Recently it has been demonstrated that particle factories, such as DAPHNE and
PEP-II, operating at fixed center-of-mass energies, are able to measure
hadronic cross sections as a function of the hadronic system energy using the
raditive return. This paper is an experimental overview of the progress in this
aera. Preliminary results from KLOE for the process e+e- -> \rho \gamma ->
\pi+\pi-\gamma and a fit to the pion form factor are presented. Some first
results from the BABAR collaboration are also shown.Comment: Invited talk presented at RADCOR/Loops and Legs 2002, Kloster
  Banz/Germany, September 8-13 2002, 6 pages, 2 Figures; v1: references added,
  typos correcte

A. Aloisio

A. Antonelli

A. Denig

A. Di Domenico

A. Doria

A. Farilla

A. Ferrari

A. Franceschi

A. Nedosekin

A. Passeri

A. Sciubba

A. Ventura

Adinolfi

Akhmetshin

Aloisio

B. Sciascia

B. Valeriani

Benayoun

Bennett

Berends

Binner

C. Bacci

C. Bini

C. Bloise

C. Di Donato

C. Forti

C. Gatti

C. Kuo

Carloni Calame

Cataldi

Czarnecki

Czyż

D. Leone

Davier

Denig

E. De Lucia

E. Gorini

E. Graziani

E. Pasqualucci

E. Petrolo

E. Santovetti

E. Spiriti

E. Valente

Eidelman

F. Ambrosino

F. Bossi

F. Ceradini

F. Cervelli

F. Cevenini

F. Grancagnolo

F. Lacava

F. Lu

F. Murtas

F. Nguyen

F. Ruggieri

F. Scuri

G. Bencivenni

G. Capon

G. Carboni

G. Cataldi

G. Chiefari

G. De Robertis

G. De Zorzi

G. Felici

G. Finocchiaro

G. Lanfranchi

G. Saracino

G. Venanzoni

G. Xu

G.L. Tong

G.W. Yu

Höfer

I. Sfiligoi

J. Lee-Franzini

Khoze

Kühn

L. Ingrosso

L. Merola

L. Paoluzi

L. Passalacqua

L. Pontecorvo

L. Tortora

M. Antonelli

M. Casarsa

M. Dreucci

M. Incagli

M. Martemianov

M. Matsyuk

M. Moulson

M. Napolitano

M. Palutan

M. Primavera

M.L. Ferrer

O. Erriquez

P. Branchini

P. Campana

P. Ciambrone

English

arXiv

The cross section σ(e+e-→π+π-γ) has been measured with the KLOE detector at the electron-positron collider DAΦNE, at an energy W=mφ=1.02 GeV. We perform this measurement as a function of the π+π- invariant mass, Mππ. The photon in the above process is due to Initial State Radiation. Dividing by a theoretical radiator function, we obtain the cross section σ(e+e-→π+π-) for the mass range  with an overall accuracy of 1.3%. We also calculate the hadronic contribution of the two-pion channel to the anomalous magnetic moment of the muon for the given mass range amupipi = (388.7+-0.8+-3.5+-3.5)*10^-10

Denig, A

GORINI, Edoardo

PRIMAVERA, Margherita

VENTURA, Andrea

Archivio Istituzionale della Ricerca- Università del Salento

April 14, 2005 10:29 WSPC/139-IJMPA 02367International Journal of Modern Physics AVol. 20, Nos. 8 & 9 (2005) 1935–1938c© World Scientific Publishing CompanyMEASUREMENT OF THE HADRONIC CROSS SECTIONVIA RADIATIVE RETURN AT DAΦNEACHIM G. DENIGPresented for the KLOE Collaboration∗Universität Karlsruhe, IEKP, Postfach 3640, 76021 Karlsruhe, GermanyThe cross section σ(e+e− → π+π−γ) has been measured with the KLOE detector at theelectron-positron collider DAΦNE, at an energy W = mφ = 1.02 GeV. We perform thismeasurement as a function of the π+π− invariant mass, Mππ . The photon in the aboveprocess is due to Initial State Radiation. Dividing by a theoretical radiator function, weobtain the cross section σ(e+e− → π+π−) for the mass range 0.35 < M2ππ < 0.95 GeV2with an overall accuracy of 1.3%. We also calculate the hadronic contribution of thetwo-pion channel to the anomalous magnetic moment of the muon for the given massrange: aππµ = (388.7 ± 0.8stat ± 3.5syst ± 3.5theo) · 10−10 .Keywords: Muon anomaly; hadronic cross section; pion electromagnetic formfactor.1. Hadronic Cross Section at DAΦNEThe recent precision measurement of the muon anomaly aµ at the BrookhavenNational Laboratory with a precision of 0.5 ppm 1 has led to renewed interest inaccurate measurements of the cross section for e+e− annihilation into hadrons.Hadronic contributions to the photon spectral functions due to quark loops arenot calculable in the framework of perturbative QCD. A dispersion relation canhowever be derived, giving the hadronic contribution, ahadrµ , as an integral over thehadronic cross section e+e− → hadrons. The process e+e− → π+π− below 1 GeV∗The KLOE Collaboration: A. Aloisio, F. Ambrosino, A. Antonelli, M. Antonelli, C. Bacci, G. Ben-civenni, S. Bertolucci, C. Bini, C. Bloise, V. Bocci, F. Bossi, P. Branchini, S. A. Bulychjov,R. Caloi, P. Campana, G. Capon, T. Capussela, G. Carboni, G. Cataldi, F. Ceradini, F. Cervelli,F. Cevenini, G. Chiefari, P. Ciambrone, S. Conetti, E. De Lucia, P. De Simone, G. De Zorzi,S. Dell’Agnello, A. Denig, A. Di Domenico, C. Di Donato, S. Di Falco, B. Di Micco, A. Doria,M. Dreucci, O. Erriquez, A. Farilla, G. Felici, A. Ferrari, M. L. Ferrer, G. Finocchiaro, C. Forti,A. Franceschi, P. Franzini, C. Gatti, P. Gauzzi, S. Giovannella, E. Gorini, E. Graziani, M. Incagli,W. Kluge, V. Kulikov, F. Lacava, G. Lanfranchi, J. Lee-Franzini, D. Leone, F. Lu, M. Martemi-anov, M. Matsyuk, W. Mei, L. Merola, R. Messi, S. Miscetti, M. Moulson, S. Müller, F. Murtas,M. Napolitano, A. Nedosekin, F. Nguyen, M. Palutan, E. Pasqualucci, L. Passalacqua, A. Passeri,V. Patera, F. Perfetto, E. Petrolo, L. Pontecorvo, M. Primavera, F. Ruggieri, P. Santangelo, E. San-tovetti, G. Saracino, R. D. Schamberger, B. Sciascia, A. Sciubba, F. Scuri, I. Sfiligoi, A. Sibidanov,T. Spadaro, E. Spiriti, M. Testa, L. Tortora, P. Valente, B. Valeriani, G. Venanzoni, S. Veneziano,A. Ventura, S. Ventura, R. Versaci, I. Villella, G. Xu.1935April 14, 2005 10:29 WSPC/139-IJMPA 023671936 A. G. Denigsπ [GeV2]dσ(e+ e- →π+π-γ)/ds π [nb/GeV2 ]   01020304050607080900.3 0.4 0.5 0.6 0.7 0.8 0.9sπ [GeV2]σ(e+e-→π+π-) [nb]   02004006008001000120014000.3 0.4 0.5 0.6 0.7 0.8 0.9Fig. 1. Left: KLOE measurement of the cross section dσ(e+e− → π+π−γ)/dsπ , plotted as afunction of the two-pion invariant mass sπ . Right: The cross section σ(e+e− → π+π−) extractedfrom this measurement after division by an appropriate radiator function and applying somefurther radiative corrections.is of special importance since it contributes ∼ 60% to the total integral. Taking theso-far most precise measurement of this channel from the CMD-2-collaboration 2(with a 0.6% systematic error), one finds a deviation of 2.7 standard deviations 3between the experimental value of aµ and its standard model prediction.Particle factories such as DAΦNE or the B-factories typically operate at fixedcentre-of-mass energies: W = mφ in the case of DAΦNE. Initial state radiation, ISR,is a complementary approach at particle factories which allows studying hadronicfinal states over the entire energy range (from 2mπ to W ). For a photon with theenergy Eγ , radiated before annihilation of the e+e− pair, the invariant mass of theπ+π− system is given by: M2ππ = sπ = W2 − 2WEγ . In general, from the π+π−γcross section one can deduce the π+π− cross section by means of a radiator functionwhich describes the initial state radiation process in the reaction e+e− → π+π−γ.Our present analysis is based on the observation of ref. 4 5, that for small polarangles of the radiated photon, the ISR process dominates over the FSR process,which on an event-by-event basis is an indistinguishable background to our ISRapproach. In the following we present the cross section measurement of the reac-tion e+e− → π+π−γ with θγ < 15◦ or θγ > 165◦. No explicit photon detectionis done since the KLOE electromagnetic calorimeter (EmC) does not cover an-gles smaller (larger) than 20o (160o). We cut on the di-pion production angle,θππ, which is calculated from the momenta of the two charged tracks. If only onephoton is emitted, the following relation holds exactly: θγ = 180◦ − θππ. An effi-cient and almost background free signal selection can be obtained without photontagging.April 14, 2005 10:29 WSPC/139-IJMPA 02367Measurement of the Hadronic Cross Section via Radiative Return at DAΦNE 19372. Analysis of π+π−γ eventsWe have analyzed KLOE data taken in 2001 with an integrated luminosity of ∼140pb−1. After fiducial volume and selection cuts we collect ∼ 1.5 million events. Toobtain the cross section, we subtract the residual background from the sπ spectrumand divide by the selection efficiency and the integrated luminosity. We brieflycomment in the following on some individual analysis items. Further details can befound in 6. For a detailed description of the KLOE detector, which consists of a highresolution tracking detector (σpT /pT ≤ 0.4%) and an electromagnetic calorimeter(σE/E = 5.7%/√E(GeV)), we refer to ref. 7.Detection of two charged tracks: with polar angles in the range 50◦ − 130◦,coming from a vertex in the fiducial volume R < 8 cm, |z| < 7 cm. The probabilityto reconstruct a vertex in the drift chamber is ∼ 98% and has been studied withπ+π−π0 and π+π− data. The tracking efficiency is 96% and uniform in sπ.Identification of pion tracks: A Likelihood Method (calibrated on real data),using the time of flight of the particle and the shape of the energy deposit in the elec-tromagnetic calorimeter, has been developed to reject e+e− → e+e−γ background.The efficiency of this PID method is ∼ 98%.Background subtraction: µ+µ−γ and π+π−π0 events are rejected by a cut ina kinematic variable called track mass, mtrk This variable is calculated from thereconstructed pion momenta, ~p+, ~p−, applying 4-momentum conservation underthe hypothesis that the final state consists of two particles with the same mass andone photon.Luminosity Measurement: The integrated luminosity is measured with theKLOE detector using large angle Bhabha (LAB) events (50◦ < Θ+,− < 130◦).Due to the excellent momentum resolution of KLOE and the high spatial resolu-tion in determining the polar angle of Bhabha tracks in the EmC, the precisionfor this selection is 0.3% . We assign a total systematic error for the luminositymeasurement of δL = 0.5%th ⊕ 0.3%exp, where the theory error comes from theprecision of the BABAYAGA event generator 9 used for the calculation of radiativecorrections.The value for the total experimental systematic error is 0.9%. In Fig. 1 (left) themeasured cross section dσ(e+e− → π+π−γ)/dsπ is displayed.3. Extraction of the Cross Section e+e− → π+π− and aππµThe π+π−γ cross section data has to be divided by a radiator function in order toextract the cross section e+e− → π+π−. We obtain this radiator function from theMC code PHOKHARA 4 8. Two further radiative corrections have to be applied fora correct evaluation of the dispersion integral: (i) vacuum polarization correctionsmust be subtracted from data ( in order to arrive at the bare cross section) and(ii) the cross section π+π− must be inclusive with respect to FSR. The resultingtwo-pion cross section can be seen in Fig. 1 (right).April 14, 2005 10:29 WSPC/139-IJMPA 023671938 A. G. DenigWe have evaluated the hadronic two-pion contribution to the muon anomaly, aππµ ,by inserting the bare cross section e+e− → π+π− into the dispersion integral.In the energy interval 0.35 < sπ < 0.95GeV2 we find 6: aππµ = (388.7 ± 0.8stat ±3.5syst±3.5theo)·10−10. The theoretical error obtains contributions from the radiatorfunction (0.5% accuracy), from luminosity (0.6%) and from the knowledge of thevacuum polarization (0.2%) and FSR corrections (0.3%). In order to compare ourresult with the CMD-2-measurement, we calculate aππµ in the energy interval 0.37 <sπ < 0.93GeV2. The KLOE result (in 10−10 units) is in good agreement with theCMD-2 value:KLOE aππµ = 375.6± 0.8stat ± 4.9syst+theoCMD-2 reanalysis 2003 2 aππµ = 378.6± 2.7stat ± 2.3syst+theoWe conclude that the KLOE measurement presented here confirms a ∼ 3σ devi-ation between the experimental and theoretical value of the anomalous magneticmoment of the muon. In the energy region above the ρ peak (> 0.65GeV2) it isespecially interesting to compare measurements from e+e− data (CMD-2, KLOE)with the spectral functions from hadronic τ decays (ALEPH, CLEO, OPAL), whichare also used in the evaluation of the dispersion integral using the CVC theorem(after having corrected for isospin breaking effects). KLOE confirms the discrep-ancy previously seen between CMD-2 and τ data. Our data in this energy regionare systematically lower of about 10 − 15% than τ data while being in agreementwithin few percent with CMD-2 10.References1. G.W. Bennett et al [Muon g-2 Coll.], Phys. Rev. Lett 89 (2002) 1018042. R.R. Akhmetshin et al [CMD-2 Coll.], Phys. Lett. B578 (2004) 2853. M. Davier, S. Eidelman, A. Höcker and Z. Zhang, Eur. Phys. J. C31 (2003) 5034. S. Binner, J.H. Kühn, K. Melnikov, Phys. Lett. B 459 (1999) 2795. G. Cataldi, A. Denig, W. Kluge, S. Müller, G. Venanzoni, Frascati Physics Series Vol.XVI (2000) 5696. A. Aloisio et al [KLOE Coll.], hep-ex/0407048, accepted for publication inPhys. Lett.B7. M. Adinolfi et al. [KLOE Coll.], Nucl. Instr. Meth. A488 (2002) 51, Nucl. Instr. Meth.A482 (2002) 3648. G. Rodrigo, A. Gehrmann-De Ridder, M. Guilleaume, J.H. Kühn, Eur. Phys. J. C22(2001) 81, G. Rodrigo, H. Czyż, J.H. Kühn and M. Szopa, Eur. Phys. J. C24 (2002)71, J.H. Kühn, G. Rodrigo, Eur. Phys. J. C25 (2002) 215, H. Czyż, A. Grzelińska,J. H. Kühn, G. Rodrigo, Eur. Phys. J. C27 (2003) 563, H. Czyż, A. Grzelińska,J. H. Kühn, G. Rodrigo, Eur. Phys. J. C33 (2004) 333, H. Czyż, A. Grzelińska,J. H. Kühn, G. Rodrigo, hep-ph/04040789. C.M.C. Calame, C. Lunardini, G. Montagna, O. Nicrosini, F. Piccinini, Nucl.Phys.B584 (2000) 45910. A. Höcker, The Hadronic Contribution to the Muon g-2, hep-ph/0410081

Measurement of the hadronic cross section via radiative return at DAFNE

S. Bertolucci

V. Bocci

S.A. Bulychjov

R. Caloi

V. Casavola

S. Conetti

P. De Simone

S. Dell'Agnello

S. Di Falco

P. Franzini

P. Gauzzi

S. Giovannella

S.W. Han

W. Kluge

V. Kulikov

W. Mei

R. Messi

S. Miscetti

S. Müller

V. Patera

P. Santangelo

R.D. Schamberger

T. Spadaro

P. Valente

Crossref