Measurement of [eta] meson production in [gamma][gamma] interactions and [Gamma]([eta] [arrow right] [gamma][gamma]) with the KLOE detector

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

We present a measurement of [eta] meson production in photon-photon interactions produced by electron-positron beams colliding with ... GeV. The measurement is done with the KLOE detector at the -factory DA[Phi]NE with an integrated luminosity of 0.24 fb^sup -1^. The e ^sup +^ e ^sup -^ [arrow right] e ^sup +^ e ^sup -^ [eta] cross section is measured without detecting the out-going electron and positron, selecting the decays [eta] [arrow right] [pi] ^sup +^ [pi] ^sup -^ [pi] ^sup 0^ and [eta] [arrow right] [pi] ^sup 0^ [pi] ^sup 0^ [pi] ^sup 0^. The most relevant background is due to e ^sup +^ e ^sup -^ [arrow right] [eta]γ when the monochromatic photon escapes detection. The cross section for this process is measured as [sigma](e ^sup +^ e ^sup -^ [arrow right] [eta]γ) = (856±8^sub stat^±16^sub syst^) pb. The combined result for the e ^sup +^ e ^sup -^ [arrow right] e ^sup +^ e ^sup -^ [eta] cross section is [sigma](e ^sup +^ e ^sup -^ [arrow right] e ^sup +^ e ^sup -^ [eta]) = (32.72±1.27^sub stat^±0.70^sub syst^) pb. From this we derive the partial width [Gamma]([eta] [arrow right] γγ) = (520±20^sub stat^±13^sub syst^) eV. This is in agreement with the world average and is the most precise measurement to date.

Published for SISSA by Springer

Received: November 8, 2012

Accepted: December 12, 2012

Published: January 17, 2013

D. Babusci,h D. Badoni,r,s I. Balwierz-Pytko,g G. Bencivenni,h C. Bini,p,q C. Bloise,hF. Bossi,h P. Branchini,u A. Budano,t,u L. Caldeira Balkesthl,w G. Capon,hF. Ceradini,t,u P. Ciambrone,h E. Czerwiski,g E. Dan,h E. De Lucia,hG. De Robertis,b A. De Santis,p,q A. Di Domenico,p,q C. Di Donato,l,m R. Di Salvo,sD. Domenici,h O. Erriquez,a,b G. Fanizzi,a,b A. Fantini,r,s G. Felici,h S. Fiore,p,qP. Franzini,p,q P. Gauzzi,p,q G. Giardina,j,d S. Giovannella,h F. Gonnella,r,sE. Graziani,u F. Happacher,h L. Heijkenskjld,w B. Histad,w L. Iafolla,hM. Jacewicz,w T. Johansson,w A. Kupsc,w J. Lee-Franzini,h,v B. Leverington,hF. Loddo,b S. Lo redo,t,u G. Mandaglio,j,d,c M. Martemianov,k M. Martini,h,oM. Mascolo,r,s R. Messi,r,s S. Miscetti,h G. Morello,h D. Moricciani,s P. Moskal,gF. Nguyen,u,1,2 A. Passeri,u V. Patera,n,h I. Prado Longhi,t,u A. Ranieri,bC. F. Redmer,i P. Santangelo,h I. Sarra,h M. Schioppa,e,f B. Sciascia,h M. Silarski,gC. Taccini,t,u,1 L. Tortora,u G. Venanzoni,h W. Wilicki,x M. Wolkew and J. Zdebikg

aDipartimento di Fisica, Universit di Bari, Bari, Italy

bINFN Sezione di Bari, Bari, Italy

cCentro Siciliano di Fisica Nucleare e Struttura della Materia, Catania, Italy

dINFN Sezione di Catania, Catania, Italy

eDipartimento di Fisica, Universit della Calabria, Cosenza, Italy

f INFN Gruppo collegato di Cosenza, Cosenza, Italy

gInstitute of Physics, Jagiellonian University, Cracow, Poland

hLaboratori Nazionali di Frascati dellINFN, Frascati, Italy

iInstitut fr Kernphysik, Johannes Gutenberg Universitat Mainz, Mainz, Germany

jDipartimento di Fisica e Scienze della Terra dellUniversit di Messina, Messina, Italy

kInstitute for Theoretical and Experimental Physics (ITEP), Moscow, Russia

lDipartimento di Fisica, Universit Federico II, Napoli, Italy

mINFN Sezione di Napoli, Napoli, Italy

nDipartimento di Scienze di Base ed Applicate per lIngegneria dellUniversit Sapienza, Roma, Italy

1Corresponding authors.

2Present Address: Laboratrio de Instrumentao e Fsica Experimental de Partculas, Lisbon, Portugal.

Open Access doi:http://dx.doi.org/10.1007/JHEP01(2013)119

Web End =10.1007/JHEP01(2013)119

Measurement of meson production in interactions and ( ! ) with the KLOE detector

JHEP01(2013)119

The KLOE-2 collaboration

oDipartimento di Scienze e Tecnologie applicate, Universit Guglielmo Marconi, Roma, Italy

pDipartimento di Fisica, Universit Sapienza, Roma, Italy

qINFN Sezione di Roma, Roma, Italy

rDipartimento di Fisica, Universit Tor Vergata, Roma, Italy

sINFN Sezione di Roma Tor Vergata, Roma, Italy

tDipartimento di Fisica, Universit Roma Tre, Roma, Italy

uINFN Sezione di Roma Tre, Roma, Italy

vPhysics Department, State University of New York at Stony Brook, New York, U.S.A.

wDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden

xNational Centre for Nuclear Research, Warsaw, Poland

E-mail: mailto:[email protected]

Web End [email protected] , [email protected]

Abstract: We present a measurement of meson production in photon-photon interactions produced by electron-positron beams colliding with s = 1 GeV. The measurement is done with the KLOE detector at the -factory DA NE with an integrated luminosity of 0.24 fb1. The e+e e+e cross section is measured without detecting the out

going electron and positron, selecting the decays +0 and 000. The

most relevant background is due to e+e when the monochromatic photon es

capes detection. The cross section for this process is measured as (e+e ) = (856 8stat 16syst) pb. The combined result for the e+e e+e cross section is

(e+e e+e) = (32.72 1.27stat 0.70syst) pb. From this we derive the partial width

( ) = (520 20stat 13syst) eV. This is in agreement with the world average and is the most precise measurement to date.

Keywords: e+-e- Experiments

ArXiv ePrint: 1211.1845

JHEP01(2013)119

Contents

1 Introduction 1

2 Signal and background model 2

3 The KLOE detector 3

4 Data sample and event preselection 4

5 Cross section for e+e ! e+e with ! +0 45.1 Event selection 45.2 Reconstruction of +0 decay 6

5.3 Cross section evaluation 8

6 Cross section for e+e ! e+e with ! 000 106.1 Event selection 106.2 Reconstruction of 30 decay 11

6.3 Cross section evaluation 12

7 Determination of ( ! ) 14

8 Measurement of the cross section for e+e ! 15

8.1 Reconstruction of +0 events 15

8.2 Evaluation of the cross section 16

9 Summary 18

1 Introduction

Photon-photon production of neutral mesons provides basic information on their structure. The strength of the coupling, measured by the partial decay width (X ), is related

to the quark content of the meson and gives information on the relations between the hadronic state and its qq representation. For the light pseudoscalar mesons 0, and , the coupling to real photons is measured in their decays, while the coupling to space-like photons can be measured in interactions. This is of particular interest in evaluating the light-by-light contribution to the anomalous magnetic moment of the muon [1]. Photon-photon interactions in electron-positron colliders were pioneered at the Frascati collider Adone in the 70s [24] and since then have been used to study the production of hadrons in almost all e+e colliders in a variety of conditions in low- and high-q2 processes [57].

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In particular, measurements of the partial width of and mesons have been done measuring the e+e e+e() cross section [813].

We present a measurement of the cross section e+e e+e with the KLOE detector

at the -factory DA NE. The cross section (e+e e+e) is a convolution of the

di erential luminosity and the cross section. The partial decay width (

) is obtained by extrapolating the value of ( ) for real photons.

DA NE is an e+e collider designed to operate at high luminosity at the mass of the resonance, 1020 MeV. We analyzed data collected with DA NE operating o the peak, at s = 1 GeV, to reduce the large background from decays. The nal state e+ and e are not detected, being emitted with high probability in the forward directions outside the acceptance of the detector. The production of the meson is identied in two decay modes, +0 and 000, that exploit in a complementary way the tracking

system and calorimeter of the detector. The most relevant background is the radiative process e+e and, in both measurements, the yield of mesons is controlled by the

e+e cross section measured in the same data sample with a dedicated analysis. The

data sample used in the analyses corresponds to an integrated luminosity of 0.24 fb1.

2 Signal and background model

For electron and positron beams colliding with energy E, the cross section for production of a state X in interactions with photon 4-momenta q1 and q2 is

(e+e e+eX) = [integraldisplay] X(q1, q2) (q1, q2)

d~q1

E1

JHEP01(2013)119

d~q2

E2 , (2.1)

where the di erential luminosity (q1, q2) has been calculated in [1416] using di erent approximations and is proportional to (/2)2(ln E/me)2. For a narrow resonance of spin 0 the formation cross section is

X = 82mX X (w2 m2X) |F (q21, q22)|2 , (2.2)

where X is the radiative width, and w2 = (q1 + q2)2. The transition form factor, F (q21, q22), is equal to one for real photons and is usually parametrized in the form

F (q21, q22) = 1

1 bq21

11 bq22

, (2.3)

inspired by the Vector Dominance Model [17]. The parameter b for the meson has been measured at high q2 values in experiments with single-tagging [1820] and in the leptonic radiative decays + [2123] at low q2 values, closer to those of

this measurement. The results do not show appreciable dependence on q2 and the value assumed in this analysis, b = (1.94 0.15) GeV2, was obtained as an average of the

measurements at low q2.

The detector response for signal and background events is fully simulated with the Monte Carlo (MC) program Geanfi [24]. While Geanfi contains the event generator for all background processes, a new generator for e+e e+eX events is developed and

2

interfaced to the detector simulation. Events are generated with exact matrix element according to full 3-body phase space distributions [25]. This results in the production of mesons with non negligible transverse momentum. The relative error due to high-order radiative corrections to equation (2.1) is estimated to be 1% [26]. All background processes have been extensively studied in other analyses. A source of irreducible background is the reaction e+e when the monochromatic photon is emitted at small angles and is

not detected. The cross section for this process is measured in the same data sample with two independent methods and the results agree with each other providing an important consistency check of the analysis. The beam-induced backgrounds were measured during data taking and background events are added to simulated events in the MC on a run-byrun basis.

3 The KLOE detector

The KLOE detector consists of a large volume cylindrical drift chamber, surrounded by a lead-scintillating bers nely segmented calorimeter. A superconducting coil around the calorimeter provides a 0.52 T axial magnetic eld. The beam pipe at the interaction region is spherical in shape with 10 cm radius, it is made of a Beryllium-Aluminum alloy of 0.5 mm thickness. Low-beta quadrupoles are located at 50 cm distance from the interaction

region. Two small lead-scintillating tiles calorimeters (QCAL) [27] are wrapped around the quadrupoles.

The drift chamber (DC) [28], 4 m in diameter and 3.3 m long, has 12,582 drift cells arranged in 58 concentric rings with alternated stereo angles and is lled with a low-density gas mixture of 90% Helium-10% isobutane. The chamber shell is made of carbon berepoxy composite with an internal wall of 1.1 mm thickness at 25 cm radius. The spatial resolutions are xy 150 m and z 2 mm.1 The momentum resolution for long tracks

is (pT )/pT 0.4%. Vertices are reconstructed with a spatial resolution of 3 mm.

The calorimeter [29] is divided into a barrel and two end-caps and covers 98% of the solid angle. The readout granularity is (4.4 4.4) cm2, for a total of 2440 cells arranged in

ve layers. Each cell is read out at both ends by photomultipliers. The energy deposits are obtained from the signal amplitude while the arrival times and the position along the bers are obtained from the time di erences. Cells close in time and space are grouped into energy clusters. The cluster energy E is the sum of the cell energies. The cluster time t and position ~r are energy-weighted averages. Energy and time resolutions are E/E = 0.057/

pE (GeV)

pE (GeV) 100 ps, respectively. The cluster space resolution is k = 1.4

pE (GeV) along the bers and = 1.3 cm in the orthogonal direction.

The trigger [30] uses both calorimeter and chamber information. For this analysis the events are selected by the calorimeter trigger, requiring two energy deposits with E >50 MeV in the barrel or E > 150 MeV in the end-caps. A higher-level cosmic-ray veto rejects events with at least two energy deposits above 30 MeV in the outermost calorimeter layer. Data are then analyzed by an event classication lter [24], which selects and streams various categories of events in di erent output les.

1KLOE uses a coordinate system where z is the bisector of the electron and positron beams, x and y dene the transverse plane.

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and t = 57 ps/

cm/

4 Data sample and event preselection

The data were collected at s = 1000.1 MeV with electron and positron beams colliding at a small angle with an average transverse momentum of 12.7 MeV in the horizontal plane. The average instantaneous luminosity was 7 1031 cm2s1 and the analysis is based on

an integrated luminosity of 242.5 pb1 measured with a precision of 0.3% recording large angle Bhabha scattering events [31].

Data are selected with a background rejection lter [24] before event reconstruction. A 1/20 sample of unltered data, corresponding to about 11 pb1, is also reconstructed to dene the preselection lter used for the analysis and to evaluate its e ciency for event selection. The preselection lter requires

at least two energy clusters, neutral (not associated to any track) and prompt (with |t r/c| < 5t);

all prompt neutral clusters are required to have energy E > 15 MeV and polar angle

20 < < 160;

at least one prompt neutral cluster with energy greater than 50 MeV;

a ratio of the two highest energy neutral prompt clusters to the total calorimeter

energy R = (E 1 + E 2)/Etot > 0.3;

100 MeV < Etot < 900 MeV, to reject low energy background events and the high

rate processes e+e e+e(), e+e .

5 Cross section for e+e ! e+e with ! +0

5.1 Event selection

In addition to the preselection, candidate decays +0 should fulll the following

requirements

two and only two neutral prompt clusters with |t r/c| < 3t and polar angle

23 < < 157;

at least two tracks with opposite curvature that are extrapolated inside a cylinder

=

px2 + y2 < 8 cm and |z| < 8 cm centered around the average beam collision

point;

the distance of the rst DC hit to the average beam collision point to be less than 50

cm for both tracks (in case of two or more tracks with the same curvature, the track with best quality parameters is chosen);

sum of the two tracks momenta |~p1| + |~p2| < 700 MeV.

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0.3

0.3

20

2 )

2 )

m2 mis (Gev

m2 mis (Gev

0.25

0.25

0.2

910

0.2

10

8

89

0.15

7

0.15

7

6

6

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0.1

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0.05

4

0.05

4

3

3

0

0

-0.05

2 -0.05

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-0.1

-0.1

-0.15

-400 -300 -200 -100 0 100 200 300 400 1

1

-0.15

-400 -300 -200 -100 0 100 200 300 400

pL(MeV)

pL(MeV)

Figure 1. Correlation between the longitudinal momentum, pL , and the squared missing mass, m2mis for the reconstructed events that pass the selection cuts of the analysis, for MC signal events (left) and data (right). The e+e events, when the monochromatic photon escapes detection,

are clearly visible in the data.

To minimize any selection bias and to optimize the selection e ciency, there is no requirement for the tracks to be associated to clusters in the calorimeter nor that they form a vertex. The number of selected events is 3.9 106. A small fraction of fully neutral nal

states can survive the two tracks requirement in case of photon conversion N e+eN or 0 Dalitz decay.

Many background contributions have been considered. The e+e process is

a source of irreducible background when decays to +0 and the monochromatic photon, E = 350 MeV, is emitted at small polar angles and is not detected. However, the correlation of the squared missing mass, m2mis and the longitudinal momentum pL

can be used to separate the signal from the background. For the background pL =

E cos 350 MeV and m2mis 0 while the signal, for small values of pT , is characterized

by m2mis (s m )2 + (s/m ) p2L , as shown in gure 1.

The process e+e 0, with +0, has four photons in the nal state and

therefore produces the same nal state as the signal when two photons are not detected. The cross section has been measured with data from the same run [32], (e+e 0

+00) = (5.72 0.05) nb. The e+e KLKS events can mimic the signal either

when the KL decays to close to the collision point and KS decays to 00, or when the KL escapes detection and KS 00 is followed by photon conversion in an e+e pair

or by a 0 Dalitz decay. The e+e K+K events can mimic the signal when both kaons

decay close to the collision point, either K 0 or K 0 in coincidence with

K . Also Bhabha radiative events, e+e e+e, given the large cross section,

can be a source of background in case of accidental or split clusters.

5

10 6

10 5

10 4

10 6

10 5

events/0.5

events/0.5

0 5 10 15 20 25 30

c2 gg (data)

0 5 10 15 20 25 30

c2 gg (MC signal)

Figure 2. Distribution of 2 for data (top) and MC signal events (bottom).

5.2 Reconstruction of ! +0 decay

To identify the 0 meson, clusters are paired choosing the combination that minimizes the di erence between the two-cluster invariant mass and the 0 mass. This is performed using a pseudo-2 variable

2 = (m m

)22m with m =

0 , m = m . Figure 3

shows the distribution of 2 from the kinematic t for MC signal events and for data. We require 2 < 20 to reduce the ( +0) background. This process has a long

tail in the 2 distribution due to events with the monochromatic photon in the detector acceptance and one photon from the 0 decay undetected, that are not rejected by the 2 < 8 requirement.

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10 4

10 3

E iE i +E jE j[parenrightbigg] . (5.1)

The energy resolution function is given in section 3, the invariant mass resolution is dominated by the calorimeter energy resolution while the angle measurement gives a negligible contribution. Figure 2 shows the distribution of the 2 variable for MC signal events and for data. In the following analysis we select events with 2 < 8.

The two tracks momenta are combined with the 0 to identify +0 decay

candidates, assigning the charged pion mass to the tracks. A kinematic t is done requiring the invariant mass of equal to the mass. In the t the energies, Ei, the times, ti, and the coordinates of the cluster centroid position xi, yi, zi, for the two clusters are varied. The track momenta are not varied in the minimization since they are measured with much better precision than the cluster energies. There are four constraints: the promptness of the two clusters, ti ri/c = 0, and the mass values m = m

m

2

0

events/0.5

events/0.5

600

500

400

300

200

100

2500

2000

0 0 5 10 15 20 25 30 35 40 45 50

c2 h (data)

0 0 5 10 15 20 25 30 35 40 45 50

c2 h (MC signal)

Figure 3. Distribution of the 2 of the kinematic t for data (top) and MC signal events (bottom).

At this stage of the selection, radiative Bhabha scattering, e+e e+e, and e+e annihilation followed by photon conversion are still a source of background.

Separation of charged pion from electron/positron tracks is done using a likelihood method when a cluster is associated to the track [33]. A cluster is associated if the distance between the centroid and the extrapolation of the track to the calorimeter wall is less than 50 cm. The e- likelihood is based on three variables: i) the di erence of time of ight,ii) the energy of the cluster; iii) the fractions of energy deposited in the rst and in the fth calorimeter layers. In this analysis events with a cluster associated to each track and a value of the likelihood estimator log L/Le < 0 for both clusters are rejected. The back

ground from e+e annihilation is reduced requiring that the most energetic cluster

satises the conditions E 1 < 230 MeV and 27.5 < 1 < 152.5.

Opposite curvature track pairs can originate from split tracks. This is due to the track nding algorithm that looks for secondary vertices of kaon decays. Background of split tracks is reduced applying a topological cut based on the correlation between the tracks opening angle, , and the distance between the rst DC hits associated to the two tracks by the tracking algorithm. The background from kaon decays in e+e KLKS and e+e K+K is reduced applying a cut on the two tracks opening angle > 50.

Kaon decays are characterized by non prompt energy clusters, thus both the time and the energy assigned by the kinematical t to the neutral clusters are modied by the t constraints. This e ect is observed in the time and energy pulls built with the two neutral clusters

2t =

Xi2 (tfiti tmeasi)22t , 2E = [summationdisplay]i2 (Efiti Emeasi)22E, (5.2)

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1500

1000

500

Final state Selection Global e ciency (%) e ciency (%)

e+e 34.4 0.3 20.8 0.3

( +0) 13.3 1.93 ( +) 43.9 0.0090 ( neutral) 0.185 0.00030

0 3.08 0.023

KLKS 0.169 0.0059

K+K 0.423 0.0075 e+e 0.447 < 0.0004

Table 1. Selection e ciency, in %, for the signal and the most relevant backgrounds. The column Selection includes the e ciency of the trigger, the background lter and the data lters described in sections 4 and 5.1. The global e ciency for e+e is derived before the cut on the e- likelihood.

where the superscript meas and t indicate the values measured and returned by the t, respectively. The pulls are required to satisfy 2t < 7 and 2E < 8.

The selection e ciencies are evaluated with the MC simulation and are listed in table 1 for the signal and the most relevant background sources. The column Selection includes the e ciency of the trigger, the background lter and the data lters described in sections 4 and 5.1. The trigger e ciency is controlled by comparison of the calorimeter trigger with a complementary trigger based on the drift chamber hit patterns [30]. A sample of unltered data is used to control the lter e ciency.

The signal is simulated with di erent values of the b parameter2 of the form factor in equation (2.3) and the t to derive the signal yield is repeated for each value. The values of e ciencies shown in table 1 correspond to b = 1.94 GeV2.

5.3 Cross section evaluation

The analysis cuts described in section 5.2 select 2977 events. The number of signal events is derived with a 2-dimensional t to the data. The variables used to discriminate the signal from background are the squared missing mass and the transverse momentum in the interval 0.15 GeV2 < m2mis < 0.25 GeV2 and pT < 300 MeV that contains 2720 events.

The t to the data is done using the simulated shapes for the signal and backgrounds, the weights are left free except for ( +0) whose cross section and error, measured in

the same data sample (see section 8), is used as a constraint in the t. The t returns the fraction of data events fi = ni/ntot with the constraint

Pi fi = 1.

The projections of the m2mis pT distribution are shown in gure 4 for the data

and the backgrounds weighted by their fractions fi, and the pL distribution is shown in gure 5. The most relevant background is e+e characterized by m2mis 0 and

pL 350 MeV. Table 2 lists the fraction of events returned by the t using the signal

e ciency evaluated with b = 1.94 GeV2, the t is repeated for all the other b values used in evaluating the e ciency. The distributions of the variables used in the event selection

2The values chosen are b = 0, 0.7, 1.0, 1.5, 1.64, 1.80, 1.94, 2.00, 2.24 GeV2.

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events/5 MeV

events/0.08 GeV 2

90

160

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

80

140

70

120

60

100

50

80

40

60

30

20

40

JHEP01(2013)119

10

20

0

0 0 50 100 150 200 250 300

m2 mis (GeV 2)

pT (MeV)

Figure 4. Projections of the 2-dimensional t. Left: distribution of the transverse momentum of the + system. Right: distribution of the squared missing mass. The contribution of the signal is blue, e+e is red, e+e 0 is black, e+e e+e is green, e+e K+K

is light blue and e+e KSKL is purple.

pL (MeV)

events/10 MeV

100

80

60

40

20

0 -400 -300 -200 -100 0 100 200 300 400

Figure 5. Distribution of the longitudinal + momentum. The contribution of the signal is blue, e+e is red, e+e 0 is black, e+e e+e is green, e+e K+K is light

blue and e+e KSKL is purple.

are compared for data and MC simulation, weighted by the fractions fi returned by the t, and good agreement is observed. The t nds 394 29 signal events.

9

Final state Fraction of events (%) e+e 14.49 1.06

32.02 0.54

0 20.48 1.81

KLKS 11.36 1.70

K+K 15.13 1.81

e+e 7.54 0.87

Table 2. Fraction of events, in %, for the signal and the most relevant backgrounds.

Variable Range /(%)2 6.6 - 10.8 +0.67 -0.73 2 18.5 - 23.5 +0.06 -0.68

E 1 210 MeV - 250 MeV -1.17 -0.33 1 26.5/153.5 - 28.5/151.5 +1.21 +0.46 2t 6 - 8 +1.10 -1.22 2E 7 - 9 +1.89 -1.39 + 48 - 52 -0.21 +0.20

Table 3. Systematic errors determined varying the cuts for each variable for the (e+e e+e e+e+0) measurement.

The contributions to the systematic error are evaluated by varying the analysis cuts by the r.m.s. width of the distributions of each variable: 2 , 2 , E 1, 1, , 2t, 2E, accounting for their correlation. This results in a systematic relative error of 2.4% to

+2.6%. The contributions are listed in table 3.

The MC simulation statistical error of 1.4% (table 1) is added in quadrature, the uncertainties in the form factor and in the branching ratio are kept separate to account for correlations between the two decay modes. The change of the result due to the variation of b in the transition form factor formula leads to a 2.0% fractional error. We obtain (e+e e+e e+e+0) = (7.84 0.57stat 0.23syst 0.16FF) pb. Using for the branching fraction the value BR( +0) = 0.2274 0.0028 [34], we obtain

(e+e e+e) = (34.5 2.5stat 1.0syst 0.7FF 0.4BR) pb . (5.3)

6 Cross section for e+e ! e+e with ! 000

6.1 Event selection

In addition to the preselection described in section 4, candidate decays 30 should

fulll the following requirements

six and only six neutral prompt clusters with E > 15 MeV, |t r/c| < 3t and polar

angle 23 < < 157;

no tracks in the drift chamber.

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Final state Selection Global e ciency (%) e ciency (%)

e+e 30.9 0.3 28.6 0.3

( 000) 10.9 2.14 0 0.145 0.0077

KLKS 0.0126 0.0073 a0(980) 2.70 0.85 f0(980) 0.147 0.0070

2.13 0.212

Table 4. Selection e ciency, in %, for the signal and the most relevant backgrounds. The column Selection includes the e ciency of the trigger, the background lter and the data lters described in sections 4 and 6.1.

The number of selected events is 9857. Many background contributions have been considered. As in the charged decay analysis, the e+e process is a source of

irreducible background when decays to 30 and the recoil photon is not detected. The process e+e 0 with 0 produces 5 photons in the nal state and is important in

case of accidental or split clusters. The cross section has been measured with the same data set [32]: (e+e 0 00) = (0.550 0.005) nb. The process e+e a0(980)

0 can mimic the signal when decays to 30 and three photons are not detected, or it decays to with split or accidental clusters. Similarly for e+e f0(980) 00 and

e+e when decays to neutrals. Also the process e+e KLKS with KS 00

and undetected KL can mimic the signal in case of split or accidental clusters.

6.2 Reconstruction of ! 30 decay

The six photons are paired choosing the combination that minimizes the di erence between the invariant mass of the pairs and the mass of the 0 as described in section 5.2. In the following analysis we select events with 26 < 14. A kinematic t is done requiring the 6 invariant mass to be equal to the mass. In the t the energies, Ei, the times, ti, and the coordinates of the centroid positions xi, yi, zi, for the six clusters are varied. There are seven constraints: the promptness of the six clusters ti ri/c = 0 and m6 = m . Figure 6

shows the distribution of 2 from the kinematic t for MC signal events and for data, we require 2 < 20 to reduce the background.

MC simulation shows that e+e gives a large contribution to the tail of the

distribution when the monochromatic photon is in the acceptance and is wrongly paired with a photon from decay. In this case it also produces an enhancement at large values of the 6 invariant mass distribution. To reduce the background we require the highest energy neutral cluster to have E 1 < 260 MeV and the six-photon invariant mass m6 < 630 MeV.

The selection e ciencies are evaluated with the MC simulation described in section 2 and are listed in table 4 for the signal and the most relevant background sources.

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events/0.5

events/0.5

160

140

120

100

80

60

40

20

500

400

0 0 5 10 15 20 25 30 35 40 45 50

c2 h (data)

0 0 5 10 15 20 25 30 35 40 45 50

c2 h (MC signal)

Figure 6. Distribution of 2 for data (top) and MC signal events (bottom).

6.3 Cross section evaluation

The number of signal events is derived with a 2-dimensional t to the data. The distributions used to discriminate the signal from background are the squared missing mass and the longitudinal momentum in the interval -0.15 GeV2 < m2mis < 0.35 GeV2 and -450 MeV < pL < 450 MeV that contains 2166 events. The t to the data is done using the simulated shapes for the signal and backgrounds and the t returns the fraction of data events fi = ni/ntot with the constraint

Pi fi = 1.

The contribution of all backgrounds, except production, is very small, below the statistical sensitivity of the t. The contribution of 0 derived from the value of the e+e 0 cross section [32] is f!

0 = 0.47%. The contributions of a0(980), and KLKS expected extrapolating the measurements at the peak are negligible.

The t with two components gives fee = (33.4 1.5)% and f = (66.6 1.9)% using the signal e ciency evaluated with b = 1.94 GeV2. The t is repeated for all the other values. The projections of the m2mis pL distribution are shown in gure 7 for the data

and the background weighted by their relative factors fi, and the pT distribution is shown in gure 8.

The contributions to the systematic error are evaluated by varying the analysis cuts by the r.m.s. width of the distributions of each variable: 2 , 2 , E 1, m6 , accounting for their correlation. This results in a systematic relative error of 1.5% to +2.6%. The

contributions are listed in table 5.

The MC simulation statistical error of 1.0% (table 4) is added in quadrature, the errors due to knowledge of the form factor and to the branching ratio are kept separate. The changes of the result due to the variation of b in the transition form factor formula lead

12

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300

200

100

events/15 MeV

events/0.0125 GeV 2

140

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

120

120

100

100

80

80

60

60

40

40

JHEP01(2013)119

20

20

0

0 -400 -300 -200 -100 0 100 200 300 400

pL (MeV)

m2 mis (GeV 2)

Figure 7. Projections of the 2-dimensional t. Left: distribution of the 6 longitudinal momentum. Right: distribution of the squared missing mass. The contribution of the signal is blue, e+e

is red.

pT (MeV)

events/5 MeV

120

100

80

60

40

20

0 0 20 40 60 80 100 120 140 160 180 200

Figure 8. Distribution of the 6 transverse momentum. The contribution of the signal is blue, e+e is red

to a 0.7% fractional error. We obtain (e+e e+e e+e30) = (10.43 0.48stat 0.29syst 0.07FF) pb. The analysis of the systematic uncertainties of the e+e

measurement leads to a relative error of 0.6%: we obtain (e+e 30) =

(278.08.1stat 1.7syst) pb. Using for the branching fraction the value BR( 000) =

13

Variable Range /(%)2 12 - 16 -0.51 +0.83 2 17 - 23 -0.26 -0.68

M6 610 MeV - 650 MeV -1.33 +2.38

Table 5. Systematic errors determined varying the cuts for each variable for the (e+e e+e e+e30) measurement. Varying the cut on E 1 gives a negligible contribution.

0.3257 0.0023 [34], we obtain

(e+e e+e) = (32.0 1.5stat 0.9syst 0.2FF 0.2BR) pb (6.1) and

(e+e ) = (853 25stat 5syst 6BR) pb . (6.2)

7 Determination of ( ! )

The two values of the cross section in equations (5.3) and (6.1) are combined accounting for the following sources of correlation:

systematic uncertainties are correlated due to the requirements on the neutral prompt

clusters, the photon energy, time and position resolutions common to both selections and t procedures;

the determination of the signal e ciencies for the two measurements that share the

same transition form factor;

the systematic error in the measurement of the luminosity [31];

the correlation between the +0 and 30 branching ratios [34]. From the combination of the two measurements we derive

(e+e e+e) = (32.7 1.3stat 0.7syst) pb . (7.1) The partial width of the meson, ( ), can be determined from equations (2.1)

and (2.2). The di erential luminosity is calculated following reference [25], the program computes also the transition form factor as parametrized in equation (2.3), for the same values of the b parameter used in evaluating the e+e e+e cross section. Since the

values of the 4-momenta q1 and q2 sampled in the two decay modes analyzed in sections 5 and 6 can be slightly di erent, the partial width is determined separately for the two decays. The theoretical error in evaluating ( ) has been added to the systematic

error due to the form factor. From the two values of the e+e e+e cross section, (5.3)

and (6.1), we derive

+0 ( ) = (548 40stat 16syst 14FF 7BR) eV , 000 ( ) = (509 23stat 14syst 8FF 4BR) eV .

The two measurements are combined accounting for their correlations to derive

( ) = (520 20stat 13syst) eV . (7.3)

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(7.2)

8 Measurement of the cross section for e+e !

The most relevant background in the measurement of the e+e e+e cross section is

due to the radiative process e+e . The value of the cross section has been used as

a constraint in the t in case of the +0 decay while it has been derived as a

by-product of the analysis of the 30 decay. The cross section has been measured by

the SND experiment [35] at VEPP-2M in the range s = (0.6 1.38) GeV, but with less

precision than needed to control the analysis of e+e e+e.The cross section for e+e is measured exploiting the +0 decay

using the same data sample and the same preselection procedure described in sections 4 and 5.1 with the only di erence that in this case events with three and only three neutral prompt clusters are selected. The event selection aims at nding two tracks of opposite curvature, compatible with being due to , two neutral prompt clusters compatible with being originated by a 0 decay, and a third neutral prompt cluster compatible with the photon recoiling against the +0 system.

Several background processes have been considered. e+e 0 with +0

is characterized by two tracks and four photons and can simulate the signal if one photon is not detected. e+e +0 has the same conguration as the signal. e+e KLKS

can mimic the signal when KL decays to close to the collision point and KS decays to 00 but one photon is not detected. e+e K+K can mimic the signal when both

kaons decay close to the collision point to 0, 0 and one photon is not detected, or decay to 0, and the additional photon originates from split or accidental clusters. e+e +0 and e+e + can mimic the signal in case of one or two accidental

or split clusters. e+e e+e has a very large cross section and can be an important

background if the electron (positron) is misidentied as a pion and the two additional photons originate from split or accidental clusters. e+e has also a large cross

section and may originate background in case of photon conversions and there are split or accidental clusters. Beside these, production with decaying to + or to 30 should be discriminated from the +0 signal by the number of prompt neutral clusters.

8.1 Reconstruction of ! +0 events

The identication of the 0 meson follows the procedure described in section 5.2. No cut is applied to the value of 2 . A kinematic t is applied to the selected combination of three neutral prompt clusters and two tracks, with the assignment of the charged pion mass. The t uses 15 variables, the energy Ei, time ti and cluster coordinates xi, yi, zi of the three clusters, and has 7 constraints, promptness of three clusters ti ri/c = 0, energy and momentum conservation:

Pi E i + E+ + E = s and

Pi ~p i + ~p+ + ~p = ~pe+e .

The track momenta are not varied in the minimization procedure. Figure 9 shows the distribution of the 2 of the kinematic t for MC signal events and for data. In the following analysis we select events with 2 < 50.

The background of e+e e+e and e+e is reduced using the e- likelihood

estimator as described in section 5.2, and requiring the angle between the two tracks to be < 160, and the angle between any photon pair to be > 20. The background

15

JHEP01(2013)119

events/2

events/2

25000

20000

15000

10000

5000

70000

60000

0 0 20 40 60 80 100 120 140 160 180 200

c2 (data)

0 0 20 40 60 80 100 120 140 160 180 200

c2 (MC signal)

Figure 9. Distribution of 2 for the data (top) and MC signal events (bottom).

of e+e 30 with photon conversion is reduced requiring the sum of the photon

energies

Pi E i < 660 MeV. At this stage of the analysis, the residual background is dominated by the processes e+e + and e+e +0 with split clusters,

characterized by a neutral energy smaller than for the signal, and e+e +0

characterized by the same nal state as the signal. These backgrounds are reduced by requiring for the sum of the track momenta |~p+|+|~p| < 440 MeV. The e ect of these cuts

is controlled by the distribution of the energy of the unpaired photon shown in gure 10 where E 3 is the value returned by the t and has a resolution greatly improved by the good time and position resolution of the calorimeter. The peaks at the energies of the photon recoiling against the and the are clearly visible over a small background at E 3 = 194 MeV and E 3 = 350 MeV, respectively.

The selection e ciencies are evaluated with the MC simulation described in section 2 and are listed in table 6 for the signal and the most relevant background sources.

8.2 Evaluation of the cross section

The number of signal events is derived with a 2-dimensional t to the data. The distributions used to discriminate the signal from background are the energy of the un-paired photon and the invariant mass of the two charged pions in the interval 50 MeV < E 3 < 400 MeV and 280 MeV < m < 520 MeV that contains 55150 events. The t to the data is done using the simulated shapes for the signal and backgrounds and the weights are left free. The projections of the E 3 m distribution are shown in g

ure 11 for the data and the backgrounds weighted by their relative factors returned by the t. The result of the t gives 13536 121 signal events resulting in a cross section

(e+e +0) = (194.7 1.8stat) pb.

16

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50000

40000

30000

20000

10000

3500

3000

2500

2000

1500

1000

500

events/MeV

JHEP01(2013)119

0 50 100 150 200 250 300 350 400

data E g3 (MeV)

Figure 10. Distribution of the energy of the unpaired photon for data before (black) and after (red) the cut on the sum of the tracks momenta. The e+e peak is clearly visible, with

E = 194 MeV.

Final state Selection Global e ciency (%) e ciency (%)

( +0) 36.71 0.02 28.68 0.02

+0 6.08 1.19

0 19.80 1.07 ( +) 0.723 0.069

( neutral) 0.111 0.002

Table 6. Selection e ciency, in %, for the signal and the most relevant backgrounds. The column

Selection includes the e ciency of the trigger, the background lter and the data lter described in section 4.

The only relevant backgrounds are from e+e +0 and e+e 0

+00. The distributions of the signal and e+e +0 are well reproduced

both in shape and relative normalization, while the fraction of 0 events results slightly higher than expected. If the measured value and its error, (e+e 0 +00) =

(5.72 0.05) nb [32], are introduced as a constraint, the t returns a value 1.36% higher

for the e+e cross section. This di erence is accounted for in the systematic error.

Other contributions to the systematic error are evaluated by varying the analysis cuts by the r.m.s. width of the distributions of each variable, 2, , , |~p+|+|~p|, accounting for their correlation. This results in a relative error of 1.45% and (e+e

+0) = (194.7 1.8stat 2.8syst) pb. Using the branching fraction for +0,

we derive

(e+e ) = (856 8stat 12syst 11BR) pb (8.1)

17

2250

2000

1750

1500

1250

1000

750

500

250

1000

events/MeV

events/2 MeV

800

600

400

200

JHEP01(2013)119

0 50 100 150 200 250 300 350 400

E g3 (MeV)

Figure 11. Projections of the 2-dimensional t. Left: distribution of the energy of the unpaired photon. Right: distribution of the invariant mass m+ . The contribution of the signal e+e

is blue, e+e 0 is green and e+e +0 is purple.

This value, obtained from a direct measurement, agrees well with the value (6.2) obtained from the analysis of 30. The result interpolates well with the measurements

of the SND experiment [35] and has a better precision.

9 Summary

The cross section (e+e e+e) has been measured at s = 1 GeV with the KLOE

detector based on an integrated luminosity of 0.24 fb1. The mesons are selected using the two decays +0 and 000 that exploit in a complementary way the

tracking and the calorimeter measurements. Many background processes are considered, the most relevant being e+e when the photon is emitted at small polar angles

and escapes detection. As a consistency check, we have measured the cross section for e+e in two independent ways, the two values agree well with each other and we

derive (e+e ) = (856 8stat 16syst) pb. This value interpolates well previous measurements by the SND experiment and is more precise. The cross section for e+e

e+e is obtained independently for the two decay modes with a 2-dimensional t to the squared missing mass and the momentum projections. Combining the two measurements we obtain (e+e e+e) = (32.721.27stat 0.70syst) pb. This value is used to extract

the partial width ( ) = (520 20stat 13syst) eV. This is in agreement with the world average of (510 26) eV and is the most precise measurement to date.

Acknowledgments

We wish to thank Fulvio Piccinini and Antonio Polosa for the countless support with the Monte Carlo code for the signal generation and for enlightening discussions. We warmly

18

0 300 325 350 375 400 425 450 475 500

mpp (MeV)

thank our former KLOE colleagues for the access to the data collected during the KLOE data taking campaign. We thank the DA NE team for their e orts in maintaining low background running conditions and their collaboration during all data taking. We want to thank our technical sta : G.F. Fortugno and F. Sborzacchi for their dedication in ensuring e cient operation of the KLOE computing facilities; M. Anelli for his continuous attention to the gas system and detector safety; A. Balla, M. Gatta, G. Corradi and G. Papalino for electronics maintenance; M. Santoni, G. Paoluzzi and R. Rosellini for general detector support; C. Piscitelli for his help during major maintenance periods. This work was supported in part by the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT- 2004-506078; by the European Commission under the 7th Framework Programme through the Research Infrastructures action of the Capacities Programme, Call: FP7-INFRASTRUCTURES-2008-1, Grant Agreement No. 227431; by the Polish National Science Centre through the Grants No. 0469/B/H03/2009/37, 0309/B/H03/2011/40, DEC-2011/03/N/ST2/02641, 2011/01/D/ST2/00748 and by the Foundation for Polish Science through the MPD programme and the project HOMING PLUS BIS/2011-4/3.

Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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