aa r X i v : . [ h e p - e x ] O c t Proton and kaon timelike form factors from BABAR
S. I. Serednyakov (on behalf of BABAR collaboration) Novosibirsk State University,Budker Institute of Nuclear Physics630090 Novosibirsk, Russia
The latest BABAR results on the proton and kaon timelike form factors (FF) are presented. The special emphasizeis made on comparison of the spacelike and timelike FFs and the rise of the proton FF near threshold. The behaviorof the cross section of e+e- annihilation into hadrons near the nucleon-antinucleon threshold is discussed.
The cross sections of the e + e − annihilation into hadrons are described in terms of the electromagnetic formfactors (FF). In case of production of proton-antiproton pair e + e − → pp (1)the cross section depends on two such functions, electric ( G E ) and magnetic ( G M ) FFs: σ pp ( s ) = πα β C s (cid:20) | G M ( s ) | + τ | G E ( s ) | (cid:21) (2)where s is the e + e − center-of-mass (c.m.) energy squared, β = q − m B / s , C is the Coulomb interactionfactor [ C = y / ( − e − y ) with y = πα ( + β ) / β for protons, and C = τ = s /4 m B .From the measurement of the total cross section the linear combination of squared form factors F ( s ) = τ | G M ( s ) | + | G E ( s ) | τ + F ( s ) is called the effective form factor. It is this function that is measuredin most of experiments.In case of production of kaons pair e + e − → K + K − (4)the expression for the cross section has the following form: σ KK ( s ) = πα β s | F K ( s ) | (5)There are many models describing timelike (TL) FFs, but definite predictions exist only for asymptoticregion s → ∞ : [email protected] XIInd International Workshop “High-Energy Physics and Quantum Field Theory”, June 24 – July 1, 2015, Samara, Russia
FENICEDM2DM1ADONE73BESBABAR M pp– (GeV/c ) C r o ss s ec ti on ( pb ) M pp– (GeV/c ) P r o t on f o r m f ac t o r -2 -1 Figure 1: (Color online)
Left : The e + e − → pp cross section near threshold measured by BABAR [1] andin other experiments. Right : The proton effective form factor [Eq.3] measured by BABAR [1] and in otherexperiments. The curve is the QCD motivated fit [Eq.6]. G E , M ( s ) = G E , M ( − s ) ∼ α s ( s ) / s , (6) F K ( s ) = ( π f K α s ( s )) / s (7)where α s ∼
1/ ln ( s / Λ ) is the strong coupling constant, f K =156 MeV is the K → l ν decay constant.In the BABAR experiment the initial state radiation (ISR) method was developed and used to measure e + e − → hadrons cross sections at energies lower than the collider (c.m.) energy. In this talk the latestresults on the proton and charged kaon TL FFs from BABAR are presented. There are two BABAR experiments [1, 2] on the proton FF, which use different ISR techniques. In the firstmethod called large angle (LA) ISR, the ISR photon and proton-antiproton pair is required to be detected.LA ISR is effective at lower masses m pp < GeV / c . The cross section for the process (1) measured usingLA ISR in the near threshold region [1] is shown in Fig.1 (left). It slowly varies from the threshold up to2.1 GeV/c and then sharply goes down from 0.85 to 0.1 nb. Such a behaviour of the cross section can beexplained by the final state nucleon-antinucleon interaction [3]. The proton FF value is close to 0.5 at thethreshold (Fig.1 (right)). Then it decreases by two orders of magnitude up to 4.5 GeV/c . Some deviationsfrom the s − fit seen at 2.15 GeV/c and 2.9 GeV/c can be understood as contributions of p ∆ (1232) and N (1520) N (1520) intermediate states respectively.In the second BABAR measurement of the proton FF, the ISR photon is required to be emitted at smallangles (SA ISR) and undetected. The SA ISR is effective in the pp mass range above 3 GeV/c .2 XIInd International Workshop “High-Energy Physics and Quantum Field Theory”, June 24 – July 1, 2015, Samara, Russia
BESCLEONUE835E760BABAR (LA ISR)BABAR (SA ISR)SLAC 1993 M pp– (GeV/c ) | G M | -3 -2 s ( nb ) (a)
2E (GeV) s ( nb ) (b)
2E (GeV) s ( nb ) (c) Figure 2: (Color online)
Left : The proton magnetic form factor measured by BABAR [2] and in otherexperiments. The curve is the QCD fit. The SLAC 1993 points are the spacelike form factor data from ep scattering experiment. Right : The cross sections near nucleon-antinucleon threshold [5] for e + e − → π (a),for e + e − → pp , nn (b), and for the sum of pp , nn and 6 π processes (c).The proton FF measured by BABAR using the SA ISR [2] is shown in Fig.2 (left). For comparison, thespacelike (SL) proton FF data are shown. The TL and SL FFs should be equil in the asymptotic limit. Below4 GeV/c the TL values are higher than the SL values by two times (Fig.2 (left)). But beginning from 5GeV/c the tendency of approaching TL data to SL data is seen.As it seen in the Fig.1 (left) the e + e − → pp cross section, measured by BABAR, has a step-like shape witha step height of about 0.85 nb. The similar behaviour is observed for the e + e − → nn cross section [4]. Thesum of these cross sections shown in Fig.2 (right,b) has the step height near 1.7 nb. One can expect that sucha step must be compensated by a similar negative step in the meson production cross section. It was noticedin the work [5] that such 1.7 nb negative step is observed in the e + e − → π cross section. So, the total crosssection (sum of e + e − → π and e + e − → pp , nn ) has no structure (Fig.2 (right,c)). Today there is no clearunderstanding, why only the e + e − → π process is sufficient to compensate the nucleon-antinucleon step. Similar to the proton FF, the charged kaon TL FF was measured at BABAR with LA and SA ISR techniques,allowing to study different K + K − mass ranges. In the first LA measurement [6] the K + K − mass range wasstudied from threshold up to 5 GeV/c . This is the most precise measurement of the e + e − → K + K − processbelow 2.6 GeV/c . The obtained FF values (Fig.3 (left)) are about 4-5 times higher then the asymptotic QCDprediction.In the second kaon FF measurement [7] using the SA ISR technique, the K + K − mass range was extendedup to 7.5 GeV/c . The measured scaled kaon FF ( M K + K − F K ) in the range 2.6-7.5 GeV/c is shown in Fig.33 XIInd International Workshop “High-Energy Physics and Quantum Field Theory”, June 24 – July 1, 2015, Samara, Russia (GeV)s’1.5 2 2.5 3 3.5 4 4.5 5 | + K | F -5 -4 -3 -2 -1 CLEOBABARFitasymptotic QCD prediction (GeV)s’1.5 2 2.5 3 3.5 4 4.5 5 | + K | F -5 -4 -3 -2 -1 CLEOSeth et al.
BABAR (SA ISR) M K + K - (GeV/c ) M K + K - | F K | ( G e V / c ) CZ (NLO)Asy (LO)Asy (NLO)00.511.5 3 4 5 6 70.70.80.9 3.5 4
Figure 3: (Color online)
Left : The charged kaon form factor versus M K + K − (GeV/c ) measured by BABAR[6]. Right : The scaled charged kaon form factor measured by BABAR [7]. Different QCD based predictionsare shown by the curves lying below data points. The region near Ψ ( ) is shown in the inset.(right). The QCD model prediction from different authors are shown by the curves lying below the experi-mental points. The references for these predictions can be found in the original BABAR paper [7]. One cansee in Fig.3 (right) that beginning from 6 GeV/c the BABAR experimental point errors begin to intersectthe QCD prediction. The main conclusion from these data is that the kaon FF begins to approach to theQCD asymptotic limit when energy increases. In recent years, thanks to development of ISR technique at BABAR, a great progress has been achieved inthe experimental study of TL electromagnetic FFs of charged hadrons. In this talk new data are presentedfor proton and charged kaon FF. A comparison with the QCD predictions is made. It was found that atenergy higher than 5 GeV for proton and 6 GeV for the charged kaon the measured FF values begin toapproach to their asymptotic QCD limit.
Acknowledgment . The author expresses his gratitude to V.P. Druzhinin for fruitfull discussion. This workis partially supported in the framework of the State order of the Russian Ministry of Science and Educationand the RFBR grants No. 15-02-01037 and Sci.School 2479.2014.2.
References [1] J. P. Lees et al., (BaBar Collaboration),
Phys. Rev. D , 092005 (2013)[2] J. P. Lees et al., (BaBar Collaboration), Phys. Rev. D , 072009 (2013)4 XIInd International Workshop “High-Energy Physics and Quantum Field Theory”, June 24 – July 1, 2015, Samara, Russia [3] V. F. Dmitriev, A. I. Milstein and S. G. Salnikov, Phys. Atom. Nucl. , 1173 (2014)[4] M. N. Achasov et al. , Phys. Rev. D, , 112007 (2014)[5] A. E. Obrazovsky, S. I. Serednyakov, JETP Letters , 315 (2014)[6] J. P. Lees et al., (BaBar Collaboration), Phys. Rev. D88