Transcript Particle Physics with Neutrons

2. Quark-Mixing
and the Unitarity of the CKM matrix
100%
50%
0%
'down' 'strange' 'bottom'
down
strange
bottom
|Vud|2 + |Vus|2 + |Vub|2 = 1-
d 

s 

b

d 

 
  UCKM  s 

 

b 
Hartmut Abele, University of Heidelberg
Vud

U CKM  Vcd
V td
V V
V V
V V
us
cs
ts



cb

tb 
ub
1
Unitarity check
Vud

U CKM  Vcd
V td
V V
V V
V V
us
cs
ts
Vub
Vus



cb

tb 
0.00001%
5%
ub
Vud
95%
Mixing of quarks
= rotation in flavor-space:
Test in first row:
|Vud|2 + |Vus|2 + |Vub|2
≈ cos2θ + sin2θ + 0 < 1
?
: Cabibbo
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2.1 Situation 1995 - 2004
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The PDG feels it has the right to redefine anything it wants
1994:
The “centimeters” on the ruler on p. 227 of the booklet
are 0.97 cm long, because:
Is there a general decline of standards?
a) The booklet were returned from the printer at 0.25 times
the speed of light
a) A theorist is in charge of the PDG
b) The PDG feels it has the right to redefine anything it wants
c) There is a general decline of standards
d) There was an international conspiracy
e) It was a congressionally mandated cost-saving measure
f) PDG gives you more cm/inch than anyone else
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Vus
2
GF Vus
2
5 2

mk C f1 (0) I (1  d )(1   R )
3
192π
Kaon semileptonic decays
- K+p0l+nl
- K0Lp-l+nl
sul+nl
= (2.12±0.08%), d= -2.0% for K+ and 0.5% for K0

I+ = 0.1605 ± 0.0009, I0 = 0.1561 ± 0.0008


= (2.56 ± 0.033)10-15 MeV, 0=(4.937 ± 0.053)10-15 MeV
f(0) = 0.961 ± 0.008, f(0) = 0.963 ± 0.004

Vus = 0.2196 ± 0.0017exp ± 0.0018th
= 0.2196 ± 0.0026 (PDG 2002)
Hartmut Abele, University of Heidelberg
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Thesis A. Sher
K+e3
CKM Unitarity: BR(Ke3)
PDG
x (1.1730.054)
Thesis Alexander Sher, 2002
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KL decay
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2.2 Some news in 2005: Vus
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Vud from-nuclear b-decay
Vud = 0.9738(4)
Ft = 3072.7(8)
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2 values
878.5  0.8 sec Serebrov et al.
885.7  0.7 sec PDG 2005 lifetime t [s]
 = 2 x 10-6
Method
year
878.5  0.7  0.3
Storage, low temp.
fomblin
2004
886.8  1.2  3.2
beam method, p trap
2003
885,4  0.9  0.4
storage method of ultracold neutrons
2000
889,2  4,8
beam method
1995
882,6  2,7
storage method of ultracold neutrons
1993
888,4  3,1  1,1
storage method of ultracold neutrons
1992
887,6  3,0
storage method of ultracold neutrons
1989
891  9
beam method
1988
885,7  0,8
world average
2004
PDG
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New projects
Ezhov et al.
prelim:
874.6 +4-1.6 s.
from lambda and
gV:
t = 880.5  1.5s
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Vud
2 values for lifetime
V ud
2
4908  2 sec 878.5  0.8 sec Serebrov et al.

t  (1  3 2 ) 885.7  0.7 sec PDG 2005
t  885.7(7) (PDG2005) :
V ud  0.9711  0.0006  0.0004  0.0002  0.00004
correlation A
lifetime t
outer radiative correction
inner radiative correction
t  878.5(8) :
V ud  0.9748  0.0006  0.0004  0.0002  0.00004
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Vud from neutron b decay
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2.3 Situation 2006
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CKM unitarity summary
Phase of consolidation
Achievements:
- New K results
- New A result
- Halving of the theoretical error in radiative
corrections
Continue to measure lifetime and correlation
coefficients until limited by theory
Lifetime
Formfactors
Q-values
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Transition probability
W dE e d e d n  p e E e (E 0  E e )2dE e d e d n
p e pn
pn
p e  pn
m
pe
e  pe
[1  a
b
  n (A
B
D
R
 N  e )]
E e En
Ee
Ee
Ee
E e En
e E e
correlation N
bncorrelation a
Fierz term b
-11%
0%
basymmetry A
-11%
nasymmetry B
97%
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triple
correlation D
SM: 0
triple
correlation R
SM: 0
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3. Correlation B in neutron b-decay
Neutron Spin

Wd~ (1 + B cos ) d
B

Neutrino
n  p e ne
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3.1Coefficient B, Serebrov et al.
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3.2 Analyzer Tools
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Polarization Analyzer
Method: Serebrov et al.
Pexp
N 0  N1
a  p 


 a p
N 0  N1 1  a  p  (  1)
A:
P
B:
P
C:
P
F
F
F F
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F
A
A
D
A
D
F F
A
D
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Comparison: Supermirrorpolarizer & Heliumspinfilter
O. Zimmer, J. Reich et al.
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Zimmer, Reich et al., Comparison
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SNS: G.L. Greene et al.: A method for the accurate determination of
the polarization using a polarized 3He spin filter
Combination of a
- short-pulse neutron source
(arrival time correlated to
neutron energy)
- polarized 3He neutron spin
filter
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3.4 M. Schumann: The Neutrino-Asymmetry B
Systematically clean method: Integration over two hemispheres
• Electron and Proton in same hemisphere
Neutron Spin
 low dependence on
Electron
energy calibration
and energy resolution
 higher sensitivity due
to larger exp. asymmetry
Proton
Bexp
N  N
 
N  N
Bexp
N  N
 
N
 N
Neutrino
• Electron and Proton in opposite hemispheres
 more statistics since
this case occurs for
~78% of the events
Neutron Spin
Electron
Neutrino
Proton
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Proton detector
Proton
n-Spin
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C foil
Scintillator
Proton detection:
• Measure electron energy
• Wait for proton
• Convert proton into
electron signal
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The ProtonElectron Converter
Detector 1
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Detector 2
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Proton “electron” spectrum
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Dissertation: J. Reich
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C; B: Same hemisphere
Neutron Spin
Proton
Electron
Neutron Spin
Electron
Neutrino
Neutrino
Proton
M. Kreuz et al., PLB 2005
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Results:
B = 0.967±0.012 C = -0.238 ±0.011
M. Kreuz et al. / Physics Letters B 619 (2005) 263–270
Detector 1 (2004)
Corr. [%]
Error [%]
Corr. [%]
Error [%]
+0.3
0.1
+0.3
0.1
Polarization
Flipper-Efficiency
Data Set:
Detector 2 (2004)
Statistics
0.1
0.1
1.17
0.37
(0.04)
acc. Coincidences
PMT afterpulses
Detector: Gain
Offset
Resolution
System:
Edge Effect
Mirror Effect
Displacement
Grid Effect
0.01
0.0
0.0
-0.17
0.05
+0.40
-0.19
0.05
0.40
+0.44
+0.16
0.05
0.358
+0.03
0.05
+0.03
0.05
B = 0.9820.005
Hartmut Abele, University of Heidelberg
0.01
0.05
+0.40
Sum:
<0.01
-0.14
A
a
<0.01
0.03
0.03
0.06
0.06
1.25
+0.77
0.55
preliminary
Dissertaion M. Schumann 2007
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Why do we measure the
Neutrino-Asymmetry B?
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3.5 Origin of nature’s lefthandedness
Standard Model:
Elektroweak interaction 100% lefthanded
Grand unified theories:
Universe was left-right symmetric at the beginning
Parity violation = 'emergent' Order parameter <100%
Neutron decay: Correlation B + A:
Mass right handed W-Boson: mR > 280 GeV/c2
Phase:
-0.20 <  < 0.07
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Why do we measure B?
•
Manifest LeftRightSymmetric Models [eg: PRL 38, 22 (1977)]
• Parity violation: spontaneous symmetry breaking
• 2 bosons (W1, W2) in the „symmetric base“; W2 very heavy
 sin    W1 
 WL   cos
    i
  
i
 WR   e sin  e cos   W2 
•
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m2W1
d 2
mW 2
SM: d= 0, mW2 = 
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3.6 Right handed current contributions
J h  d  (1   5)u  V   A
J l  e (1   5)n  v   a 
Lint 
,
,
  n
1 GV
  p (  (1   5 )  p
 n k n )n  e   (1   5 )n
2 2
2m p
1 GF
 (2.4)
V ud  (V   A  )( v   a  ).
2 2
.
Lint 

L int
1 g2

 (V  A )( v  a )
2 8m 2
1 g2

(V v  A a  (V a  A v))
2 8m 2
1
(1   5 )e
2
1
 (1   5 )e
2
Righthanded :  R e 
Lefthanded :  Le
 sin   W 1 
W L   cos 
 
    i
W R  e sin  e i cos   W 2 
  
 
mW2 1
d 2
mW 2
2
1 g
 
 [(c  (V  A)  s  (V  A))  (c  (v  a )  s  ( v  a ))]
2 8m12
2
1 g
 
 [( s  (V  A)  c  (V  A))  ( s  (v  a )  c  ( v  a ))]
2 8m2 2
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 2 d
 AA  2
 d 1
~
GF
1  VA
1  VA

Vud {V 
[( v - a) 
( v + a )]
2
1  VA
2
  VA
  VA
   A  AA
[( v - a) + AA
( v + a)]}
2
 AA  VA
Lint
G 1  η VA

2
2
G η AA  η VA
gA '

λ
2
2
gV '
VA 
rV 
1  VA
1  VA
  (1  d )
 2d  1
 
rA  AA VA
 AA  VA
 
rA  AA VA
 AA  VA
g A ' η AA  η VA

 λ  λL
gV '
1 - η VA
PF | ψ F | 2
 g V ' M F
2
λ GT/F
2


PGT / M GT
PF / M F
1  rGT
1  rF
2
2
 λL
η AA  η VA
1  η VA

2
2
PGT | ψ GT | 2
2
 g A ' 2 M GT   
2
2


1


  1
 (    )  rF  (    )  (    )  rF  (    ) 
2


 M F  g V ' 2 (1  rF )
2
2
2
2
2
2
ε2  δ2 2
 2 2
λ
ε δ 1
 λ2

2
3
1
3


1
2

 (    )  rGT  (    )  (    )  rGT  (    )
 1  (    )  rGT  (    )


2
 M GT  g A ' (1  rGT )
2
2
2
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Thesis Doehner 1991
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Correlation Coefficients and RHC
Contributions
2  g V ' 2 (1  rF )
ft n
R  0 0 
2
2
ft
g V ' 2 (1  rF )  3  g A ' 2 (1  rGT )
2
2  (1  rF )
2
R
(1  rF )  3  λ L  (1  rGT )
2
2
(1  rF )  3  λ L  (1  rGT )
2
a
2

2
2
(1  rF )  3  λ L  (1  rGT )
A  -2 
B  2 
2
2
2
1  3  λ GT/F
2
2

1  λ GT/F
2
1  3  λ GT/F
2
λ L  (λ L  1)  rGT  λ L  (rGT  λ L  rF )
(1  rF )  3  λ L  (1  rGT )
2
2
2
λ L  (λ L  1)  rGT  λ L  (rGT  λ L  rF )
(1  rF )  3  λ L  (1  rGT )
2
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2
2
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Right Handed Currents?
B=0.983(4)
B=0.983(2)
Exclusion Plot
3 Observables A, B and t
for 3 parameters, m1/m2, , 
A
B
SM
current situation (PDG 2004)
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Herczeg, Gudkov
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3.7 Decay into hydrogen and the origin of
nature’s lefthandedness
n H+n, BR 4 . 10-6
Examine hyperfine
state population
wrong neutrino helicity state!
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