1

Meson Structure with Dilepton Production

Jen-Chieh Peng

University of Illinois at Urbana-Champaign

9th Workshop on “Hadron Physics in China and Opportunities Worldwide”

Nanjing University, July 24-28, 2017

In collaboration with Wen-Chen Chang and Stephane Platchkov

Outline

• Overview of Drell-Yan experiments with meson beams

• What have we learned from these experiments

• What we would like to learn in the future• Summary and outlook

2

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

3

4

The Drell-Yan Process

5

Exp P (GeV) targets Number of D-Y events

WA11 175 Be 500 (semi-exclusive)

WA39 40 W (H2) 3839 (all beam, M > 2 GeV)

NA3 150, 200, 280 Pt (H2) 21600, 4970, 20000 (535, 121, 741)

NA10 140, 194, 286 W (D2) ~84400, ~150000, ~45900 (3200, --, 7800)

E331/E444 225 C, Cu, W 500

E326 225 W

E615 80, 252 W 4060, ~50000

Experiments at CERN and Fermilab

Relatively pure beam Relatively large cross section due to contents in ud

π

π

−

−

•

•

6

Exp P (GeV) targets D-Y events

WA39 40 W (H2)

NA3 200 Pt (H2) 1750 (40)

E331/E444 225 C, Cu, W

Require beam particle identification to reject large proton content Smaller DY cross section due to contents in Very few DY data with beam

du π

π

+

+

•

•

•

7

Exp P (GeV) targets D-Y events

WA39 40 W (H2)

NA3 150, 200 Pt 688, 90

Exp P (GeV) targets D-Y events

WA39 40 W (H2)

NA3 200 Pt 170

Exp P (GeV) targets D-Y events

WA39 40 W (H2)

NA3 150, 200 Pt 275, 32

E537 125 W, Cu, Be 380

8

Ratio of ( ) / ( ) Drell-Yan cross sectionsA p Aπ − + +

2

2 2

2

2

2

1 2 1

1 1

1 2

1

( / )( / )4 ( ) ( ) ( )4 ( ) ( )

( ) ( )( )

Black: valence

( )( ) ( )

( )

Red: s a e

N

N N

NDY

p NDY

N

p p

N

p N

d d

d

MdyRd dMdyu x u x d x x

u xu x d x

u x u xu

d x

x u x

π

π π

π

σσ

+

+=

++

2

2

Rapid rise in at large reflects the rise in valence/sea

( )ratio as increases )

:(

N

N

M

xu

xx

R

u

From E331/E444

9

Ratios of ( ) / ( ) Drell-Yan cross sectionsC Cπ π+ −+ +

1 2 2 1

1

1 2 1 2

1 2 12 22 1

( ) ( ) ( ) ( )( )

( )( )

( )( ) ( ) ( )

( ) 5 ( ) 5 ( ) 104 ( ) ( ) 5 ( ) 5 ( ) 10 4

N N

N N

DY

DY

N N

N N

S x S x S x S

CRC

V x V x V x V x AV

x BS x S x S x S x Bx V x V x V x Aπ π

π π

π π

π π

σ πσ π

+

−

+=

++ + + +

=+ + + +

( ) ( ) ( ) ( ) ( )

Defining ( ) ( ) ( ) ( ) ( )

( ) [ ( ) ( )] / 2

Considering only the and f( ) [ ( ) ( )] /

la r2

vo s

V V V

p

p

N

V

N p

p

S x u x d x d x u x

S x u

V x u x d x d x u x

V x

x d x

u x d x

u d

π π π

π π

π

π

π

π π

+ +

+ +

−

− −

−= = =

= = = =

+

= +

=

=

From E331/E444

1 / 4 1R≤ ≤

Black: Valence; Red : Sea

10

( ) versus ( ) Drell-Yan cross sectionsW p Wπ − + +

Valence quark -distributionin pion is broader than thatin antiproton (proton)

x

E537, 125 GeV

Drell-YanWπ − +

Drell-Yanp W+

11

How to determine the valence quark distribution in pion?

11 2 2 1

1

2 1 2

1 2 1 22 2 1

( ) ( ) ( ) ( )( ) 4 ( ) ( ) 5 ( ) 5 ( ) 10

( ) ( ) ( ) 5 ( ) 5 ( ) 1( ) ( 0) ( ) ( )DY N N

DY

N

NN

N

NN

D S x S x S x S xS x S x S x S x

V x V x V x V xD V x V x V x V x

π π

π

π π

π ππ

σ π

σ π

−

+

+ ∝ + + +

+ ∝ + + +

1 2

Only ( ) ( ) 3 ( ) ( )

the valence-quark term remain!DY DY ND D V x V xπσ π σ π− ++ − + ∝

Only very low statistics data for ( ) are available!DY Dσ π + +

See Londergan et al., PL B361 (1995) 110

Compare ( ) with ( ) Drell-Yan cross sectionsD Dπ π− ++ +

12

1 2

Only( ) ( ) 4 ( ) ( ) the valence-quark term remain!

uDY DY K NK D K D V x V xσ σ− ++ − + ∝

1 2

( ) is more sensitive to kaon's sea-quark content than ( )(especially data at low and large (negative ) region!)

DY DY

F

K D K Dx x x

σ σ+ −+ +

1 2 2 2

1 2 1 2

1 1

12

( ) 4 ( ) ( ) 4 ( ) ( ) ( )( ) ( ) ( ) (

( )5 ( ) 10 2 ) ( )

N N

K K

u u sDY K N K

N N N

K

K

K D V x V x V x V xV x

S x s xS x S x S x S x s x

σ − + ∝ + ++ + +

2 2

1 1 2 1

1

2

1

2

( ) 4 ( ) ( )5 ( )

( ) ( )( ) ( ) ( ) ( )1 2 ( )0

u sDY K K

N

N N

K K N K N

S x s xS

K D V x V xVx S x S x S x s xx

σ + + ∝ ++ + +

See Londergan al., PL B380 (1996) 393

How to determine the valence quark distribution in kaon?

Compare ( ) with ( ) Drell-Yan cross sectionsK D K D− ++ +

13

Attemps to extract the pion valence quark distribution

0.5 0.46( ) 0.72 (1 )F x x xπ = −

NA3, 200 GeV

E331, 225 GeVBNL, 22 GeV

WA11, 175 GeV

0.5 1.27( ) 0.90 (1 )F x x xπ = −

0.5 1.57( ) 2.43 (1 )F x x xπ = −0.45 1.17( ) (1 )F x Ax xπ = −

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Attemps to extract the pion valence quark distribution

NA3, 200 GeV

0.442 1.248( ) (1 )F x Ax xπ = −

E537, 125 GeV

E615, 252 GeV

0.6 1.26( ) (1 )F x Ax xπ = −

A global fit to all data is needed

15

• OW-P (PRD 30, 943 (1984))– LO QCD– J/Ψ data from NA3 and WA39; D-Y data

from E537 and NA3

Four pion PDF sets available at LHAPDF library

16

• SMRS (PR D45, 2349 (1992))

– NLO QCD– NA10 and E615 D-Y data,

WA70 direct photon data

Four pion PDF sets available at LHAPDF library

Need new global fits to all existing data Need new experimental data

with pion and kaon beams

•

•

17

Kaon PDF from ( ) / ( ) Drell-Yan ratiosK D Dπ− −+ +

From NA3; 150 GeV, Pt target

1 2 1 1 2 1

1

2 2

2 2

1

1 11 2

( )( )

4 ( ) ( ) 4 ( ) ( ) 5 ( ) ( )4 ( ) ( ) 5 ( ) 5

( ) ( ) ( )( ) () ))( (

DY

DYu u s u

K N K K N K

N N

N p K

N

S x s x S

K DRD

V x V x V x V x V x V xV x V x V x V x V x

xS x S xπ π ππ

σσ π

−

−

+=

+

+ + ++ +

0.18 0.07(1 ) softer -valence in kaon than in pionR x u±− ⇒

Comparison between data and theory

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19

( Pt) / ( Pt) ratios for J/ productionK π− −+ + Ψ

Ratios for D-Y

Similar behavior at large for D-Y and J/ production?Fx Ψ

From NA3; 150 GeV, Pt target

Ratios for J/Ψ

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Comparison between data and CEM calculations

same pdf for and K π− −

The / ratios of J/ production at large might indicate

a softer in than in the pion, similar to the D-Y data?FK x

u Kπ

−

Ψ

( Pt) / ( Pt) ratios for J/ productionK π− −+ + Ψ

modified pdf for K −

Modified kaon PDF has the ubar valence quark distribution multiplied by (1-x)0.18

and the strange quark distribution divided by (1-x)0.18

Dilepton data with meson beams at COMPASS

• Prospect of RF-separated kaon and antiproton beams in the future 21

See talks of M. Perdekamp and W.C. Chang

190 GeV π- beam

22

Three proton parton distributions describing transverse momentum and/or transverse spin

1) Transversity

2) Sivers function

3) Boer-Mulders function

Correlation between and q Ns S⊥ ⊥

Correlation between and q qs k⊥ ⊥

Correlation between and N qS k⊥ ⊥

Three transverse quantities:1) Nucleon transverse spin

2) Quark transverse spin 3) Quark transverse momentum

Three different correlations

N

q

q

S

s

k

⊥

⊥

⊥

⇒

23

One pion parton distribution describing transverse momentum and transverse spin

1) Boer-Mulders function

Correlation between and q qs k⊥ ⊥

Two transverse quantities:1) Quark transverse spin 2) Quark transverse momentum

One correlation

q

q

s

k

⊥

⊥

⇒

2424

It can be measured in Drell-Yan process

1 1

Boer-Mulders functions:

Drell-Yan does not require knowledge of the f

- Unpolar

ragmentation f

ized Drell-Yan:

unctions T-odd T

( ) ( )co

MDs ar

s

e predicted to change si

(2 ) DY q qd h x h xσ φ⊥ ⊥∝

•

• gn from DIS to DY (Boer-Mulders and Sivers f

Remains to be tested exunct

peri mentaions)

lly!

25

Boer-Mulders function h1┴

κ1=0.47, MC=2.3 GeV

221 12 2( , ) ( )T TkC HT

T HT C

M Mh x k c e f xk M

ααπ

−⊥ =+

1

1

1 represents a correlation between quark's and transverse spin in an unpolarized hadron (ana is a time-reversal odd, chiral-o

logous to Colldd TMD p

ins fuarton distributio

nction)n

T

h

h

h k⊥

⊥

⊥

•

•

•

1 1

1 1

can lead to an azimuthal dependence with h hf f

ν⊥ ⊥

∝

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

Can one test the predicted sign-change from DIS to D-Y for pion’s B-M function?

26

,1,

1) From NA10 pion Drell-Yan data, one deduces that the productof the pion valence quark B-M function and the proton valencequark B-M function is positive. Using -quark dominance,

( ) we have:

DYu

uh p⊥

, ,1, 1,

, ,1, 1,

,1,

Therefore, either ( )

or

a) ( ) 0; ( ) 0

b) ( )2) In polarized D

( ) < 0; ( ) < 0t

* (

he sin ( ) mo

) > 0

Y, du-

DYu

DY DYu u

DY DYu u

S

h p h

h p h

sign change

no sign c

h

hangepπ φ

π

π

π

φ

⊥ ⊥

⊥ ⊥

⊥

+

−>

−

>

−

,1, (being measured at COMPASS)

3) Need to mea

lation is sensitive

to the sign of (sure the sign of pion's B-M functi

)on in DIS

DYuh π⊥

HOW?

SIDIS on the meson cloud of proton at EIC

27

TSIDIS (Tagged Semi-Inclusive DIS)

TSIDIS

underlying process:

1) An independent check of pion's PDF2) Could a D

llow valence-sea flavor sepaetected is most likely from (or ) s

rea in

Det

ati

ected

o

n

e p e n x

u

e e

d

x

π

π π

π

π

π− + − ±

− − ±

− +

+

′+ → + + +

′+ → + +

3) Pion B-M funis most likely

ction is extracfrom valenc

ted from cos2 modulatione (or ) in u d π

φ

+

28

29

T. Sawada, W. C. Chang, et al.

Summary

30

New territory for theory and experiment * Unique opportunity at COMPASS * Complementary to JLab/EIC tagged DIS p

Meson and Kaon parton distributions

Pion's TMD (Boer-Muldrogra

ers f nctms

u

•

•

∗

ion) Exclusive Drell-Yan with and bea

Test sign-change prediction for pion B-M function

Probe pion and kaon distribution amplitudes First measurement seems feasi

m

ble at

s

J-P

ARC

Kπ − −•

∗

∗∗