Measurement of meson transition form factors at BESIII
MMeasurement of meson transition form factors at BESIII
Christoph Florian Redmer for the BESIII Collaboration
Institute for Nuclear PhysicsJohannes Gutenberg-University Mainz, 55128 Mainz, GERMANY
Meson transition form factors describe the coupling of photons andhadrons. They are an important input to the calculations of the light-by-light scattering contribution of the anomalous magnetic moment of themuon. At the BESIII experiment in Beijing, the transition form factors ofpseudoscalar mesons are studied in their Dalitz decays, in their radiativeproduction in e + e − annihilation, and in their production in two-photonscattering. All relevant kinematic regimes are covered. An overview ofthe recent results and the status of the ongoing analyses is provided.PRESENTED AT Thirteenth International Conference on the Intersections ofParticle and Nuclear Physics (CIPANP2018)Palm Springs, California, May 28–June 3, 2018 a r X i v : . [ h e p - e x ] O c t Introduction
Meson transition form factors (TFF) describe the interaction of hadronic matterwith two photons of arbitrary virtuality. They represent the difference to point-likeinteractions, as e.g. described by QED. Thus, TFFs also contain valuable informationon the structure of the mesons. Additional interest in TFF comes from the anomalousmagnetic moment of the muons a µ . Here, TFF are needed as experimental input forthe Standard Model (SM) prediction.Being one of the most precisely determined parameters in the SM, a µ is knownto 0 . a µ comes from the BNL ex-periment E821 [3]. Two new experiments are being prepared, which aim at directmeasurement with a fourfold increase of the accuracy. On the one hand, the E989experiment at Fermilab [4] reuses the BNL storage ring and tries to reduce the un-certainties with higher beam intensities and an improved apparatus. On the otherhand, the new experiment at J-PARC [5] uses a beam of ultra cold muons, whichallows to avoid the use of focusing electric fields. As a consequence, there will be twosystematically independent direct measurements of a µ .The SM prediction of a µ contains contributions of all three fundamental interac-tions. While the final result is almost completely given by the contribution of QED,the uncertainty is completely dominated by the hadronic contributions. Due to therunning of the strong coupling constant, these, in contrast to the QED and weakcontributions, cannot be calculated using perturbative methods. The hadronic con-tributions are separated into two parts, the hadronic vacuum polarization contribution a hV Pµ , and the hadronic light-by-light scattering contribution a hLbLµ . Recent activitiesin lattice QCD demonstrated the feasibility of determining the hadronic contributionson the lattice, however, the current accuracy is not yet sufficient to compete with theupcoming experimental accuracy [6]. Another approach is to exploit experimentalinformation to improve the calculations. There is a dispersive approach which allowsto systematically improve the knowledge on a hV Pµ by measuring hadronic cross sec-tions at e + e − machines [7]. The determination of a hLbLµ is more involved. In the past,hadronic models were used to evaluate the light-by-light contribution [1, 9]. All ap-proaches agree on the importance of the individual subprocesses to the light-by-lightscattering, as suggested by de Rafael [8]. The pole contributions of the pseudoscalarmesons π , η and η (cid:48) are most important, followed by the contributions of pion loopsand heavier resonances. Recently, dispersive approaches have been designed [10, 11],aiming at a model independent determination of the most important contributions,1hich also reduces the overall model dependence of a hLbLµ . The most important exper-imental observables needed as input to these calculations are the pseudoscalar mesonTFFs at arbitrary virtualities and the partial waves of the process γ ( ∗ ) γ ( ∗ ) → ππ .Experimentally, TFFs can be determined in three different processes. In the time-like regime, TFFs are measured in Dalitz decays and in the radiative production ofpseudoscalar mesons in e + e − annihilation. Both cases allow to study the TFFs asfunction of a single virtuality, which corresponds to the squared mass of the leptonpair. In the former case, the mass can vary between the rest mass of the leptons andthe rest mass of the decaying meson. In the latter case, the virtuality is fixed to theenergy of the collider.The space-like regime can be studied in e + e − scattering processes, where each ofthe beam leptons emits a photon. The two photons fuse to form a hadronic state. Inprinciple, this process allows to study meson TFFs at arbitrary space-like virtualities.Limitations are given by the detector setups. The smaller the virtualities of thephotons, the smaller are the scattering angles of the leptons. The cross sections of two-photon scattering processes decrease with increasing virtualities. The investigationof two-photon scattering is typically divided into three categories, depending on thepossibility to detect none, one, or both of the scattered leptons in the detector.The BESIII detector is well suited to study meson TFFs in the time-like andspace-like regime using all of the above approaches. The BESIII detector is a magnetic spectrometer [12] located at the Beijing ElectronPositron Collider (BEPCII) [13]. The cylindrical core of the BESIII detector consistsof a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flightsystem (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all en-closed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. Thesolenoid is supported by an octagonal flux-return yoke with resistive plate countermuon identifier modules interleaved with steel. The acceptance of charged particlesand photons is 93% over 4 π solid angle. The charged-particle momentum resolutionat 1 GeV /c is 0 . dE/dx resolution is 6% for the electrons from Bhabhascattering. The EMC measures photon energies with a resolution of 2 .
5% (5%) at1 GeV in the barrel (end cap) region. The time resolution of the TOF barrel part is68 ps, while that of the end cap part is 110 ps.The accelerator BEPCII provides e + e − collisions at center-of-mass energies be-tween √ s = 2 . GeV and 4.6 GeV. The luminosity is optimized for data taking atthe peak of the ψ (3770) resonance, i.e. √ s = 3 .
773 GeV. The design luminosity of10 cm − s − has been reached. Over the past years large data samples have been col-lected at the J/ψ resonance [15], ψ (3686) resonance [16], as well as at and above the2 ) (GeV/c - e + e γ M( ) E ve n t s / ( M e V / c ) ) (GeV/c - e + M(e ) | | F ( q Figure 1: (From Ref. [19]) left:
Invariant mass of e + e − γ . The dashed green lineshows the background contribution from the fit result. The solid red histogram sowsthe remaining background form photon conversion. right: η (cid:48) TFF as function of theinvariant mass of e + e − and fitted with Eq.1 (blue line). ψ (3770) resonance [17, 18], which are used to pursue the BESIII physics program, fo-cusing on charm physics, charmonium and charmoniumlike spectroscopy, light hadronphysics, QCD tests, and precise τ mass measurements. A recent example of the investigation of Dalitz decays of pseudoscalar mesons atBESIII, is the measurement of the decay η (cid:48) → γe + e − [19]. It is the first measurementof the η (cid:48) Dalitz decay with an e + e − pair in the final state. The mesons are taggedby the monochromatic photon in the radiative decay of the J/ψ resonance. From thedata set of 1 . · inclusive J/ψ decays, 864 ±
36 events with a Dalitz decay ofthe η (cid:48) are reconstructed. The most severe background contribution is due to photonconversion in the beam pipe and the detector material. By tracking the lepton pairsback to a common vertex, which is required to be less than 2 cm away from theinteraction point in radial direction, this background could be sufficiently suppressed.The branching ratio is determined as B ( η (cid:48) → γe + e − ) = 4 . ± . stat ± . syst .The mass of the lepton pair is fitted with a single pole approximation of the TFF | F ( q ) | η (cid:48) = Λ (Λ − γ )(Λ − q ) − Λ γ , (1)where Λ and γ correspond to the mass and with of an effective vector meson con-tributing to the decay. The fit results in Λ = (0 . ± . stat ± . syst ) GeV and γ = (0 . ± . stat ± . syst ) GeV. The slope parameter of the TFF is determinedas 1 . ± . stat ± . syst , which is in good agreement with the Lepton-G result,3ased on the Dalitz decay with a muon pair, and the extrapolation of the space-likeCELLO result to the time-like region. The accuracy is at the level of the space-likeextrapolation, which is an improvement compared to the previous time-like result. The study of the radiative decays ψ (3686) → γπ , ηη (cid:48) is a recent result on the ra-diative production of pseudoscalar mesons [21]. The motivation of this analysis alsocomes form the need to improve the understanding of radiative transitions of char-monium resonances. A data set of 448 · inclusive ψ (3686) decays is analyzed. Thepseudoscalar mesons are reconstructed from their most abundant decay modes, wheresimilarities in the topologies between the final states are exploited: π → γγ, η → πππ and η (cid:48) → ηππ , with charged and neutral pions in the η/η (cid:48) decays, respectively. Thefully neutral final state of ψ (3686) → γπ requires additional constraints to suppressbackground from photon conversion. The most severe background contribution comesfrom e + e − → γγ . It can be suppressed by counting the single hits in the MDC in theazimuthal section between the two photon candidates, which are assigned to the π .In total 56053 . ± . η (cid:48) , 382 . ± . η , and 423 . ± . ψ (3686) → π γ . In the latter two cases thenumbers correspond to significances of 7 . σ and 6 . σ , respectively. The branchingratios are determined as B ( ψ (3686) → η (cid:48) γ ) = 125 . ± . stat ± . syst , B ( ψ (3686) → ηγ ) = 0 . ± . stat ± . syst , and B ( ψ (3686) → π γ ) = 0 . ± . stat ± . syst .The analysis is currently extended to the continuum region. The process e + e − → γπ , η, η (cid:48) can be used to study the momentum dependence of TFFs in the range4 . ≤ q [GeV ] ≤ .
16. The pQCD prediction that time- and space-like TFFsbehave identical for large momentum transfers q can be tested. If this is alreadysatisfied in the energy range covered at BESIII, it also allows to shed light on the“BaBar-Belle puzzle” [24, 25], where the space-like TFFs deviate for q < −
10 GeV . Compared to the annihilation cross sections, two-photon scattering is a rare process.Thus, only the largest data sets are used to study space-like TFFs of pseudoscalarmesons at BESIII. The momentum dependence of the TFF is studied in a single-tagtechnique, where only one lepton is scattered into the detector and can be measuredalong with the decay products of the produced meson. Using energy and momentumconservation, the momentum of the unmeasured lepton can be reconstructed. Byplacing a corresponding condition on the polar angle, a minimum momentum transfer,and thus the exchange of a quasi-real photon, is required. The same method wasapplied by CELLO [22], CLEO [23], BaBar [24], and Belle [25], however, in the4 ) (GeV/c η - π + π M( E v en t s / . G e V / c -1 ) ) (GeV/c η - π + π M( E v en t s / . G e V / c -1 ) ) (GeV/c η π π M( E v en t s / . G e V / c -1 ) ) (GeV/c η π π M( E v en t s / . G e V / c -1 ) ) (GeV/c π - π + π M( E v en t s / . G e V / c ) ) (GeV/c π - π + π M( E v en t s / . G e V / c ) ) (GeV/c π π π M( E v en t s / . G e V / c ) ) (GeV/c π π π M( E v en t s / . G e V / c ) ) (GeV/c γγ M( E v en t s / . G e V / c ) ) (GeV/c γγ M( E v en t s / . G e V / c Figure 2: (From Ref. [21]) Mass distributions of individual final states. Left toright: ψ (3686) → γη (cid:48) , ψ (3686) → γη and ψ (3686) → γπ . Top(Bottom): Neutral(Charged) decay modes. The red line illustrates the total fit result. The blue line is thecontinuum background. The green histogram shows the contribution of χ cJ → π π .momentum range of Q = − q ≤ , which is of special importance for a hLbLµ [26],the available information is scarce.The investigation of the π TFF selects event candidates with one lepton and atleast two photons. The data set of 2 .
93 fb − at √ s = 3 .
773 GeV is evaluated. An over-whelming background contribution of radiative Bhabha scattering is effectively sup-pressed by requiring the polar angle of the unmeasured lepton to be | cos θ miss | ≤ . π decay to be | cos θ H | ≤ .
8. Addi-tional background from incompletely reconstructed hadronic final states is rejectedusing the observable R , based on energy and momentum conservation, which wasintroduced by BaBar [24] to suppress radiative effects in two-photon scattering.Remaining background is subtracted in a data-driven approach. In every bin ofmomentum transfer Q the number of π signals in the invariant mass of the decayphoton candidates is fitted. By normalizing the event yield to the reconstructionefficiency and the integrated luminosity, the differential cross section is calculated.The TFF as a function of Q is obtained by dividing out the point-like cross section.Figure 3 shows the preliminary result of the measurement displayed as Q · | F ( Q ) | .Statistical errors as well as the total uncertainty estimate are shown, while the latterdoes not yet contain the uncertainties due to radiative effects. These are underevaluation based on the recently released Ekhara3.0 [27].The BESIII result covers momentum transfers between 0 . ≤ Q [GeV ] ≤ .
1. Itcan be seen from Fig. 3 that information on the π TFF is provided with unprece-5 ] [GeV Momentum Transfer Q ) | [ G e V ] | F ( Q Q CELLO 91CLEO 98BESIII, stat. err. onlyBESIII, stat + syst B E S I I I P r e l i m i n a r y Figure 3: Preliminary result of the π TFF from BESIII (red: statistical uncer-tainty; black: total uncertainty). The results of the CELLO [22] and CLEO [23]collaborations are show for comparison.dented accuracy for Q ≤ . , which is the region most relevant for a hLbLµ . Forlarger values of Q the accuracy is still compatible with previous measurements.An analysis of the TFF of the η and η (cid:48) mesons is performed analogously. Cur-rently, only the charged decay modes η → π + π − π and η (cid:48) → π + π − η are considered,allowing for a common analysis strategy looking for the decay of π /η in two pho-tons. Based on the data taken at √ s = 3 .
773 GeV a competitive statistical accuracyin the momentum range 0 . ≤ Q [GeV ] ≤ . γγ ∗ → π + π − . So far, only the production by two quasireal photons was studied [28]. The analysis at BESIII follows the single-tag strategy,successfully applied to investigate the production of single pseudoscalar mesons. Themain background contributions stem from the two-photon production of muon pairs,and the radiative Bhabha scattering process, in which the photon couples to a ρ -meson, decaying into two pions. While the first kind of background contributioncan be efficiently rejected by combining different detector information for particleidentification in a boosted decision tree, which can be trained by established MCgenerators [29], the latter kind of background is irreducible. It is removed by fittingand subtracting the ρ peak in the π + π − invariant mass. The remaining events allowto study for the first time the reaction γγ ∗ → π + π − at momentum transfers 0 . ≤ Q [GeV ] ≤ .
0, invariant masses between 2 m π ≤ M ππ [GeV] ≤ .
0, at a full coverage6f the pion helicity angle cos θ ∗ . An equivalent analysis of neutral meson systems, i.e. γγ ∗ → π π and γγ ∗ → π η is in preparation. At BESIII, meson TFFs are studied in different kinematic regions. Important input tothe calculations of the hadronic light-by-light scattering contribution to a µ is provided.Based on existing data, unprecedented accuracy is achieved. The continued datataking allows to further improve the accuracy and investigate more rare processes.An important next step in the investigation of two-photon scattering is the mea-surement of doubly-virtual meson TFFs. Due to the small cross section, publishedinformation was not available until recently [30]. The BESIII collaboration has col-lected more than 10 fb − at √ s ≥ .
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