max-planck-institut für kernphysik, heidelberg two scales of the hadronic structure search for...
TRANSCRIPT
Max-Planck-Institut für Kernphysik, Heidelberg
Two scales of the hadronic structure
Search for clean signatures in the data
Bogdan Povh
Max-Planck-Institut für Kernphysik, Heidelberg
• 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
Max-Planck-Institut für Kernphysik, Heidelberg
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)
Max-Planck-Institut für Kernphysik, Heidelberg
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)
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
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.
Max-Planck-Institut für Kernphysik, Heidelberg
Diffraction
At high energies and large Mx diffraction is dominated by gluon bremsstrahlung.
Mx
Colorless exchange
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
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.
Max-Planck-Institut für Kernphysik, Heidelberg
Diffraction
...
Max-Planck-Institut für Kernphysik, Heidelberg
Diffraction
Inclusive cross section for the reaction pp->pX at ISR
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
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.
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
Proton-proton cross section
Schematic total cross sections of pions, kaons, protons/antiprotons and photons on the proton
Max-Planck-Institut für Kernphysik, Heidelberg
Proton-proton cross section
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
Max-Planck-Institut für Kernphysik, Heidelberg
Proton-proton cross section
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:
Max-Planck-Institut für Kernphysik, Heidelberg
Proton-proton cross section
Differential cross sections of elastic pp and pp scattering.
Imaginary part of partial amplitude as a function of the impact parameter.
Max-Planck-Institut für Kernphysik, Heidelberg
pp (solid circles) and pp (open circles) cross sections at s1/2 > 10 GeV
elastic slope and our predictions
Proton-proton cross section
Max-Planck-Institut für Kernphysik, Heidelberg
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.
Max-Planck-Institut für Kernphysik, Heidelberg
Photoproduction of J/
Differential cross sections for the exclusive photoproduction of J/
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
2.0
Max-Planck-Institut für Kernphysik, Heidelberg
Max-Planck-Institut für Kernphysik, Heidelberg
Gluon shadowing
x
Boost
Reduction of the gluon density by x
Max-Planck-Institut für Kernphysik, Heidelberg
Gluon shadowing
PQCD gives huge shadowing.
Observed small.
For shadowing one needs also transverse overlap.
Max-Planck-Institut für Kernphysik, Heidelberg
Conclusion "anschaulich"
J
Chew-Frautschi plot
Max-Planck-Institut für Kernphysik, Heidelberg
Conclusion "anschaulich"
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,...
Max-Planck-Institut für Kernphysik, Heidelberg
Conclusion "anschaulich"
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
Max-Planck-Institut für Kernphysik, Heidelberg
Backup Slides
Max-Planck-Institut für Kernphysik, Heidelberg
Max-Planck-Institut für Kernphysik, Heidelberg
Color glass codensate = gluon shadowing as function of k
One would expect:
N
A
GA
G
1
0 k
Max-Planck-Institut für Kernphysik, Heidelberg
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
Max-Planck-Institut für Kernphysik, Heidelberg
Measurements of , b0, ’ and (0) obtained separately from the electron and muon decay
channels.
Photoproduction of J/