Lepton Angular Distributions in Drell-Yan Process

Transcription

1 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

2 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

3 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

4 ngular Distribution in the Naïve Drell-Yan 4

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 Lam-ung relation from CDF Z-production p + p e + + e + X at s.96 ev arxiv: (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 )

13 Recent CMS (LS) data for Z-boson production in p+p collision at 8 ev λ ν (arxiv: , PL B 750 (05) 54) Striking q dependencies for λ and ν were observed at two rapidity regions Is Lam-ung relation violated? 3

14 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

15 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 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

16 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

17 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

18 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

19 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

20 How is the angular distribution expression derived? dσ + a cosθ0 + cos θ0 dω cosθ cosθcosθ + sinθsinθ cos( φ φ ) 0 0

21 ll eight angular distribution terms are obtained! dσ dω 0 ( + cos θ ) + ( 3cos + sin θ cosφ sin θ cosφ sinθ cosφ sin θ sin φ sin θ sinφ sinθ sinφ 4 cosθ θ ) are entirely described by θ, φ 0 7 and a

22 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

23 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 Lam-ung relation ( ) is satisfied when φ 0 0 Forward-backward asymmetry, a, is reduced by a factor of cos θ for ,, are odd function of φ and must vanish from symmetry consideration Some equality and inequality relations among 0 7 can be obatined 3

24 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 Some bounds on the coefficients can be obtained 0 < a a < < < 0 / < < 3 4 < < < < a a / 4

25 5 β β g Z q q ) ( ) 0 γ β β (B) () (B) () β β β β ) /( sin q Q q + β ; 3 3 q Q q q Q q Q ν λ

26 6 β β q Z qg ) ( ) 0 γ β β β β ; q Q q q Q q Q ν λ (B) () (B) () q β β g ) 5 /( 5 0 q Q q +

27 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

28 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

29 ) 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

30 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

31 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

32 Compare with CMS data on, 3 and 4 3

33 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

34 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

35 35

36 Summary 36

37 Pion-induced D-Y See Lambertsen and Vogelsang, arxiv: 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

38 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

39 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