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 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 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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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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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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Measurement of the charge asymmetry in top quark pair production in pp collisions at $\sqrt(s) =$ 8 TeV using a template method

The CMS collaboration Khachatryan, Vardan ; Sirunyan, Albert M ; Tumasyan, Armen ; et al.
Phys.Rev.D 93 (2016) 034014, 2016.
Inspire Record 1388178 DOI 10.17182/hepdata.69208

The charge asymmetry in the production of top quark and antiquark pairs is measured in proton-proton collisions at a center-of-mass energy of 8 TeV. The data, corresponding to an integrated luminosity of 19.6 inverse femtobarns, were collected by the CMS experiment at the LHC. Events with a single isolated electron or muon, and four or more jets, at least one of which is likely to have originated from hadronization of a bottom quark, are selected. A template technique is used to measure the asymmetry in the distribution of differences in the top quark and antiquark absolute rapidities. The measured asymmetry is A[c,y] = [0.33 +/- 0.26 (stat) +/- 0.33 (syst)]%, which is the most precise result to date. The results are compared to calculations based on the standard model and on several beyond-the-standard-model scenarios.

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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 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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Forward–backward asymmetry of Drell–Yan lepton pairs in pp collisions at $\sqrt{s} = 8$ $\,\mathrm{TeV}$

The CMS collaboration Khachatryan, Vardan ; Sirunyan, Albert M ; Tumasyan, Armen ; et al.
Eur.Phys.J.C 76 (2016) 325, 2016.
Inspire Record 1415949 DOI 10.17182/hepdata.73121

A measurement of the forward-backward asymmetry A[FB] of oppositely charged lepton pairs (mu mu and e e) produced via Z/gamma* boson exchange in pp collisions at sqrt(s) = 8 TeV is presented. The data sample corresponds to an integrated luminosity of 19.7 inverse femtobarns collected with the CMS detector at the LHC. The measurement of A[FB] is performed for dilepton masses between 40 GeV and 2 TeV and for dilepton rapidity up to 5. The A[FB] measurements as a function of dilepton mass and rapidity are compared with the standard model predictions.

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Final Results on $\mu$ and Tau Pair Production by the Jade Collaboration at {PETRA}

The JADE collaboration Hegner, S. ; Naroska, B. ; Schroth, F. ; et al.
Z.Phys.C 46 (1990) 547-554, 1990.
Inspire Record 284560 DOI 10.17182/hepdata.15279

The cross-sections and the forward-backward charge asymmetries of muon and tau pairs produced ine+e− collisions at\(\sqrt s= 35 GeV\) have been measured by the JADE Collaboration. The cross-sections,\(\sigma _\mu(\sqrt s= GeV) = 69.79 \pm 1.35 \pm 1.40 pb\) and\(\sigma _\mu(\sqrt s= GeV) = 71.72 \pm 1.48 \pm 1.61 pb\), are in agreement with the QED α3 prediction. The charge asymmetries areAμ=−(9.9±1.5±0.5)% andAτ=−(8.1±2.0±0.6)% in agreement with the value −9.2% predicted by the standard model, usingMZ=91.0 GeV and sin2θW=0.230.

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The Forward - backward asymmetry of e+ e- ---> b anti-b and e+ e- ---> c anti-c using leptons in hadronic Z0 decays

The OPAL collaboration Acton, P.D. ; Akers, R. ; Alexander, G. ; et al.
Z.Phys.C 60 (1993) 19-36, 1993.
Inspire Record 356097 DOI 10.17182/hepdata.14320

The forward-backward asymmetries of$$e^ + e^ - \to Z^0 \to b\bar b and e^ + e^ - \to Z^0 \to c\bar c$$

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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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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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Inclusive Electron Production From Heavy Quarks in $e^+ e^-$ Annihilation at 34.6-{GeV} Center-of-mass Energy

The TASSO collaboration Althoff, M. ; Braunschweig, W. ; Kirschfink, F.J. ; et al.
Phys.Lett.B 146 (1984) 443-449, 1984.
Inspire Record 202782 DOI 10.17182/hepdata.30507

The production of electrons by bottom and charm hadrons has been studied in e + e − annihilation at 34.6 GeV center of mass energy. It is observed that the b quark fragmentation function is peaked at large values of the scaling variable z with 〈 z b 〉 = 0.84 +0.15 + 0.15 −0.10 − 0.11 . For c quarks 〈 z c 〉 = 0.57 +0.10 + 0.05 −0.09 − 0.06 is observed. A forward-backward charge asymmetry of A = −0.25 ± 0.22 was measured in b production.

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Measurement of the angular distribution of electrons from $W \to e \nu$ decays observed in $p\bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV

The D0 collaboration Abbott, B. ; Abolins, M. ; Abramov, V. ; et al.
Phys.Rev.D 63 (2001) 072001, 2001.
Inspire Record 533572 DOI 10.17182/hepdata.41717

We present the first measurement of the electron angular distribution parameter alpha_2 in W to e nu events produced in proton-antiproton collisions as a function of the W boson transverse momentum. Our analysis is based on data collected using the D0 detector during the 1994--1995 Fermilab Tevatron run. We compare our results with next-to-leading order perturbative QCD, which predicts an angular distribution of (1 +/- alpha_1 cos theta* + alpha_2 cos^2 theta*), where theta* is the polar angle of the electron in the Collins-Soper frame. In the presence of QCD corrections, the parameters alpha_1 and alpha_2 become functions of p_T^W, the W boson transverse momentum. This measurement provides a test of next-to-leading order QCD corrections which are a non-negligible contribution to the W boson mass measurement.

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Beam-Spin Asymmetries in the Azimuthal Distribution of Pion Electroproduction

The HERMES collaboration Airapetian, A. ; Akopov, Z. ; Amarian, M. ; et al.
Phys.Lett.B 648 (2007) 164-170, 2007.
Inspire Record 735612 DOI 10.17182/hepdata.41783

A measurement of the beam-spin asymmetry in the azimuthal distribution of pions produced in semi-inclusive deep-inelastic scattering off protons is presented. The measurement was performed using the {HERMES} spectrometer with a hydrogen gas target and the longitudinally polarized 27.6 GeV positron beam of HERA. The sinusoidal amplitude of the dependence of the asymmetry on the angle $\phi$ of the hadron production plane around the virtual photon direction relative to the lepton scattering plane was measured for $\pi^+,\pi^-$ and $\pi^0$ mesons. The dependence of this amplitude on the Bjorken scaling variable and on the pion fractional energy and transverse momentum is presented. The results are compared to theoretical model calculations.

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Spin correlation in $t\bar{t}$ production from $p\bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV

The D0 collaboration Abbott, B. ; Abolins, M. ; Abramov, V. ; et al.
Phys.Rev.Lett. 85 (2000) 256-261, 2000.
Inspire Record 524260 DOI 10.17182/hepdata.42996

The D0 collaboration has performed a study of spin correlation in tt-bar production for the process tt-bar to bb-bar W^+W^-, where the W bosons decay to e-nu or mu-nu. A sample of six events was collected during an exposure of the D0 detector to an integrated luminosity of approximately 125 pb^-1 of sqrt{s}=1.8 TeV pp-bar collisions. The standard model (SM) predicts that the short lifetime of the top quark ensures the transmission of any spin information at production to the tt-bar decay products. The degree of spin correlation is characterized by a correlation coefficient k. We find that k>-0.25 at the 68% confidence level, in agreement with the SM prediction of k=0.88.

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Asymmetries in the production of Lambda0, Xi-, and Omega- hyperons in 500-GeV/c pi minus: Nucleon interactions

The E791 collaboration Aitala, E.M. ; Amato, S. ; Anjos, J.C. ; et al.
Phys.Lett.B 496 (2000) 9-18, 2000.
Inspire Record 532973 DOI 10.17182/hepdata.42997

Using data from Fermilab fixed-target experiment E791, we have measured particle-antiparticle production asymmetries for lambda zero, cascade minus, and omega minus hyperons in pi minus-nucleon interactions at 500 GeV/c. The asymmetries are measured as functions of Feynman-x (x_F) and pt^2 over the ranges of -0.12 GE x_F LE 0.12 and 0 GE pt^2 LE 4 (GeV/c)^2. We find substantial asymmetries, even at x_F = 0. We also observe leading-particle- type asymmetries which qualitatively agree with theoretical predictions.

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Asymmetries in the production of Lambda0 in 250-GeV/c pi+-, K+- and p - Nucleon interactions

The E769 collaboration Alves, G.A ; Amato, S ; Anjos, J.C ; et al.
Phys.Lett.B 559 (2003) 179-186, 2003.
Inspire Record 615414 DOI 10.17182/hepdata.41928

Using data from Fermilab fixed-target experiment E769, we have measured particle-antiparticle production asymmetries for Lambda0 hyperons in 250 GeV/c pi+-, K+- and p -- nucleon interactions. The asymmetries are measured as functions of Feynman-x (x_F) and p_t^2 over the ranges -0.12<=x_F<=0.12 and 0<=p_t^2<=3 (GeV/c)^2 (for positive beam) and -0.12<=x_F<=0.4 and 0<=p_t^2<=10 (GeV/c)^2 (for negative beam). We find substantial asymmetries, even at x_F around zero. We also observe leading-particle-type asymmetries. These latter effects are qualitatively as expected from valence-quark content of the target and variety of projectiles studied.

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Production and Muonic Decay of Heavy Quarks in e+ e- Annihilation at 34.5-GeV

The TASSO collaboration Althoff, M. ; Braunschweig, W. ; Kirschfink, F.J. ; et al.
Z.Phys.C 22 (1984) 219, 1984.
Inspire Record 194775 DOI 10.17182/hepdata.16252

The production of prompt muons ine+e− annihilation has been studied at centre of mass energies near 34.5 GeV. The measured semi-muonic branching ratios ofb andc quarks areB(b»Xμv) =0.117±0.028±0.01 andB(c→Xμv)=0.082 ±0.012a−0.01+0.02. The fragmentation functions of heavy quarks are hard, <zb>=0.85a−0.12–0.07+0.10+0.02 and <zc> =0.77a−0.07–0.11+0.05+0.03. Limits have been set on flavour changing neutral current decays:B(b→Xµ+µ−) <0.02 andB(b→Xµ+µ− (95% confidence level).

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Forward - backward charge asymmetry in $e^+e^- \to$ hadron jets

The AMY collaboration Stuart, D. ; Breedon, R.E. ; Kim, G.N. ; et al.
Phys.Rev.Lett. 64 (1990) 983, 1990.
Inspire Record 283082 DOI 10.17182/hepdata.19965

The forward-backward asymmetry of quarks produced in e+e− annihilations, summed over all flavors, is measured at √s between 50 and 60.8 GeV. Methods of determining the charge direction of jet pairs are discussed. The asymmetry is found to agree with the five-flavor standard model.

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Measurement of the target asymmetry of eta and pi0 photoproduction on the proton

Bock, A. ; Anton, G. ; Beulertz, W. ; et al.
Phys.Rev.Lett. 81 (1998) 534-537, 1998.
Inspire Record 474492 DOI 10.17182/hepdata.19492

At the tagged photon facility PHOENICS at the Bonn accelerator ELSA a measurement of the target asymmetry of the reaction γp→pη from threshold to 1150 MeV has been performed. Simultaneously the reaction γp→pπ0 has been measured in the first resonance region. Results are presented for both reactions. The target asymmetry data are suited to put considerable constraints on the model parameters used for the theoretical description of meson photoproduction.

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Heavy Quark Charge Asymmetries With the Cello Detector

The CELLO collaboration Behrend, H.J. ; Criegee, L. ; Field, J.H. ; et al.
Z.Phys.C 47 (1990) 333-342, 1990.
Inspire Record 282536 DOI 10.17182/hepdata.15243

The production ofb andc quarks ine+e− annihilation has been studied with the CELLO detector in the range from 35 GeV up to the highest PETRA energies. The heavy quarks have been tagged by their semileptonic decays. The charge asymmetries forb quarks at 35 and 43 GeV have been found to beAb=−(22.2±8.1)% andAb=−(49.1±16.5)%, respectively, using a method incorporating jet variables and their correlations for the separation of the heavy quarks from the back ground of the lighter quarks. Forc quarks we obtainAc=−(12.9±8.8)% andAc=+(7.7±14.0)%, respectively. The axial vector coupling constants of the heavy quarksc andb are found to beac=+(0.29±0.46) andab=−(1.15±0.41) taking\(B^0 \overline {B^0 } \) mixing into account. The results are in agreement with the expectations from the standard model.

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