Lepton ngular Distributions in Drell-Yan Process Jen-Chieh Peng University of Illinois at Urbana-Champaign QCD Evolution 08 Santa Fe May 0-4, 08 Based on the paper of JCP, Wen-Chen Chang, Evan McClellan, Oleg eryaev, Phys. Lett. B758 (06) 384, PRD 96 (07) 05400, and preprints
First Dimuon Experiment p+ U µ + + µ + X 9 GeV proton Lederman et al. PRL 5 (970) 53 Experiment originally designed to search for neutral weak boson (Z 0 ) Missed the J/Ψ signal! Discovered the Drell-Yan process
he Drell-Yan Process d σ dx dx DY.. 4πα e q x q x + q x q x 9sx x a [ ( ) ( ) ( ) ( )] a a a a a 3
ngular Distribution in the Naïve Drell-Yan 4
Drell-Yan angular distribution Lepton ngular Distribution of naïve Drell-Yan: dσ σ + λ θ λ dω 0 ( cos ); Data from Fermilab E77 (nn. Rev. Nucl. Part. Sci. 49 (999) 7-53) 5
Helicity conservation and parity θ dσ ~ ( + cosθ ) dding all Dilepton rest frame four helicity configurations: dσ ~ + cos θ dσ ~ ( cosθ ) dσ ~ ( + cosθ ) dσ ~ ( cosθ ) 6
Drell-Yan lepton angular distributions Θ and Φ are the decay polar and azimuthal angles of the μ - in the dilepton rest-frame Collins-Soper frame general expression for Drell-Yan decay angular distributions: dσ 3 ν + λ cos θ + µ sin θ cosφ+ sin θ cos φ σ dω 4π Lam-ung relation: Reflect the spin-/ nature of quarks (analog of the Callan-Gross relation in DIS) Insensitive to QCD - λ ν corrections 7
Decay angular distributions in pion-induced Drell-Yan dσ 3 ν + λ cos θ + µ sin θ cosφ+ sin θ cos φ σ dω 4π N0 π - +W Z. Phys. 37 (988) 545 Dashed curves are from pqcd calculations ν 0 and ν increases with p 8
Decay angular distributions in pion-induced Drell-Yan Is the Lam-ung relation (-λ-ν0) violated? 40 GeV/c 94 GeV/c 86 GeV/c Data from N0 (Z. Phys. 37 (988) 545) Violation of the Lam-ung relation suggests interesting new origins (Brandenburg, Nachtmann, Mirkes, Brodsky, Khoze, Muller, Eskolar, Hoyer,Vantinnen, Vogt, etc.) 9
Boer-Mulders function h Boer pointed out that the cos φ dependence can be caused by the presence of the Boer-Mulders function. h h h can lead to an azimuthal dependence with ν f f ν α M M h ( xk, ) c e f( x) C H α k H π k + MC ν 6κ QM C ( Q + 4 MC) κ 0.47, M C.3 GeV Boer, PRD 60 (999) 040 ν>0 implies valence BM functions for pion and 0 nucleon have same signs
zimuthal cosφ Distribution in p+d Drell-Yan Fermilab E866 Lingyan Zhu et al., PRL 99 (007) 0830; PRL 0 (009) 800 With Boer-Mulders function h : ν(π - W µ + µ - X)~ [valence h (π)] * [valence h (p)] ν(pd µ+µ-x)~ [valence h (p)] * [sea h (p)] Sea-quark BM function is much smaller than valence BM function
Lam-ung relation from CDF Z-production p + p e + + e + X at s.96 ev arxiv:03.5699 (PRL 06 (0) 480) λ ν λ ν Strong p (q ) dependence of λ and ν Lam-ung relation (-λ ν) is satisfied within experimental uncertainties (MD is not expected to be important at large p )
Recent CMS (LS) data for Z-boson production in p+p collision at 8 ev λ ν (arxiv:504.035, PL B 750 (05) 54) Striking q dependencies for λ and ν were observed at two rapidity regions Is Lam-ung relation violated? 3
Recent data from CMS for Z-boson production in p+p collision at 8 ev Yes, the Lam-ung relation is violated (-λ > ν)! Can one understand the origin of the violation of the Lam-ung relation? 4
Interpretation of the CMS Z-production results dσ 0 ( + cos θ ) + ( 3cos θ ) + sin θ cosφ dω + sin θ cosφ + 3 sinθ cosφ + 4 cosθ + sin θ sin φ + sin θ sinφ + sinθ sinφ Question s: How is the above expression derived? Can one express 5 0 7 in terms of some quantities? Can one understand the q dependence of,,,etc? 0 Can one understand the origin of the violation of Lam-ung relation? 6 7 5
How is the angular distribution expression derived? Define three planes in the Collins-Soper frame ) Hadron Plane Contains the beam P and target P momenta B ngle β satisfies the relation ta n β q / Q Q is the mass of the dilepton ( Z) when q 0, β 0 ; when q, β 90 6
How is the angular distribution expression derived? Define three planes in the Collins-Soper frame ) Hadron Plane Contains the beam P and target P momenta B ngle β satisfies the relation tan β q / Q ) Quark Plane q and q have head-on collision along the zˆ axis zˆ and zˆ axes form the quark plane zˆ axis has angles θ and φ in the C-S frame 7
How is the angular distribution expression derived? Define three planes in the Collins-Soper frame ) Hadron Plane Contains the beam P and target P momenta B ngle β satisfies the relation tan β q / Q ) Quark Plane q and q have head-on collision along the zˆ axis zˆ axis has angles θ and φ in the C-S frame 3) Lepton Plane + l and l are emitted back-to-back with equal P l and zˆ form the lepton plane l is emitted at angle θ and φ in the C-S frame 8
How is the angular distribution expression derived? dσ + a cosθ0 + cos dω cosθ cosθcosθ + sinθsinθ cos( φ φ ) 0 θ zimuthally symmetric! How to express the angular distribution in terms of θ and φ? Use the following relation: 0 9
How is the angular distribution expression derived? dσ + a cosθ0 + cos θ0 dω cosθ cosθcosθ + sinθsinθ cos( φ φ ) 0 0
ll eight angular distribution terms are obtained! dσ dω 0 ( + cos θ ) + ( 3cos + sin θ cosφ + + + + + sin θ cosφ sinθ cosφ + 3 5 6 7 sin θ sin φ sin θ sinφ sinθ sinφ 4 cosθ θ ) are entirely described by θ, φ 0 7 and a
ngular distribution coefficients 0 7 sin 0 sin θ cos φ sin θ cos φ a sinθ cosφ 3 a θ cosθ 4 sin θ sin φ 5 sin θ sin φ a sinθ sinφ 6 7
Some implications of the angular distribution coefficients 0 7 sin θ 0 (or λ ν 0) 0 sin θ cos φ sin θ cos φ a sinθ cosφ 3 a cosθ 4 sin θ sin φ sin θ sin φ a sinθ sinφ 5 6 7 Lam-ung relation ( ) is satisfied when φ 0 0 Forward-backward asymmetry, a, is reduced by a factor of cos θ for 5 6 7 4,, are odd function of φ and must vanish from symmetry consideration Some equality and inequality relations among 0 7 can be obatined 3
Some implications of the angular distribution coefficients 0 7 sin 0 a sinθ cosφ 3 a θ sin θ cos φ sin θ cos φ cosθ 4 sin θ sin φ sin θ sin φ a sinθ sinφ 5 6 7 Some bounds on the coefficients can be obtained 0 < a a < < < 0 / < < 3 4 < < < < a a / 4
5 β β g Z q q ) ( ) 0 γ β β (B) () (B) () β β β β ) /( sin q Q q + β 0 0 0 3 ; 3 3 q Q q q Q q Q + + + + ν λ
6 β β q Z qg ) ( ) 0 γ β β β β 0 0 0 5 0 ; 5 5 3 q Q q q Q q Q + + + + ν λ (B) () (B) () q β β g ) 5 /( 5 0 q Q q +
Compare with CMS data on λ (Z production in p+p collision at 8 ev) λ λ Q Q Q Q q + 3q 5q + 5q for for qq qg Zg Zq For both processes λ at q 0 (θ 0⁰) λ -/3 at q (θ 90⁰) 7
Compare with CMS data on ν (Z production in p+p collision at 8 ev) ν ν q Q + 3q 0q Q + 5q for for qq qg Zg Zq Solidcurve corresponds sin θ cosφ sin θ to 0.77 8
) Processes Origins of the non-coplanarity at order α s or higher ) Intrinsic from interacting partons k (Boer-Mulders functions in the beam and target hadrons) 9
Compare with CMS data on Lam-ung relation Solid curves correspond to a mixture of 58.5% qg and 4.5% qq processes, and sin θ cosφ sin θ 0.77 Violation of Lam-ung relation is well described 30
Compare with CDF data Solid curves correspond to a mixture of 7.5% qg and 7.5% qq processes, and sin θ cosφ sin θ 0.85 Violation of Lam-ung relation is not ruled out 3
Compare with CMS data on, 3 and 4 3
Future prospects Extend this study to W-boson production Preliminary results show that the data can be well described Extend this study to fixed-target Drell-Yan data Extraction of Boer-Mulders functions must take into account the QCD effects Extend this study to dihadron production in e - e + collision (inverse of the Drell-Yan) nalogous angular distribution coefficients and analogous Lam-ung relation 33
Future prospects Extend this study to semi-inclusive DIS at high p (involving two hadrons and two leptons) Relevant for EIC measurements Rotational invariance, equality, and inequality relations formed by various angular distribution coefficients Comparison with pqcd calculations 34
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Summary 36
Pion-induced D-Y See Lambertsen and Vogelsang, arxiv: 605.065 he ν data should be between the qq and qg curves, if the effect is entirely from pqcd. he qq process should dominate. Surprisingly large pqcd effect is predicted! Extraction of the B-M functions must remove the pqcd effect. 37
Pion-induced D-Y he λ data should be between the qq and qg curves, if the effect is entirely from pqcd. lso λ must be less than (from positivity)!! he data suggest the presence of other effects (or poor data) 38
Pion-induced D-Y he L- violation should be between the qq and qg curves, if the effect is entirely from pqcd (we assume the same non-coplanarity as in the LHC). pqcd effect can only be positive, while the data are large and negative! Large violation of L- (due to λ > ) cannot be explained by pqcd. Need better data 39