Two scales of the hadronic structure

Max-Planck-Institut für Kernphysik, Heidelberg

Two scales of the hadronic structure

Search for clean signatures in the data

Bogdan Povh


• Introduction

• Diffractive cross section is surprisingly small

• Hadronic cross sections rise slowly

• Diffractive cone hardly shrinks with energy

• Gluon shadowing is weak

• Conclusion "anschaulich"

Gluonic mini-clouds of the valence quarks


Introduction

The first evidences for the smallness of the gluonic clouds come from the ISR-experiments

but they have been formally interpreted within the Regge-phenomenology with no connection to hadronic structure (small triple pomeron coupling)


Introduction

I will reinterpret the data in a less formal way, showing that the weakness of diffraction is related to smallness of gluonic clouds. I will argue that the radius of the gluonic spots suggested by data is about 0.3 fm. This is small as compared to to the confinement radius of 1 fm (in fact one has to compare these numbers squared)


Introduction

Theoretically small r0=0.3 fm is not a surprise.

1. Lattice-calculation2. Instanton-liquid model3. Quark model with gluons of mg=0.8

GeV


Introduction

Any high energy reaction via the strong interaction carries the information on the size of the gluon cloud. But, in general, cannot be unambiguously interpreted.

Diffraction seems to be the unique wayto probe directly the gluonic structure of hadrons.


Diffraction

At high energies and large Mx diffraction is dominated by gluon bremsstrahlung.

Mx

Colorless exchange


At low energies the neutral object is qq exchange (Regge exchange) but the cross section drops with energy ~ s-1/2 and Mx dependence

Diffraction

The gluon bremsstrahlung gives different Mx dependence because the gluon is a vector particle

32

1

xx

dd

MdM

d

22

1

xx

dd

MdM

d


Diffraction

The 1/M2 mass distribution at fixed s and t is the signature of gluon bremsstrahlung.

Analogy to photon bremsstrahlung

22

2 11

,1

xx

ddx

MdM

dM

d

d

in spite of the difference of photon and gluon.


Diffraction

...


Diffraction

Inclusive cross section for the reaction pp->pX at ISR


Diffraction

2

1

2

2

2

2 )()(

x

xtotPp

n

x

Ppp

x M

M

M

stg

dtdM

d

scaling gluon bremsstrahlung

gPpp gP

pp

(gPpp)2 ~ tot

P: Pomeron

ln (s/Mx2) = rapidity gap

gPpp


Diffraction

mbdtdM

dM

tg

sM

x

xPpp

nxtot

Pp 2)(

)/(2

22

2

2

The Pomeron-proton total cross section

naïve expectation:

mbtotp

totPp 50

4

9


Diffraction

The gluon cloud of the valence quark is small.

r02 = 0.1 fm2

Neither the single gluon comes far from the quark nor two gluons can couple to the color singlet if they are more than 0.3 fm apart.


Diffraction in DIS

Similar results are obtained in diffraction in DIS from the H1 and ZEUS data by Hauptmann und Soper.

p

p

qx

qr0 = 0.2 fm


Proton-proton cross section

Schematic total cross sections of pions, kaons, protons/antiprotons and photons on the proton



2Rtot

20

20

2 )( nrRsR

02

1xx

n

2ln/ln 0

x

xn

Random walk

The transverse distances between the quarks s independentThe s dependence comes from the gluon bremsstrahlung

20

20

0

20

0

20

20

020

20

2 lnln2ln

1)(

R

r

s

sR

s

srR

x

xrRsR

R0

R



Our model: Kopeliovich, Potashnikova, bp and Predazzi

00

0

200 4

93

s

s

s

srCtot

20

0 4

9ln

3

4

!

1rC

s

s

n

n

n

sqNn

17.03

4

s

23

2202 rn

rB chn 0

2 ln'23

2

s

srB ch

220

20 1.0

43'

GeVrrs

Our prediction: 225.0' GeVExperiment:



Differential cross sections of elastic pp and pp scattering.

Imaginary part of partial amplitude as a function of the impact parameter.


pp (solid circles) and pp (open circles) cross sections at s1/2 > 10 GeV

elastic slope and our predictions



Photoproduction of J/

It is good to have a hadron-proton elasctic scattering far away from the unitary limit.

pJp /*

and ’ agree with our parameters before the unitary correction.



Differential cross sections for the exclusive photoproduction of J/



Values of the slope b, of the t distribution, plotted as a function of W.

1.0'

ln'4ln'20

00

0

W

WB

s

sBB


2.0



Gluon shadowing

x

Boost

Reduction of the gluon density by x


Gluon shadowing

PQCD gives huge shadowing.

Observed small.

For shadowing one needs also transverse overlap.


Conclusion "anschaulich"

J

Chew-Frautschi plot



Chew-Frautschi plot

The Regge trajectory simulates the collective effect of exchanging all members of a family of particles. When t is negative it is the square of the momentum transferred in the exchange. Positive t is the squared mass of the physical particles of spin 1, 3, 5,...



For linear potential (string) gives m2 ~ J

slope

fm

GeV

GeV

1

9.02

1' 2

naive expectation for 'P = 4/9 0.9 GeV-2 = 0.4 GeV-2

measured 'P = 0.1 GeV-2

P = 8 GeV/fm


Backup Slides



Color glass codensate = gluon shadowing as function of k

One would expect:

N

A

GA

G

1

0 k


Diffraction

22

4

222

2

2

222

222

11

,

/

1)1(

MdM

d

d

dM

dMdMd

ddM

Ek

E

kM

x

m

xx

kM

x

hT

h

Tx

hTx

h 1-x

xkT

-kT

Mx


Measurements of , b0, ’ and (0) obtained separately from the electron and muon decay

channels.


Documents

Two scales of the hadronic structure