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
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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
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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
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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
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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
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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
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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
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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
]2
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Data
! ! !" # !MC K
! 0" !" # !MC K
Trigger cut
First clear observation of the cusp
at 2π threshold
MC O(p6), ĉ=2
m2π
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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
0
20
40
60
80
100
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
0.4 0.45 0.5 0.55
)2 E
ntr
ies
/ (
5 M
eV
/c
0
20
40
60
80
100
]2
mass [GeV/c!-e+Invariant e
0.2 0.25 0.3 0.35
)2 E
ntr
ies
/ (
5 M
eV
/c
0
5
10
15
20
Cut
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
ies
/ (
5 M
eV
/c
0
5
10
15
20
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
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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
200
300
400
500
600
700
MC
Data
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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
20
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
EUROFLAVOUR08 Simone Bifani 17
“Raw” values (no BKG/trigger correction, stat error only)
z distribution is sensitive to the Form Factors and contains all the dynamical information
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)%
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Measurements
NA48/2
‘75 ‘92 ‘99 ‘08
BR
(10-
7 )
Measurements
NA48/2
‘92 ‘99 ‘00 ‘08
δ
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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
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› 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
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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
L1 E
ffic
ien
cy
0
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1
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L2 E
ffic
ien
cy
0
0.1
0.2
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0.5
0.6
0.7
0.8
0.9
1
]2
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Data
0" !" # !
MC K
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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
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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
EUROFLAVOUR08 Simone Bifani 29
z0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Events
0
100
200
300
400
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600
MC
Data
m2π
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No dynamical information from the angle between (e+, π±) in (e+, e–) frame
z distribution is sensitive to the Form Factors and contains all the dynamical information
!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
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