Simone Bifani - IPPP Conference Management System (Indico) · 2008. 9. 22. · EUROFLAVOUR08 11...

Simone Bifani University of Bern

on Behalf of the NA48/2 Collaboration Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz,

Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Vienna

EuroFlavour 2008 IPPP, Durham (United Kingdom), 22nd – 26th September 2008

EUROFLAVOUR08 Simone Bifani 2

› NA48/2 Experimental Setup

› K± -> π±γγ: Branching Ratio

› K± -> π±e+e-γ: Branching Ratio and Spectrum Shape

› K± -> π±e+e-: Branching Ratio and Form Factors


NA48 (1997-2001): Direct CP-Violation in neutral K

>  Re(ε’/ε) = (14.7 ± 2.2)·10-4

NA48/1 (2002): Rare KS decays

>  BR(KS -> π0e+e-) = (5.8+2.8-2.3 ± 0.8)·10-9

>  BR(KS -> π0µ+µ-) = (2.8+1.5-1.2 ± 0.2)·10-9

NA48/2 (2003-2004): Direct CP-Violation in charged K

> Ag(K± -> π±π+π-) = (-1.5 ± 2.1)·10-4

> Ag(K± -> π±π0π0) = (1.8 ± 1.8)·10-4

P326 / NA62 (2006-2012): Very Rare K Decays

>  K+ -> π+νν

1997 ε’/ε KL & KS

1998 KL & KS

1999 KL & KS KS HI

2000 KL Only KS HI

2001 KL & KS KS HI

2002 KS & Hyperons HI

2003-2004 K+ & K-

2006-2010 Design & Construction

2007-2008 Ke2/Kµ2 Tests

2011-2012 K+ -> π+νν


Beams coincide within ~ 1 mm all along 114 m

decay volume

Simultaneous K+ and K- beams: large charge symmetrization of experimental conditions

2÷3 M K/spill (π/K ~ 10) π decay products stay in pipe

Flux ratio: K+/K– ~ 1.8

Second chromat: Cleaning

Beam Spectrometer

δPK/PK = 0.7% δx,y ~ 100 µm

~7⋅1011 p/spil

400 GeV/c

Front-End Achromat: Momentum Selection

Quadrupole, Quadruplet:

Focusing µ Sweeping

PK = (60±3) GeV/c

54 60 66

Width ~ 5 mm

K+/K- ~ 1 mm


Beam pipe

Magnetic Spectrometer (4 DCHs): >  4 view / DCH -> high efficiency >  σP/P = 1.0% + 0.044%·P [GeV/c] Hodoscope: >  Fast trigger >  σt = 150ps Electromagnetic Calorimeter (LKr): > High granularity, quasi-homogeneous >  σE/E = 3.2%/√E + 9%/E + 0.42% [GeV] Hadron Calorimeter, Muon and Photon Vetoes

Trigger: >  Fast hardware trigger (L1): hodoscope & DCHs multiplicity >  Level 2 trigger (L2): on-line processing of DCHs & LKr information


A view of the NA48/2 beam line

Run periods: > 2003: ~ 50 days > 2004: ~ 60 days

Total collected statistics: > K± -> π±π+π-: ~ 4·109

> K± -> π±π0π0: ~ 1·108

>200 TB of data recorded

Rare K± decays can be measured down to BR ~ 10–9


In the Chiral Perturbation Theory framework the differential rate of the K±(p) -> π±(p3) γ(q1) γ(q2) process (no O(p2) contribution) is:

› The leading contribution @ O(p4) is given by A(z,ĉ) (loops) which is responsible for a cusp at mγγ = m2π

› C (WZW) corresponds to ~10% of A @ O(p4) › B, D = 0 @ O(p4)

› O(p6) unitarity corrections can increase the BR by 30÷40%

G. Ecker, A. Pich, E. de Rafael, Nucl. Phys. B303 (1988), 665

G. D’Ambrosio and J. Portoles, Nucl. Phys. B386 (1996), 403

€

y =p ⋅ q1 − q2( )m

K ±2

z =q1 + q2( )2

mK ±2 =

mγγ2

mK ±2

€

∂2Γ∂y∂z

=m

K ±

8π( )3⋅ z2 ⋅ A + B 2

+ C 2( ) + y 2 − 14λ 1,z,rπ

2( )

2

⋅ B 2+ D 2( )

relevant only @ low mγγ


Both decay spectrum and rate strongly depend on the single ĉ parameter (O(1)):

BR(K+ -> π+γγ) = (5.26 + 1.64·ĉ + 0.32·ĉ2 + 0.49)·10-7 ≥ 4·10-7

unitarity corrections mγγ spectrum

cusp-like behaviour at 2π threshold

m2π

EUROFLAVOUR08 11

Previous measurement by E787 (31 candidate, 5.1 ± 3.3 background events):

BR(π+γγ) = (1.10 ± 0.32)·10-6 Event Sample (~40% of the full statistics): ›  K± -> π±π0 as normalization ›  K flux: ΦK = 2.06·1010 ›  1164 candidate events ›  3.3% background (K± -> π±π0γ)

Shape Analysis: › MC O(p6) and ĉ = 2 for comparison › Data shape follows ChPT prediction ›  Possibility of precise ĉ measurement

but no quantitative result yet

BR(K± -> π±γγ)= (1.07 ± 0.04stat ± 0.08syst)·10-6 assuming O(p6) distribution and ĉ = 2

Simone Bifani

]2

[GeV/c!!"m0.475 0.48 0.485 0.49 0.495 0.5 0.505 0.51

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Data

! ! !" # !MC K

! 0" !" # !MC K

mK = 493.7 ± 4.3 MeV/c2

χ2/ndf = 25.2 / 21

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! ! !" # !MC K

! 0" !" # !MC K

Trigger cut

First clear observation of the cusp

at 2π threshold

MC O(p6), ĉ=2

m2π


BR(K± -> π±e+e-γ) = (1.19 ± 0.12stat ± 0.04syst)·10-8

Never observed before. Naïve estimation of the BR:

K± -> π±γ*γ -> π±e+e-γ BR(π±e+e-γ) = BR(π±γγ)·2α ~ 1.6·10-8

Theoretical expectation: BR(π±e+e-γ) = (0.9÷1.6)·10-8

Event Sample (full statistics): › K± -> π±π0

D as normalization › K flux: ΦK = 1.48·1011 › 120 candidate events › 6.1% background (K± -> π±π0

Dγ)

Model-Independent BR (meeγ > 260 MeV/c2):

]2

mass [GeV/c!-e+e!"Invariant

0.4 0.45 0.5 0.55

)2 E

ntr

ies

/ (

5 M

eV

/c

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Cut

Data

D

0"0"+" #+K

!D

0"+" #+K

-e+e0"+" #+K-e+e+" #+K

$+eD

0" #+K

]2

mass [GeV/c!-e+e!"Invariant

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Data

!D

0"+" #+

K-e+e0"+" #+K

-e+e+" #+K

D

0"+" #+

K

D

0"0"+" #+

K

]2

mass [GeV/c!-e+Invariant e

0.2 0.25 0.3 0.35

)2 E

ntr

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/ (

5 M

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/c

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Gabbiani, PRL D59, 094022

Shape Analysis: ĉ has been extracted by fitting data to the absolute O(p4) ChPT prediction

]2

mass [GeV/c! -

e+

Invariant e

0.25 0.3 0.35

9 1

0!

)

2 B

r /

(5 M

eV

/c"

0

0.5

1

1.5

Cut

ĉ = 0.9 ĉ = 1.8

EUROFLAVOUR08 13 Simone Bifani

ĉ = (0.90 ± 0.45) χ2/ndf = 8.1 / 17

Prob = 96.4%

Gabbiani, Phys. Rev. Lett. D59 (1999), 094022

Phys. Lett. B659 (2008), 493

1.2σ away from BNL E787 value in K+ -> π+γγ: ĉ = 1.8 ± 0.6

K± -> π±γ* -> π±l+l–: suppressed FCNC process proceeding through one-photon exchange. Weak interactions at low energy, ChPT tests

Form Factors: 1)  Linear: W(z) = GF·mK

2·f0·(1 + δ·z) 2)  ChPT O(p6): W(z) = GF·mK

2·(a+ + b+·z) + Wππ(z) 3)  Dubna ChPT: W(z) = W(Ma, Mρ, z)

(f0, δ) or (a+, b+) or (Ma, Mρ) fully determine a Model-Dependent BR

Goals: › Model-Independent BR(z > 0.08) in visible kinematic range ›  Parameters of models and BRs in the full kinematic range

dΓ/dz ~ P(z)·|W(z)|2 z = (mee/mK)2 P(z) = phase space factor

Dubnickova et al. hep-ph/0611175


D’Ambrosio et al. JHEP 8 (1998), 4

2), GeV/c-e+e!!M(0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53

Ev

en

ts

0

100

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400

500

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700

MC

Data


Event Sample (full statistics): › K± -> π±π0

D as normalization › K flux: ΦK = 1.70·1011 › 7146 candidate events › 0.6% background/signal (K± -> π±π0

D, K± -> π0De±ν + particle mis-ID)

2), GeV/c

D0!!!M(

0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56

Ev

en

ts

210

310

410

510

610

3D"K D!2K

MC

Data

z distribution is sensitive to the Form Factors and contains all the dynamical information

Model-Independent BRMI(z > 0.08) computed by integrating dΓ/dz

δ = 2.42 ± 0.15 f0 = 0.529 ± 0.012

ρ(δ, f0) = –0.963

a+ = –0.576 ± 0.012 b+ = –0.830 ± 0.053

ρ(a+, b+) = –0.913

Ma = (0.951 ± 0.028) [GeV] Mρ = (0.705 ± 0.010) [GeV]

ρ(Ma, Mρ) = 0.998 z

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

2/d

z, G

eV

/c!

d

0

10

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30

40

50

60

-2410!

(1)

(2)

(3) /ndf=22.0/192"

/ndf=29.0/192"

/ndf=33.4/192"

Linear (1):

ChPT (2):

Dubna ChPT (3):

The models can not be distinguished with the

available data set


“Raw” values (no BKG/trigger correction, stat error only)


Including uncertainty due to the model dependence (full z range):

CPV parameter (first measurement):

BRMI·107 = 2.26 ± 0.03stat ± 0.03syst ± 0.06ext = 2.26 ± 0.08

δ = 2.35 ± 0.15stat ± 0.09syst = 2.35 ± 0.18 f0 = 0.532 ± 0.012stat ± 0.008syst ± 0.007ext = 0.532 ± 0.016

BR1·107 = 3.02 ± 0.04stat ± 0.04syst ± 0.08ext = 3.02 ± 0.10

a+ = –0.579 ± 0.012stat ± 0.008syst ± 0.007ext = –0.579 ± 0.016 b+ = –0.798 ± 0.053stat ± 0.037syst ± 0.017ext = –0.798 ± 0.067

BR2·107 = 3.11 ± 0.04stat ± 0.04syst ± 0.08ext = 3.11 ± 0.10

Ma = 0.965 ± 0.028stat ± 0.018syst ± 0.002ext = 0.965 ± 0.033 [GeV/c] Mρ = 0.711 ± 0.010stat ± 0.007syst ± 0.002ext = 0.711 ± 0.013 [GeV/c]

BR3·107 = 3.15 ± 0.04stat ± 0.04syst ± 0.08ext = 3.15 ± 0.10

BR(K± -> π±e+e-) = (3.08 ± 0.04stat ± 0.04syst ± 0.08ext ± 0.07model)·10–7

Δ(K± -> π±e+e-) = (BR+–BR–) / (BR++BR–) = (–2.1 ± 1.5stat ± 0.3syst)%


Measurements

NA48/2

‘75 ‘92 ‘99 ‘08

BR

(10-

7 )

Measurements

NA48/2

‘92 ‘99 ‘00 ‘08

δ


Measurement BR·107

Bloch et al., PL 56 (1975), B201 2.70 ± 0.50

Alliegro et al., PRL 68 (1992), 278 2.75 ± 0.26

Appel et al. [E865], PRL 83 (1999), 4482 2.94 ± 0.15

NA48/2 preliminary 3.08 ± 0.12

Measurement δ

Alliegro et al., PRL 68 (1992), 278 1.31 ± 0.48

Appel et al. [E865], PRL 83 (1999), 4482 2.14 ± 0.20

Ma et al. [E865], PRL 84 (2000), 2580 2.45+1.30–0.95

NA48/2 preliminary 2.35 ± 0.18


› Precise study of the K± -> π±γγ decay (BR ~ 10–6) ›  Clear evidence for a cusp at mγγ = m2π, first possibility for shape study › Measured BR in agreement with ChPT › Shape analysis and a larger sample coming soon

› First observation of the K± -> π±e+e–γ decay (BR ~ 10–8) › An independent evidence for the cusp at mγγ = m2π › Measurement of Shape and the BR finalized

› Precise study of the K± -> π±e+e– decay (BR ~ 10–7) › Sample & precision comparable to world’s best ones ›  BR and Form Factors in agreement with ChPT and other

measurements ›  First limit on the CPV Asymmetry obtained

PASCOS08 Simone Bifani 23

In the Chiral Perturbation Theory framework the differential rate of the K±(p) -> π±(p3) γ(q1) γ(q2) process (no O(p2) contribution) is:

The leading contribution @ O(p4) is given by: €

dΓdz

=m

K ±5

2 8π( )3⋅ z2 ⋅ λ1 2 1,z,rπ

2( ) ⋅ A z( )2

+ C z( )2[ ]

€

z =q1 + q2( )2

mK ±2 =

mγγ2

mK ±2 , 0 < z < 1− rπ( )2, rπ =

mπ ±

mK ±

, λ a,b,c( ) = a2 + b2 + c 2 − 2 ab + ac + bc( )

€

A z, ˆ c ( ) =G8aem

2π ⋅ z⋅ rπ

2 −1− z( ) ⋅ F zrπ

2

+ 1− z − rπ

2( ) ⋅ F z( ) + ˆ c ⋅ z

π loop K loop tree level counterterm

K± -> π±γγ

K± -> π±γ*γ -> π±e+e-γ



MC K+→→→→ ππππ+ππππ0

MC K+→→→→ ππππ+γγγγγγγγ

• Bad trigger conditions:- Selected through neutral trigger:

L1 required more than 2 clusters in e.m. calorimeter !!!! 50% efficiency.L2 rejected K±→→→→ ππππ±ππππ0 decays (BR=20.92%!!)

cutting on ECMππππ: 80% efficient.

Br (K±!ππππ±γγ)

mfake= !!2mKECMπ [GeV/c2]

C. Morales. Rencontres de Moriond. QCD 2008. 13

• Due to low amount of statistics, trigger efficiencies not measured with K±→ π± γγ data.- Solution: use background events

& study dependencies on kinematic variables:

EffL1(ptrack,dc1c2), EffL2(ptrack,zvertex,rbeampipe)

& use MC K±→ π± γγ to “reshape” variables and integrate

BR(BR(ππππ±±±±γγγγγγγγ) = ) = 11 x x (#(#ππππ±±±±γγγγγγγγ) ) -- (#(#bkgbkg))!!fluxflux AccAcc((ππππ±±±±γγγγγγγγ) x ) x EffEff

Eπ [GeV]

EffL1,L2 = "n ( #MC(v1,...vn) x EffL1,L2(v1,...vn))

"n ( #MC(v1,...vn) )

]2 [GeV/c!!m0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

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Data

0" !" # !

MC K

EUROFLAVOUR08 26 Simone Bifani

BG suppression: › many BG sources considered and

evaluated with MC › meeγ > 260 MeV/c2 (low BG area) › cut on θeγ to reject K± -> π±e+e-

› 480 MeV/c2 < mπeeγ < 505 MeV/c2 (K mass)

Event selection: › at least 3 tracks with Qtot=±1

and compatible decay vertex › at least 1 cluster not associated

to track › E/p > 0.94 for e±, E/p < 0.8 for π±

› 54 GeV < Etot < 66 GeV


Common selection criteria: 3-track vertex [consistent in space/time]

1 π candidate, 2 opposite sign electron candidates Electron (pion) ID based on E deposition : E/p > 0.95 (E/p < 0.85)

Signal selection: Kinematic suppression of π±π0

D background: mee > 140 MeV/c2. Limitations on reconstructed

π±e+e– invariant mass, total & transverse momentum

Normalization selection: Selection of good γ candidate. Limitations on reconstructed

e+e–γ and π±e+e–γ masses, total & transverse momentum

The K± -> π±e+e– is measured normalizing to K± -> π±π0D -> π±e+e–γ,

thus particle ID efficiencies cancel in the first order


z0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Events

0

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600

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Data

m2π


No dynamical information from the angle between (e+, π±) in (e+, e–) frame


!e"cos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Events

0

50

100

150

200

250

300

€

dΓdϑ

~ sin2ϑ = 1− cos2ϑ( )

z = (mee / mK)2

Parameter Electron ID

Beam Simulation

Radiative Corrections

Background to K± -> π±e+e–

Trigger Inefficiency

Fitting Procedure

External (PDG)

BRMI·107 0.02 0.01 0.01 –0.01±0.01 –0.01±0.01 - 0.06 Model (1): Linear

δ 0.01 0.04 0.05 –0.04±0.04 –0.03±0.03 0.03 - f0 0.001 0.006 0.004 +0.002±0.002 +0.001±0.001 0.003 0.007

BR1·107 0.02 0.02 0.01 –0.01±0.01 –0.01±0.01 0.02 0.08 Model (2): O(p6) ChPT [D’Ambrosio, Ecker, Isidori, Portoles, hep-ph/9808289]

a+ 0.001 0.005 0.004 –0.001±0.001 –0.002±0.002 0.004 0.007 b+ 0.009 0.015 0.022 +0.017±0.017 +0.015±0.015 0.010 0.017

BR2·107 0.02 0.02 0.01 –0.01±0.01 –0.01±0.01 0.02 0.08 Model (3): Dubna ChPT [Pervushin et al., hep-ph/0611175]

Ma/GeV 0.004 0.009 0.009 +0.008±0.008 +0.006±0.006 0.006 0.002 Mρ/GeV 0.002 0.003 0.004 +0.003±0.003 +0.003±0.003 0.002 0.002 BR3·107 0.02 0.02 0.01 –0.01±0.01 –0.01±0.01 0.02 0.08


Simone Bifani - IPPP Conference Management System (Indico) · 2008. 9. 22. · EUROFLAVOUR08 11...

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