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Had K(S)O-Hac1(S)Ds Hadronic Cross Section Measurements with ISR and the Implications on 9µ 2 - K. Griessinger representing the BA BA R Collaboration Mainz University, Institute for Nuclear Physics, J. -J.-Becherwe9 45, 55099 Mainz, Germany The B-Factories have produced data of unprecedented precision for the measurement of hadronic cross sections. This data, extracted via Initial State Radiation ISR , can be used ( ) to predict the anomaly of the muon gyromagnetic factor, - 2. In this note, the recent -measurements of the channels e+ e- gand,,. e+ e- K+ K- are summa­ BA BA R --+ 7T+7T-7r+7r- --+ rized, which improve the accuracy of the Standard Model prediction of 2 significantly. g,,. - 1 Introduction The muon gyromagnetic factor 9µ can be determined directly fromspin precession measurements and theoretically in the Standard Model. For the latter, the QED and weak contributions to aµ = (9µ 2)/2 can be calculated perturbatively to great precision (a ED (116 584 718.951 ± 0.080) 0-111 and a eak (154 ± 2) 10 112, respectively). In contrast� , the= contribution from 1 - = · strong interaction at ;low energies cannot- be calculated perturbatively due to the magnitude of the ·running strong coupling constant as (s). Therefore a dispersion integral (obtained via the optical theorem) is employed to calculate the hadronic low energy part of aµ from the experimentally determined hadronic cross section O"had( s): 1 E2 aµhad (s Ecu2 t) K(s)o-hac1(s)ds . � = -347r 1m �cut K(s) denotes the analytically known 3 Kernel function, which exhibits an asymptotic l/s decrease. The value of Ecut is chosen such that as(s) is sufficiently small for s > E;ut and thus the remaining part a ad(s > E;ut) can be calculated in a perturbative expansion. This combination leads to a valuet of approximately a ad (6930 ± 49) . 10-112. t = On the purely experimental side, aµ is determined by measuring the differenceof the Larmor and Cyclotron frequency of precessing muons. This led to a very precise measurement in the E821 experiment at Brookhaven National Laboratory with the result aµ (116 592 089±54stat ± 33 ) 10-ll 2. = syst · The direct and theoretical results deviate by approximately 3.50-. Since this discrepancy merely provides a hint at yet no evidence for a deficiency in the Standard Model, more precise data from both sides is of utmost importance. 2 Experimental Setup The B-Factories and Belle are located at SLAC National Accelerator Center in Stanford, BA BA R USA and at KEK in Tsukuba, Japan, respectively. achieved an integrated luminosity of BABAR 530 fb-1, whereas Belle even exceeded 1 ab-1. While running (mostly) at the 'Y'(4S)resonance, this produced a large data set for the study of hadronic cross sections via the process of Initial State� Radiation (ISR). This process takes place when one of the particles in the initial state (e+e- radiates a photon. Since the photon carries a certain amount of CMS-energy E; , the squared center-of-mass energy ist lowered to 2faE; . Owed to the continuous spectrum ) s s' = s of possible photon energies, this gives access to a broad- range of invariant masses over which hadronic cross sections may be measured. 287 � 35 - _i\11 , r! �1 2 0.5 1.5 2 2.5 .. 0.5 1 1.5 2 2.5 4 j LL '"" 1 o�Li o d�c� Jl� ..� - """ _ 3 I 1000 �1 2 l� 0.5 1 1.5 2 2.5 nl0.5 1.5 2 2.5 4 tD 20 � � O 3 I 0 0 0 15 -[2LJ1 .8-'32 G<Vi<' 4 -RL]0.5 1.5 2 2.5 500 �· 0.5 1 2 2.5 2000 1000 ,,- - 250''·. � - 100 3 I �1.5 10 1000 \� ... 0 20000 0 2 4 0.5 1 1.5 2 2.5 0.5 1.5 2 2.5 I \ 50(I 1 · 1 ··� 3 tz;:J KJ I 0 0 0 1 2 3 4 0.5 2 2.5 o.s -�1 �Y2 i 2.5 1.5 2.5 3.5 4.5 1 • •· . ·--. M,_,,(Gevt<:2J' ECM (GeV) 200[z:]'-"""�(GeV/cv'<'2) "'l&:J- "'�1 Figure 1: Left panel: The cross section e+e- -+ measured· at Statistical uncertainties only, w+7r-7r+7r- BA BA R . l t.5 1.5 systematics are listed in Tab. 1. Right panel: Internal structures, data in red, simulation!'11i,(GeVtc2) in bla ck. From top to bottom: slices in the 4tt invariant mass. Left to right: mass, 2rr mass and 21T not originating from p0• 3?r 3 Measurement of the channel e+e- --+7r+7r -7r+7f- 4 The channel e+e- --+ 7r+7r-7f+7r- is not only interesting for its cross section, but also due to its rich internal structures. These are explored by investigating the invariant masses of different particle combinations from the final state as a function of the total invariant mass of the hadronic system, see Fig. 1 (right). In the three-pion mass (left column, 4 entries per event for all combinations), the a1 (1260) is observed clearly, especially in the high-mass slices. The charge neutral two-pion mass, which also contains 4 combinations per event, exhibits a very 0 pronounced p signature. This peak contains approximately one fourth of all entries in each 0 0 0 histogram. Since e+e- --+ p p is forbidden at tree level, this means that there must be one p 0 in each event. When excluding the 7r+7r- combination from the p , the third column of Fig. 1 0 (right) is produced. Here, the additional resonances apart from the p show up much more clearly. In the spectrum, especially the /0(980) and /2(1270) can be observed quite nicely at intermediate and large total hadronic energies. The cross section itself is shown in Fig. 1 (left) with its statistical uncertainties. The systematics are listed in Tab. 1. This very precise measurement improves the low-energy (0.6GeV < < l.8GeV) prediction of a ad 7r+7r-7f+7r- from a ad 7r+7r-7r+7r- (133.5 ± 10-11, calculated using the previous world data set (including the= smaller l.Ostat ± 5.2s,,/8st · ( ( data yset from 2006), to a ad 7r+7f-7r+7rt - (136.4 ) 0.38tatt ± 3.68 ) 10-)1 1, only with BA BA R ± yst · the measurement) . BA BA R ( t ) = Table 1: Systematic uncertainties of the e e cross section measured at + - ---r 7T+7r-7r+7T- BABAR . Mha<l <LlGeV l.1GeV :::;h M a<l :::; 2.8GeV >2.8GeV 11 % 2.4% 4% 0"8yst 4 Measurement of the channel e+ e- --+K+ K- 5 Another channel that had yet to be measured with high precision was the production of two charged Kaons. At it has now been analyzed using � 232 fb-1, yielding the cross section BA BA R with a very large ¢ peak shown in Fig. 2. Remarkably small uncertainties down to 0. 7 % in 288 o :-�-,��_,.,�,,---�-�-��j� ?'1 ' i' - 0 � 10' ' -� j '(·· \"; ,,,:-;:; lCt>\. l Figure 2: Cross section e+ e- --+ K+ K- measured at· (left, J/.,P and .,P(2S) removed) and the corresponding BABAR squared Kaon form factor (right) including a BW-fit (blue) . Statistical and systematic uncertainties shown. Bf\BAR I� OL'i/..EiABARFil Fit ,� $ND c; osl SNO 0.6l- I ! jJ 04fc 1,l ' lI � 02r- l � i Ir1 ! l i � 0 4� �\r:1 0 g· 1 -06� i -1 ���cL-��,_,__-"-'=�- <-Lo--->�-��c'.-"-� -0.8,1 1.05 1.1 1.15 1.25 1.3 1.35 1.4 1.2 J;i C:e\\ ·I Figure 3: Deviation between the fit to the squared Kaon form factor measured at and SND data in the ¢ BABA R region (left) and in a wider energy range (right), also including OLYA. the <f; peak region were achieved especially by very diligently studying Kaon particle (mis-)­ identificationand the !SR-luminosity, which is calculated from e+e- -+ µ+µ-"( event rates. Fromthis cross section, the corresponding formfactor is extracted, see Fig. 2. It is parametrized by a sum of Breit-Wigner distributions: FK(s) (arp · BWrp(s) + arp' · BW4,,(s) + arp" · BWrpn (s))/3 + (ap · BWp(s) + ap' · BWp'(s) + ap" · BWpn(s) + ap'" · BWpm(s))/2 + (aw · BWw(s) +aw' · BWw'(s) + aw" · BWwn(s) + aw"' · BWwm(s))/6 with arp+ arp' + arp" 1 , ap + ap' + ap" + ap"' 1 , + aw' + aw" + aw"' 1 . = = aw = Using the fit to the BABAR data, the results from other experiments can be compared to BA BAR . This is shown in Fig. 3 and some interesting deviations are found. There is a small wiggle around the <f; mass, which is due to calibration differences of the experiments and is covered by the experimental uncertainties. More importantly for the determination of 9µ 2, there seems to be a normalization differencebetween data fromB ABAR and the experiments from- Novosibirsk (SND and CMD2). While in the low-mass region around the <f; SND and CMD2 show a smaller formfact or, above l.15 GeV the form factor from SND is considerably � larger (CMD2 has not yet publishedR their result in the full energy range). Furthermore the measurement of the form factor can be compared to theoretical predic­ tions 6,7 in the high-energy regime. For large values of R, 289 with n = 2 is predicted in a perturba­ CLEO tive approach. While the measurement con­ • BABAR firmsthe exponent with a fitted (in the regime OF• it QCD Vs'>2.5 GeV) value of n = 2.10 ± 0.23 and - asymptotic prediction agrees with the point from CLEO at Vs' 3.8 GeV, the overall scaling is offby roughly ,:::::;a factor of 20, as seen in Fig.
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