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Register a new userToward $e^+e^-to pi^+pi^-$ annihilation inspired by higher $rho$ mesonic states around 2.2 GeV
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Very recently, the {it BABAR} Collaboration indicated that there exist an explicit enhancement structure near 2.2 GeV when focusing on the $e^+e^-topi^+pi^-$ process again, which inspires our interest in studying the production of higher $rho$ mesonic states. Since the branching ratio of $pi^+pi^-$ channel of $D-$wave $rho$ states are much smaller than $S-$wave states, we choose $rho(1900)$ and $rho(2150)$ as the intermediate states in $e^+e^-topi^+pi^-$, where $rho(1900)$ and $rho(2150)$ are treated as $rho(3S)$ and $rho(4S)$ states, respectively. Our result indicates that the $BABAR$s data of $e^+e^-topi^+pi^-$ around 2 GeV can be depicted well, which shows that this enhancement structure near 2.2 GeV existing in $e^+e^-topi^+pi^-$ can be due to the contribution from two $rho$ mesons, $rho(1900)$ and $rho(2150)$. Additionally, this conclusion can be enforced by the consistence of the extracted values of $Gamma_{e^+e^-}mathcal{B}(pi^+pi^-)$ of $rho(1900)$ and $rho(2150)$ in the whole fitting processes and the corresponding theoretical calculations. The present study of $e^+e^-topi^+pi^-$ data may provide valuable information to establish the $rho$ meson family.
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The cross section of the process e+e- -> pi+pi- has been measured using about 114000 events collected by the CMD-2 detector at the VEPP-2M e+e- collider in the center-of-mass energy range from 0.61 to 0.96 GeV. Results of the pion form factor determination with a 0.6% systematic uncertainty are presented. Implications for the hadronic contribution to the muon anomalous magnetic moment are discussed.
C-odd asymmetry can be studied from an accurate measurement of the angular distribution due to the interference between the S- and P-waves in e+e- --> pi+ pi- at order alpha^3. The asymmetry is dominated by the pion rescattering diagram which is enhanced by the presence of the ln(s/m^2_e), and is quite large (10% at theta=30^0 and sqrt{s} < M_{f_2}) compared to alpha/pi=0.3%. This process can also be used for alternatively measuring the size of the rescattering term and the phase of the S-wave amplitude, but does not help to solve the present discrepancy between the hadronic spectral functions from e+e- and tau-decay data.
We report measurements of the observed cross sections for $e^+e^-toomega pi^+pi^-$, $omega K^+K^-$, $omega pbar p$, $K^+K^-rho^0pi^0$, $K^+K^-rho^+pi^-+c.c.$, $K^{*0}K^-pi^+pi^0+c.c.$, $K^{*+}K^-pi^+pi^-+c.c.$, $phipi^+pi^-pi^0$ and $Lambda bar Lambda pi^0$ at $sqrt s=$ 3.773 and 3.650 GeV. Upper limits (90% C.L.) are given for observed cross sections and for $psi(3770)$ decay branching fractions for production of these final states. These measurements are made by analyzing the data sets of 17.3 pb$^{-1}$ collected at $sqrt{s}=3.773$ GeV and 6.5 pb$^{-1}$ collected at $sqrt{s}=3.650$ GeV with the BES-II detector at the BEPC collider.
We consider the $pi^+pi^-pi_0gamma$ final state in electron-positron annihilation at cms energies not far from the threshold. Both initial and final state radiations of the hard photon is considered but without interference between them. The amplitude for the final state radiation is obtained by using the effective Wess-Zumino-Witten Lagrangian for pion-photon interactions valid for low energies. In real experiments energies are never such small that $rho$ and $omega$ mesons would have negligible effect. So a phenomenological Breit-Wigner factor is introduced in the final state radiation amplitude to account for the vector mesons influence. Using radiative 3$pi$ production amplitudes, a Monte Carlo event generator was developed which could be useful in experimental studies.
This work reports the first observation of azimuthal asymmetries around the thrust axis in $e^+e^-$ annihilation of pairs of back-to-back charged pions in one hemisphere, and $pi^0$ and $eta$ mesons in the opposite hemisphere. These results are complemented by a new analysis of pairs of back-to-back charged pions. The $pi^0$ and $eta$ asymmetries rise with the relative momentum $z$ of the detected hadrons as well as with the transverse momentum with respect to the thrust axis. These asymmetries are sensitive to the Collins fragmentation function $H_1^{perp}$ and provide complementary information to previous measurements with charged pions and kaons in the final state. In particular, the $eta$ final states will provide additional information on the flavor structure of $H_1^{perp}$. This is the first measurement of the explicit transverse-momentum dependence of the Collins fragmentation function from Belle data. It uses a dataset of 980.4~fb$^{-1}$ collected by the Belle experiment at or near a center-of-mass energy of 10.58 GeV.
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