1ceinterferen-- OP

Pomeron/Odderon interference in diffractive mesonpairs production

In collaboration withPhilipp Hägler, MIT

Bernard Pire, Ecole Polytechnique

Lech Szymanowski, Ecole Polytechnique&Soltan Institute for Nuclear Studies, Warsaw

Oleg Teryaev, BLTP, JINR, Dubna

Hägler/Pire/Szymanowski/Teryaev, Eur.Phys.J. C26: 261-270,2002 and Phys.Lett. B535:117-126,2002

2ceinterferen-- OP

Odderon OPomeron P colorlessflavourless

C-even C-odd

effective theorypQCD: BFKL P/BKP Ovs Generalized Partton Distr. Reggeons

pure O contributionsare rather small

Fracture functions=q,G distributions in PP/O=C/T-odd Fracture functions

P contributionsare dominant

(2,3)-gluon exchangeGPD: + quark one!

asymmetries in harddiffractive 2-pion electroproduction:

Specifics of H1(ZEUS)/HERMES/COMPASS

phase-shiftdependence

Generalized (2-pion) distribution amplitudesimpact-factors

Overview

3ceinterferen-- OP

Pomeron and Odderon

predicts

P/O-like2/3-gluon-exchange

0s

t

t

s ?1

2

3

4

t

s1

2

3

4s

1

2

3

4OP,

t

phenomenologicalRegge-approach

perturbativeQCD

predictsP/O-exchange

perturbative P/O

P andperturbative P

O andperturbative O

1P

O

A

A

?

4ceinterferen-- OP

Previous approaches to the O (non-exhaustive)

Czyzewski/Kwiecinski/Motyka/Sadzikowski, Phys.Lett.B398, 1997

Engel/Ivanov/Kirschner/Szymanowski, Eur.Phys.J.C4, 1998

Bartels/Braun/Colferai/Vacca, Eur.Phys.J.C20,2000

Brodsky/Rathsman/Merino, Phys.Lett.B461,1999

Ivanov/Nikolaev/Ginzburg,hep-ph/0110181, 0207345

Schäfer/Mankiewicz/Nachtmann,Phys.Lett.B2724,19912

OA

P

OAA

A

OP,

P 'P?

)(OP/J

P 'P

P 'P)(PO

underlying idea: C-Odd

Ginzburg/Ivanov,Nucl.Phys.B388:376-390,1992

c

'P ?

'NNJ

pQCD

?

pQCD

P

non-QCD

non-QCD

non-QCD

P/O-interference in hard diffractive

pion-pair electroproduction

5ceinterferen-- OP

P

?

'P

T/L

P 'P

P 'P ?

q

q

T/LJ

'NNJ

'NNJ

1k 2k 3k

p

t

s

QCD: Collinear vs high-energy factorization

'NN/// JJPSA T/L

OPOPOP

approx.-Born 22QCDQs

0s

t

"," OP

2Q

DDIS=Diffractive

DeepInelastic

Scattering

HEallongitudink

Ctransversek

i

i

)(0

)(02

2

6ceinterferen-- OP

)k,k,k(J)k,k,k(Jkkk)(

)pkkk(kdkdkd

!

sA

)k,k(J)k,k(Jkk)(

)pkk(kdkdisA

'NN

'NN

T/L

T/L

32132123

22

21

6

3212

32

22

122

212122

21

2

212

22

12

23

8

2

OOO

PPP

The amplitudes

2

2

22

2

)(

e, transversare

momentagluon squared the

pt

Pqs

kk

k

ii

i

*

P 'P

flow momentum transverse

*qP

'P

p

p

p

ep

'pe

lowerupper ,....)k,k(J,....)k,k(J....)kk(

....kk)(

....kdkdsA

n 2121212

22

21

22

12

2

ionfactorizat-

llenergy/sma-high k/x

7ceinterferen-- OP

The upper impact-factors, longitudinal polarized photon

3

1222222222221

1

0

20321

3

1111

3

1

4

i ii

I

C

abc

)pzk()zpk(pzpz)k,k(P

)m,,z()k,k,k(PzzdzN

QdiegJ L

O

OO

Pomeron

Odderon

2

2

2

2

22

222

22

210

qq

pp

pp

qQ

mm,Qzzm

pm

)m,,z(

duqq

,I

in ionapproximat collinear

of fraction momentum allongitudin

squared virtuality-photon

mass-quark

dipion the of mass invariant

amplitudes-ondistributi-

2 p,z

1k 2k 3k

pL

a b c

z p,

pQCD-calculation

)z()z(AdzJ softhardupper 1

0ionfactorizat collinear

8ceinterferen-- OP

22

22

1

222

222

222

0

10

2

310

2

222

0

220

mFcoszz)m,,z(

cosPmBWemBWeR)zz(zz)m,,z(

I

fmi

fmiI

The Generalized (2-pion) distribution-amplitudes

shifts-phase wave- and -

factor-form pion timelike

amplitudes-Wigner-Breit

in of fraction momentum

frame rest 2 the in of angledecay polar

ds

F

BW

qq,.R

s'

m

m,cos

,

f ,

20

22

2

20

50

4112

MM

MM

mimm

mmBW

222

22

2p

Diehl/Gousset/Pire, Phys.Rev.D62,073014,2000

evolutionGegenbauer-polynomials partial wave expansion dispersion relations

Diehl/Gousset/Pire/Teryaev Phys.Rev.Lett..81,1782,1998

asymptotic expansion

p,zp

z p,

qq

002

22 )()x(e

dx)m,,z( xizP

q

q

9ceinterferen-- OP

Which resonances contribute?

O-exchange

C O

parity-G

pions#)(G

?....f,f,a, 200q

q

),(C)(G ),(I 10

GI,C:a 10 GI,C:f 00

P-exchange

only C=- and I=1 possible

)G(I,C: 1

only C=+ and I=0 possible

10ceinterferen-- OP

The 2-pion-distribution-amplitudes, continued

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

0

1

2

3

4

5

6

7

P1+P2*m+(P3+P4*m)*atan((m-P5)*P6)

fit of delta0 in

comparison to fitfrom Hyams et al.

Chi^2 = 0.00085P1-0.13325 ±0.04713P23.18816 ±0.04268P30.40399 ±0.02791P40.25554 ±0.02374P50.99637 ±0.00052P6159.90324 ±23.34

phas

e sh

ift 0

m2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

0.0

0.5

1.0

1.5

2.0

2.5

3.0

P1+P2*m+(P3+P4*m)*atan((m-P5)*P6)

2-fitvs

2-data

P11.8268 ±0.46632P2-0.22728 ±0.32446P31.23832 ±0.30507P4-0.13906 ±0.18783P51.27679 ±0.00571P611.42772 ±0.75429

phas

e sh

ift 2

m2

300 400 500 600 700 800 900 1000

0

10

20

30

40

50

with and without'-contributionF

F

m2 [MeV]

)m( 20 )m( 22 0.4 0.6 0.8 1.2 1.4 1.6

50

100

150

200

' with

)m( 21

Kühn/Santamaria, Z.Phys. C48, 1990,Hyams et al., Nucl.Phys. B64,1973

cosPmBWemBWeR)zz(zz)m,,z( f

mif

miI2

22

222

222

02

222

0

220

2

310

22

22

1 10 mFcoszz)m,,z(I

' without

11ceinterferen-- OP

213

232

221

2

2

321

3

1321321321

3

22

21

2

2

221

2

22

2

1

200034

2

1

2

13

2

kkkkkkA

A)k,k,k(F

)k,k,k(F),kkkk,k(F),,kkk(FN

digJ

kkA

A

kkA

A

N

igJ

iii

C

abcsoft'NN

C

absoft'NN

O

P

The lower impact-factors

coupling veperturbati-non a is ; softgm

A2

according to Gunion/Soper, Phys.Rev.D15, 1977 and Fukugita/Kwiecinski, Phys.Lett.B83, 1979

) (limit invariant gauge

gluons of exchange undersymmetric

are factors impact proton the

0

ik

model-dependent

P 'P ? 'NNJ

1k 2k 3k

P 'P

1k 2k 3k

a b c

pptot from 7030 ..soft

12ceinterferen-- OP

Dcosd

Ncoscosd

,y,,,m,t,Q,sd

,y,,,m,t,Q,sdcos

y,,m,t,Q

C

,

,

1

1

1

122

2

22

2

22

2

PO

OPOP

AA

p

sinBWsinBWAA*AARe

FF) pion the in (hidden shift-phase-wave- the is 1

122100

122100 sinBWsinBWA

A~

P

O specific m2 -dependence

The charge asymmetry

*AARep)cos()y()y(

*AA*AARe)cos(py)y(*AARe)y(N

TT

LTLTLLC

OP

POOPOP

22 212114

128116

2222

22

212112

12818

TT

LTLTLL

AAp)cos()y()y(

*AA*AARe)cos(py)y(AA)y(D

OP

OOPPOP

yy

Qpe 1

2p

13ceinterferen-- OP

complementary m2-dependence

The spin asymmetry

Dcosd

Ncoscosd

,y,,,m,t,Q,sd

,y,,,m,t,Q,sdcos

y,,m,t,Q

S

,

,

1

1

1

122

2

22

2

22

2

*AA*AAIm)sin(pyN TLTL

SPOOP

18

122100 cosBWcosBWA

A~

P

O

14ceinterferen-- OP

Some numerical results

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

f0

= 0.05 GeV

Q2 = 3 GeV

2

t = -0.8 GeV2

soft

= 0.3...0.7

QCD = 0.2...0.35 GeV

asym

met

ry

m2

peak-0f

peak-2f

antipeak-

0.4 0.6 0.8 1.0 1.2 1.4-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Q2 = 3,5,10 GeV

2

t = -0.8 GeV2

= 0y = 0.5

char

ge a

sym

met

ry

m2 [GeV]

0.00.10.2

0.30.4

0.50.6

0.70.8

0.90

50100

150200

250300

350-0.4

-0.2

0.0

0.2

0.4

0.6

Q2 = 5 GeV

2

t = -0.8 GeV2

m2 = 1.275 GeV

char

ge a

sym

met

ry

y

longitudinal polarization

0.4 0.6 0.8 1.0 1.2 1.4-0.02

-0.01

0.00

0.01

0.02

0.03

Q2 = 3,5,10 GeV

2

t = -0.8 GeV2

= /2y = 0.5

spin

asy

mm

etry

m2 [GeV]

15ceinterferen-- OP

0.4 0.6 0.8 1.0 1.2 1.4

-0.05

0.00

0.05

0.10

solid line: 0°

with extra phasesfrom -20° to 20°

Q2 = 5 GeV

2

t = -0.8 GeV2ch

arge

asy

mm

etry

(L)

m2 [GeV]

0.4 0.6 0.8 1.0 1.2 1.4

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

fromKloet/Loiseau

= 1Q

2 = 5 GeV

2

t = -0.8 GeV2

= 0y = 0.5

char

ge a

sym

met

ry

m2 [GeV]

Higher order corrections & extra phases

to LLA,-Pomeron-exchange is purely Im-Odderon-exchange is purely Re

higher order corrections introduce additional phases

%~)t,s(A

)t,s(A30

0

0

Im

Re

non-resonant background

16ceinterferen-- OP

Competing/supplementary processes

Primakoff-contribution

collinear approach,off-forward scattering

so far not calculated, estimated to be small

dominant/valid at „large“ x dies out at small x

P 'P ?

q

q

'NNJ

P 'P

q

q

?pF

predicted (without f0) rather welllarge x data from HERMES

-expected at COMPASS!

Lehmann-Dronke/Schäfer et al.,Phys.Rev.D63(2001)

17ceinterferen-- OP

Lehmann-Dronke/Schäfer et al.,Phys.Rev.D63(2001)

peak?- the is Where 0f

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

f0

= 0.05 GeV

Q2 = 3 GeV

2

t = -0.8 GeV2

soft

= 0.3...0.7

QCD = 0.2...0.35 GeV

asym

met

ry

m2

x small at out dies result collinear 2 twist

Anisovich/Sarantsev,hep-ph/0203139neededbut unclear yet nature -(980)0f

? peak-0f

asym

met

ry

! peak-2f

Reason-dominance of gluon GPD(C=-)HIGH twist is required

18ceinterferen-- OP

Summary

charge and spin asymmetries-sensitive test for C-T/odd Fracture Functions

Pomeron/Odderon or various GPD‘s Complementarity of H1(ZEUS)/HERMES/COMPASS

Higher twist C-odd gluonic GPD required (relation to O?!)more sophisticated GDAs/proton-impact-factorsKaon asymmetriesStudies of f0 - resonance contribution to asymmetries-Key to its structure?

Outlook

a rather large asymmetry is predictedin the vicinity of the f0,2-resonances

P/O-pQCD framework – large Q, small x -small Q (almost real photons)- COMPASS - phenomenological P/O?!

GPD-same GDA as in pQCD P/O-relatively small x – leading twist contribution to asymmetries go to zero (as ratio of quark/gluon GPD‘s)