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Introduction to High Energy PhysicsIntroduction to High Energy PhysicsFinal Project - Fall 2007Final Project - Fall 2007

Purdue University – West Lafayette IN 12/03/2007Purdue University – West Lafayette IN 12/03/2007

Introduction to Direct CP Introduction to Direct CP Violation inViolation in

ultra-rare Kaon decaysultra-rare Kaon decays

Grelli Alessandro Purdue University

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SummarySummary

1)1)Introduction to C, P and CP.Introduction to C, P and CP.2) CP violation:CP violation:

- Kaon system.- Kaon system.

- Violation in the mixing and direct- Violation in the mixing and direct

3)3)Ultra-rare kaon decays.Ultra-rare kaon decays.4) KK++

LL→→ππ++νννν.

5) 5) KK00LL→→ππ00νννν

- experiments: - experiments: KTeVKTeV and and KOPIOKOPIO

6) ConclusionConclusion

Summary:Summary:

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P e C symmetriesP e C symmetries

P and C symmetries:

PP: Physical laws are invariant under coordinates inversion.

Lee e Yung [2] (1956) Hypotesis of C violation in weak interactionWu et al.[3] (1957) Experimental proof.

CC: 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 TurlayChristenson, 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. KCP Violation. K00 system as example 1/2 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 :

200 SKK

• As CP eighenstates :

)(2

1)(

2

1 002

001 KKKKKK

• 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. KCP Violation. K00 system as example 2/2 system as example 2/2

• According to Gell-Mann and Pais[1] prevision the mean lifetime of this states is really different:

ss 82

111 10)04.017.5(10)009.0927.8(

)(1

1)(

1

12112 KKKKKK S

S

SL

L

L

• 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)

• Experimentally the “indirect” CP violation effect is :

)10( 3

Indirect violation

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Direct CP vilationDirect 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 decaysUltra-rare kaon decays

K+L→π+νν (BR~10-10) and K0

L→ 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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KK++LL→→ππ++νννν, K, K00

LL→→ππ00νννν: Feynman dyagramns: Feynman dyagramns

Z-Penguin and W box

Dyagramns: s→dνν

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KK++LL→→ππ++νννν, K, K00

LL→→ππ00νννν

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→π

0vv ) is related directly to the parameter that take into account

The CP violation in Standard Model.

Hadronic element can be obtained from Kl3 decays.

Very low theoretical uncertains.

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1.1. B.R. from Standard Model:B.R. from Standard Model: ( 2.8 ± 1.7 ) x 10( 2.8 ± 1.7 ) x 10-11-11

2.2. Experimental Signature:Experimental Signature: Only 2 photons.

Without particular technique we don’t know decay vertex and K

energy.3. Background3. Background::

From K decays.• 34% of KL decays has 1 or more p0 .

– K0L π0 π0 ( B.R. = 9.3 x 10-4)

– K0L π+π - π0 ( B.R. = 1.25 x 10-1)

• Miss identification.– K0

L e+π– ( B.R. = 3.9 x 10-1) – K0

L e+π– ( B.R. = 3.6 x 10-3) Neutrons in the beam halo . Hyperons decays (Л π0 n).

Experimental challengesExperimental challenges

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KTev Fermilab (USA)KTev Fermilab (USA)

800 Gev protons, KL average momentum ~ 70Gev/c .

Revelation channel KL0νν

→e+e-γ (Dalitz decay).

• Odoscopio: Drift Chambers + Magnet.

• Electromagnetic Calorimeter (CsI).

• Veto (high prestations).

Upper limit < 5.9 x 10Upper limit < 5.9 x 10-7-7..

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KOPIO Proposal BNL (USA)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 ~ 101099 additional rejection from kinematical constrints 101022!!.!!.

0 0 even0 0 odd000 LK 00 LK

**2

*1 0 EvsEE • Example:

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ConclusionsConclusions

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 k0

l .

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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BibliographyBibliography

[1] [1] M. Gell-Mann and A. Pais, M. Gell-Mann and A. Pais, Phys. RevPhys. Rev. 97, 1387 . 97, 1387 (1955)(1955)..

[2][2] T.D. Lee and C.N. Yang, T.D. Lee and C.N. Yang, Phys. Rev.Phys. Rev. 104, 254 104, 254 (1956)(1956)..

[3][3] C.S. Wu et al., C.S. Wu et al., Phys. RevPhys. Rev. 105, 1413 . 105, 1413 (1957)(1957)

[4][4] J.H. Christenson, J.W. Cronin, V.L. Fitch, and R. Turlay, J.H. Christenson, J.W. Cronin, V.L. Fitch, and R. Turlay, Phys. Rev. Phys. Rev. Lett.Lett. 13. 138 13. 138 (1964)(1964)..

[5][5] Gilmann-Wise, Gilmann-Wise, Phys.RevPhys.Rev.D21:3150, .D21:3150, 1980.1980.

[6][6] KOPIO Collaboration, KOPIO Conceptual Design Report KOPIO Collaboration, KOPIO Conceptual Design Report (2005)(2005)..

[7][7] Greenlee, Greenlee, Phys.RevPhys.Rev.D42:3724, .D42:3724, 1990.1990.

[8][8] Littenberg, Littenberg, Phys.RevPhys.Rev.D39:3322,.D39:3322,1989.1989.

[9][9] K.Sakashita, PhD Thesis, Osaka University K.Sakashita, PhD Thesis, Osaka University (2006)(2006)..

[10][10] G.C. Branco et al., CP Violation, Clarendon Press, Oxford G.C. Branco et al., CP Violation, Clarendon Press, Oxford (1999)(1999)..

[11][11] Kazunori Hanagaki, PhD Thesis, Osaka University. Kazunori Hanagaki, PhD Thesis, Osaka University. (1998)(1998)..

[12][12] T.Inagaki et al. KEK proposal, “Measurement of the K T.Inagaki et al. KEK proposal, “Measurement of the KLL→ → 0νν decay”” (1996)(1996)..

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........ B

ackup slides ....

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CKM Matrix – Standard ModelCKM Matrix – Standard Model

Operatore di corrente debole attraverso cui vengono descritte le transizioni tra quarks di diverso sapore:

The W boson cupling is obtained with the lagrangian:

The Vij matrix in 1 is the CKM matrix:

1

Weak current operator describing quarks flavor transitions can beWritten as in the following:

SM Electroweak sector. SM Electroweak sector. (..hint..)

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...Sorry for the Italian language...Sorry for the Italian language SM Electroweak sector. (..hint..)SM Electroweak sector. (..hint..)

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 TriangleUnitarity TriangleUnitarity triangleUnitarity triangle

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Past, Present and Future experimentsPast, Present and Future experiments

KOPIO