The physics underlying the fall and eventual rise in various total
cross-sections at high energies has been investigated over a decade using a
model based on the Bloch-Nordsieck resummation in QCD. Here a brief review of
our latest results is presented and comparison made with experimental data on
$pp$, $\gamma proton$ and $\gamma \gamma$ total cross-sections.Comment: Presented by G. Pancheri at ISMD04, Sonoma State University. Under
  publication in Acta Physica Polonica. LaTeX format, 10 *.eps files, 7 page

Godbole, R.

Grau, A.

Pancheri, G.

Srivastava, Y. N.

Acta Physica Polonica B

English

arXiv

Presented by G. Pancheri at the XXXIV International Symposium on Multiparticle Dynamics, Sonoma County, California (USA), july 26- august 1, 2004.The physics underlying the fall and eventual rise in various total cross-sections at high energies has been investigated over a decade using a model based on the Bloch–Nordsieck resummation in QCD. Here a brief review of our latest results is presented and comparison made with experimental data on pp, γ proton and γγ total cross-sections.This work was supported in part by EU Contract CEE-311. RG wishes to acknowledge the partial support of the Department of Scie
nce and Technology, India, under project number SP/S2/K-01/2000-II. AG acknowledges
support from MCYT under project number FPA2003-09298-c02-01

Godbole, R. M.

Institutional Repository of the University of Granada

Total cross-sections and Bloch-Nordsieck gluon resummation

Repositorio Institucional Universidad de Granada

Vol. 36 (2005) ACTA PHYSICA POLONICA B No 2TOTAL CROSS-SECTIONS AND BLOCH–NORDSIECKGLUON RESUMMATION∗G. PancheriINFN, Frascati National Laboratories, I00044 Frascati, ItalyR.M. GodboleCentre for High Energy Physics, Indian Institute of ScienceBangalore, 560 012, IndiaA. GrauDepartamento de Física Teórica y del Cosmos, Universidad de Granada, Spainand Y.N. SrivastavaPhysics Department and INFN, University of Perugia, Perugia, Italy(Received October 26, 2004)The physics underlying the fall and eventual rise in various total cross-sections at high energies has been investigated over a decade using a modelbased on the Bloch–Nordsieck resummation in QCD. Here a brief reviewof our latest results is presented and comparison made with experimentaldata on pp, γ proton and γγ total cross-sections.PACS numbers: 12.38.–t, 13.60.Hb, 13.85.Lg1. IntroductionTotal cross-sections at high energies provide significant information aboutthe distribution of the constituents and the nature of their interaction at veryshort distances. Even though QCD is the fundamental theory for stronginteractions, our lack of knowledge about the confinement of quarks and∗ Presented by G. Pancheri at the XXXIV International Symposium on MultiparticleDynamics, Sonoma County, California, USA, July 26–August 1, 2004.(735)736 G. Pancheri et al.glue has not allowed a first principle determination of hadronic total cross-sections and hence one has to resort to phenomenological models. Overseveral years we have developed and refined a model based on a Bloch–Nordsieck (BN) resummation of soft partons. Through it, we have been im-proving our understanding of the observed variations in the cross-sections,in a quantitative way. Details of our work and its evolution, can be followedthrough references [1–8]. A short summary of data for various processes andtheir comparison with our model predictions are discussed in the subsequentsections. Given the paucity of space, we shall only focus on the energy de-pendences in pp, γp and γγ reactions and the uncertainities therein present.2. QCD and the energy dependence of total cross-sectionsIn Fig. 1, we show a comparison of the energy dependence in differentprocesses. The data show a clear initial fall and eventual rise in the totalcross-sections for all processes.2040608010012014016018020010 102103104105√s ( GeV )σ tot(mb)ZEUS γ  proton (extr.)proton-protonproton-proton from cosmic. M. Block et al.proton-antiprotonPhotoproduction data before HERAZEUS 96 preliminaryH1 94Zeus 92 and 94L3 γ γ  189, 192-202 GeVOPAL γ γ  189 GeVTPC γ γDESY 84 γ γDESY 86 γ γγ  proton divided  by (2/3 Phrunning)γ γ  divided  by (2/3 Phrunning)2Fig. 1. pp/p̄p,γp and γγ total cross-sections. The scaling factor to compare photonson the same scale is obtained from quark counting rules and VMD.The uncertainties in the data for γp [9–12] and γγ [13, 14] are shown inFig. 2 and Fig. 3.Theoretically, perturbative QCD provides a natural mechanism to ex-plain the rise with energy of total cross-sections. As the hadronic c.m. en-ergy increases from 5 to 104 GeV the number of parton collisions increases.In this approach. it is the rise with energy of the jet cross-sectionσjet =√s/2∫ptmindpt1∫4p2t/sdx11∫4p2t/(x1s)dx2∑i,j,k,lfi|a(x1)fj|b(x2)dσ̂ij→kl(ŝ)dpt, (2.1)which drives the rise of the total cross-section. This quantity dependsstrongly on ptmin, the minimum transverse momentum of the produced jetsTotal Cross-Sections and Bloch–Nordsieck Gluon Resummation 7370.060.080.10.120.140.160.180.20.2210 102√s ( GeV )σ totγp(mb)ZEUS BPC 95Photoproduction data before HERAZEUS 96 PreliminaryH1 94ZEUS 92 and 94EMM GRS(top line) k0=0.4 GeV  ptmin=1.5 GeV A=0 GRV(lower) k0=0.66 GeV ptmin=2.0 GeV A non 0Aspen ModelFig. 2. Photoproduction data compared with predictions from the Aspen modeland the EMM.10020030040050060070080090010001 10 102103Cudell et al.BKKSEMMLEP2-L3 189 GeV and 192-202 GeV TPCDesy 1984DESY 86LEP2-OPAL 189 GeVAspenBSWGLMNRegge/Pomeron, SaS510152025303540300 400 500 600 700 800√s (GeV)σ tot(ee→ γγ→ hadrons)(nb)EMM GRS Totaltop line BKKS Modellower line Aspen ModelTagged Beamsminγγ  = 50 GeV2smaxγγ  = 0.64 seeFig. 3. At left we show γγ cross-section data compared with predictions fromdifferent models. At right the corresponding predictions for e+e− hadronic cross-sections in the EMM, Aspen and BKKS models.and can be calculated by convoluting the parton densities for protons andphotons. To satisfy unitarity, the jet cross-sections are embedded into theeikonal formalism. In this Eikonal Minijet Model (EMM) the total cross-section is given byσtot = 2∫d2~b[1 − e−n(b,s)/2], (2.2)where n(b, s) is the average number of inelastic collisions at impact parame-ter b. Introducing a separation between the soft and hard contributions and738 G. Pancheri et al.assuming factorization of the impact parameter and energy dependence wecan writen(b, s) = nsoft + nhard = Asoft(b)σsoft + Ajet(b)σjet , (2.3)where σjet drives the rise and the function A(b) represents the impact pa-rameter distribution of partons in the collision.In the simplest EMM formulation A(b) is obtained through convolutionof the electromagnetic form factors of the colliding particles, i.e.Aab(b) ≡ A(b; ka, kb) =1(2π)2∫d2~qeiq·bFa(q, ka)Fb(q, kb) . (2.4)This model is unable to describe — without further adjustments — theexperimental data for total cross-sections in all the energy range. This canbe seen in Fig. 2 where data for γp cross-section are compared with a bandcorresponding to different sets of parameters in the EMM. Similarly, weshow in Fig. 3 γγ cross section data and its comparison with various models,EMM [3], Regge–Pomeron [15], Aspen [16], BSW [17], GLMN [18], Cuddellet al. [19], BKKS [20]. The predictions for e+e− → hadrons cross-sectionappear in Fig. 3 for the Aspen [16], EMM [3] and BKKS [20] models.2.1. Energy dependence of soft gluon emissionA more realistic EMM is obtained taking into account soft gluon emis-sion from initial state valence quarks. In this model, the impact parameterdistribution of partons is obtained as the Fourier transform of the transversemomentum distribution of the colliding partons computed through soft gluonresummation techniques. The resulting expression isABN =e−h(b,s)∫d2~b e−h(b,s), (2.5)whereh(b, s) =83πqmax∫0dkkαs(k2) ln(qmax +√q2max − k2qmax −√q2max − k2)[1 − J0(kb)] . (2.6)The upper limit qmax is the maximum energy allowed to each single soft gluonemitted in the collision and can be calculated for hard processes (those withTotal Cross-Sections and Bloch–Nordsieck Gluon Resummation 739ppartont ≥ ptmin) by averaging over the valence parton densities, i.e.M ≡ 〈qmax(s)〉 =√s2∑i,j∫dx1x1fi/a(x1)∫dx2x2fj/b(x2)√x1x21∫zmindz(1 − z)∑i,j∫dx1x1fi/a(x1)∫dx2x2fj/b(x2)1∫zmin(dz)(2.7)with zmin = 4p2tmin/(sx1x2). As qmax depends on the energy of the collidingpartons, the impact parameter distribution Eq.(2.5) will be energy depen-dent. The behaviour of qmax with energy is shown in Fig. 4 where the upperline is the one obtained with Eq.(2.7) and the lower curve are the qmax valuesthrough which the soft part nsoft(b, s) has been calculated phenomenologi-cally to describe pp scattering at low energy. Using these values of qmax, inFig. 4 we show the predictions of the model for pp and p̄p total cross-sectionswith GRV [21] densities.00.20.40.60.811.21.41.61.821 10 102103√s ( GeV )q max(GeV)qmax for hard processesand GRV densitiesptmin=1.15 GeV qmaxsoft40608010012014010 102103104√s ( GeV )σ tot(mb)σtot=σsoftABNsoft+σjetABNjetpp     σsoft=σ0pp–    σsoft =σ0(1+2/√s)p=3/4Λ=100 MeVσ0=48 mbptmin= 1.15 GeV, GRV densitiesproton-antiprotonproton-protonFig. 4. At left we show the energy dependence of the maximum energy allowed tosingle gluon emission for hard or soft processes. At right we show pp and p̄p totalcross-sections data compared with predictions from EMM with Bloch–Nordsiecksoft gluon resummation.The EMM model with Bloch–Nordsieck soft gluon resummation havealso been applied to γp and γγ collisions. Theoretical results are comparedwith experimental data and shown in Fig. 5 for γp and in Fig. 6, for γγ, usingtwo different partonic densities for the photon, GRS [22] and CJKL [23].740 G. Pancheri et al.0.060.080.10.120.140.160.180.20.2210 102√s ( GeV )σ totγp(mb)ZEUS BPC 95Photoproduction data before HERAZEUS 96 PreliminaryH1 94ZEUS 92 and 94with BN resummation Soft from pp soft eikonal times 2/3  GRS ptmin=1.2,1.3,1.4,1.5 GeV     Phad=1/2400.060.080.10.120.140.160.180.20.2210 102√s ( GeV )σ totγp(mb)ZEUS BPC 95Photoproduction data before HERAZEUS 96 PreliminaryH1 94ZEUS 92 and 94with BN resummation  CJKL ptmin=1.6,1.8,2 GeV      Phad=1/240Fig. 5. We show photoproduction data compared with the soft gluon improvedEMM for different values of ptmin using GRS densities for the photon (at left) andCJKL densities (at right).02004006008001000120014001600180020001 10 102√s ( GeV )σ total(nb)LEP2-L3 189 GeV and 192-202 GeVLEP2-OPAL 189 GeV TPCDesy 1984Desy 1986Phad constant=1/240GRS ptmin=1.2,1.3,1.4,1.5 GeV BNsoft from BN in p/pbar02004006008001000120014001600180020001 10 102√s ( GeV )σ total(nb)LEP2-L3 189 GeV and 192-202 GeVLEP2-OPAL 189 GeV TPCDesy 1984Desy 1986Phad constant=1/240CJLK ptmin=1.6,1.8,2 GeV BN, soft from p/pbarFig. 6. We show γγ cross-section data compared with the soft gluon improvedEMM using GRS photon densities (at left) and CJKL densities (at right).3. ConclusionIn this brief survey, we have presented a comparison of our model pre-dictions with available data for various processes. The BN resummed gluondistributions appear to describe quite adequately the rise and fall visible inthe data. Experimentally, there are still significant uncertainites. Theoret-ically, we need a better understanding of the qmax parameter for the softpart.Total Cross-Sections and Bloch–Nordsieck Gluon Resummation 741This work was supported in part by EU Contract CEE-311. RG wishesto acknowledge the partial support of the Department of Science and Tech-nology, India, under project number SP/S2/K-01/2000-II. AG acknowledgessupport from MCYT under project number FPA2003-09298-c02-01.REFERENCES[1] G. Pancheri, Y.N. Srivastava, Phys. Lett. B158, 402 (1986).[2] A. Corsetti, A. Grau, G. Pancheri, Y.N. Srivastava, Phys. Lett. B382, 282(1996).[3] A. Corsetti, R.M. Godbole, G. Pancheri, Phys. Lett. B435, 441 (1998).[4] A. Grau, G. Pancheri, Y.N. Srivastava, Phys. Rev. D60, 114020 (1999);[5] R.M. Godbole, A. Grau, G. Pancheri, Y.N. Srivastava, Invited talk at theInternational Workshop on QCD, Martina Franca, Italy, June, 2001[arXiv: hep-ph/0205196]; [hep-ph/0408355].[6] R.M. Godbole, A. de Roeck, A. Grau, G. Pancheri, J. High Energy Phys.0306, 061 (2003) [arXiv: hep-ph/0305071].[7] A. Grau, S. Pacetti, G. Pancheri, Y.N. Srivastava, Nucl. Phys. B (Proc. Suppl.)126, 84 (2004).[8] R.M. Godbole, A. Grau, G. Pancheri, Y.N. Srivastava, Nucl. Phys. B (Proc.Suppl.) 126, 94 (2004).[9] ZEUS Collaboration, Phys. Lett. B293, 465 (1992); Z. Phys. C63, 391 (1994);Nucl. Phys. B627, 3 (2002) [hep-ex/0202034].[10] H1 Collaboration, Z. Phys. C69, 27 (1995).[11] ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B487, 53 (2000)[arXiv:hep-ex/0005018].[12] ZEUS Collaboration (C. Ginsburg et al. ), Proc. 8th International Workshopon Deep Inelastic Scattering, April 2000, Liverpool, editors: J.A. Gracey andT. Greenshaw, World Scientific, 2001.[13] L3 Collaboration, M. Acciarri et al., Phys. Lett. B408, 450 (1997); Phys. Lett.B519, 33 (2001) [hep-ex/0102025]; L3 Collaboration, A. Csilling, Nucl. Phys.Proc. Suppl. B82, 239 (2000).[14] OPAL Collaboration. G. Abbiendi et al., Eur. Phys. J. C14, 199 (2000).[15] G. Schuler, T. Sjöstrand, Z. Phys. C68, 607 (1995); Phys. Lett. B376, 193(1996); Z. Phys. C73, 677 (1997).[16] M.M. Block, E.M. Gregores, F. Halzen, G. Pancheri, Phys. Rev. D58, 17503(1998); M. Block, E.M. Gregores, F. Halzen, G. Pancheri, Phys. Rev. D60,54024 (1999).[17] C. Bourelly, J. Soffer, T.T. Wu, Mod. Phys. Lett. A15, 9 (2000).[18] E. Gotsman, E. Levin, U. Maor, E. Naftali, Eur. Phys. J. C14, 511 (2000)[hep-ph/0001080].742 G. Pancheri et al.[19] J.R. Cudell et al., arXiv:hep-ph/0212101; Phys. Rev. Lett. 89, 201801 (2002)[arXiv:hep-ph/0206172].[20] B. Badelek, M. Krawczyk, J. Kwiecinski, A.M. Stasto, Phys. Rev. D62, 074021(2000); arXiv:hep-ph/0001161.[21] M. Glück, E. Reya, A. Vogt, Phys. Rev. D46, 92 1973.[22] M. Glueck, E. Reya, I. Scheinbein, Phys. Rev. D60, 054019 (1999).[23] F. Cornet, P. Jankowski, M. Krawczyk, A. Lorca, Phys. Rev. D68, 014010(2003) [arXiv:hep-ph/0212160].

The physics underlying the fall and eventual rise in various total cross-sections at high energies has been investigated over a decade using a model based on the Bloch-Nordsieck resummation in QCD. Here a brief review of our latest results is presented and comparison made with experimental data on pp, gamma proton and gammagamma total cross-sections

Pancheri, G

Godbole, RM

Grau, A

Srivastava, YN

Open Access Repository of IISc Research Publications

Total Cross-Sections And Bloch–Nordsieck Gluon Resummation

The physics underlying the fall and eventual rise in various total crosssections at high energies has been investigated over a decade using a model based on the Bloch-Nordsieck resummation in QCD. Here a brief review of our latest results is presented and comparison made with experimental data on pp, γ proton and γγ total cross-sections

Publications of the IAS Fellows

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 3
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 2
00
4 Total Cross-sections and Bloch-Nordsieck Gluon
Resummation
G. PANCHERI
INFN, Frascati National Laboratories, I00044Frascati, Italy
and
R.M. GODBOLE
Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560 012,
India
and
A. GRAU
Departamento de F´ısica Teo´rica y del Cosmos, Universidad de Granada, Spain
and
Y.N. SRIVASTAVA
Physics Department and INFN, University of Perugia, Perugia, Italy
The physics underlying the fall and eventual rise in various total cross-
sections at high energies has been investigated over a decade using a model
based on the Bloch-Nordsieck resummation in QCD. Here a brief review
of our latest results is presented and comparison made with experimental
data on pp, γ proton and γγ total cross-sections.
1. Introduction
Total cross-sections at high energies provide significant information about
the distribution of the constituents and the nature of their interaction at
very short distances. Even though QCD is the fundamental theory for
strong interactions, our lack of knowledge about the confinement of quarks
and glue has not allowed a first principle determination of hadronic to-
tal cross-sections and hence one has to resort to phenomenological models.
2 pancheri1 printed on February 2, 2008
Over several years we have developed and refined a model based on a Bloch
Nordsieck(BN) resummation of soft partons. Through it, we have been im-
proving our understanding of the observed variations in the cross-sections,
in a quantitative way. Details of our work and its evolution, can be followed
through references [1, 2, 3, 4, 5, 6, 7, 8]. A short summary of data for various
processes and their comparison with our model predictions are discussed in
the subsequent sections. Given the paucity of space, we shall only focus on
the energy dependences in pp, γp and γγ reactions and the uncertainities
therein present.
2. QCD and the energy dependence of total cross-sections
In Fig.(1), we show a comparison of the energy dependence in different
processes. The data show a clear initial fall and eventual rise in the total
cross-sections for all processes.
20
40
60
80
100
120
140
160
180
200
10 10 2 10 3 10 4 10 5
√s ( GeV )
s
to
t(m
b)
ZEUS g   proton (extr.)
proton-proton
proton-proton from cosmic. M. Block et al.
proton-antiproton
Photoproduction data before HERA
ZEUS 96 preliminary
H1 94
Zeus 92 and 94
L3 g  g   189, 192-202 GeV
OPAL g  g   189 GeV
TPC g  g
DESY 84 g  g
DESY 86 g  g
g   proton divided  by (2/3 Phrunning)
g  g   divided  by (2/3 Phrunning)2
Fig. 1. pp/p¯p,γp and γγ total cross-sections. The scaling factor to compare photons
on the same scale is obtained from quark counting rules and VMD.
The uncertainties in the data for γp [9, 10, 11, 12] and γγ[13, 14] are
shown in Fig.(2) and Fig.(3).
Theoretically, perturbative QCD provides a natural mechanism to ex-
plain the rise with energy of total cross-sections. As the hadronic c.m. en-
ergy increases from 5 to 104 GeV the number of parton collisions increases.
In this approach. it is the rise with energy of the jet cross-section
σjet =
∫ √s/2
ptmin
dpt
∫ 1
4p2
t
/s
dx1
∫ 1
4p2
t
/(x1s)
dx2
∑
i,j,k,l
fi|a(x1)fj|b(x2)
dσˆij→kl(sˆ)
dpt
,
(2.1)
which drives the rise of the total cross-section. This quantity depends
strongly on ptmin, the minimum transverse momentum of the produced jets
pancheri1 printed on February 2, 2008 3
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
10 10 2√s ( GeV )
s
to
t
g
p
(m
b)
ZEUS BPC 95
Photoproduction data before HERA
ZEUS 96 Preliminary
H1 94
ZEUS 92 and 94
EMM
 GRS(top line) k0=0.4 GeV  ptmin=1.5 GeV A=0
 GRV(lower) k0=0.66 GeV ptmin=2.0 GeV A non 0
Aspen Model
Fig. 2. Photoproduction data compared with predictions from the Aspen model
and the EMM.
100
200
300
400
500
600
700
800
900
1000
1 10 10
2
10
3
Cudell et al.
BKKS
EMM
LEP2-L3 189 GeV and
 192-202 GeV
 TPC
Desy 1984
DESY 86
LEP2-OPAL 189 GeV
Aspen
BSW
GLMN
Regge/Pomeron, SaS
5
10
15
20
25
30
35
40
300 400 500 600 700 800
√s (GeV)
s
to
t(e
e→
 
gg→
 
ha
dr
on
s)(
nb
)
EMM GRS Total
top line BKKS Model
lower line Aspen Model
Tagged Beam
s
min
gg
 = 50 GeV2
s
max
gg
 = 0.64 see
Fig. 3. At left we show γγ cross-section data compared with predictions from
different models. At right the corresponding predictions for e+e− hadronic cross-
sections in the EMM, Aspen and BKKS models.
and can be calculated by convoluting the parton densities for protons and
photons. To satisfy unitarity, the jet cross-sections are embedded into the
eikonal formalism. In this Eikonal Minijet Model (EMM) the total cross-
section is given by
σtot = 2
∫
d2~b[1− e−n(b,s)/2] (2.2)
where n(b, s) is the average number of inelastic collisions at impact parame-
ter b. Introducing a separation between the soft and hard contributions and
assuming factorization of the impact parameter and energy dependence we
can write
n(b, s) = nsoft + nhard = Asoft(b)σsoft +Ajet(b)σjet (2.3)
4 pancheri1 printed on February 2, 2008
where σjet drives the rise and the function A(b) represents the impact pa-
rameter distribution of partons in the collision.
In the simplest EMM formulation A(b) is obtained through convolution
of the electromagnetic form factors of the colliding particles, i.e.
Aab(b) ≡ A(b; ka, kb) =
1
(2π)2
∫
d2~qeiq·bFa(q, ka)Fb(q, kb) (2.4)
This model is unable to describe - without further adjustments - the experi-
mental data for total cross-sections in the all energy range. This can be seen
in Fig.(2) where data for γp cross-section are compared with a band corre-
sponding to different sets of parameters in the EMM. Similarly, we show in
Fig.(3) γγ cross section data and its comparison with various models, EMM
[3], Regge-Pomeron[15], Aspen[16], BSW[17], GLMN[18], Cuddell et al.[19],
BKKS[20]. The predictions for e+e− → hadrons cross-section appear in
Fig. (3) for the Aspen[16], EMM [3] and BKKS [20] models.
2.1. Energy dependence of soft gluon emission
A more realistic EMM is obtained taking into account soft gluon emis-
sion from initial state valence quarks. In this model, the impact parameter
distribution of partons is obtained as the Fourier transform of the trans-
verse momentum distribution of the colliding partons computed through
soft gluon resummation techniques. The resulting expression is
ABN =
e−h(b,s)∫
d2~b e−h(b,s)
(2.5)
where
h(b, s) =
8
3π
∫ qmax
0
dk
k
αs(k
2) ln(
qmax +
√
q2max − k2
qmax −
√
q2max − k2
)[1− J0(kb)] (2.6)
The upper limit qmax is the maximum energy allowed to each single soft
gluon emitted in the collision and can be calculated for hard processes (those
with ppartont ≥ ptmin) by averaging over the valence parton densities,i.e.
M ≡< qmax(s) >=
√
s
2
∑
i,j
∫ dx1
x1
fi/a(x1)
∫ dx2
x2
fj/b(x2)
√
x1x2
∫ 1
zmin
dz(1− z)∑
i,j
∫ dx1
x1
fi/a(x1)
∫ dx2
x2
fj/b(x2)
∫ 1
zmin
(dz)
(2.7)
with zmin = 4p
2
tmin/(sx1x2). As qmax depends on the energy of the col-
liding partons, the impact parameter distribution Eq.(2.5) will be energy
dependent. The behaviour of qmax with energy is shown in Fig.(4) where
pancheri1 printed on February 2, 2008 5
the upper line is the one obtained with Eq.(2.7) and the lower curve are
the qmax values through which the soft part nsoft(b, s) has been calculated
phenomenologically to describe pp scattering at low energy. Using these
values of qmax, in Fig.(4) we show the predictions of the model for pp and
p¯p total cross-sections with GRV [21] densities.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 10 10
2
10
3
√s ( GeV )
q m
a
x(G
eV
)
qmax for hard processes
and GRV densities
ptmin=1.15 GeV
 qmax
soft
40
60
80
100
120
140
10 10
2
10
3
10
4
√s ( GeV )
s
to
t(m
b)
s tot= s softABN
soft
+ s jetABN
jet
pp     s soft= s 0
pp–    s soft =s 0(1+2/√s)
p=3/4
L =100 MeV
s 0=48 mb
ptmin= 1.15 GeV, GRV densities
proton-antiproton
proton-proton
Fig. 4. At left we show the energy dependence of the maximum energy allowed to
single gluon emission for hard or soft processes. At right we show pp and p¯p total
cross-sections data compared with predictions from EMM with Bloch-Nordsieck
soft gluon resummation.
The EMM model with Bloch-Nordsieck soft gluon resummation have
also been applied to γp and γγ collisions. Theoretical results are compared
with experimental data and shown in Fig.(5) for γp and in Fig.(6), for γγ
using two different partonic densities for the photon, GRS[22] and CJKL[23].
3. Conclusion
In this brief survey, we have presented a comparison of our model pre-
dictions with available data for various processes. The BN resummed gluon
distributions appear to describe quite adequately the rise and fall visible in
the data. Experimentally, there are still significant uncertainites. Theoret-
ically, we need a better understanding of the qmax parameter for the soft
part.
4. Acknowledgments
This work was supported in part by EU Contract CEE-311. RG wishes
to acknowledge the partial support of the Department of Science and Tech-
6 pancheri1 printed on February 2, 2008
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
10 10 2√s ( GeV )
s
to
t
g
p
(m
b)
ZEUS BPC 95
Photoproduction data before HERA
ZEUS 96 Preliminary
H1 94
ZEUS 92 and 94
with BN resummation
 Soft from pp soft eikonal times 2/3
  GRS ptmin=1.2,1.3,1.4,1.5 GeV     Phad=1/240
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
10 10 2√s ( GeV )
s
to
t
g
p
(m
b)
ZEUS BPC 95
Photoproduction data before HERA
ZEUS 96 Preliminary
H1 94
ZEUS 92 and 94
with BN resummation
  CJKL ptmin=1.6,1.8,2 GeV      Phad=1/240
Fig. 5. We show photoproduction data compared with the soft gluon improved
EMM for different values of ptmin using GRS densities for the photon (at left) and
CJKL densities (at right).
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1 10 10 2√s ( GeV )
s
to
ta
l(n
b)
LEP2-L3 189 GeV and 192-202 GeV
LEP2-OPAL 189 GeV
 TPC
Desy 1984
Desy 1986
Phad constant=1/240
GRS ptmin=1.2,1.3,1.4,1.5 GeV BN
soft from BN in p/pbar
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1 10 10 2√s ( GeV )
s
to
ta
l(n
b)
LEP2-L3 189 GeV and 192-202 GeV
LEP2-OPAL 189 GeV
 TPC
Desy 1984
Desy 1986
Phad constant=1/240
CJLK ptmin=1.6,1.8,2 GeV BN, soft from p/pbar
Fig. 6. We show γγ cross-section data compared with the soft gluon improved
EMM using GRS photon densities (at left) and CJKL densities (at right).
nology, India, under project number SP/S2/K-01/2000-II. AG acknowledges
support from MCYT under project number FPA2003-09298-c02-01.
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Total Cross-sections and Bloch-Nordsieck Gluon Resummation

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