xl international symposium on multiparticle dynamics inclusive cross sections of proton-proton and...
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XL International Symposium on Multiparticle Dynamics
Inclusive cross sections of proton-proton and
proton-antiproton scattering
Victor A. Abramovsky
Natalia V. RadchenkoNovgorod State University
Russia
ISMD 2010 2
Inclusive cross sections and multiplicity distributions are different for pp and pbarp
Pomeranchuk theorem:
total cross sections
differential elastic cross sections the same
elastic cross sections for pp and pbarp
It is also generally accepted that inclusive
cross sections and multiplicity distributions are the
same for pp and pbarp.
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Low Constituents Number Model (LCNM)1. On the first step before the collision there is small number
of constituents in initial hadrons. In every hadron this is component either with only valence quarks or with valence quarks and one additional gluon.
2. On the second step the hadrons interaction is carried out by gluon exchange between the valence quarks and initial gluons. The hadrons gain the color charge.
3. On the third step after interaction the colored hadrons move apart and when the distance between them becomes larger than the confinement radius, the lines of color electric field gather into the string. This string breaks out into secondary hadrons.
(Abramovsky, Kancheli 1980, Abramovsky, Radchenko 2009)
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Three types of inelastic subprocesses
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Results in LCNM
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Pseudorapidity density at LHC energies
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The importance of inclusive cross sections• From the LCNM it follows, that multiplicity distributions are
different for pp and pbarp because of subprocess with three quark strings in pbarp (blue line).
• Three quark strings produce events with high multiplicity in tail of distribution.
• In order to make the difference more visible, we have to use observable instead of
• is measured independently of in inclusive measurementsnPn nP
nPn nP
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Inclusive cross sections in events with fixed number of particles
Topological inclusive cross section of one charged particle production
Total inclusive cross section and its normalization
Normalization of topological inclusive cross section
2
210
3
33
!
1
!1
122
mnmn
m
incln Ad
mnpd
dE
03
33
3
33 2222
n
incln
incl
pd
dE
pd
dE
nsdincl
npd
dpd
3
33
2
20 !
1
!
1
mnmn
mn Ad
mn
n
incln npd
dpd
3
33
nnsdn
incln
nsdPnn
pd
dpd
3
331
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Inclusive cross sections in bins
UA5 Coll. gave data in 9 bins of charged multiplicities:
2 ≤ n ≤ 10, 12 ≤ n ≤ 20, … 72 ≤ n ≤ 80 and n ≥ 82.
We define inclusive cross section in this bins
Inclusive cross sections in bins are normalized as follows
pd
d
pd
d incl
i
incli
3
39
13
)(3
823
3
3
)9(3
,n
incln
incl
pd
d
pd
d
nsdi
bininnn
nsdincli
nPnpd
dpd
)(
3
)(33
...,20
123
3
3
)2(3
n
incln
incl
pd
d
pd
d ,
10
23
3
3
)1(3
n
incln
incl
pd
d
pd
d
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Difference in inclusive cross sections of pp and pbarp
Ratio of (1) to (2) gives
Solution of the integral equation (3) (perhaps, the only solution)
pdd
dpd
d
d incliincli
2
)(32
)(
)1()()(
2
)(32
3
)(33 nsdi
pp
inclipp
inclipp
inclipp n
d
dd
pdd
dpdd
pd
dpd
)2()()(
2
)(32
3
)(33 nsdi
pp
inclipp
inclipp
inclipp n
d
dd
pdd
dpdd
pd
dpd
)3()(
)(
)()(
d
dd
n
n
d
dd
inclipp
ipp
ipp
inclipp
)4()(
)(
)()(
d
d
n
n
d
d inclipp
ipp
ipp
inclipp
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Inclusive cross sections in different bins
2 ≤ n ≤ 10 0.76 ± 0.01
12 ≤ n ≤ 20 0.86 ± 0.01
22 ≤ n ≤ 30 0.99 ± 0.01
32 ≤ n ≤ 40 1.09 ± 0.01
42 ≤ n ≤ 50 1.10 ± 0.01
52 ≤ n ≤ 60 1.18 ± 0.01
62 ≤ n ≤ 70 1.35 ± 0.02
72 ≤ n ≤ 80 1.45 ± 0.02
n ≥ 82 1.26 ± 0.02
)()( ipp
ipp nn
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Inclusive cross sections summed over all bins
We obtained the numerical
value of relation
by summing over all nine
bins of multiplicity.
For
This result will be used on
the next slides.
5.2
d
d
d
d inclpp
inclpp
01.012.1
d
d
d
d inclpp
inclpp
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Inclusive cross section with transverse momentum
From the AGK cancellation rules it follows the factorization of
transverse dependence in inclusive cross section.
Returning to formulas (1) and (2) we can write down
From this relation it can strictly be proved that
so we can obtain
pdd
d
n
n
pdd
d inclipp
ipp
ipp
inclipp
2
)(3
)(
)(
2
)(3
pfpf pppp
d
d
d
d
dpd
d
pdpd
d
p
inclpp
inclpp
inclpp
inclpp
22
21
21
d
dpf
dpd
d
p
inclincl
2
2
1
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Experimental evidences of difference in pp and pbarp
ATLAS Coll. ALICE Coll.
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Conclusion
• We think that ATLAS Coll. discovered a new effect – the difference in multiparticle production in pp and pbarp interactions. ALICE Coll. confirmed this effect.
• We propose to experimentalists to measure inclusive cross section in bins with high multiplicities, where the difference will be the most evident.
ISMD 2010 16
Acknowledgements
• V.A.A. gratefully acknowledges financial support from the RFBR, grant 10-02-68536-z.
• N.V.R. gratefully acknowledges financial support from the Ministry of education and science of the Russian Federation, grant P1200.