We present measurements of Collins asymmetries in the inclusive process $e^+e^- \rightarrow h_1 h_2 X$, $h_1h_2=KK,\, K\pi,\, \pi\pi$, at the center-of-mass energy of 10.6 GeV, using a data sample of 468 fb$^{-1}$ collected by the BaBar experiment at the PEP-II $B$ factory at SLAC National Accelerator Center. Considering hadrons in opposite thrust hemispheres of hadronic events, we observe clear azimuthal asymmetries in the ratio of unlike- to like-sign, and unlike- to all charged $h_1 h_2$ pairs, which increase with hadron energies. The $K\pi$ asymmetries are similar to those measured for the $\pi\pi$ pairs, whereas those measured for high-energy $KK$ pairs are, in general, larger.
Light quark ($uds$) Collins asymmetries obtained by fitting the U/L and U/C double ratios as a function of ($z_1$,$z_2$) for kaon pairs. In the first column, the $z$ bins and their respective mean values for the kaon in one hemisphere are reported; in the following column, the same variables for the second kaon are shown; in the third column the mean value of $\sin^2\theta_{th}/(1+\cos^2\theta_{th})$ is summarized, calculated in the RF12 frame; in the last two columns the asymmetry results are summarized. The mean values of the quantities reported in the table are calculated by summing the corresponding values for each $KK$ pair and dividing by the number of $KK$ pairs that fall into each ($z_1$,$z_2$) interval. Note that the $A^{UL}$ and $A^{UC}$ results are strongly correlated since they are obtained by using the same data set.
Light quark ($uds$) Collins asymmetries obtained by fitting the U/L and U/C double ratios as a function of ($z_1$,$z_2$) for kaon pairs. In the first column, the $z$ bins and their respective mean values for the kaon in one hemisphere are reported; in the following column, the same variables for the second kaon are shown; in the third column the mean value of $\sin^2\theta_{2}/(1+\cos^2\theta_{2})$ is summarized, calculated in the RF0 frame; in the last two columns the asymmetry results are summarized. The mean values of the quantities reported in the table are calculated by summing the corresponding values for each $KK$ pair and dividing by the number of $KK$ pairs that fall into each ($z_1$,$z_2$) interval. Note that the $A^{UL}$ and $A^{UC}$ results are strongly correlated since they are obtained by using the same data set.
Light quark ($uds$) Collins asymmetries obtained by fitting the U/L and U/C double ratios as a function of ($z_1$,$z_2$) for $K\pi$ hadron pairs. In the first column, the $z$ bins and their respective mean values for the hadron ($K$ or $\pi$) in one hemisphere are reported; in the following column, the same variables for the second hadron ($K$ or $\pi$) are shown; in the third column the mean value of $\sin^2\theta_{th}/(1+\cos^2\theta_{th})$ is summarized, calculated in the RF12 frame; in the last two columns the asymmetry results are summarized. The mean values of the quantities reported in the table are calculated by summing the corresponding values for each $K\pi$ pair and dividing by the number of $K\pi$ pairs that fall into each ($z_1$,$z_2$) interval. Note that the $A^{UL}$ and $A^{UC}$ results are strongly correlated since they are obtained by using the same data set.
Exclusive production of $\rho^0$ mesons was studied at the COMPASS experiment by scattering 160 GeV/$c$ muons off transversely polarised protons. Five single-spin and three double-spin azimuthal asymmetries were measured as a function of $Q^2$, $x_{Bj}$, or $p_{T}^{2}$. The $\sin \phi_S$ asymmetry is found to be $-0.019 \pm 0.008(stat.) \pm 0.003(syst.)$. All other asymmetries are also found to be of small magnitude and consistent with zero within experimental uncertainties. Very recent calculations using a GPD-based model agree well with the present results. The data is interpreted as evidence for the existence of chiral-odd, transverse generalized parton distributions.
Single-spin azimuthal asymmetries for a transversely (T) polarised target and unpolarised (U) beam.
Single-spin azimuthal asymmetries for a transversely (T) polarised target and unpolarised (U) beam.
Single-spin azimuthal asymmetries for a transversely (T) polarised target and unpolarised (U) beam.
We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from the proton. The kinematic point (theta_lab = 12.3 degrees and Q^2=0.48 (GeV/c)^2) is chosen to provide sensitivity, at a level that is of theoretical interest, to the strange electric form factor G_E^s. The result, A=-14.5 +- 2.2 ppm, is consistent with the electroweak Standard Model and no additional contributions from strange quarks. In particular, the measurement implies G_E^s + 0.39G_M^s = 0.023 +- 0.034 (stat) +- 0.022 (syst) +- 0.026 (delta G_E^n), where the last uncertainty arises from the estimated uncertainty in the neutron electric form factor.
Longitudinally polarized beam. C=L and C=R means left- and right polarization. The second systematic uncertainty arises from the estimated uncertainty inthe neutron electromagnetic from factor.
Results are presented from data recorded in 2009 by the PHENIX experiment at the Relativistic Heavy Ion Collider for the double-longitudinal spin asymmetry, $A_{LL}$, for $\pi^0$ and $\eta$ production in $\sqrt{s} = 200$ GeV polarized $p$$+$$p$ collisions. Comparison of the $\pi^0$ results with different theory expectations based on fits of other published data showed a preference for small positive values of gluon polarization, $\Delta G$, in the proton in the probed Bjorken $x$ range. The effect of adding the new 2009 \pz data to a recent global analysis of polarized scattering data is also shown, resulting in a best fit value $\Delta G^{[0.05,0.2]}_{\mbox{DSSV}} = 0.06^{+0.11}_{-0.15}$ in the range $0.05<x<0.2$, with the uncertainty at $\Delta \chi^2 = 9$ when considering only statistical experimental uncertainties. Shifting the PHENIX data points by their systematic uncertainty leads to a variation of the best-fit value of $\Delta G^{[0.05,0.2]}_{\mbox{DSSV}}$ between $0.02$ and $0.12$, demonstrating the need for full treatment of the experimental systematic uncertainties in future global analyses.
PI0 ASYM(LL) measurements from 2005.
PI0 ASYM(LL) measurements from 2006.
PI0 ASYM(LL) measurements from 2009.
We present a measurement of the cross section and transverse single-spin asymmetry ($A_N$) for $\eta$ mesons at large pseudorapidity from $\sqrt{s}=200$~GeV $p^{\uparrow}+p$ collisions. The measured cross section for $0.5<p_T<5.0$~GeV/$c$ and $3.0<|\eta|<3.8$ is well described by a next-to-leading-order perturbative-quantum-chromodynamics calculation. The asymmetries $A_N$ have been measured as a function of Feynman-$x$ ($x_F$) from $0.2<|x_{F}|<0.7$, as well as transverse momentum ($p_T$) from $1.0<p_T<4.5$~GeV/$c$. The asymmetry averaged over positive $x_F$ is $\langle{A_{N}}\rangle=0.061{\pm}0.014$. The results are consistent with prior transverse single-spin measurements of forward $\eta$ and $\pi^{0}$ mesons at various energies in overlapping $x_F$ ranges. Comparison of different particle species can help to determine the origin of the large observed asymmetries in $p^{\uparrow}+p$ collisions.
ASYM(PEAK) and ASYM(BG) for ETA mesons measured as a function of XF in the range 0.3 < ABS(XF) < 0.7 from the 4X4B triggered dataset. The values represented are the weighted mean of the South and North MPC (Muon Piston Calorimeter). The uncertainties listed are statistical only.
ASYM for ETA mesons measured as a function of XF in the range 0.2 < ABS(XF) < 0.7. Uncertainties listed are those due to the statistics, the XF uncorrelated uncertainties due to extracting the yields, and the correlated relative luminosity uncertainty.
ASYM for ETA mesons measured as a function of PT for ABS(XF) > 0.2. Uncertainties listed are those due to the statistics, the PT uncorrelated uncertainties due to extracting ASYM, and the correlated relative luminosity uncertainty.
We present the midrapidity charged pion invariant cross sections and the ratio of $\pi^-$-to-$\pi^+$ production ($5<p_T<13$ GeV/$c$), together with the double-helicity asymmetries ($5<p_T<12$ GeV/$c$) in polarized $p$$+$$p$ collisions at $\sqrt{s} = 200$ GeV. The cross section measurements are consistent with perturbative calculations in quantum chromodynamics within large uncertainties in the calculation due to the choice of factorization, renormalization, and fragmentation scales. However, the theoretical calculation of the ratio of $\pi^-$-to-$\pi^+$ production when considering these scale uncertainties overestimates the measured value, suggesting further investigation of the uncertainties on the charge-separated pion fragmentation functions is needed. Due to cancellations of uncertainties in the charge ratio, direct inclusion of these ratio data in future parameterizations should improve constraints on the flavor dependence of quark fragmentation functions to pions. By measuring charge-separated pion asymmetries, one can gain sensitivity to the sign of $\Delta G$ through the opposite sign of the up and down quark helicity distributions in conjunction with preferential fragmentation of positive pions from up quarks and negative pions from down quarks. The double-helicity asymmetries presented are sensitive to the gluon helicity distribution over an $x$ range of $\sim$0.03--0.16.
Double-helicity asymmetries and statistical uncertainties for $\pi^+$ and $\pi^-$ hadrons. The primary systematic uncertainties, which are fully correlated between points, are $1.4\times10^{-3}$ from relative luminosity and a $^{+7.0\%}_{-7.7\%}$ scaling uncertainty from beam polarization.
We present measurements of $\pi^-$ and $\pi^+$ elliptic flow, $v_2$, at midrapidity in Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200, 62.4, 39, 27, 19.6, 11.5 and 7.7 GeV, as a function of event-by-event charge asymmetry, $A_{ch}$, based on data from the STAR experiment at RHIC. We find that $\pi^-$ ($\pi^+$) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at $\sqrt{s_{_{\rm NN}}} = \text{27 GeV}$ and higher. At $\sqrt{s_{_{\rm NN}}} = \text{200 GeV}$, the slope of the difference of $v_2$ between $\pi^-$ and $\pi^+$ as a function of $A_{ch}$ exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. Similar centrality dependence is also observed at lower energies.
The distribution of observed charge asymmetry from STAR data.
Pion $v_2${2} as a function of observed charge asymmetry.
$v_2$ difference between $\pi^-$ and $\pi^+$ as a function of charge asymmetry with the tracking efficiency correction, for 30-40% central Au+Au collisions at 200 GeV. The errors are statistical only.
We present the measurement of the transverse single-spin asymmetry of weak boson production in transversely polarized proton-proton collisions at $\sqrt{s} = 500~\text{GeV}$ by the STAR experiment at RHIC. The measured observable is sensitive to the Sivers function, one of the transverse momentum dependent parton distribution functions, which is predicted to have the opposite sign in proton-proton collisions from that observed in deep inelastic lepton-proton scattering. These data provide the first experimental investigation of the non-universality of the Sivers function, fundamental to our understanding of QCD.
The amplitude of the transverse single-spin asymmetry for $W^{+-}$ boson production as a function of $P_T^W$, in the |$y^W$| < 1 region, measured by STAR in proton+proton collisions at $\sqrt{s}=500$ GeV with a recorded luminosity of 25 $pb^{-1}$. The average boson's rapidity value for each $P_T^W$ bin is $y^W=0.0$.
The amplitude of the transverse single-spin asymmetry for $W^{+-}$ boson production as a function of $y^W$, in the 0.5 GeV/c < $P_T^W$ < 10 GeV/c region, measured by STAR in proton+proton collisions at $\sqrt{s}=500$ GeV with a recorded luminosity of 25 $pb^{-1}$. The average boson's transverse-momentum value for each $y^W$-bin is $P_T^W=5.3$ GeV/c.
The amplitude of the transverse single-spin asymmetry for $Z^0$ boson production, measured by STAR in proton+proton collisions at $\sqrt{s}=500$ GeV with a recorded luminosity of 25 $pb^{-1}$.
We report a new high-precision measurement of the mid-rapidity inclusive jet longitudinal double-spin asymmetry, $A_{LL}$, in polarized $pp$ collisions at center-of-mass energy $\sqrt{s}=200$ GeV. The STAR data place stringent constraints on polarized parton distribution functions extracted at next-to-leading order from global analyses of inclusive deep inelastic scattering (DIS), semi-inclusive DIS, and RHIC $pp$ data. The measured asymmetries provide evidence for positive gluon polarization in the Bjorken-$x$ region $x>0.05$.
Inclusive jet $A_{LL}$ vs. parton jet $p_T$ for |eta|<0.5.
Inclusive jet $A_{LL}$ vs. parton jet $p_T$ for 0.5<|eta|<1.0.
$A_{LL}$ model predictions for |eta|<0.5.
We report high-precision measurements of the longitudinal double-spin asymmetry, $A_{LL}$, for midrapidity inclusive jet and dijet production in polarized $pp$ collisions at a center-of-mass energy of $\sqrt{s}=200\,\mathrm{GeV}$. The new inclusive jet data are sensitive to the gluon helicity distribution, $\Delta g(x,Q^2)$, for gluon momentum fractions in the range from $x \simeq 0.05$ to $x \simeq 0.5$, while the new dijet data provide further constraints on the $x$ dependence of $\Delta g(x,Q^2)$. The results are in good agreement with previous measurements at $\sqrt{s}=200\,\mathrm{GeV}$ and with recent theoretical evaluations of prior world data. Our new results have better precision and thus strengthen the evidence that $\Delta g(x,Q^2)$ is positive for $x > 0.05$.
Parton inclusive-jet $p_T$ and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $0.5<|\eta|<1$.
Parton inclusive-jet $p_T$ and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $|\eta|<0.5$.
Parton dijet invariant mass $M_{inv}$ and $A_{LL}$ values with associated uncertainties for the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology.
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