Post on 21-Jan-2016
description
Recent results from NA48/2 on pion scattering lengths using Ke4 decay
and cusp in K±->π±π0π0
Stefano VendittiStefano Venditti
University of Pisa & University of Pisa & INFNINFN
QCD@WORK 2007
On behalf of the NA48/2 collaboration:
Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa Saclay,
Siegen, Torino, Wien
QCD@WORK 2007Stefano Venditti 17/06/2007
Outline
• The NA48/2 experiment;
• Ke4: theory and NA48/2 analysis;
• Ke4: results for form factors and interpretation in terms of pion scattering lengths (a0,a2);
• Cusp: K3pi theory and analysis;
• Cusp: fit procedure and extraction of (a0-
a2);
• Conclusions.
NA48/2 beam line
K+
K−
PK spectra, 603 GeV/c
54 60 66
QCD@WORK 2007Stefano Venditti 17/06/2007
Detectors
K+/K- flux~1.8
Width ~ 5mm
K+/K- ~ 1mm
Beams coincide within 1 cm over 114 m of
decay volume
Incoming SPS 400 GeV protons
NA48 DETECTORS
•Spectrometer:
4 DCHs -> redundancy.
σp/p=1.0%+0.044%× p(p in GeV);
•Liquid Krypton EM calorimeter:
16000 cells -> high granularity.
σE/E=3.2%/√E + 9%/E + 0.42%;
•Hodoscopes (charged, neutral):
Trigger, time measurement.
•Muon veto, Hadronic calo, Kabes, photon vetoes.
Stefano Venditti 17/06/2007QCD@WORK 2007
QCD@WORK 2007Stefano Venditti 17/06/2007
NA48/2 DATA:
20032003 run: run: ~ 50 ~ 50 daysdays
20042004 run: run: ~ 60 ~ 60 daysdays
Ke4:
0.68 M events
(from 2003 data only)
K3pi:
~ 108 events
(greatest K3pi sample ever collected)
EVENTS SELECTED FOR K±->π±π±e±ν AND K±->π±π0π0:
QCD@WORK 2007Stefano Venditti 17/06/2007
Ke4:Theory
4 body decay->5 independent variables
Using Cabibbo-Maksymowicz variables:
Sπ(Mππ2),Se(Meν2),cosθπ,cosθe,ΦHadronic ME:<π+π-|Aλ+Vλ|K>=(1/MK)[FPλ+GQλ+R(K-P)λ+(H/M2)ελμνσKμPνQσ]
F,G,R: axial form factorsH: vector form factor
K
e+
π-
π+
ν
θπ θe
Φ
Partial wave expansion of amplitude:
F = Fseiδs + Fpe
iδp cosθπ +d-wave terms
G = Gpeiδg + d-wave terms
H = Hpeiδh + d-wave termsFit parameters: Fs , Fp , Gp , Hp
, δ=δs-δp
R negligible
(relevant in Kμ4)
f.f. expansion wrt Se, q2:
Fs=fs+f’sq2+f’’sq
4+fe(Se/
4mπ2)+…
Fp=fp+f’pq2+…
Gp=gp+g’pq2+…
Hp=hp+h’pq2+…
q2=(Sπ/4mπ2)-1
(Pλ=dipion 4V; Qλ=dilepton 4V; Kλ=kaon 4V)
QCD@WORK 2007Stefano Venditti 17/06/2007
Ke4 Analysis: selection and BG rejectionKe4-> 3 charged tracks (2 opposite sign pions),1 ν. BR ~ 4 ·
10-5
K±
e±
ν
π- π+
• Spectrometer for momenta measurement;
• LKR info used to tag electron and pions (E/p);
• Missing energy and Pt (because of neutrino).
BG checked with data: wrong sign events have same total charge but wrong electron charge (es:e+π-π- for K- decay):their contribution to total BG is the same or is to be rescaled by a factor 2 wrt “real” BG, depending on the process.
PkMke4
Background, main sources:
• π±π+π-, with π->eν in-flight decay or π misidentified as e;
• π±π0,π±π0π0,with π0->e+e-γ Dalitz decay and,e misidentified and γ(s) undetected.
QCD@WORK 2007Stefano Venditti 17/06/2007
Data/MC comparison
Mππ Meν
cosθπ cosθe
GeVGeV
QCD@WORK 2007Stefano Venditti 17/06/2007
Ke4 analysis: fitting procedureIso-populated 10(Mππ)x5(Meν)x5(cosθe)x5(cosθπ)x12(Φ)=15000 bins
in the C-M variables used. Form factor values used to minimize a log-likehood estimator well-suited for small numbers.
K+: Data: 435654 events,29 evts/box
MC: 10.0 M events,~667 evts/box
K-: Data: 241856 events,16 evts/box
MC: 5.6 M events,~373 evts/box
K+/K-~1.8 (both data and MC)
MC/Data~23 (both K+ and K-)
Ten independent fits in Mππ bins, assuming constant f.f. over single bins.
• no normalization->only relative f.f. and their variation wrt kinematical variables;
• residual variation (linear slope) observed wrt Mev for Fs: 2-dim fit performed;
• Fs from bin/bin normalization after fit.
Fs2~(1+f’s q2 + f’’s q4 +f’e Se/4mπ
2)2
QCD@WORK 2007Stefano Venditti 17/06/2007
fp,hp≠0, no q2
dependencegp linear wrt q
2
Correlation:
gp
g’p
-0.914
QCD@WORK 2007Stefano Venditti 17/06/2007
Ke4: form factors results• Relative form factors:
f.f./Fs(0);
• measured separatedly for K+,K- and then combined;
• Fs obtained from bin/bin normalization,Fp,Gp,Hp deconvoluted from observed Fs(q2,Se) variation.
SYSTEMATIC CHECKS
• Two independent analyses;
• Acceptance control;
• BG level and shape control;
• Radiative correction included;
• Possible bin-to-bin correlation considered.
f’s/fs=0.165±0.011±0.006
f’’s/fs=-0.092±0.011±0.007
f’e/fs=0.081±0.011±0.008
fp/fs=-0.048±0.004±0.004
gp/fs=0.873±0.013±0.012
g’p/fs=0.081±0.022±0.014
hp/fs=-0.411±0.019±0.007
value±stat.±syst.
All f.f. parameters measured within5% to 15% relative precision
QCD@WORK 2007Stefano Venditti 17/06/2007
Ke4: δ phase shift and a0,a2 extraction• Extraction of pion scattering lengths from δ=(δ0
0-δ11) phase
shift can be done through external experimental and theoretical (e.g. Roy equation) inputs, which relate δ and (a0,a2);
• The Universal Band parameterization corresponds to a 1-dimensional fit of δ with a fixed relation between a0 and a2.
QCD@WORK 2007Stefano Venditti 17/06/2007
Ke4: comparison with other experiments• Thanks to the independent bin analysis, the scattering
length extraction can be performed on old data even if the collaboration doesn’t exist anymore;
• E865 quotes values ranging from a0=0.203 to a0=0.237, NA48 seems to obtain slightly higher values;
• Further checks are ongoing to understand the two different results, expecially in the last Mππ bin.
a0=0.25
a0=0.20
QCD@WORK 2007Stefano Venditti 17/06/2007
Plane (a0,a2): theory and experiments• Several equations
relating a0 and a2 exist (ACGL,DFGS,…)
• A 2-dimensional fit (on a0 and a2) can also be performed (dotted lines in figure,centered on best χ2 and including 68% of events);
• E865 and NA48/2 point at slightly different regions of the universal band; removing the last E865 bin brings the two results closer and decreases χ2.Isospin breaking corrections neglected so far. This contribution was considered negligible until short time ago. Calculations to apply this correction are ongoing.
QCD@WORK 2007Stefano Venditti 17/06/2007
K3pi:selection
Dik
ZijZkl
LKR
• For each photon pair (e.g. i,j) a decay vertex reconstructed along beam axis assuming π0 mass:
m02=2EiEk(1-cosβ)~EiEk(Dik)
2/(Zik)2
Zik;
• Pair of photons minimizing ΔZ=Zjl-Zik chosen;
• Compatibility within ± 6 MeV wrt PDG kaon
mass requested.
ΔZ
γ
γγ
γ
DjlK
m0: pion massEi,Ej: γ energiesZik: π0 vertex distance from LKR
ππ invariant mass
Excellent at low Mππ values
++0000 invariant mass, GeV/c invariant mass, GeV/c22
Resolution: 0.9 MeV/c2 MKPDG ± 6 MeV
cut
59.3M K59.3M K++ contribution
32M K32M K--
QCD@WORK 2007Stefano Venditti 17/06/2007
Primary goal: asymmetry measurement Dalitz
variables:
u=(s3-s0)/π2
v=(s2-s0)/π23s0=Mk2+Mπ2+2Mπ0
2
si=(Pk-Pi)2
(i=1,2,3;3=odd pion)
Matrix element:
|M(u,v)|2 ~1+gu+hu2+kv2+...
K+
π+(even)
π+(even)
π-(odd)
−+
−+
+−
=gg
ggAg Ag≠0->direct CP
violation
v
uK±→±00 dalitz plot
Comparison between Dalitz plot distribution for K+ and K- to look for direct CP violation.
•SM Ag predictions in range 10-6-10-5;
•Beyond SM models enhance the prediction;
QCD@WORK 2007Stefano Venditti 17/06/2007
Slope difference: Δg=(2.2±2.1stat±0.7syst)·10-4
Charge asymmetry: Ag=(1.8±1.7stat±0.5syst)·10-4
4-ple ratio:
R4=RUS*RUJ*RDS*RDJ≈ n(1+g/f(u))4
Acceptance equalization XXYY
JuraJura
SaleveSaleve
Achromats: KAchromats: K+ + UpUpB+
BKK++KK--
In each ratio the charged pions are deflected towards the same side of the detector (left-right asymmetry cancels out)
In each ratio the event at the numerator and denominator are collected in subsequent period of data taking (global time variations)
The whole data taking is subdivided periods in which all the field configurations are present.
3-fold cancellation:
• L-R asymmetry;
• Beam shape asimmetry;
• Global time variations.
N(A+B+K+)N(A+B-K-)RUS=
N(A+B-K+)N(A+B+K-)RUJ=
N(A-B+K+)N(A-B-K-)RDS=
N(A-B-K+)N(A-B+K-)RDJ=
RESULTS:
QCD@WORK 2007Stefano Venditti 17/06/2007
“Bonus” goal: cusp in M2π0π0
distribution2003: 16.0 mln events
0.0800.0790.0780.0770.076 0.0790.0780.0770.076
80k
60k
40k
20k
0
40k
80k
120k
160k
200k
80k
120k
110k
100k
90k
25k
45k
2004 (80%): 43.6 mln events
M2(00), (GeV2)
70k
30k
35k
40k
+– threshold+– threshold
• Cusp analysis not foreseen at the beginning of the experiment;
• First cusp observation on 2003 data, 2004 data now included (~80% of the whole statistics);
• A cusp can be seen in M2(π0π0) distribution at 4Mπ+ value and is the effect of the interference of (at least) two amplitudes.
M2(00), (GeV2)
M2(00), (GeV2)
M2(00), (GeV2)
Negative interference under
2m+
QCD@WORK 2007Stefano Venditti 17/06/2007
Cusp theory: final state rescatteringM(K±
π±π0π0)=M1+M2M0 =direct emission amplitude =
A0(1+g0u/2+h’u2/2+k’v2/2) Not the same
parameterization used for asymmetry! Amplitude parameterized (rather than matrix element)
M1 =rescattering amplitude = -2/3(a0-a2)m+M+√ 1-(M00/2m+)
2
K±
K±
π±
π±
π0π+
π-
π0
π0
π0
S-wave ππ scattering lengths
K->3π± amplitude
at threshold
: no rescattering: 1-loop
rescattering
M2π0π0(GeV2)
M2=4m2π+
N. Cabibbo, PRL 93 (2004) 121801
QCD@WORK 2007Stefano Venditti 17/06/2007
Cusp theory: higher order diagrams • 1 and 2-loop processes included;
• Five S-vawe scattering lengths (ax,
a++, a+-, a+0, a00), expressed as
linear combinations of a0 and a2;
• Isospin symmetry breaking (~2%) considered;
• Radiative corrections missing -> a0-a2 precision >= 5 %.
Arbitrary scale
0.074 0.076 0.078 0.080
Cusp
Negative amplitude
No rescattering Imaginary amplitude
K±
K±
K±
π±
π±
π±
π0
π0
π0
π0
π0
π0
Examples of 2-loop diagrams:
N. Cabibbo and G. Isidori, JHEP 503 (2005) 21
π*
π*
π*
π*
π*π*
π*
π*
π*
π*
π*
Two loop effect on cusp
No cusp
Cusp (2-loop correction)
M2π0π0(GeV2)
QCD@WORK 2007Stefano Venditti 17/06/2007
Cusp: fit procedure• Detector response computed with a full GEANT MC; resolution matrix (computed on s3 variable) applied on MC-generated data;
• Five free parameters (g0, h’,m+(a0-a2),m+a2,N) in MC data.
Use of MINUIT to minimize χ2 based on difference data-MC.
χ2(g0, h’,m+(a0-a2),m+a2,N)=∑
δF2data+δ2N2F2MC
bins
(Fdata-NFMC)2
Resolution smears MC bins:
FiMC=∑ RijGj
G=G(M00,g0,h’,m+(a0-
a2),m+a2)
generated MC bin:
Generated s3=M2(00)
(GeV2)
Reconstructed
s3
QCD@WORK 2007Stefano Venditti 17/06/2007
Cusp: dealing with pionium• Pionium created when relative velocity between two opposite-
sign pions is ~0. It is created by EM interaction, decays (~10-16 sec) by strong interaction;
• No Coulomb corrections -> Pionium cannot be accounted for in this model -> 7 bins (±3.5 resolution σ’s around dipion mass) excluded from Data/MC comparison.
If excess in data all interpreted as pionium, one gets:
R=(K+A2)/(K+–) = (1.820.21)10–5
Theoretical prediction:R=0.810–5 [Z.K. Silagadze, JETP Lett. 60 (1994) 689]
7 bins excluded (0.0775-0.0785 GeV2)
QCD@WORK 2007Stefano Venditti 17/06/2007
Cusp: results
(a0–a2)m+ = 0.261 0.006stat. 0.003syst.
0.013ext.
a2m+= –0.037 0.013stat. 0.009syst. 0.018ext.Using a chiral symmetry constraint [Colangelo et al., PRL 86 (2001) 5008]:
a2 = –0.0444 + 0.236(a0–0.22) – 0.61(a0–0.22)
2 – 9.9(a0–0.22)3
(2003+2004 data, 80% of statistics)
(a0–a2)m+ = 0.263 0.003stat. 0.0014syst.
0.013ext.
• Analysis technique;
• Trigger inefficiency;
• Resolution;
• LKR non-linearity;
• Geometric acceptance;
• MC sample;
• LKR showers
• V-dependence of amplitude.
Systematic
checks
QCD@WORK 2007Stefano Venditti 17/06/2007
Conclusions
• The NA48 results for a0 and a2 following two different paths (ke4 and cusp) are consistent;
• Agreement is also found with DIRAC result, which computes a0 and a2 measuring pionium lifetime;
• Both analyses are still ongoing, room for improvements.