Kinematic Azimuthal Asymmetries and Lam-Tung Relation
O. V. Teryaev
备注：
3 pages, Published in Proceedings of XI WORKSHOP ON HIGH ENERGY SPIN PHYSICS (SPIN-05, Dubna, September 27 - October 1, 2005, http://theor.jinr.ru/meetings/2005/spin2005/ ), p.171-174
The origin of Lam-Tung relation for the angular asymmetry of Drell-Yan dileptons is analyzed. The asymmetry constrained by this relation is shown to belongto the class of kinematic azimuthal asymmetries, emerging due to the deviation of the reference axis from the natural physical one. The validity and violation of Lam-Tung relation due to radiative and power QCD corrections is discussed. The relation is generalized to the case when the virtual photon is not the transverse oneand the possible applications are suggested.
We study the Drell-Yan production cross section and structure functions in proton (deuteron)-nucleus collisions using the Color Glass Condensate formalism. The nucleus is treated in the Color Glass Condensate framework which includes both higher twist effects due to the inclusion of multiple scatterings and leading twist pQCD shadowing due to the small x resummation, while the proton (or deuteron) is treated within the DGLAP improved parton model. In particular, the Drell-Yan structure functions are used in order to investigate the Lam-Tung relation at small x, which is known to be identically…
We study the azimuthal asymmetry in the Drell-Yan lepton pair production in hadronic scattering processes at moderate transverse momentum region, taking into account the contributions from the twist-three quark-gluon correlations from the unpolarized hadrons. The contributions are found to dominate the asymmetry, and are not power suppressed by q_\perp/Q at small q_\perp where q_\perp and Q are the transverse momentum and invariant mass of the lepton pair. Accordingly, the Lam-Tung relation will be violated at this momentum region, and its violation depends on the twist-three functions. Howeve…
The Lam-Tung relation breaking coefficient $A_{\mathrm{LT}} = A_0 - A_2$ in the Drell-Yan dilepton angular distributions in the $Z^0$ boson mass region at the LHC is analyzed in the $k_T$-factorization approach. This observable was recently measured with high precision by ATLAS collaboration. Within the $k_T$-factorization approach we perform an approximate ${\cal O}(α_{\mathrm{em}}α_s^2)$ calculation of the off-shell parton hard matrix elements in which we include the leading tree level contributions of valence quarks and off-shell gluons: the $q_{\mathrm{val}} g^* \to qZ^0$ channel and the $…
Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be readily obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam-Tung relation. While the vi…
The observation of the violation of Lam-Tung relation in the $πN$ Drell-Yan process triggered many theoretical speculations. The TMD Boer-Mulders functions characterizing the correlation of transverse momentum and transverse spin for partons in unpolarized hadrons could nicely account for the violation. The COMPASS experiment at CERN will measure the angular distributions of dimuons from the unpolarized Drell-Yan process over a wide kinematic region and study the beam particle dependence. Significant statistics is expected from a successful run in 2015 which will bring further understanding of…
High precision data of dilepton angular distributions in $γ^*/Z$ production were reported recently by the CMS Collaboration covering a broad range of the dilepton transverse momentum, $q_T$, up to $\sim 300$ GeV. Pronounced $q_T$ dependencies of the $λ$ and $ν$ parameters, characterizing the $\cos^2θ$ and $\cos 2ϕ$ angular distributions, were found. Violation of the Lam-Tung relation was also clearly observed. We show that the $q_T$ dependence of $λ$ allows a determination of the relative contributions of the $q \bar q$ annihilation versus the $qG$ Compton process. The violation of the Lam-Tun…
The coefficients determining the dilepton decay angular distribution of vector particles obey certain positivity constraints and a rotation-invariant identity. These relations are a direct consequence of the covariance properties of angular momentum eigenstates and are independent of the production mechanism. The Lam-Tung relation can be derived as a particular case, simply recognizing that the Drell-Yan dilepton is always produced transversely polarized with respect to one or more quantization axes. The dilepton angular distribution continues to be characterized by a frame-independent identit…
High precision data of lepton angular distributions in inclusive $Z$ boson production, reported by the CMS and ATLAS Collaborations, showed pronounced transverse momentum ($q_T$) dependencies of the $A_0$ and $A_2$ coefficients. Violation of the Lam-Tung relation, $A_0 = A_2$, was also found. An intuitive understanding of these results can be obtained from a geometric approach. We predict that $A_0$ and $A_2$ for $Z$ plus single gluon-jet events are very different from that of $Z$ plus single quark-jet events, allowing a new experimental tool for checking various algorithms which attempt to di…
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The rotational properties of angular momentum eigenstates imply the existence of a frame-independent relation among the parameters of the decay distribution of vector mesons into fermions. This relation is a generalization of the Lam-Tung identity, a result specific to Drell-Yan production in perturbative QCD, here shown to be equivalent to the dynamical condition that the dilepton always originates from a transversely polarized photon.
We discuss the angular distribution of dilepton pairs in p+A collisions at LHC at low momentum transfer and transverse momentum. This includes helicity amplitudes and angular coefficients as well as a look at the Lam-Tung sum rule. We use leading twist NLO calculations and higher twist corrections by double scattering in large nuclei.
The anomalously large cos(2 phi) asymmetry measured in the Drell-Yan process is discussed. Possible origins of this large deviation from the Lam-Tung relation are considered with emphasis on the comparison of two particular proposals: one that suggests it arises from a QCD vacuum effect and one that suggests it is a hadronic effect. Experimental signatures distinguishing these effects are discussed.
The lepton angular distributions of the Drell-Yan process in the fixed-target experiments are investigated by NLO and NNLO perturbative QCD. We present the calculated angular parameters $λ$, $μ$, $ν$ and the degree of violation of the Lam-Tung relation, $1-λ-2ν$, for the E615 experiment as well as predictions for the COMPASS experiment. Many salient features of transverse momentum and rapidity dependence could be qualitatively understood by a geometric approach.
Transverse polarization (TP) can be used to study interference of (S,P) or T type couplings from new physics with the SM contribution. In e+e- -> t tbar, a CP-odd azimuthal asymmetry can constrain the scale Lambda of new (S,P) or T contact interactions to be higher than about 7 TeV for total c.m. energy of 500 GeV, integrated luminosity of 500 inverse fb, and assuming 80% e- and 60% e+ polarizations in opposite directions. In e+e- -> gamma Z without chirality violation, but with CP-violating anomalous gamma-gamma-Z couplings, an azimuthal asymmetry can probe the anomalous coupling down to abou…
The lepton angular distributions of the Drell-Yan process in fixed-target experiments are investigated by NLO and NNLO perturbative QCD. We present the calculated angular parameters $λ$, $μ$, $ν$ and the degree of violation of the Lam-Tung relation, $1-λ-2ν$, for the NA10, E615 and E866 experiments. Predictions for the ongoing COMPASS and SeaQuest experiments are also presented. The transverse momentum ($q_T$) distributions of $λ$ and $ν$ show a clear dependence on the dimuon mass ($Q$) while those of $μ$ have a strong rapidity ($x_F$) dependence. Furthermore, $λ$ and $ν$ are found to scale wi…
We present the leading order unpolarized and polarized cross sections in electroweak semi-inclusive deep inelastic leptoproduction. The azimuthal dependences in the cross section differential in the transverse momentum of the vector boson arise due to intrinsic transverse momenta of the quarks. However, the presented asymmetries are not suppressed by inverse powers of the hard scale. We discuss the different opportunities to measure specific asymmetries as offered by neutral compared to charged current processes and point out the optimal kinematical regions. The present and (proposed) future H…
We reanalyze the anomalous angular distribution of lepton pairs produced in a pion-induced Drell-Yan process by taking into account the Glauber gluon effect in the $k_T$ factorization theorem. Compared to the previous study, we adopt the realistic parton distribution functions (PDFs) for a proton from the CTEQ and for a pion from the xFitter, include the QCD evolutions of the strong coupling and the PDFs, and integrate the differential cross section over the kinematic regions for the NA10, E615 and COMPASS experiments. These improvements then allow rigorous confrontations of theoretical result…
We present Monte Carlo simulations of both the Sivers and the Boer-Mulders effects in the polarized Drell-Yan $π^\pm p^\uparrow \to μ^+ μ^- X$ process at the center-of-mass energy $\sqrt{s} \sim 14$ GeV reachable at COMPASS with pion beams of energy 100 GeV. For the Sivers effect, we adopt two different parametrizations for the Sivers function to explore the statistical accuracy required to extract unambiguous information on this parton density. In particular, we verify the possibility of checking its predicted sign change between Semi-Inclusive Deep-Inelastic Scattering (SIDIS) and Drell-Yan …
We present a comparison of data of lepton angular distributions of Drell-Yan/$Z$ production with the fixed-order pQCD calculations by which the baseline of pQCD effects is illustrated. As for the $Z$ production, we predict that $A_0$ and $A_2$ for $Z$ plus single gluon-jet events are very different from that of $Z$ plus single quark-jet events, allowing a new experimental tool for checking various algorithms which attempt to discriminate quark jets from gluon jets. Using an intuitive geometric approach, we show that the violation of the Lam-Tung relation, appearing at large transverse-momentum…
We calculate the transverse momentum Q_{\perp} dependence of the helicity structure functions for the hadroproduction of a massive pair of leptons with pair invariant mass Q. These structure functions determine the angular distribution of the leptons in the pair rest frame. Unphysical behavior in the region Q_{\perp} --> 0 is seen in the results of calculations done at fixed-order in QCD perturbation theory. We use current conservation to demonstrate that the unphysical inverse-power and \ln(Q/Q_{\perp}) logarithmic divergences in three of the four independent helicity structure functions shar…
Fixed-target unpolarized Drell-Yan experiments often feature an acceptance depending on the polar angle of the lepton tracks in the laboratory frame. Typically leptons are detected in a defined angular range, with a dead zone in the forward region. If the cutoffs imposed by the angular acceptance are independent of the azimuth, at first sight they do not appear dangerous for a measurement of the cos(2ϕ)-asymmetry, relevant because of its association with the violation of the Lam-Tung rule and with the Boer-Mulders function. On the contrary, direct simulations show that up to 10 percent asymmet…
