" Mein Gott " denkt sich Frau Professor Dr Schaile

14/09/2011 - 17:08 von Die Sieben | Report spam
Ich mailte ihr ja mehrmals, daß ich die Formeln für die K Zerfalls-
Verhàltnisse " in der Schublade " hàtte.

Netterweise überließ sie mir in der Vorlesung ein Büchlein der "
Particle Data Group " :

K0s pi0 pi0 31%
pi+ pi- 68%
pi+ pi- pi0 3*10 hoch -7%

K0l pi+- e-+ nüe 38%
pi+- mü-+ nümü 27%
pi0 pi+- e-+ nü 5*10 hoch -5 %

" Jetzt sitzt der Typ mit seinen E-Mails schon wieder in meiner
Vorlesung " dachte sich die Frau Professor wàhrend der Zwischenpause,
" Mein Gott, jetzt kommt er auch noch zur Tafel runter ".

Lesen sie die antworten

#1 Die Sieben
14/09/2011 - 22:16 | Warnen spam
On 14 Sep., 17:08, Die Sieben wrote:
Ich mailte ihr ja mehrmals, daß ich die Formeln für die K Zerfalls-
Verhàltnisse " in der Schublade " hàtte.

Netterweise überließ sie mir in der Vorlesung ein Büchlein der "
Particle Data Group " :

K0s > pi0 pi0  31%
pi+  pi- 68%
pi+  pi-  pi0  3*10 hoch -7%

K0l > pi+-  e-+  nüe  38%
pi+-  mü-+  nümü  27%
pi0  pi+-  e-+  nü   5*10 hoch -5 %

" Jetzt sitzt der Typ mit seinen E-Mails schon wieder in meiner
Vorlesung " dachte sich die Frau Professor wàhrend der Zwischenpause,
" Mein Gott, jetzt kommt er auch noch zur Tafel runter ".

L.Wolfenstein schreibt noch 2010 aus Amerika ( seine Schriften wurden
aus Deutschen Bibliotheken entfernt ) :

Updated May 2010 by L. Wolfenstein (Carnegie-Mellon University),
T.G. Trippe (LBNL), and C.-J. Lin (LBNL).
The symmetries C (particle-antiparticle interchange) and
P (space inversion) hold for strong and electromagnetic interactions.
After the discovery of large C and P violation in the
weak interactions, it appeared that the product CP was a good
symmetry. In 1964 CP violation was observed in K0 decays at
a level given by the parameter  ≈ 2.3 × 10−3.
A unified treatment of CP violation in K, D, B, and
Bs mesons is given in “CP Violation in Meson Decays” by
D. Kirkby and Y. Nir in this Review. A more detailed review
including a thorough discussion of the experimental techniques
used to determine CP violation parameters is given in a book
by K. Kleinknecht [1]. Here we give a concise summary of the
formalism needed to define the parameters of CP violation in
KL decays, and a description of our fits for the best values of
these parameters.
1. Formalism for CP violation in Kaon decay:
CP violation has been observed in the semi-leptonic decays
→ π∓±ν, and in the nonleptonic decay K0L
→ 2π. The
experimental numbers that have been measured are
→ π−+ν) − Γ(K0L
→ π+−ν)
→ π−+ν) + Γ(K0L
→ π+−ν)
η+− = A(K0L
→ π+π

→ π+π

= |η+−| eiφ+− (1b)
η00 = A(K0L
→ π0π0)/A(K0S
→ π0π0)
= |η00| eiφ00 . (1c)
CP violation can occur either in the K0 –K
mixing or
in the decay amplitudes. Assuming CPT invariance, the mass
eigenstates of the K0–K0 system can be written
|KS = p|K0 + q|K0 , |KL = p|K0 − q|K0 . (2)
If CP invariance held, we would have q = p so that KS would
be CP-even and KL CP-odd. (We define |K0 as CP |K0).
CITATION: K. Nakamura et al. (Particle Data Group), JPG 37, 075021
(2010) (URL: http://pdg.lbl.gov)
July 30, 2010 14:34
– 2–
CP violation in K0–K0 mixing is then given by the parameter
(1 + )
(1 − )
. (3)
CP violation can also occur in the decay amplitudes
A(K0 → ππ(I)) = AIeiδI, A(K0 → ππ(I)) = A

IeiδI , (4)
where I is the isospin of ππ, δI is the final-state phase shift,
and AI would be real if CP invariance held. The CP-violating
observables are usually expressed in terms of  and  defined
η+− =  + 

, η00 =  − 2

. (5a)
One can then show [2]
 =  + i (Im A0/Re A0) , (5b)


= iei(δ2−δ0)(ReA2/ReA0) (ImA2/ReA2−ImA0/Re A0) ,
AL = 2Re /(1 + ||2) ≈ 2Re  . (5d)
In Eqs. (5a), small corrections [3] of order  × Re (A2/A0) are
neglected, and Eq. (5d) assumes the ΔS = ΔQ rule.
The quantities Im A0, Im A2, and Im depend on the choice
of phase convention, since one can change the phases of K0 and
by a transformation of the strange quark state |s → |s eiα;
of course, observables are unchanged. It is possible by a choice
of phase convention to set ImA0 or ImA2 or Im  to zero,
but none of these is zero with the usual phase conventions
in the Standard Model. The choice ImA0 = 0 is called the
Wu-Yang phase convention [4], in which case  = . The value
of  is independent of phase convention, and a nonzero value
demonstrates CP violation in the decay amplitudes, referred to
as direct CP violation. The possibility that direct CP violation
is essentially zero, and that CP violation occurs only in the
mixing matrix, was referred to as the superweak theory [5].
By applying CPT invariance and unitarity the phase of  is
given approximately by
φ ≈ tan
−1 2(mKL
−mKS )
≈ 43.51 ± 0.05

, (6a)
July 30, 2010 14:34
– 3–
while Eq. (5c) gives the phase of  to be
φ = δ2 − δ0 +
≈ 42.3 ± 1.5

, (6b)
where the numerical value is based on an analysis of π–π scattering
using chiral perturbation theory [6]. The approximation
in Eq. (6a) depends on the assumption that direct CP violation
is very small in all K0 decays. This is expected to be good to a
few tenths of a degree, as indicated by the small value of  and
of η+−0 and η000, the CP-violation parameters in the decays
KS → π+π−π0 [7], and KS → π0π0π0 [8]. The relation in
Eq. (6a) is exact in the superweak theory, so this is sometimes
called the superweak-phase φSW. An important point for the
analysis is that cos(φ–φ)  1. The consequence is that only
two real quantities need be measured, the magnitude of  and
the value of (/), including its sign. The measured quantity
|η00/η+−|2 is very close to unity so that we can write
|η00/η+−|2 ≈ 1 − 6Re (

/) ≈ 1 − 6

/ , (7a)

/) ≈ 1
(1 − |η00/η+−|) . (7b)
From the experimental measurements in this edition of the
Review, and the fits discussed in the next section, one finds
|| = (2.228 ± 0.011) × 10
−3 , (8a)
φ = (43.5 ± 0.7)

, (8b)

/) ≈ 

/ = (1.65 ± 0.26) × 10
−3 , (8c)
φ+− = (43.4 ± 0.7)

, (8d)
φ00–φ+− = (0.2 ± 0.4)

, (8e)
AL = (3.32 ± 0.06) × 10
−3 . (8f)
Direct CP violation, as indicated by /, is expected in
the Standard Model. However, the numerical value cannot be
reliably predicted because of theoretical uncertainties [9]. The
value of AL agrees with Eq. (5d). The values of φ+− and
φ00 − φ+− are used to set limits on CPT violation [see “Tests
of Conservation Laws”].
July 30, 2010 14:34
– 4–
2. Fits for K0L
CP-violation parameters:
In recent years, K0L
CP-violation experiments have improved
our knowledge of CP-violation parameters, and their
consistency with the expectations of CPT invariance and unitarity.
To determine the best values of the CP-violation parameters
in K0L
→ π+π− and π0π0 decay, we make two types
of fits, one for the phases φ+− and φ00 jointly with Δm and τS ,
and the other for the amplitudes |η+−| and |η00| jointly with
the K0L
→ ππ branching fractions.
Fits to φ+−, φ00, Δφ, Δm, and τS data: These are joint fits
to the data on φ+−, φ00, the phase difference Δφ = φ00 – φ+−,
the K0L
mass difference Δm, and the K0S
mean life τS ,
including the effects of correlations.
Measurements of φ+− and φ00 are highly correlated with
Δm and τS. Some measurements of τS are correlated with Δm.
The correlations are given in the footnotes of the φ+− and
φ00 sections of the K0L
Listings, and the τS section of the K0S
In most cases, the correlations are quoted as 100%, i.e.,
with the value and error of φ+− or φ00 given at a fixed value of
Δm and τS , with additional terms specifying the dependence of
the value on Δm and τS . These cases lead to diagonal bands in
Figs. [1] and [2]. The KTeV experiment [10] quotes its results
as values of φ+−, Δm, and τS with correlations, leading to the
ellipses labeled “b.”
The data on τS, Δm, and φ+− shown in Figs. [1] and [2]
are combined with data on φ00 and φ00 – φ+− in two fits, one
without assuming CPT, and the other with this assumption.
The results without assuming CPT are shown as ellipses labeled
“a.” These ellipses are seen to be in good agreement with the
superweak phase
φSW = tan


= tan

2ΔmτS τL
¯h(τL – τS )

. (9)
In Figs. [1] and [2], φSW is shown as narrow bands labeled “j.”
July 30, 2010 14:34
– 5–
φ+ _ (degrees)
mKL - mKS (1010 hs-1)
0.520 0.525 0.530 0.535 0.540
c e
g f
Figure 1: φ+− vs Δm for experiments which
do not assume CPT invariance. Δm measurements
appear as vertical bands spanning Δm±
1σ, cut near the top and bottom to aid the eye.
Most φ+− measurements appear as diagonal
bands spanning φ+− ± σφ. Data are labeled by
letters: “b”–FNAL KTeV, “c”–CERN CPLEAR,
“d”–FNAL E773, “e”–FNAL E731, “f”–CERN,
“g”–CERN NA31, and are cited in Table 1.
The narrow band “j” shows φSW. The ellipse
“a” shows the χ2 = 1 contour of the fit result.
Color version at end of book.
Table 2 column 2, “Fit w/o CPT,” gives the resulting fitted
parameters, while Table 3 gives the correlation matrix for this
fit. The white ellipses labeled “a” in Fig. 1 and Fig. 2 are the
χ2 = 1 contours for this fit.
For experiments which have dependencies on unseen fit
parameters, that is, parameters other than those shown on the
x or y axis of the figure, their band positions are evaluated
using the fit results and their band widths include the fitted
July 30, 2010 14:34
– 6–
Table 1: References, Document ID’s, and sources
corresponding to the letter labels in the figures.
The data are given in the φ+− and Δm sections
of the KL Listings, and the τS section of the KS
Label Source PDG Document ID Ref.
a thisReview OUR FIT
e FNAL E731 GIBBONS 93,93C [13,14]
f CERN GEWENIGER 74B,74C [15,16]
g CERN NA31 CAROSI 90 [17]
h CERN NA48 LAI 02C [18]
i CERN NA31 BERTANZA 97 [19]
j thisReview SUPERWEAK 10
uncertainty in the unseen parameters. This is also true for the
φSW bands.
If CPT invariance and unitarity are assumed, then by
Eq. (6a), the phase of  is constrained to be approximately
equal to
φSW = (43.5165±0.0002)


where we have linearized the Δm and τS dependence of Eq. (9).
The error ±0.0002 is due to the uncertainty in τL. Here Δm
has units 1010 ¯h s−1 and τS has units 10−10 s.
If in addition we use the observation that Re(/)  1 and
cos(φ − φ)  1, as well as the numerical value of φ given in
Eq. (6b), then Eqs. (5a), which are sketched in Fig. 3, lead to
the constraint
φ00 – φ+− ≈ −3 Im

≈ −3 Re

tan(φ – φ)
≈ 0.006
◦ ± 0.008

, (11)
so that φ+− ≈ φ00 ≈ φ ≈ φSW.
July 30, 2010 14:34
– 7–
φ+ _ (degrees)
τKs (10-10 s)
0.892 0.896 0.900 0.904
Figure 2: φ+− vs τS . τS measurements appear
as vertical bands spanning τS
± 1σ, some
of which are cut near the top and bottom to
aid the eye. Most φ+− measurements appear as
diagonal or horizontal bands spanning φ+−±σφ.
Data are labeled by letters: “b”–FNAL KTeV,
“c”–CERN CPLEAR, “d”–FNAL E773, “e”–
FNAL E731, “f”–CERN, “g”–CERN NA31,
“h”–CERN NA48, “i”–CERN NA31, and are
cited in Table 1. The narrow band “j” shows
φSW. The ellipse “a” shows the fit result’s
χ2 = 1 contour. Color version at end of book.
In the fit assuming CPT, we constrain φ = φSW using the
linear expression in Eq. (10), and constrain φ00 − φ+− using
Eq. (11). These constraints are inserted into the Listings with
the Document ID of SUPERWEAK 10. Some additional data
for which the authors assumed CPT are added to this fit or
substitute for other less precise data for which the authors did
not make this assumption. See the Listings for details.
July 30, 2010 14:34
– 8–
Table 2: Fit results for φ+−, Δm, τS , φ00,
Δφ = φ00 − φ+−, and φ without and with the
CPT assumption.
Quantity(units) Fit w/o CPT Fit w/ CPT
φ+−(◦) 43.4 ± 0.7 (S=1.3) 43.51 ± 0.05 (S=1.1)
Δm(1010¯h s−1) 0.5290 ± 0.0015 (S=1.1) 0.5292 ± 0.0009 (S=1.2)
τS(10−10s) 0.8958 ± 0.0005 0.8953 ± 0.0005 (S=1.1)
φ00(◦) 43.7 ± 0.8 (S=1.2) 43.52 ± 0.05 (S=1.1)
Δφ(◦) 0.2 ± 0.4 0.006 ± 0.014 (S=1.8)
φ(◦) 43.5 ± 0.7 (S=1.3) 43.51 ± 0.05 (S=1.1)
χ2 17.4 21.9
# Deg. Free. 13 17
Figure 3: Sketch of Eqs. (5a). Not to scale.
The results of this fit are shown in Table 2, column 3, “Fit
w/CPT,” and the correlation matrix is shown in Table 4. The
Δm precision is improved by the CPT assumption.
July 30, 2010 14:34
– 9–
Table 3: Correlation matrix for the results of
the fit without the CPT assumption
φ+− Δm τS φ00 Δφ φ
φ+− 1.000 0.778 −0.391 0.837 −0.002 0.977
Δm 0.778 1.000 −0.424 0.665 0.024 0.766
−0.391 −0.424 1.000 −0.327 0.001 −0.382
φ00 0.837 0.665 −0.327 1.000 0.546 0.934
Δφ −0.002 0.024 0.001 0.546 1.000 0.211
φ 0.977 0.766 −0.382 0.934 0.211 1.000
Table 4: Correlation matrix for the results of
the fit with the CPT assumption
φ+− Δm τS φ00 Δφ φ
φ+− 1.000 0.924 0.054 0.711 −0.283 0.964
Δm 0.924 1.000 −0.231 0.834 −0.020 0.958
τS 0.054 −0.231 1.000 0.056 0.009 0.059
φ00 0.711 0.834 0.056 1.000 0.473 0.873
Δφ −0.283 −0.020 0.009 0.473 1.000 −0.018
φ 0.964 0.958 0.059 0.873 −0.018 1.000
Fits for /, |η+−|, |η00|, and B(KL → ππ)
We list measurements of |η+−|, |η00|, |η00/η+−|, and /.
Independent information on |η+−| and |η00| can be obtained
from measurements of the K0L
and K0S
lifetimes (τL, τS ), and
branching ratios (B) to ππ, using the relations
→ π+π−)
→ π+π−)
, (12a)
→ π0π0)
→ π0π0)
. (12b)
For historical reasons, the branching ratio fits and the
CP-violation fits are done separately, but we want to include
the influence of |η+−|, |η00|, |η00/η+−|, and / measurements
on B(K0L
→ π+π−) and B(K0L
→ π0π0) and vice versa. We
July 30, 2010 14:34
– 10–
approximate a global fit to all of these measurements by first
performing two independent fits: 1) BRFIT, a fit to the K0L
branching ratios, rates, and mean life, and 2) ETAFIT, a fit to
the |η+−|, |η00|, |η+−/η00|, and / measurements. The results
from fit 1, along with the K0S
values from this edition, are used
to compute values of |η+−| and |η00|, which are included as
measurements in the |η00| and |η+−| sections with a document
ID of BRFIT 10. Thus, the fit values of |η+−| and |η00| given
in this edition include both the direct measurements and the
results from the branching ratio fit.
The process is reversed in order to include the direct
| η | measurements in the branching ratio fit. The results from
fit 2 above (before including BRFIT 10 values) are used along
with the K0L
and K0S
mean lives and the K0S
→ ππ branching
fractions to compute the K0L
branching ratio Γ(K0L

→ π+π−). This branching ratio value is included
as a measurement in the branching ratio section with a document
ID of ETAFIT 10. Thus, the K0L
branching ratio fit values
in this edition include the results of the direct measurement of
|η00/η+−| and /. Most individual measurements of |η+−| and
|η00| enter our fits directly via the corresponding measurements
of Γ(K0L
→ π+π−)/Γ(total) and Γ(K0L
→ π0π0)/Γ(total), and
those that do not have too large errors to have any influence
on the fitted values of these branching ratios. A more detailed
discussion of these fits is given in the 1990 edition of this
Review [20].
1. K. Kleinknecht, “Uncovering CP violation: experimental
clarification in the neutral K meson and B meson
systems,” Springer Tracts in Modern Physics, vol. 195
(Springer Verlag 2003).
2. B. Winstein and L. Wolfenstein, Rev. Mod. Phys. 65, 1113
3. M.S. Sozzi, Eur. Phys. J. C36, 37 (2004).
4. T.T. Wu and C.N. Yang, Phys. Rev. Lett. 13, 380 (1964).
5. L. Wolfenstein, Phys. Rev. Lett. 13, 562 (1964);
L. Wolfenstein, Comm. Nucl. Part. Phys. 21, 275 (1994).
July 30, 2010 14:34
– 11–
6. G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys.
B603, 125 (2001).
7. R. Adler et al., (CPLEAR Collaboration), Phys. Lett.
B407, 193 (1997);
P. Bloch, Proceedings of Workshop on K Physics (Orsay
1996), ed. L. Iconomidou-Fayard, Edition Frontieres, Gifsur-
Yvette, France (1997) p. 307.
8. A. Lai et al., Phys. Lett. B610, 165 (2005).
9. G. Buchalla, A.J. Buras, and M.E. Lautenbacher, Rev.
Mod. Phys. 68, 1125 (1996);
S. Bosch et al., Nucl. Phys. B565, 3 (2000);
S. Bertolini, M. Fabrichesi, and J.O. Egg, Rev. Mod. Phys.
72, 65 (2000).
10. A. Alavi-Harati et al., Phys. Rev. D67, 012005 (2003);
See also erratum, Alavi-Harati et al., Phys. Rev. D, to be
published, for corrections to correlation coefficients.
11. A. Apostolakis et al., Phys. Lett. B458, 545 (1999).
12. B. Schwingenheuer et al., Phys. Rev. Lett. 74, 4376 (1995).
13. L.K. Gibbons et al., Phys. Rev. Lett. 70, 1199 (1993) and
footnote in Ref. 12.
14. L.K. Gibbons, Thesis, RX-1487, Univ. of Chicago, 1993.
15. C. Geweniger et al., Phys. Lett. 48B, 487 (1974).
16. C. Geweniger et al., Phys. Lett. 52B, 108 (1974).
17. R. Carosi et al., Phys. Lett. B237, 303 (1990).
18. A. Lai et al., Phys. Lett. B537, 28 (2002).
19. L. Bertanza et al., Z. Phys. C73, 629 (1997).
20. J.J. Hernandez et al., Particle Data Group, Phys. Lett.
B239, 1 (1990).
July 30, 2010 14:34

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