Introduction to High Energy Physics
Final Project - Fall 2007
Introduction to Direct CP Violation in
ultra-rare Kaon decays
Grelli Alessandro
Purdue University
02/07/2016
Grelli
Purdue University –Alessandro
West Lafayette
IN 12/03/2007
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Summary
Summary:
1) Introduction to C, P and CP.
2) CP violation:
- Kaon system.
- Violation in the mixing and direct
3) Ultra-rare kaon decays.
4) K+L→π+νν.
5) K0L→π0νν
- experiments: KTeV and KOPIO
6) Conclusion
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P e C symmetries
P and C symmetries:
P: Physical laws are invariant under coordinates inversion.
Lee e Yung [2] (1956) Hypotesis of C violation in weak interaction
Wu et al.[3] (1957) Experimental proof.
C: Physical invariance over C simmetry: it’s only matter of convention the
definition of particle and anti-particle.
C violation: Neutrino elicity. If you apply C to neutrino you will
have the anti-neutrino with wrong elicity
In 1957 first proposal of CP conservation (Landau). In 1964 Christenson,
Cronin, Fitch e Turlay [4] prove that CP is not true simmetry of nature using
the decay K0→+- (CP Violation).
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CP Violation. K0 system as example 1/2
• Il K0 ~ (sd) e K0 ~ (ds) are eigenstates produced by strong interaction
with strangeness S = +1 ed S = -1.
• The Weak interaction doesn’t preserve S so :
K0  K 0
S  2
• As CP eighenstates :
K1 
1
( K0  K 0 )
2
K2 
1
( K0  K 0 )
2
• CP(K1) = +1 and CP(K2) = -1. if CP is a true simmetry K1 can only
decay in states with CP = +1 and K2 only in CP = -1 states.
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CP Violation. K0 system as example 2/2
• According to Gell-Mann and Pais[1] prevision the mean lifetime of this
states is really different:
 1  (8.927  0.009) 1011 s
 2  (5.17  0.04) 108 s
• Perfect sistem to study CP violation. We can produce beams of pure
K2 and check if happens CP =+1 state decays. (CP violation found in
1964)
Indirect violation
KL 
1
1  L
( K 2   L K1 )
KS 
1
1  S
( K1   S K 2 )
• Experimentally the “indirect” CP violation effect is :
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(103 )
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Direct CP vilation
• In the 70s was born the hypotesis that CP violation can be explained in
SM with the CKM matrix (Cabibbo-Kobajashy -Maskawa).
• This hypotesis introduce the possibility of a DIRECT CP violation (i.e a
violation the decay amplitude). Usually this kind of Violation is
considered with a parameter ε’.
• A value of ε’/ε different from 0 should be a demostration of Direct CP
Violation.
Na48 @ CERN results:
Re(ε’/ε) = (15.3±2.6)x10-4
KTev @ Fermilab results:
Re(ε’/ε) = (20.7±2.8)x10-4
Really little effect but ≠ 0
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Ultra-rare kaon decays
K+L→π+νν (BR~10-10) and K0L→ π0νν (BR~10-11) are FCNC processes
(Flavor Changing Neutral Current) forbidden at tree level in SM and so
they can happen only at second order (1 loop in Feynman dyagram see
next slide).
K0L→ π0νν dominated by Direct CP Violation ( indirect violation suppressed
by a factor ε2 = 106 ).
Direct evidence of K+L→π+νν:
From BNL experiments: 3 events
Proposal for experiment at CERN.
No direct evidence for K0L→π0νν:
Upper limit from KTev (Fermilab)
Several experiments and proposals
in the world .
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K+L→π+νν, K0L→π0νν: Feynman dyagramns
Z-Penguin and W box
Dyagramns: s→dνν
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K+L→π+νν, K0L→π0νν
Hadronic element can be obtained from Kl3 decays.
Very low theoretical uncertains.
For K0l→π0vv theoretical errors smaller than the charge twin (the loop
over c quark in the matrix element is neglegible ~0.1%, only errors from Top
physics) and effect of indirect violation less than 1%. Open a window on
DIRECT CP violation!!!!
Theoretical errors 2-3%
BR(K0l→π0vv ) is related directly to the parameter that take into account
The CP violation in Standard Model.
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Experimental challenges
1.
2.
3.
B.R. from Standard Model: ( 2.8 ± 1.7 ) x 10-11
Experimental Signature:
Only 2 photons.
Without particular technique we don’t know decay vertex and K
energy.
Background:
From K decays.
• 34% of KL decays has 1 or more p0 .
–
–
•
K0L π0 π0
K0L π+π - π0
( B.R. = 9.3 x 10-4)
( B.R. = 1.25 x 10-1)
Miss identification.
– K0L e+π– ( B.R. = 3.9 x 10-1)
– K0L e+π– ( B.R. = 3.6 x 10-3)
Neutrons in the beam halo .
Hyperons decays (Л π0 n).
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KTev Fermilab (USA)
•
•
•
Odoscopio: Drift
Chambers + Magnet.
Electromagnetic
Calorimeter (CsI).
Veto (high prestations).
Upper limit < 5.9 x 10-7.
800 Gev protons, KL average momentum ~ 70Gev/c .
Revelation channel KL0νν
→e+e-γ (Dalitz decay).
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KOPIO Proposal BNL (USA)
Proposal for KOPIO experiment at
BNL (Long Island NY).
Similar experiments at KeK and J-Park in
Japan.
Background Rejection factor from veto
~ 109 additional rejection from
kinematical constrints 102!!.
• Example:
K L0   0 0
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K L0   0
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E  E 2 vs E 0
0 0 odd
*
1
*
*
0 0 even
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Conclusions
A precise measure of ultra-rare kaon decays BR can permit a
determination of the value of direct CP violation with an error similar
(order of magnitude) to the error that we have from B meson sistem.
This is crucial to have a model indipendent determination of direct CP
violation and consequently is a test of CP Standard Model sector.
Some non Standard Models have different predictions for the branching
ration of k0l .
Due to the very low BR (~10-9, 10-11) the experimental detection is very
challenging and is at the limits of the actual tecnology.
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Bibliography
[1]
[2]
[3]
[4]
M. Gell-Mann and A. Pais, Phys. Rev. 97, 1387 (1955).
T.D. Lee and C.N. Yang, Phys. Rev. 104, 254 (1956).
C.S. Wu et al., Phys. Rev. 105, 1413 (1957)
J.H. Christenson, J.W. Cronin, V.L. Fitch, and R. Turlay, Phys. Rev. Lett. 13. 138
(1964).
[5] Gilmann-Wise, Phys.Rev.D21:3150, 1980.
[6] KOPIO Collaboration, KOPIO Conceptual Design Report (2005).
[7] Greenlee, Phys.Rev.D42:3724, 1990.
[8] Littenberg, Phys.Rev.D39:3322,1989.
[9] K.Sakashita, PhD Thesis, Osaka University (2006).
[10] G.C. Branco et al., CP Violation, Clarendon Press, Oxford (1999).
[11] Kazunori Hanagaki, PhD Thesis, Osaka University. (1998).
[12] T.Inagaki et al. KEK proposal, “Measurement of the KL→ 0νν decay” (1996).
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CKM
Matrix – Standard
Model
SM Electroweak
sector. (..hint..)
Operatore
dioperator
corrente describing
debole attraverso
cui vengono
descritte
le
Weak
current
quarks flavor
transitions
can be
transizioni tra quarks di diverso sapore:
Written as in the following:
1
The W boson cupling is obtained with the lagrangian:
The Vij matrix in 1 is the CKM matrix:
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SM Electroweak sector. (..hint..)
...Sorry for the Italian language
Wolfenstein paramerization of CKM matrix. All the CP violation effects are
Taken into account in η parameter (the complex phase):
This is a Unitary 3x3 matrix: Imposing the unitarity condition you can
paint the unitarity triangle. The BR of KOPIO decay can mesure the
height of the tringle.
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Unitarity Triangle
triangle
Unitarity
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Past, Present and Future experiments
KOPIO
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