1

Lepton Angular Distributions in Drell-Yan Process

Jen-Chieh Peng

QCD Evolution 2018 Santa Fe

May 20-24, 2018

University of Illinois at Urbana-Champaign

Based on the paper of JCP, Wen-Chen Chang, Evan McClellan, Oleg Teryaev, Phys. Lett. B758 (2016) 384, PRD 96 (2017) 054020, and preprints

First Dimuon Experiment

29 GeV protonp U Xµ µ+ −+ → + +

Lederman et al. PRL 25 (1970) 1523

Experiment originally designed to search for neutral weak boson (Z0)

Missed the J/Ψ signal !

“Discovered” the Drell-Yan process

2

3

The Drell-Yan Process

[ ]2 2

21 2 1 2

1 2 1 2. .

4 ( ) ( ) ( ) ( )9 a a a a a

aD Y

d e q x q x q x q xdx dx sx x

σ πα = +

∑

4

Angular Distribution in the “Naïve” Drell-Yan

5

Lepton Angular Distribution of “naïve” Drell-Yan:Drell-Yan angular distribution

Data from Fermilab E772

(Ann. Rev. Nucl. Part. Sci. 49 (1999) 217-253)

20 (1 cos ); 1d

dσ σ λ θ λ= + =Ω

6

Helicity conservation and parity

θ2)cos1(~ θσ +d

2)cos1(~ θσ −d

2)cos1(~ θσ +d

2)cos1(~ θσ −d

θσ 2cos1~ : ionsconfigurathelicity four all Adding

+d

Dilepton rest frame

7

Drell-Yan lepton angular distributions

Collins-Soper frame

Θ and Φ are the decay polar and azimuthal angles of the μ-

in the dilepton rest-frame

2 21 3 1 cos sin 2 cos sin cos 24 2

ddσ νλ θ µ θ φ θ φ

σ π = + + + Ω

A general expression for Drell-Yan decay angular distributions:

Reflect the spin-1/2 nature of quarks (analog of the Callan-Gross relation in DI

Ins

Lam-Tung relation:

ensitive to QCD - S

c)

orrection

2

s

1 λ ν−

=

−

−

Decay angular distributions in pion-induced Drell-Yan

8

Z. Phys.

37 (1988) 545

T0 and increases with pν ν≠

Dashed curves are from pQCD

calculations

NA10 π- +W

2 21 3 1 cos sin 2 cos sin cos 24 2

ddσ νλ θ µ θ φ θ φ

σ π = + + + Ω

9

Decay angular distributions in pion-induced Drell-Yan

Data from NA10 (Z. Phys. 37 (1988) 545)

Is the Lam-Tung relation (1-λ-2ν=0) violated?140 GeV/c 194 GeV/c 286 GeV/c

Violation of the Lam-Tung relation suggests interesting new origins (Brandenburg, Nachtmann, Mirkes, Brodsky, Khoze, Muller, Eskolar, Hoyer,Vantinnen, Vogt, etc.)

221 12 2( , ) ( )T TkC HT

T HT C

M Mh x k c e f xk M

ααπ

−⊥ =+

10

Boer-Mulders function h1

κ1=0.47, MC=2.3 GeV

1 11

1 1

Boer pointed out that the cos2 dependence can be caused by the presence of the Boer-M

can lead to an azimuthal dependence wi

ulders

th

function.

h hhf f

ν⊥ ⊥

⊥ • ∝

•

φ

2 2

1 2 2 216( 4 )

T C

T C

Q MQ M

ν κ=+

Boer, PRD 60 (1999) 014012

ν>0 implies valence BM functions for pion and nucleon have same signs

ν

11

With Boer-Mulders function h1:

ν(π-Wµ+µ-X)~ [valence h1(π)] * [valence h1

(p)]

ν(pdµ+µ-X)~ [valence h1(p)] * [sea h1

(p)]

Azimuthal cos2Φ Distribution in p+d Drell-YanLingyan Zhu et al., PRL 99 (2007) 082301;

PRL 102 (2009) 182001

Sea-quark BM function is much smaller than valence BM function

Fermilab E866

12

Lam-Tung relation from CDF Z-productionTeV 1.96sat =++→+ −+ Xeepp

λ 1 2λ ν− −ν

• Strong pT (qT) dependence of λ and ν• Lam-Tung relation (1-λ = 2ν) is satisfied within

experimental uncertainties (TMD is not expected to be important at large pT)

arXiv:1103.5699 (PRL 106 (2011) 241801)

Recent CMS (ATLAS) data for Z-boson production in p+p collision at 8 TeV

• Striking qT dependencies for λ and ν were observed at two rapidity regions

• Is Lam-Tung relation violated? 13

(arXiv:1504.03512, PL B 750 (2015) 154)

λ ν

14

Recent data from CMS for Z-boson production in p+p collision at 8 TeV

• Yes, the Lam-Tung relation is violated (1-λ > 2ν)!• Can one understand the origin of the violation of

the Lam-Tung relation?

15

Interpretation of the CMS Z-production results

0

0 1 2

7 Can one express in terms of some quantities How is the above expression derived?

Can one understand the dependence of , , ,etc?

Can one understan

Quest

d the origin of the viola

ion :

?t

s

Tq A A AA A

•

•• −

• ion of Lam-Tung relation?

φθφθφθ

θφθφθ

φθθθσ

sinsinsin2sin2sinsin

coscossin2cossin2

cos2sin)cos31(2

)cos1(

762

5

4322

1202

AAA

AAA

AAdd

+++

+++

+−++∝Ω

16

How is the angular distribution expression derived?

Define three planes in the Collins-Soper frame

Contains the beam and target momenta Angle satisfies the relatio

1) Hadron Plane

n

n ta /B T

T

P Pq Qβ β

•• =

is the mass of the dilepton ( ) when 0, 0 ;

when , 90T

T

Q Zqq

β

β

•

• → →

→∞ →

17

How is the angular distribution expression derived?

Define three planes in the Collins-Soper frame

Contains the beam and target momenta Angle satisfies the relation tan /

ˆ and have head-on collision along the axisˆ ˆ and a

1) Hadron Plane

2) Quar

xes form

k Pl

the

ane

quark

B T

T

P Pq Q

q q zz z

β β•• =

′•′•

1 1

planeˆ axis has angles and in the C-S frame

z θ φ′•

18

How is the angular distribution expression derived?

Define three planes in the Collins-Soper frame

1 1

Contains the beam and target momenta Angle satisfies the relation tan /

ˆ and have head

1) Hadron Pl

-on collisio

ane

2) Quark Planen along the axis

ˆ axis has angles and

B T

T

P Pq Q

q q zz

β β

θ φ

•• =

′•′•

in the C-S frame

and are emitted back-to-back with equal | |ˆ and form the lepton plane

is emitted at ang

3) Lepton Plan

le and in the C-S fra

e

me

l l Pl zl θ φ

− +

−

−

•

•

•

19

How is the angular distribution expression derived?

02

0cos1 cosaddσ θ θ∝ + +Ω

0 1 1 1cos cos cos sin sin cos( )θ θ θ θ θ φ φ= + −

How to express the angular distribution in terms of θ and φ?

Azimuthally symmetric !

Use the following relation:

20

How is the angular distribution expression derived?0

20cos1 cosad

dσ θ θ∝ + +Ω

0 1 1 1cos cos cos sin sin cos( )θ θ θ θ θ φ φ= + −

21

All eight angular distribution terms are obtained!

φθφθφθ

θφθ

φθ

φθ

θθσ

sinsinsin2sin

2sinsin

coscossin

2cossin2

cos2sin

)cos31(2

)cos1(

7

6

25

43

22

1

202

AAA

AA

AA

Add

+++

++

+

+

−++∝Ω

aAA and,by describedentirely are 1170 φθ−

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Angular distribution coefficients A0 – A72

0 1

1 1 1

22 1 1

3 1 1

4 1

25 1 1

6 1 1

7 1 1

sin

1 sin 2 cos2sin cos 2

sin cos

cos1 sin sin 221 sin 2 sin2

sin sin

A

A

A

A a

A a

A

A

A a

θ

θ φ

θ φ

θ φ

θ

θ φ

θ φ

θ φ

=

=

=

=

=

=

=

=

23

Some implications of the angular distribution coefficients A0 – A7

20 1

1 1 1

22 1 1

3 1 1

4 1

25 1 1

6 1 1

7 1 1

sin

1 sin 2 cos2sin cos 2

sin cos

cos1 sin sin 221 sin 2 sin2

sin sin

A

A

A

A a

A a

A

A

A a

θ

θ φ

θ φ

θ φ

θ

θ φ

θ φ

θ φ

=

=

=

=

=

=

=

=

0 2

0 2

1

5 6 1

1 4

7

(or 1 2 0)

Forward-backward asymmetry, ,is reduced by a factor of cos f

Lam-Tung relation ( ) is satisfied when 0

, , are odd function of and must vanish f

or

rom sym

A A

A

A

aA

A A

A λ

θ

φ

ν

φ• =

−

•

=

•

• ≥ − ≥

0 7

Some equality and inequality relations among

metry considerat

can be o

io

ba n

n

ti edA A•

−

24

Some implications of the angular distribution coefficients A0 – A7

20 1

1 1 1

22 1 1

3 1 1

4 1

25 1 1

6 1 1

7 1 1

sin

1 sin 2 cos2sin cos 2

sin cos

cos1 sin sin 221 sin 2 sin2

sin sin

A

A

A

A a

A a

A

A

A a

θ

θ φ

θ φ

θ φ

θ

θ φ

θ φ

θ φ

=

=

=

=

=

=

=

=

aAaaAa

AA

A

<<−<<−<<−

<<−<<

4

3

2

1

0

112/12/1

10

Some bounds on the coefficients can be obtained

25

ββ

gZqq )( )1 0∗→ γ

ββ

(B)

(T)

(B)

(T)ββ

ββ

)/(sin 2222TT qQq +=β

22

2

0

222

22

0

0

322

22;

322

232

T

T

T

T

qQq

AA

qQqQ

AA

+=

+=

+−

=+−

= νλ

26

ββ

qZqg )( )2 0∗→ γ

ββ

ββ

22

2

0

222

22

0

0

15210

22;

15252

232

T

T

T

T

qQq

AA

qQqQ

AA

+=

+=

+−

=+−

= νλ

(B)

(T)

(B)

(T)

q

ββg

)5/(5 22220 TT qQqAA +≈=

Compare with CMS data on λ

27

ZqqGqQqQ

ZgqqqQqQ

T

T

T

T

→+−

=

→+−

=

for15252

for32

2

22

22

22

22

λ

λ

For both processesλ = 1 at qT = 0 (θ1=0⁰)λ = -1/3 at qT = ∞ (θ1=90⁰)

(Z production in p+p collision at 8 TeV)

Compare with CMS data on ν

28

ZqqGqQ

q

ZgqqqQ

q

T

T

T

T

→+

=

→+

=

for152

10

for32

2

22

2

22

2

ν

ν

(Z production in p+p collision at 8 TeV)

77.0sin2cossin

toscorrespond curve Solid

12

112 =θφθ

Origins of the non-coplanarity

29

higheror order at Processes1) 2sα

(Boer-Mulders fun2) Intrinsic fr

ctions in the bom inter

eam and acting pa

target hart

dr so

)ns

onTk

Compare with CMS data on Lam-Tung relation

30

77.0sin2cossin

and processes, 41.5%and 58.5% of mixturea

tocorrespond curves Solid

12

112 =θφθ

qqqG

Violation of Lam-Tung relation is well described

Compare with CDF data

31

85.0sin2cossin

and processes, 72.5%and 27.5% of mixturea

tocorrespond curves Solid

12

112 =θφθ

qqqG

Violation of Lam-Tung relation is not ruled out

Compare with CMS data on A1, A3 and A4

32

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)– Analogous angular distribution coefficients and

analogous Lam-Tung relation33

Future prospects

• Extend this study to semi-inclusive DIS at high pT (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

36

Summary

Pion-induced D-Y

The data should be between the and curves, if the effect is entirely from pQCD. The p Surprisingly large pQCD effect is predicted

roc

Extraction of the B-M funct

ess should dom

i!

inate.qq qG

qqν

•

•

•ons must remove the pQCD effect. 37

See Lambertsen and Vogelsang,

arXiv: 1605.02625

Pion-induced D-Y

The data should be between the and curves, if the effect is entirely from pQCD. Also m The data sugge

ust be lst the p

ess than 1 (fromresence of other

positi effects (or poor dat

vity)!!qq qGλ

λ•

• a) 38

Pion-induced D-Y

The L-T violation should be between the and 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 t.

he da ta

qq qG

•

•

Large violation of L-T (due to 1) cannot be explained

are large and

by pQCD. Need

negat

betteiv

re

ata!

dλ• >39