Measurement of the $W$ charge asymmetry in the $W \to \mu \nu$ decay mode in $pp$ collisions at $\sqrt s=7$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Phys.Lett.B 701 (2011) 31-49, 2011.
Inspire Record 892704 DOI 10.17182/hepdata.85594

This letter reports a measurement of the muon charge asymmetry from W Boson produced in proton-proton collisions at a centre-of-mass energy of 7 TeV with the ATLAS experiment at the LHC. The asymmetry is measured in the W Boson to muon decay mode as a function of the muon pseudorapidity using a data sample corresponding to a total integrated luminosity of 31 pb-1. The results are compared to predictions based on next-to-leading order calculations with various parton distribution functions. This measurement provides information on the u and d quark momentum fractions in the proton.

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Measurement of the charge asymmetry in highly boosted top-quark pair production in $\sqrt{s} =$ 8 TeV $pp$ collision data collected by the ATLAS experiment

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Phys.Lett.B 756 (2016) 52-71, 2016.
Inspire Record 1410588 DOI 10.17182/hepdata.77021

In the $pp \rightarrow t\bar{t}$ process the angular distributions of top and anti-top quarks are expected to present a subtle difference, which could be enhanced by processes not included in the Standard Model. This Letter presents a measurement of the charge asymmetry in events where the top-quark pair is produced with a large invariant mass. The analysis is performed on 20.3 fb$^{-1}$ of $pp$ collision data at $\sqrt{s} =$ 8 TeV collected by the ATLAS experiment at the LHC, using reconstruction techniques specifically designed for the decay topology of highly boosted top quarks. The charge asymmetry in a fiducial region with large invariant mass of the top-quark pair ($m_{t\bar{t}} > $ 0.75 TeV) and an absolute rapidity difference of the top and anti-top quark candidates within $-$2 $ < |y_t| - |y_{\bar{t}}| <$ 2 is measured to be 4.2 $\pm$ 3.2%, in agreement with the Standard Model prediction at next-to-leading order. A differential measurement in three $t\bar{t}$ mass bins is also presented.

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Measurement of the charge asymmetry in top-quark pair production in the lepton-plus-jets final state in pp collision data at $\sqrt{s}=8\,\mathrm TeV{}$ with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Eur.Phys.J.C 76 (2016) 87, 2016.
Inspire Record 1392455 DOI 10.17182/hepdata.75528

This paper reports inclusive and differential measurements of the $t\bar{t}$ charge asymmetry $A_{\textrm{C}}$ in 20.3 fb$^{-1}$ of $\sqrt{s} = 8$ TeV $pp$ collisions recorded by the ATLAS experiment at the Large Hadron Collider at CERN. Three differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the $t\bar{t}$ system. The $t\bar{t}$ pairs are selected in the single-lepton channels ($e$ or $\mu$) with at least four jets, and a likelihood fit is used to reconstruct the $t\bar{t}$ event kinematics. A Bayesian unfolding procedure is performed to infer the asymmetry at parton level from the observed data distribution. The inclusive $t\bar{t}$ charge asymmetry is measured to be $A_{\textrm{C}} = 0.009 \pm 0.005$ (stat.$+$syst.). The inclusive and differential measurements are compatible with the values predicted by the Standard Model.

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Measurement of the forward-backward asymmetry of electron and muon pair-production in $pp$ collisions at $\sqrt{s}$ = 7 TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
JHEP 09 (2015) 049, 2015.
Inspire Record 1351916 DOI 10.17182/hepdata.76996

This paper presents measurements from the ATLAS experiment of the forward-backward asymmetry in the reaction $pp\rightarrow Z/\gamma^{*}\rightarrow l^{+}l^{-}$, with $l$ being electrons or muons, and the extraction of the effective weak mixing angle. The results are based on the full set of data collected in 2011 in $pp$ collisions at the LHC at $\sqrt{s}$ = 7 TeV, corresponding to an integrated luminosity of 4.8 fb$^{-1}$. The measured asymmetry values are found to be in agreement with the corresponding Standard Model predictions. The combination of the muon and electron channels yields a value of the effective weak mixing angle of $0.2308 \pm 0.0005 \mathrm{(stat.)} \pm 0.0006 \mathrm{(syst.)} \pm 0.0009\mathrm{(PDF)}$, where the first uncertainty corresponds to data statistics,the second to systematic effects and the third to knowledge of the parton density functions. This result agrees with the current world average from the Particle Data Group fit.

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Observation of a Centrality-Dependent Dijet Asymmetry in Lead-Lead Collisions at $\sqrt{s_{NN}}=2.77$ TeV with the ATLAS Detector at the LHC

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Phys.Rev.Lett. 105 (2010) 252303, 2010.
Inspire Record 878733 DOI 10.17182/hepdata.63790

Using the ATLAS detector, observations have been made of a centrality-dependent dijet asymmetry in the collisions of lead ions at the Large Hadron Collider. In a sample of lead-lead events with a per-nucleon center of mass energy of 2.76 TeV, selected with a minimum bias trigger, jets are reconstructed in fine-grained, longitudinally-segmented electromagnetic and hadronic calorimeters. The underlying event is measured and subtracted event-by-event, giving estimates of jet transverse energy above the ambient background. The transverse energies of dijets in opposite hemispheres is observed to become systematically more unbalanced with increasing event centrality leading to a large number of events which contain highly asymmetric dijets. This is the first observation of an enhancement of events with such large dijet asymmetries, not observed in proton-proton collisions, and which may point to an interpretation in terms of strong jet energy loss in a hot, dense medium.

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Measurement of the production and lepton charge asymmetry of $W$ bosons in Pb+Pb collisions at $\mathbf {\sqrt{\mathbf {s}_{\mathrm {\mathbf {NN}}}}=2.76\;TeV}$ with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Eur.Phys.J.C 75 (2015) 23, 2015.
Inspire Record 1311623 DOI 10.17182/hepdata.66358

A measurement of $\textit{W}$ boson production in lead-lead collisions at $\sqrt{s_{\mathrm{NN}}}=$2.76 TeV is presented. It is based on the analysis of data collected with the ATLAS detector at the LHC in 2011 corresponding to an integrated luminosity of 0.14 $\mathrm{nb}^{-1}$ and 0.15 $\mathrm{nb}^{-1}$ in the muon and electron decay channels, respectively. The differential production yields and lepton charge asymmetry are each measured as a function of the average number of participating nucleons $< N_{\mathrm{part}} >$ and absolute pseudorapidity of the charged lepton. The results are compared to predictions based on next-to-leading-order QCD calculations. These measurements are, in principle, sensitive to possible nuclear modifications to the parton distribution functions and also provide information on scaling of $\textit{W}$ boson production in multi-nucleon systems.

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Search for contact interactions and large extra dimensions in the dilepton channel using proton-proton collisions at $\sqrt{s}$ = 8 TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Eur.Phys.J.C 74 (2014) 3134, 2014.
Inspire Record 1305430 DOI 10.17182/hepdata.65760

A search is conducted for non-resonant new phenomena in dielectron and dimuon final states, originating from either contact interactions or large extra spatial dimensions. The LHC 2012 proton-proton collision dataset recorded by the ATLAS detector is used, corresponding to 20 fb$^{-1}$ at $\sqrt{s}$ = 8 TeV. The dilepton invariant mass spectrum is a discriminating variable in both searches, with the contact interaction search additionally utilizing the dilepton forward-backward asymmetry. No significant deviations from the Standard Model expectation are observed. Lower limits are set on the $\ell\ell q q$ contact interaction scale $\Lambda$ between 15.4 TeV and 26.3 TeV, at the 95% credibility level. For large extra spatial dimensions, lower limits are set on the string scale $M_{S}$ between 3.2 TeV to 5.0 TeV.

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Measurement of the inclusive $W^\pm$ and Z/gamma cross sections in the electron and muon decay channels in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Phys.Rev.D 85 (2012) 072004, 2012.
Inspire Record 928289 DOI 10.17182/hepdata.58162

The production cross sections of the inclusive Drell-Yan processes W to l nu and Z/gamma to ll (l=e,mu) are measured in proton-proton collisions at sqrt(s) = 7 TeV with the ATLAS detector. The cross sections are reported integrated over a fiducial kinematic range, extrapolated to the full range and also evaluated differentially as a function of the W decay lepton pseudorapidity and the Z boson rapidity, respectively. Based on an integrated luminosity of about 35 pb^-1 collected in 2010, the precision of these measurements reaches a few per cent. The integrated and the differential W+- and Z/gamma cross sections in the e and mu channels are combined, and compared with perturbative QCD calculations, based on a number of different parton distribution sets available at NNLO.

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Measurement of the forward - backward asymmetries for charm and bottom quark pair productions at S**(1/2) = 58-GeV with electron tagging

The TOPAZ collaboration Nakano, E. ; Enomoto, R. ; Iwasaki, M. ; et al.
Phys.Lett.B 340 (1994) 135-142, 1994.
Inspire Record 39496 DOI 10.17182/hepdata.28532

We have measured, with electron tagging, the forward-backward asymmetries of charm- and bottom-quark pair productions at $\langle \sqrt{s} \rangle$=58.01GeV, based on 23,783 hadronic events selected from a data sample of 197pb$~{-1}$ taken with the TOPAZ detector at TRISTAN. The measured forward-backward asymmetries are $A_{FB}~c = -0.49 \pm 0.20(stat.) \pm 0.08 (sys.)$ and $A_{FB}~b = -0.64 \pm 0.35(stat.) \pm 0.13 (sys.)$, which are consistent with the standard model predictions.

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Measurement of the forward - backward asymmetry of e+ e- ---> c anti-c at s**(1/2) = 57.95-GeV

The TOPAZ collaboration Nakano, E. ; Enomoto, R. ; Abe, K. ; et al.
Phys.Lett.B 314 (1993) 471-476, 1993.
Inspire Record 361662 DOI 10.17182/hepdata.28846

Measurements of the forward-backward asymmetry of e + e − → cc events were carried out at a mean √s energy of 57.95 GeV at TRISTAN, KEK. The cc events were tagged either by the full-reconstruction of D ∗± or the inclusive P T spectrum of π s ± from D ∗± → D 0 ( D 0 )π s ± . The forward-backward asymmetry was measured to be A FB c = −0.49 −0.13 +0.14 (stat.) ± 0.06 (syst.), consistent with the standard model.

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Measurement of A(c) with charmed mesons at SLD

The SLD collaboration Abe, Kenji ; Abe, Koya ; Abe, Toshinori ; et al.
Phys.Rev.D 63 (2001) 032005, 2001.
Inspire Record 533573 DOI 10.17182/hepdata.41721

We present a direct measurement of the parity-violation parameter $A_c$ in the coupling of the $Z^0$ to $c$-quarks with the SLD detector. The measurement is based on a sample of 530k hadronic $Z^0$ decays, produced with a mean electron-beam polarization of $|P_e| = 73 %$. The tagging of $c$-quark events is performed using two methods: the exclusive reconstruction of $D^{\ast+}$, $D^+$, and $D^0$ mesons, and the soft-pions ($\pi_s$) produced in the decay of $D^{\ast+}\to D^0 \pi_s^+$. The large background from $D$ mesons produced in $B$ hadron decays is separated efficiently from the signal using precision vertex information. The combination of these two methods yields $A_c = 0.688 \pm 0.041.$

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Measurement of the lepton forward-backward asymmetry in $B \rightarrow X_s \ell^+ \ell^-$ decays with a sum of exclusive modes

The Belle collaboration Sato, Y. ; Ishikawa, A. ; Yamamoto, H. ; et al.
Phys.Rev.D 93 (2016) 032008, 2016.
Inspire Record 1283183 DOI 10.17182/hepdata.64698

We report the first measurement of the lepton forward-backward asymmetry ${\cal A}_{\rm FB}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B \rightarrow X_s \ell^+ \ell^-$ with a sum of exclusive final states, where $\ell$ is an electron or a muon and $X_s$ is a hadronic recoil system with an $s$ quark. The results are based on a data sample containing $772\times10^6$ $B\bar{B}$ pairs recorded at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. ${\cal A}_{\rm FB}$ for the inclusive $B \rightarrow X_s \ell^+ \ell^-$ is extrapolated from the sum of 10 exclusive $X_s$ states whose invariant mass is less than 2 GeV/$c^2$. For $q^2 > 10.2$ GeV$^2$/$c^2$, ${\cal A}_{\rm FB} < 0$ is excluded at the 2.3$\sigma$ level, where $\sigma$ is the standard deviation. For $q^2 < 4.3$ GeV$^2$/$c^2$, the result is within 1.8$\sigma$ of the Standard Model theoretical expectation.

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Measurement of the polarized forward - backward asymmetry of Z0 ---> b anti-b using a lifetime tag and momentum weighted track charge

The SLD collaboration Abe, K. ; Abt, I. ; Ahn, C.J. ; et al.
1995.
Inspire Record 398301 DOI 10.17182/hepdata.18618
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Measurement of the left-right forward - backward asymmetry for charm quarks with D*+ and D+ mesons

The SLD collaboration Abe, K. ; Abt, I. ; Ahn, C.J. ; et al.
Phys.Rev.Lett. 75 (1995) 3609-3613, 1995.
Inspire Record 404272 DOI 10.17182/hepdata.19646

We present a direct measurement of Ac=2vcac(vc2+ac2) from the left-right forward-backward asymmetry of D*+ and D+ mesons in Z0 events produced with the longitudinally polarized SLAC Linear Collider beam. These Z0→cc¯ events are tagged on the basis of event kinematics and decay topology from a sample of hadronic Z0 decays recorded by the SLAC Large Detector. We measure Ac0=0.73±0.22(stat)±0.10(syst).

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Direct measurement of leptonic coupling asymmetries with polarized Zs

The SLD collaboration Abe, K. ; Akagi, T. ; Allen, N.J. ; et al.
Phys.Rev.Lett. 79 (1997) 804-808, 1997.
Inspire Record 442260 DOI 10.17182/hepdata.19552

We present direct measurements of the $Z~0$-lepton coupling asymmetry parameters, $A_e$, $A_\mu$, and $A_\tau$, based on a data sample of 12,063 leptonic $Z~0$ decays collected by the SLD detector. The $Z$ bosons are produced in collisions of beams of polarized $e~-$ with unpolarized $e~+$ at the SLAC Linear Collider. The couplings are extracted from the measurement of the left-right and forward-backward asymmetries for each lepton species. The results are: $A_e=0.152 \pm 0.012 {(stat)} \pm 0.001 {(syst)}$, $A_\mu=0.102 \pm 0.034 \pm 0.002$, and $A_\tau=0.195 \pm 0.034 \pm 0.003$.

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An Improved direct measurement of leptonic coupling asymmetries with polarized Z bosons

The SLD collaboration Abe, Koya ; Abe, Kenji ; Abe, T. ; et al.
Phys.Rev.Lett. 86 (2001) 1162-1166, 2001.
Inspire Record 534735 DOI 10.17182/hepdata.41720

We present final measurements of the Z boson-lepton coupling asymmetry parameters Ae, Amu, and Atau with the complete sample of polarized Z bosons collected by the SLD detector at the SLAC Linear Collider. From the left-right production and decay polar angle asymmetries in leptonic Z decays we measure Ae = 0.1544 +- 0.0060, Amu = 0.142 +- 0.015, and Atau = 0.136 +- 0.015. Combined with our left-right asymmetry measured from hadronic decays, we find Ae = 0.1516 +- 0.0021. Assuming lepton universality, we obtain a combined effective weak mixing angle of sin**2 theta^{eff}_W = 0.23098 +- 0.00026.

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Measurement of Parity-Violating Asymmetry in Electron-Deuteron Inelastic Scattering

Wang, D. ; Pan, K. ; Subedi, R. ; et al.
Phys.Rev.C 91 (2015) 045506, 2015.
Inspire Record 1327482 DOI 10.17182/hepdata.72848

The parity-violating asymmetries between a longitudinally-polarized electron beam and an unpolarized deuterium target have been measured recently. The measurement covered two kinematic points in the deep inelastic scattering region and five in the nucleon resonance region. We provide here details of the experimental setup, data analysis, and results on all asymmetry measurements including parity-violating electron asymmetries and those of inclusive pion production and beam-normal asymmetries. The parity-violating deep-inelastic asymmetries were used to extract the electron-quark weak effective couplings, and the resonance asymmetries provided the first evidence for quark-hadron duality in electroweak observables. These electron asymmetries and their interpretation were published earlier, but are presented here in more detail.

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Observation of Transverse Spin-Dependent Azimuthal Correlations of Charged Pion Pairs in $p^\uparrow+p$ at $\sqrt{s}=200$ GeV

The STAR collaboration Adamczyk, L. ; Adkins, J.K. ; Agakishiev, G. ; et al.
Phys.Rev.Lett. 115 (2015) 242501, 2015.
Inspire Record 1357596 DOI 10.17182/hepdata.73282

We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in $p^\uparrow+p$ collisions at RHIC. These correlations directly probe quark transversity distributions. We measure signals in excess of five standard deviations at high transverse momenta, at high pseudorapidities eta>0.5, and for pair masses around the mass of the rho-meson. This is the first direct transversity measurement in p+p collisions. Comparing the results to data from lepton-nucleon scattering will test the universality of these spin-dependent quantities.

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Separated cross-sections in pi0 electroproduction at threshold at Q**2 = 0.05-GeV**2/c**2

The A1 collaboration Weis, M. ; Bartsch, P. ; Baumann, D. ; et al.
Eur.Phys.J.A 38 (2008) 27-33, 2008.
Inspire Record 751930 DOI 10.17182/hepdata.51606

The differential cross sections \sigma_0=\sigma_T+\epsilon \sigma_L, \sigma_{LT}, and \sigma_{TT} of \pi^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of \theta=90^\circ. By an additional out-of-plane measurement with polarized electrons \sigma_{LT'} was determined. This showed for the first time the cusp effect above the \pi^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.

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Measurement of azimuthal asymmetries in inclusive charged dipion production in $e^+e^-$ annihilations at $\sqrt{s}$ = 3.65 GeV

The BESIII collaboration Ablikim, M. ; Achasov, M.N. ; Ai, X.C. ; et al.
Phys.Rev.Lett. 116 (2016) 042001, 2016.
Inspire Record 1384778 DOI 10.17182/hepdata.73802

We present a measurement of the azimuthal asymmetries of two charged pions in the inclusive process $e^+e^-\rightarrow \pi\pi X$ based on a data set of 62 $\rm{pb}^{-1}$ at the center-of-mass energy $\sqrt{s}=3.65$ GeV collected with the BESIII detector. These asymmetries can be attributed to the Collins fragmentation function. We observe a nonzero asymmetry, which increases with increasing pion momentum. As our energy scale is close to that of the existing semi-inclusive deep inelastic scattering experimental data, the measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon and are valuable to explore the energy evolution of the spin-dependent fragmentation function.

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A Measurement of the Weak Axial Couplings of the $b$ and $c$ Quark

The JADE collaboration Elsen, E. ; Allison, J. ; Ambrus, K. ; et al.
Z.Phys.C 46 (1990) 349-360, 1990.
Inspire Record 282535 DOI 10.17182/hepdata.15241

The forward-backward charge asymmetries of theb andc quarks are measured with the JADE detector at PETRA at\(\sqrt s= 35\) GeV and 44 GeV using both electrons and muons to tag the heavy quarks. At\(\sqrt s= 35\) GeV, a simultaneous fit for the two asymmetries yields the resultAb=−9.3±5.2% (state.) ndAc=−9.6±4.0% (stat.). The systematic errors are comparable with the statistical uncertainties. Combining the measurements at both energies and alternately constraining the weak coupling of thec andb quark to their Standard Model values (ac=1,ab=−1) increases the precision of the measurement of coupling constant of the other quark. Using this procedureab=−0.72±0.34 andac=0.79±0.40, where the numbers are corrected for\(B\bar B - mixing\) and the errors include both statistical and systematic contributions. The mixing parameter for continuum\(b\bar b - production\) is determined to be χ-0.24±0.12 if both heavy quark coupling constants are constrained to their values in the Standard Model.

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A Measurement of the Charmed Quark Asymmetry in $e^+ e^-$ Annihilation

The JADE collaboration Ould-Saada, F. ; Allison, J. ; Ambrus, K. ; et al.
Z.Phys.C 44 (1989) 567, 1989.
Inspire Record 278937 DOI 10.17182/hepdata.15357

The charmed quark charge asymmetry has been measured at the average centre of mass energy of 35 GeV with the JADE detector at thee+e− storage ring PETRA. Charmed quarks were identified byD*± tagging using the ΔM technique.D*± mesons were reconstructed through their decay intoD0 mesons resulting in (Kπ) π and (K π π π) π final states. The measured charge asymmetryA=−0.149±0.067 is in agreement with the expectation from the electroweak interference effect in quantum flavour dynamics (QFD).

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Measurement of forward - backward charge asymmetry in the process of b quark production in e+ e- annihilation around s**(1/2) = 60-GeV

The VENUS collaboration Shirakata, M. ; Utsumi, M. ; Abe, K. ; et al.
Phys.Lett.B 278 (1992) 499-505, 1992.
Inspire Record 322085 DOI 10.17182/hepdata.29242

We have measured the forward-backward charge asymmetry in the process of b-quark production in e + e − annihilation at TRISTAN. It was made possible by detecting prompt leptons from b-quarks. The obtained asymmetry is A = −0.55±0.15±0.08. If corrected for B-meson mixing effects with the assumptions given in the text, the asymmetry becomes A = f −0.78±0.21±0.11, which is consistent with the prediction of the standard model, namely the assignment of the b-quark to the isospin doublet of the third quark generation.

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Inclusive hadron photoproduction from longitudinally polarized protons and deuterons

The E155 collaboration Anthony, P.L. ; Arnold, R.G. ; Averett, T. ; et al.
Phys.Lett.B 458 (1999) 536-544, 1999.
Inspire Record 495554 DOI 10.17182/hepdata.28074

We report measurements of the asymmetry A_parallel for inclusive hadron production on longitudinally polarized proton and deuteron targets by circularly polarized photons. The photons were produced via internal and external bremsstrahlung from an electron beam of 48.35 GeV. Asymmetries for both positive and negative signed hadrons, and a subset of identified pions, were measured in the momentum range 10<P<30 GeV at 2.75 and 5.5 degrees. Small non-zero asymmetries are observed for the proton, while the deuteron results are consistent with zero. Recent calculations do not describe the data well.

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A Measurement of the $e^+ e^- \to b \bar{b}$ Forward - Backward Charge Asymmetry at $\sqrt{s}=29$-{GeV}

The MAC collaboration Band, H.R. ; Camporesi, T. ; Chadwick, G.B. ; et al.
Phys.Lett.B 218 (1989) 369-373, 1989.
Inspire Record 276692 DOI 10.17182/hepdata.29845

High p ⊥ inclusive muon events produced in e + e − annihilations at √ s =29 GeV have been analyzed to obtain a measurement of the b b forward-backward charge asymmetry. The result A b =0.034±0.070±0.035 differs from the theoretical expectation (−0.16) unless substantial B 0  B 0 mixing is assumed.

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