pp Elastic Scattering at LHC in a Nucleon-Structure Model

a r X i v :0708.1156v 1 [h e p -p h ] 8 A u g 2007Blois07/EDS07

Proceedings

M.M.Islam a ,J.Ka ˇs par b and R.J.Luddy c a Department of Physics,University of Connecticut,Storrs,CT 06269,USA,(islam@ad796d7a168884868762d661)b TOTEM Collaboration,CERN,Geneva,Switzerland (Jan.Kaspar@cern.ch)

Institute of Physics,Academy of Sciences of the Czech Republic,Prague

c Department of Physics,University of Connecticut,Storrs,CT 06269,USA,(RJLuddy@ad796d7a168884868762d661)pp Elastic Scattering at LHC in a Nucleon–Structure Model (Presente

d by M.M.Islam)Abstract W

e predict pp elastic differential cross sections at LHC at c.m.en-ergy 14TeV and momentum transfer range |t |=0–10GeV 2in a nucleon-structure model.In this model,the nucleon has an outer cloud o

f quark-antiquark condensed ground state,an inner shell of topolog-ical baryonic charge (r ?0.44F )probed by the vector meson ω,and a central quark-ba

g (r ?0.2F )containing valence quarks.We also predict d σ/d t in the Coulomb-hadronic interference ad796d7a168884868762d661rge |t |elastic scattering in this model arises from valence quark-quark scat-tering,whic

h is taken to be due to the hard-pomeron (BFKL pomeron with next to leading order corrections).We present results of taking into account multiple hard-pomeron exchanges,i.e.unitarity correc-tions.Finally,we compare our prediction of pp elastic d σ/d t at LHC with the predictions of various other models.Precise measurement of pp d σ/d t at LHC by the TOTEM group in the |t |region 0–5GeV 2will be able to distinguish between these models.High energy pp and ˉp p elastic scattering have been at the forefront of accelerator research since the early seventies with the advent of CERN Intersecting Storage Rings (ISR)and mea-surement of pp elastic differential cross section in the c.m.energy range

√s =27.4GeV in a ?xed target

experiment at large momentum transfers:|t |=5.5–14GeV 2[2].Next came the CERN SPS Collider,where ˉp p elastic scattering was measured at c.m.energies 546GeV and 630GeV –a jump of one order of magnitude in c.m.energy from ISR [3–5].The Fermilab Tevatron followed next where ˉp p elastic scattering was measured at c.m.energy 1.8TeV ,but in a rather small mo-mentum transfer range:|t |=0–0.5GeV 2[6,7].We are now at the threshold of a new period of accelerator research with the LHC starting up soon and with the planned measurement of pp elastic scattering by the TOTEM group at c.m.energy 14TeV and momentum transfer range |t |?0–10GeV 2[8,9].

My collaborators and I have been studying pp and ˉp p elastic scattering since late seventies.From our phenomenological investigation,we have arrived at two results:1)a physical picture

of the nucleon,2)an effective?eld theory model underlying the physical picture[10].The physical picture shows that the nucleon has an outer cloud,an inner shell of baryonic charge, and a central quark-bag containing the valence quarks(Fig.1).The radius of the shell is about 0.44F and that of the quark-bag is0.2F.The underlying?eld theory model turns out to be a gauged Gell–Mann–Levy linearσ-model with spontaneous breakdown of chiral symmetry and with a Wess–Zumino–Witten(WZW)anomalous action.The model attributes the outer nu-cleon cloud to a quark–antiquark condensed ground state analogous to the BCS ground state in superconductivity–an idea that was?rst proposed by Nambu and Jona-Lasinio.The WZW ac-tion indicates that the baryonic charge is geometrical or topological in nature,which is the basis of the Skyrmion model.The action further shows that the vector mesonωcouples to this topo-logical charge like a gauge boson,i.e.like an elementary vector meson.As a consequence,one nucleon probes the baryonic charge of the other viaω-exchange.In pp elastic scattering,in the small momentum transfer region,the outer cloud of one nucleon interacts with that of the other giving rise to diffraction scattering.As the momentum transfer increases,one nucleon probes the other at intermediate distances and theω-exchange becomes dominant.At momentun transfers even larger,one nucleon scatters off the other via valence quark-quark scattering.

Our calculated pp elastic dσ/d t at c.m.energy14TeV is shown in Fig.2by the solid line that includes all three processes:diffraction,ω-exchange,and qq scattering.The dotted curve shows dσ/d t due to diffraction only.We see that diffraction dominates in the small|t| region,but falls off rapidly.The dot-dashed curve shows dσ/d t due toω-exchange only and indicates thatω-exchange dominates in the|t|region1.5–3.5GeV2.Beyond that,the valence quark-quark scattering takes over.The dashed curve for|t|>3.5GeV2represents dσ/d t with single valence quark-quark scattering,whereas the solid curve represents dσ/d t with all multiple valence quark-quark scattering.

Let us next examine how the three processes are described in our calculations[10].Diffrac-tion is described by using the impact parameter representation and a phenomenological pro?le function:

T D(s,t)=i p W ∞0b d b J0(b q)ΓD(s,b);(1) q is the momentum transfer(q=

+1

1+e(b?R)/a)

),a=a0+a1(ln s?iπ

2

(derivative dispersion relation)

a0+a1ln s

3.T D(s,t)～i s ln2s f(|t|ln2s)(Auberson-Kinoshita-Martin scaling)

(s,t)=T pp D(s,t)(crossing even)

4.Tˉp p

D

Incidentally,the pro?le function(2)has been used by Frankfurt et al.to estimate the ab-sorptive effect of soft hadronic interactions(gap survival probability)in the central production of Higgs at LHC[11].

The ω-exchange amplitude in our model has the form

T ω(s,t )～exp[i χD (s,0)]s F 2(t )

2 ω1

2 ωK 0(b

2!

?i ?χ34!+... .(7)The n th term in the series is

?T n (?s ,t )=?i (?1)n 2n ?12 nω ∞0b d b J 0(bq )K n 0 b

s .Dotted curves represent

the error band given by Cudell et al.[14].In Fig.5,solid and dashed curves represent our calculated ρˉp p and ρpp respectively (ρ=Re T (s,0)/Im T (s,0)).Dotted curves,as before,

represent the error band given by Cudell et al.At√

s=541GeV in the Coulomb–hadronic interference region using the Kundr′a t–Lokaj′?ˇc ek formulation(upper curve)and West–Yennie formulation(lower curve).Experimental data are from Augier et al.[15].Fig.7shows our predicted dσ/d t for pp elastic scattering at√

10

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10-1

110102

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|t| (GeV 2

)

D i f f e r e n t i a l c r o s s s e c t i o n d σ/d t (p p ) (m b /G e V 2

)

diffraction only

ω amplitude only quark-quark (single)quark-quark (unitarized)

pp 14 TeV

diffraction only

ω only

single

unitarized

Fig.1Fig.2

T o t a l c r o s s s e c t i o n s σ(p p a n d p p –

) (m b )

Fig.6Fig.7

10

10

10

10

10

10101010101010101101010|t| (GeV 2)D i f f e r e n t i a l c r o s s s e c t i o n s d σ/d t (p p ) (m b /G e V 2)Fig.8

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