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Measurement of hadronic cross section at KLOE/KLOE-2 Veronica De Leo 5 1 University of Messina, Italy 0 2 on behalf of the KLOE/KLOE-2 Collaboration n a J 9 Themeasurementoftheσ(e+e− →π+π−)crosssectionallowstodeter- 1 minethepionformfactor|F |2 andthetwopioncontributiontothemuon π anomaly a . Such a measurement has been performed with the KLOE de- ] µ x tector at DAΦNE, the Frascati φ-factory. e The preliminary results on the combination of the last analysis (KLOE12) - with two previous published (KLOE08, KLOE10) will be presented in the p following. e h [ PACS numbers: PACS numbers come here 1 v 1. Introduction 6 4 Theanomalousmagneticmomentofthemuondefinedasa ≡ gµ−2,can µ 2 4 beaccuratelymeasuredand,withintheSMframework,preciselypredicted[1]. 4 The experimental value of a ((11659208.9±6.3)×10−10) measured at the 0 µ . Brookhaven Laboratory differs from the SM estimates by 3.2 - 3.6 σ [2]. 1 If the deviation is confirmed with higher precision it would signal of new 0 5 physics. 1 The main theoretical uncertainty for a comes from hadronic contribu- µ : v tions. The leading order hadronic term can be derived from a combination i of experimental cross section data, related to e+e− annihilation to hadrons. X At DAΦNE the differential cross section (as a function of m ) for the r ππ a e+e− → π+π−γ initial state radiation (ISR) process is measured. Then, the dipion cross section σ ≡ σ(e+e− → π+π−) has been obtained from: ππ dσ(π+π−γ) s | = σ (s )H(s ,s), (1) ISR ππ π π ds π where the radiator function H is computed from QED with complete NLO corrections and depends on the initial e+e− center of mass energy (1) 2 template˙new printed on January 20, 2015 squared s. The dipion cross section σ obtained from Eq. 1 requires ππ the correction for final state radiation (FSR). Eq. 1 is also valid for the e+e− → µ+µ−γ and e+e− → µ+µ− processes with the same radiator func- tionH.Thus,wecandetermineσ fromtheratiooftheπ+π−γ andµ+µ−γ ππ differential cross sections for the same value of the dipion and dimuon in- variant mass. The pion form factor can then be determined using the following equation: 3 s(cid:48) |F (s(cid:48))|2 = σ0 (s(cid:48))(1+δ )(1−η (s(cid:48))) (2) π πα2β3 ππ(γ) VP π π where δ is the Vacuum Polarization (VP) correction , η accounts for VP π the FSR radiation assuming point-like pions. σ0 is a bare cross section, ππ i.e. corrected for the running of α and inclusive of FSR, defined as [6] em σ0(π+π−,s(cid:48)) = dσ(π+π−γ,ISR)/ds(cid:48) ×σ0(e+e− → µ+µ−γ,s(cid:48)) (3) dσ(µ+µ−γ,ISR)/ds(cid:48) where s(cid:48) = s = s . π µ Many radiative corrections drop out for this ratio method: contributions due to the radiator function (this allows to suppress the related systematic uncertainty of 0.5% for the direct σ measurement), to the integrated lu- ππ minosity (since the data for the π+π−γ and µ+µ−γ processes are collected simultaneously) and finally to the vacuum polarization. 2. Measurement of the e+e− → π+π− cross section at KLOE In the 2008 and 2010 two analyses of the σ(e+e− → π+π−γ) have been performed at DAΦNE with the KLOE detector. A cross section of the detector in the y, z plane is shown in Fig.1. TheKLOE08analysis[7]usedadatasamplecorrespondingtoanintegrated √ luminosity of 240 pb−1 collected at s = m in 2002 and selection cuts in φ which the photon is emitted within a cone of θ < 15◦ around the beamline γ (narrow cones in Fig.1) and the two charged pion tracks have 50◦ < θ < π 130◦ (wideconesinFig. 1). Inthisconfiguration,thephotonisnotdetected and the photon momentum is reconstructed from missing momentum: p(cid:126) (cid:39) γ p (cid:126) = −(p(cid:126) +p(cid:126) ). Theseselectioncutsprovidehighstatisticsdatasample miss + − for the ISR signal events, and significantly reduce contamination from the resonant process e+e− → φ → π+π−π0. Fromthebarecrosssection,thedipioncontributiontothemuonanomaly ∆ππa is measured: µ ∆ππa (0.592 < M < 0.975GeV) = (387.2±3.3)×10−10. µ ππ template˙new printed on January 20, 2015 3 Fig.1. Schematic view of the KLOE detector with selection regions. The KLOE10 analysis [8] was performed requiring events that are se- lectedtohaveaphotonatlargepolaranglesbetween50◦ < θ < 130◦ (wide γ cones in Fig.1), in the same angular region as the pions. This selection allow to access the two pion threshold. However, compared to the measurement with photons at small angles, this condition reduces statistics and increases the background from the process φ → π+π−π0. The dispersionintegralfor∆ππa iscomputedasthesumofthevaluesforσ0 µ ππ(γ) times the kernel K(s), times ∆s = 0.01GeV2 1 (cid:90) smax ∆ππa = dsσ0 (s)K(s). (4) µ 4π3 ππ(γ) smin The following value for the dipion contribution to the muon anomaly ∆ππa was found: µ ∆ππa (0.1−0.85)GeV2 = (478.5±2.0 ±5.0 ±4.5 )×10−10. µ stat exp th ThelastKLOEmeasurementofthee+e− → π+π−crosssection(KLOE12) has been obtained from the ratio between the pion and muon ISR differential cross section. The data sample is the same as for the KLOE08 analysis. The separation between the ππγ and µµγ events is obtained assuming the final state with two charged particles with equal mass M and one pho- TRK ton. The M < 115MeV identifies the muons and M > 130MeV TRK TRK the pions. The selection procedure has been compared to other techniques, such as a kinematic fit or applying a quality cut on the helix fit for both tracks, all leading to consistent results. Trigger, particle identification and tracking efficiencies have been checked using control data samples. The differential µµγ cross section is obtained from the observed event count 4 template˙new printed on January 20, 2015 N and background estimate N , as: obs bkg dσ N −N 1 µµγ obs bkg = (5) ds ∆s (cid:15)(s )L µ µ µ whereListheintegratedluminosityfromRef. [9]and(cid:15)(s )theselection µ efficiency. The bare cross section σ0 (inclusive of FSR, with VP effects ππ(γ) removed) is obtained from the bin-by-bin ratio of the KLOE08 ππγ and the described above µµγ differential cross sections. The bare cross section is used in the dispersion integral to compute ∆ππa . The pion form factor µ |F |2 is extracted using Eq. (2). π Eq. 4 gives ∆ππa = (385.1±1.1 ±2.6 ±0.8 )×10−10 in the interval µ stat exp th 0.35 < M2 < 0.95GeV2. For each bin contributing to the integral, sta- ππ tistical errors are combined in quadrature and systematic errors are added linearly. ThelastthreeKLOEestimationsonthe∆ππa (KLOE08,KLOE10,KLOE12) µ have been compared and are consistent (as you can see in the table 1). Table 1. Comparison of ∆ππa between the KLOE12 and the previous KLOE µ measurements (KLOE08, KLOE10). Measurement ∆aππ(0.35−0.95GeV2)×1010 µ KLOE12 385.1±1.1 ±2.7 stat sys+theo KLOE08 387.2±0.5 ±3.3 stat sys+theo ∆aππ(0.35−0.85GeV2)×1010 µ KLOE12 377.4±1.1 ±2.7 stat sys+theo KLOE10 376.6±0.9 ±3.3 stat sys+theo The preliminary combination of these KLOE results is reported in the fig- ure 2[10]. It is obtained using the Best Linear Unbiased Estimate (BLUE) method [11, 12]. In the Fig. 2 (left) the pion form factor measurements for the three KLOE analysis and the fractional difference (right) are shown[10]. The cross section ratio method used in the KLOE12 measurement reduces significantly the theoretical and the systematic error. The following aµ values are found: ππ aµ (0.1−0.95GeV2) = (487.8±5.7)·10−10 ππ aµ (0.1−0.85GeV2) = (378.1±2.8)·10−10. ππ 3. Conclusion Precision measurements of the pion vector form factor using the Initial State Radiation (ISR) have been performed by the KLOE/KLOE-2 Col- laboration during the last 10 years. The preliminary consolidation of the template˙new printed on January 20, 2015 5 |FKLOEXX|2−|FBLUE|2 |FBLUE|2 Fig.2. Preliminary combination of the last three KLOE results (KLOE08, KLOE10, KLOE12) on the pion form factor measurements (left) and the fractional difference (right) using the Best Linear Unbiased Estimate (BLUE) method [11, 12]. The light blue band in the fractional difference is the statistical error and the dark blue band is the combined statistical and systematic uncertainty[10]. last analysis(KLOE12) with two previously published (KLOE08, KLOE10) oneshasbeenpresented. Theresultconfirmsthecurrentdiscrepancy(∼ 3σ) between the Standard Model (SM) calculation and the experimental value of the muon anomaly a measured at BNL. µ In the near future the γγ Physics program of the KLOE-2 experiment[13] willfurthershedlightinthisfield, withe.g. thestudyoftheradiativewidth ofpseudoscalarmesonsandofthetransitionformfactors[14], thankstothe luminosity upgrade of DAφNE and the KLOE upgrade with the addition of new detectors: low energy [15] and high energy [16] e+e− taggers, an inner tracker [17], crystal calorimeters (CCALT) [18], and tile calorimeters (QCALT) [19]. REFERENCES [1] F. Jegerlehner, A. Nyffeler, Phys. Rept. 477 (2009) 1. M. Davier, A. Hoecker, B. Malaescu, Z. Zhang, Eur. Phys. J. C 71 (2011) 1515. K. Hagiwara, et al., J. Phys. G 38 (2011) 085003. [2] G.W.Bennett,etal.,MuonG-2Collaboration,Phys.Rev.D76(2006)072003. 6 template˙new printed on January 20, 2015 [3] S.J. Brodsky and E. de Rafael, Phys. 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