value of as a function of the

6. TAU DECAYS IN LEFT-RIGHT SYM-

mass of the right-handed W -b oson in units of

METRIC MODELS

GeV.

In left-right symmetric mo dels the symmetry

between the right and left handed fermions is re-

go o d idea to re t the p olarization for those ex-

stored by a second W -b oson which couples ex-

p eriments running at the Z-p ole as there might

clusively to the right-handed fermions (and left-

also b e right-handed Z-b osons around. The crit-

handed anti-fermions). The mass eigenstates W

ical assumption is, that the masses of the right-

and W might b e mixtures of the chirality eigen-

handed neutrinos are small compared to the

states W and W with a mixing angle :

L R

mass. This assumption is di erent for decays

W cos sin W

1 L

where the scale is set by the mass of the .

= (8)

W sin cos W

2 R

The t uses the Michel parameters (including

W is the well-known W -b oson of the standard ), the measurements of the helicity of the

mo del and W must b e some heavier state to ex- neutrino [21], and the mass of the W -b oson [22]

plain parity violation at low energies [20]. As as inputs to t for the mass ratio b etween the two

b oth b osons have spin 1 we are left with a pure W -b osons and the mixing angle. (For details see

vector current with universal couplings. It is a [16].) For illustration g. 12 shows the variation

11. ARGUS collab., H. Albrecht et al., Phys. Lett. of the Michel parameter in the mo del.

B 431, 1998 (179). The t slightly prefers a mass around 310

12. ARGUS collab., H. Albrecht et al., Phys. Lett. GeV. The distribution can b e seen in g. 13.

B 341, 1995 (441), Phys. Lett. B 316, 1993 The minimum is approximately 1 standard de-

(608), Phys. Lett. B 246, 1990 (278), viation deep and corresp onds to a slightly nega-

CRYSTAL BALL collab., H. Janssen et al., tive mixing angle. Right-handed W -b osons with

Phys. Lett. B 228, 1989 (273), a mass b elow 236 GeV and mixing angles outside

MAC collab., W.T. Ford et al., Phys. Rev. D 0:12 < < 0:05 can be excluded at the 90 %

36, 1987 (1971), con dence level (229 GeV at 95 % c.l.).

CLEO collab., S. Behrends et al., Phys. Rev.

D 32, 1985 (2468),

7. CONCLUSION

DELCO collab., W. Bacino et al., Phys. Rev.

Lett. 42, 1979 (749).

The Michel parameters of leptonic and

13. B. Stugu, presentation at this workshop.

hadronic decays provide an interesting window

14. S. Wasserbach, presentation at this workshop.

into physics beyond the standard mo del which

15. R. Bartoldus, presentation at this workshop.

will b ecome even more interesting as more pre-

16. A. Stahl and H. Voss, Z. Phys. C 74, 1997

cise measurements b ecome available.

(73)

17. H. Thurn and H. Kolanoski, Z. Phys. C 60,

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