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QUARK MIXING : PHENOMENOLOGY
S. Pakvasa
To cite this version:
S. Pakvasa. QUARK MIXING : PHENOMENOLOGY. Journal de Physique Colloques, 1982, 43 (C3),
pp.C3-234-C3-238. �10.1051/jphyscol:1982346�. �jpa-00221899�
JOURNAL DE PHYSIQUE
CoZZoque
C3,suppZ6ment au n o
22,Tome
43,ddeembre
2982page C3-234
Q U A R K MIXING : PHENOMENOLOGY
S. Pakvasa *
CERN,
Geneva, SwitzerZand
The low qZ effective charged current interaction in the standard model is
gee
=4 ~ ~ / f i J +J where
Fcu
To extract information about GF and Um it has to be assumed1 that a) all mvi
=0 or b) U
=1 or c) all mvi
<<Q in p-decay and other semi-leptonic decays. Then GF is fixed by u-lifetime and Uud can be measured via ft-values of allowed nuclear B-decays. Radiative corrections play an important role2 and the final result for Uud can be written as2-4
where 6c and
gRare coulamb and internal radiative nuclear corrections, AR and 6p are electro-weak corrections to 6-decay and y-decay. The most accurate ft values are those of 014 and AlZ1. Combining the recent analyses, we conclude:
The largest uncertainties are in tic and in evaluating hadronic matrix elements of quark operators.
Uus can be extracted in a similar way from K
-tae-ve and Y
-tNe-ve, albeit with less accuracy. In case of Keg, apart from Uus and GF there are two form factors f-(q2) and f+(q2), whose ratio and q2 dependence is measured. If+(0) 1 is deter-
mined theoretically5 (broken chiral SU(3) x SU(3)) to be about 0.98. Then one
find^^.^ IuUs (
=0.219 + 0.003. The hyperon semileptonic decays7 are slightly problematic. One potential problem is the rate for T(C-
+Ae-ve) which is lower than SU(3) fits would like and the other is the electron asymmetry in polarized C--decay(C-
+ne-ve) which may have the sign opposite to the expected value. Now the first can be accomodated with SU(3) breaking in the axial-vector current matrix element without affecting the overall fit drastically whereas the second, if correct, would require a profound change in our understanding of charged weak currents.
Ignoring this second problem, recent fits3,8 to hyperon decays yield values for ranging from 0.225
?0.002, to 0.227 + 0.003 or even 0.228, all of which are somewhat higher than values obtained earlied; viz. 0.222 + 0.003. For the present purposes, we adopt a crude average from Keg and hyperon decays of
A
better way to use the hyperon data is to make a two angle fit (Bv and 8 ~ ) and use only Bv to determine \u,,), thus minimizing dependence on the uncertain axial vector matrix elements.
* Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822
USAArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982346
From the bounds (at l a level) on lUudl and (UUsI in Eq. (3) and
/4)and the unitarity of Um we find
in agreement with the earliest bound9 obtained on Iuubl. In principle, luubl can also be bounded by the same-sign dimuon rate in GUN. This has a contribution from vpu
+p+b
+p+c
+u+u+x which can be bounded by the unknown rate. However, due to the high o(Cu
+u+p+), the threshold sup ression in b-production and the unfavorable y-dependence, the bound obtained on lUuby is weaker than (5) .lo A more promising way of constraining luub 1 may be to use the llunexplained" part of a(Gp
+ u+u-p+)i.e., the observed cross-section after subtracting the cross-section calculated from all conventional sources.
The unitarity limit on U d from Uud in
(3)is lucdl
<0.24. To get a non-zero lower bound it was suggested1$ that one use the valence contribution to o(vu
+u-1+) which comes from vud
-tp-c
+u-1'~. Using the recent CDHS data for the fraction of valence in o(v,,
+u-u+) viz. 52%, one finds (ucdl
>0.2.
Amore complete analysis by C D H S ~ ~ using the identity
where R
= o(3 +u+)/o(v
+ p-)and using fragmentation function they measured finds lucdl
=0.24 + 0.03. So summarizing
In the same analysis C D H S ~ ~ also find that ( I u ~ ~ ~ ~ / I u ~ ~ ~ ~ ) ( ~ S / U
+D)
=0.92 k0.06-and-from their charged current data (U
+D)/(u
+D)
=0.13 + 0.02. So if 2s
<U
+ Dthey deduce the most conservative bound I U C ~ 1 > 0.59. But from C H A W analysis13 of their neutral current data (assuming s and d have identical neutral current couplings) we know that 2~/(0 + 6) is close to 0.5. From this, it is possi- ble to use CDHS data to deduce a stronger bound14 on I u ~ ~ I viz. lucsl
>0.7*to 0.74.
A
similar bound on lucs 1 can be obtained11 from T
(D+ +~Oe've). Using an F -
dominance model for the form factors and a calculated value15 for I f+(0) 1 1 , one
finds 1 ucs 1
>0.8. The main uncertainties are the values for B(D+
+e+koe+ve) and
T
(D+). Including the unitarity limit from 1uCs 1, then3
It would be nice to check that indeed IuCsI
<1 and that unitarity is satisfied.
There are several ways of measuring the ratio IUub/Ucb ( as reviewed16 in Madison. CLEO has reported17 on a new measurement of < N K > ~ ~ ~ / < N K > c
=1.88
t0.28 from which a limit I u ~ ~ / u ~ ~ ~
<0.4 can be deduced.
Astronger result from a study of the shape and the end-point of the electron spectrum in B
+evex is reported to this conference by C U S B ~ ~ :
If B-decay is described well by quark decay, as seems likely, the lifetime r B is given approximately by
With the new limit1' on
T Bfrom JADE
T B <1.4
x10-12 s, and the smallness of IuUbl,
I
u C ~1 should satisfy
JOURNAL DE PHYSIQUE
where the upper bound comes from unitarity.
We can now use unitarity to limit Uti, e.g., we find lutdl
<0.13, lUtsl
<0.56 and 0.99
>lUtbl
>0.82. Hence lUts utdl
<0.073. However, a better bound on
lUts Utdl is obtained from saturating the dispersive part of KL
+ p+1.1-amplitude20 by one loop graphs which are dominated by t. If the fourth generation heavy quark contribution is small com ared to t then for mt
>20 GeV, it can be shown that1
IUfs
"td/0.035. lUtb lq
+1lJtsl z'+ I u ~ ~ ! ~ which should be
ilcan be measured in principle In weak decays of topponiwn: (tt)
-tt
+b
+1v etc. The rate goes as
. -
G$~S $ Iuti lz and the branching ratio can be as high as 5 to 6 % for Mtf
- - - 50 GeV.
A pos$ible signature is prompt e/y accompanied by h a d r o n ~ . ~ ~ Since rT
<10-l7 s, this may be the only way to measure the absolute value of t-couplings. Relative strengths such as IIJts/Utbl can only be measured in t
-tblv, t
+s.lv etc.
A summary of our present knowledge of Urn elements is:
If and only if there are three families, Urn can be parameterized la Kobayashi-
~askawa22
' 1 ' 3
c ~ c ~ s ~ - s ~ s ~ ~ ~ ~ s1s2 - c ~ s ~ c ~ - c ~ s ~ ~ ~ ~
where Ci and Si are cosei and sinei with 0
_<0 r/2 and 0
56
52r. The value of IUUdl fixes S1
=0.229. The other constraints on Uij restrict S2 and S3 as shown in Figs. 1 to 3. In Fig. 1 and Fig. 2, sin6 is small and 6 is near 0 and a respec- tively. In Fig. 3, sin6 is large p0.1). These constraints can be converted into other parameterizations23 for Uij .
Bounds on ei and 6 can also be derived from evaluating 6 m ~ - s and Re
Efor the KL
-KS ~ ~ s t e m . 2 4 The principal uncertainty is the evaluation of the hadronic matrix element. The bag-model evaluation is too sensitive to the parameters chosen and even the sign is ~nstable.~5 There is also the factor of 2 to 3 uncertainty due to possible long-range effects26 (e.g., TO, n,
q 1intermediate states). Two recent attempts to estimate this matrix element are very encouraging. one27 relates the AS
=2, AT
=1 matrix element for KO
++ KOto the AS
=1, AT
=3/2 matrix element
Ko
+r0 in K+
-+2r and obtains a suppression factor of 0.33 compared to vacuum saturation. The otherz8 uses QCD sum rules to place a bound on the form factor for vacuum
+KK yielding a limit of the suppression factor <0.6. Allowing for this uncertainty and allowing mt to range between 20 and 60 GeV, the range for S2 and S3 preferred2412g by the KL
-KS parameters is shown on the figures. Similar con- s t r a i n t ~ ~ ~ , ~ ~ can be obtained from KL
+ p-u+.Meanwhile, it seems to me that the real problem, viz. that of predicting quark
and lepton masses and mixings, remains open. As a beginning, we need to see the
regularities, i.e., find the "Balmer formula" for fermion spectrum. One speculation
on t-quark mass not yet ruled out is mt/mc - m,/my. This leads to the expecta-
tion31 that the threshold for naked t i.e., 2Mt is between 46 and 52 GeV. Are there
simple relations between mixings and masses? Tune in next year.
S. Pakvasa
Acknowledgment
I thank V. Barger, L.L. Chau, J. Donoghue, J. Ellis, J. Hagelin, K. Kleinknecht, J. KUhn, L. Maiani, E. Paschos, E. de Rafael, J.J. Sakurai, and J. Trampetic for enjoyable and instructive discussions. I thank CERN Theory Division for its hospi- tality during the preparation of this review and acknowledge partial support by the U.S. DOE under Contract No. DE-AM03-76SF00235.
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