Stefano Venditti University of Pisa & INFN

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Recent results from NA48/2 on pion scattering lengths using Ke4 decay and cusp in K ± ->π ± π 0 π 0 Stefano Venditti Stefano Venditti University of Pisa & University of Pisa & INFN INFN 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

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Recent results from NA48/2 on pion scattering lengths using Ke4 decay and cusp in K ± -> π ± π 0 π 0. Stefano Venditti University of Pisa & INFN. On behalf of the NA48/2 collaboration: - PowerPoint PPT Presentation

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Page 1: Stefano Venditti University of Pisa & INFN

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

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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.

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NA48/2 beam line

K+

K−

PK spectra, 603 GeV/c

54 60 66

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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

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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

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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:

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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)

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Ke4 Analysis: selection and BG rejectionKe4-> 3 charged tracks (2 opposite sign pions),1 ν. BR ~ 4 ·

10-5

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.

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Data/MC comparison

Mππ Meν

cosθπ cosθe

GeVGeV

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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

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fp,hp≠0, no q2

dependencegp linear wrt q

2

Correlation:

gp

g’p

-0.914

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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

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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.

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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

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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.

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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--

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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;

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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:

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“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)

Page 19: Stefano Venditti University of Pisa & INFN

Negative interference under

2m+

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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

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

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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

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)

Page 21: Stefano Venditti University of Pisa & INFN

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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

Page 22: Stefano Venditti University of Pisa & INFN

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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)

Page 23: Stefano Venditti University of Pisa & INFN

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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

Page 24: Stefano Venditti University of Pisa & INFN

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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.