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QCD issues in photon-photon total cross-section : why we need a photon collider Giulia Pancheri - INFN-Frascati Giulia Pancheri - INFN-Frascati December 12, 2007Hiroshima University, Higashi-Hiroshima, Japan AdA : Where e+e- collisions were born LEI 2007, Hiroshima, December 2007 1 12/28/07 Points for discussion • The data • Why the total cross-section is interesting • A QCD model for protons to account for – The rise – The saturation, i.e. Froissart bound • Application to γγ LEI 2007, Hiroshima, December 2007 2 12/28/07 The data LEI 2007, Hiroshima, December 2007 3 12/28/07 Start with present γγ σtot data Large errors, scattered values: •Difficult to establish proper normalization •Need to check data normalization from LEP (there is an issue 2007 LEI 2007, Hiroshima, December here) 4 12/28/07 The region 2-10 GeV • For a good model low energy data are crucial for normalization • A photon collider at low energy could give very useful information LEI 2007, Hiroshima, December 2007 5 12/28/07 The region 10-100 GeV • In this region one sees the beginning of the rise • Errors are large at the high end, where QCD models could be distinguished from one another • Need to have a photon collider with good beam energy resolution to fix the rate of increase LEI 2007, Hiroshima, December 2007 6 12/28/07 Beyond 100 GeV • Comparison with proton σtot can really only be done if data are available for Wγγ ~ 500 GeV LEI 2007, Hiroshima, December 2007 7 12/28/07 Why the total cross-section is interesting LEI 2007, Hiroshima, December 2007 8 12/28/07 The strong limit of QCD • The most important yet unresolved issue in hadron physics and QCD is the infrared behaviour of αs • One way to get information on αs is from total cross-section studies As I shall try to show with a toy model LEI 2007, Hiroshima, December 2007 9 12/28/07 Do all total cross-section look alike? LEI 2007, Hiroshima, December 2007 10 12/28/07 Do all total cross-section look alike? • Yes – They all start falling and s-η sε then rise with energy and • No – They fall with different slopes at low energy – They may be rising with different slopes at high energy LEI 2007, Hiroshima, December 2007 11 12/28/07 Difference at low energy is understood from unitarity and analiticity • Quantum numbers in the s-channel give rise to different resonances in the very low region • Quantum numbers in the t-channel bring in different Regge pole exchanges and a decrease with energy: through Finite Energy Sum Rules related to s- channel resonances and different quantum numbers in s and t channel LEI 2007, Hiroshima, December 2007 12 12/28/07 Difference at high energy? • Not well understood yet • Pomeron exchange was supposed to give universal behaviour but one now distinguishes – Soft Pomeron : same for everybody – Hard Pomeron :could differ • Here is where QCD comes in LEI 2007, Hiroshima, December 2007 13 12/28/07 Models for total cross-section • Is factorization all there is to go from pp to γγ? • Can one disentangle the QCD role ? • How much can ILC/LPC help ? A.de Roeck, R. Godbole, A. Grau, G.Pancheri, JHEP 2003 LEI 2007, Hiroshima, December 2007 14 12/28/07 sε : Should ε be the same for all hadronic cross-sections? • Yes if the model – is based on Regge poles and a universal Pomeron pole exchange σ=Bs-η + Asε • Not necessarily if – The model has some connection with QCD and parton densities play a role LEI 2007, Hiroshima, December 2007 15 12/28/07 A fit to LEP data shows that ε is not the same for proton and photon cross- sections LEI 2007, Hiroshima, December 2007 16 12/28/07 σ=Bs-η + Asε+ Csε1 • Fit3 C≠ 0 ε=0.093 ε1=0.418 • Fit 1 C=0 ε=0.250 • Fit2 C=0 ε=0.093 as in pp A.de Roeck, R. Godbole, A. Grau, G.Pancheri, JHEP 2003 LEI 2007, Hiroshima, December 2007 17 12/28/07 A QCD model to account for The rise The saturation, i.e. Froissart bound LEI 2007, Hiroshima, December 2007 18 12/28/07 The Bloch-Nordsiek Eikonal Minijet model includes kt resummation R.Godbole, A. Grau, G.Pancheri, Y.Srivastava PRD 2005 A. Corsetti, A. Grau, G.Pancheri, Y. Srivastava PLB 1996 A. Achilli, R. Godbole, R. Hedge. A. Grau, G.P., Y. Srivastava, TbP in PLB 1. Multiple parton interactions : optical theorem and eikonal representation for Tel(s,t) 2. Hard scattering to drive the rise due to 1/x 3. Soft gluons down to zero momentum to tame the rise LEI 2007, Hiroshima, December 2007 19 12/28/07 1. Hard component of scattering responsible for the rise of the total cross-section DGLAP Parton densities x1 x2 LEI 2007, Hiroshima, December 2007 20 12/28/07 Jet cross-sections at LO Using current DGLAP evoluted PDF’s : GRV, MRST, CTEQ LEI 2007, Hiroshima, December 2007 21 12/28/07 1. Different ε for different Hard PDFs component of scattering responsible sε type for the rise of behaviour the total cross-section LEI 2007, Hiroshima, December 2007 22 12/28/07 In mini-jet models densities make all the difference between photon and proton processes Proton-proton and γ−proton and γγ proton-antiproton Most commonly used Most commonly used densities densities • GRV • GRV • GRS • CTEQ • CJKL • MRST LEI 2007, Hiroshima, December 2007 23 12/28/07 Choose ptmin = 1÷2 GeV for mini-jets and parton densities For photons, LEP data suggest ptmi ~ 1.3 ÷ 1.8 GeV n • Gluck Reya Vogt • Gluck Reya Shielbein • Cornet Jankowski Lorca Krawczyk LEI 2007, Hiroshima, December 2007 24 12/28/07 3. eikonal transformation implies multiple scattering and requires impact parameter distribution in hadrons LEI 2007, Hiroshima, December 2007 25 12/28/07 2. soft gluon emission from scattering particles which softens the rise and gives b-distribution Soft gluon emission factor LEI 2007, Hiroshima, December 2007 26 12/28/07 Soft gluon emission factor ~ qmax is the maximum transverse momentum allowed by kinematics to single soft gluon emission in a given hard collision, averaged over the parton densities. M. Greco and P. Chiappetta LEI 2007, Hiroshima, December 2007 27 12/28/07 qmax for ptmin=1.15 geV CTEQ GRV98 GRV CTEQ LEI 2007, Hiroshima, December 2007 28 12/28/07 What about the kt 0 limit for αs ? Modeling the infrared behaviour • frozen •Our choice : singular but integrable, phenomenological choice LEI 2007, Hiroshima, December 2007 29 12/28/07 Zero momentum quanta • Soft gluons need to be Models for infrared behaviour resummed if they are indeed soft ≈1/k • Resummation implies integration over dkt • What matters will be ∫αs(kt )dkt f(kt) and not αs(0) LEI 2007, Hiroshima, December 2007 30 12/28/07 Ansatz The saturation mechanism which reinstates the Froissart bound comes from zero momentum gluons which are emitted in an indefinite number LEI 2007, Hiroshima, December 2007 31 12/28/07 Model results for the proton-proton case and application to γγ LEI 2007, Hiroshima, December 2007 32 12/28/07 How the model works • Choose ptmin = 1÷2 GeV for mini-jets • Choose parton densities • Calculate minijet x-section • Calculate qmax for soft gluons • Calculate A(b,s) for given qmax • Calculate nhard (b,s)=A(b,s) σjet(ptmin,s) • Parametrize nsoft • Evaluate n(b,s)= nsoft + nhard • Eikonalize σtot≈2∫d2b [1-e-n(b,s)/2] LEI 2007, Hiroshima, December 2007 33 12/28/07 Comparison with proton data R.Godbole, A. Grau R. Hedge G. Pancheri Y. Srivastava Les Houches 2005 Pramana 67 (2006) GGPS PRD 2005 LEI 2007, Hiroshima, December 2007 34 12/28/07 For all pdf’s • For different PDF , with soft gluon emission to give an energy dependent size and QCD hard gluon minijets to drive the rise • All the Bloch-Nordsieck type curves LEI 2007, Hiroshima, December 2007 35 12/28/07 Now apply the model to γγ LEI 2007, Hiroshima, December 2007 36 12/28/07 Applying the mini-jet+IR gluons to γγ • Factorization from pp Or • Using photon densities in minijets and soft gluon emission factors LEI 2007, Hiroshima, December 2007 37 12/28/07 Factorization from pp • Multiply band of our model predictions for pp by appropriate factor 1/330 which reproduces γp • Multiply pp by (factor)2 LEI 2007, Hiroshima, December 2007 38 12/28/07 Using photon densities in minijets and soft gluon emission factors • Choose densities • Calculate minijets • Calculate qmax for chosen densities and b- distribution from soft gluons • Calculate nhard • Eikonalize with – nsoft from pp – Normalization for nhard from Vector Meson Dominance and Quark Parton model LEI 2007, Hiroshima, December 2007 39 12/28/07 Eikonalize σtot≈2Phad∫d2b [1-e-n(b,s)/2] and compare with data Phad is a Phenomenological input describing the hadronic content of the photon in eikonal models R.Fletcher, T.Gaisser. F.Halzen, 1993 LEI 2007, Hiroshima, December 2007 40 12/28/07 Conclusions (I) • We have built a model for the total cross-section which – Incorporates hard and gluon effects – Satisfies the limits from the Froissart bound – Can be used to study other minimum bias effects – Easily extended to γ p and γ γ LEI 2007, Hiroshima, December 2007 41 12/28/07 Conclusions (II) • Predictions at ILC vary according to which densities better describe the behaviour at low x • Total cross-sections measurements in Collider mode would allow clean information on γγ cross-sections, reducing the errors due to modelling of diffractive components • Even in regular mode, difference in the model predictions are measurable and can give insights into the soft or non perturbative region of QCD. LEI 2007, Hiroshima, December 2007 42 12/28/07 Back up slides LEI 2007, Hiroshima, December 2007 43 12/28/07 The saturation mechanism which reinstates the Froissart bound LEI 2007, Hiroshima, December 2007 44 12/28/07 At very large energies : LEI 2007, Hiroshima, December 2007 45 12/28/07 soft gluon resummation effects Virtual Energy-momentum gluons conservation factor for real soft gluons Model LEI 2007, Hiroshima, December 2007 46 12/28/07 From power law to log behaviour Main result LEI 2007, Hiroshima, December 2007 47 12/28/07 The hard cross-section • Mini-jet cross-section Σ∫ densities ∫dpt dσ/dpt LEI 2007, Hiroshima, December 2007 48 12/28/07 σjet for ptmin=1.15 GeV GRV GRV98 green band MRST CTEQ LEI 2007, Hiroshima, December 2007 49 12/28/07 Soft resummation Probablity of total KT from infinite # of soft gluons ∫ d2b eiK b exp{-∫d3n(k)[1-e-ik b]} T t depends upon single gluon energy maximum : use Kinematics minimum : 0 from Bloch-Nordsieck theorem LEI 2007, Hiroshima, December 2007 50 12/28/07 Role of resummation An infinite number of soft quanta • down to zero momentum but how? next slides • Up to an energy dependent limit qmax – Higher hadron energy possibility of more small x partons with “high energy” (≈1-2 GeV) higher qmax LEI 2007, Hiroshima, December 2007 51 12/28/07 Resummation of soft gluons down to kt=0 • Gluon emission in kt changes the collinearity of initial partons • And for same energy and ptmin, acollinearity of initial partons will bring loss of luminosity of the parton beams and parton-parton cross-sections will decrease • As the energy available for soft gluon emission increases, so does the acollinearity of the parton-parton collision • The rate of rise of total cross-sections due to rising minijet cross-section is reduced (softened by) by soft gluon emissions. • Softening effect more important the more singular αs LEI 2007, Hiroshima, December 2007 52 12/28/07 Which parameters in soft emission? ptmin and p regulate how large is the maximum energy , but PDF’s also play a role • Ptmin hard scattering lowest scale • p infrared (integrable) behaviour LEI 2007, Hiroshima, December 2007 53 12/28/07 An aside on the Froisart bound and minijet cross- sections LEI 2007, Hiroshima, December 2007 54 12/28/07 About the Froissart bound and QCD minijets LEI 2007, Hiroshima, December 2007 55 12/28/07 Interpolating from the infrared to asymptotic freedom • Singular but integrable • Singularity regulated by p < 1 LEI 2007, Hiroshima, December 2007 56 12/28/07 QCD Mini-jets violate the Froissart bound • Consequence of infinite range of QCD • One needs to introduce a finite distance of the interaction • The eikonal does it through the hadron finite size LEI 2007, Hiroshima, December 2007 57 12/28/07 How about nsoft? •Parametrized with a constant σ0 •With ptmin dependence through A(b,s) LEI 2007, Hiroshima, December 2007 58 12/28/07 Minijets : how to reduce their growth? • Embedding the minijets into the eikonal but • It depends on how A(b,s) 0 as b infinity LEI 2007, Hiroshima, December 2007 59 12/28/07 Finite size of hadrons • The finite size can be introduced through the Form Factor A(b)~ e -b constant as b ~ very large : not enough to tame the rise because the growth of σjetPDF is too strong!! or energy dependent soft gluon emission where satisfaction of the energy dependent soft gluon emission where satisfaction of the Froissart bound would imply that the the finite range of the interaction is Froissart bound would imply that the the finite range of the interaction is restored through soft gluon emission down into the infrared restored through soft gluon emission down into the infrared LEI 2007, Hiroshima, December 2007 60 12/28/07 For all pdf’s • For different PDF , with soft gluon emission to give an energy dependent size and QCD hard gluon minijets to drive the rise • All the Bloch-Nordsieck type curves LEI 2007, Hiroshima, December 2007 61 12/28/07 Photons and QCD • Photons probe the QCD vacuum • How a photon becomes a hadron • Two photons have a unique signature in producing scalar or pseudoscalar resonances • If new strong WW interactions would be detected at LHC possible new scalar states could be probed to extract threshold dynamics information not unlike what happens in γγ π0π0 around the σ-meson • One can study γγ γγ if enough luminosity – Light-by-light and hadronic contributions – Insight into the trace anomaly LEI 2007, Hiroshima, December 2007 62 12/28/07 Total cross-sections are a testing ground of our understanding of QCD beyond perturbative regime • A popular models for total cross-section from L3 fits LEI 2007, Hiroshima, December 2007 63 12/28/07 σtot=102 mb at LHC GRV LEI 2007, Hiroshima, December 2007 64 12/28/07 Comparison with proton data(I) R.Godbole, A. Grau R. Hedge G. Pancheri Y. Srivastava Les Houches 2005 Pramana 67 (2006) GGPS PRD 2005 LEI 2007, Hiroshima, December 2007 65 12/28/07 Maximum soft gluon energy • q1 and q2 : any two partons • X : the 2-jet final state • Q2≥4 p2tmin • qmax depends on x1,x2 • We average over densities LEI 2007, Hiroshima, December 2007 66 12/28/07 Soft gluons give b-distributions In eikonal representation σtot≈2∫d2b [1-e-n(b,s)/2] • n(b,s)=average # of collisions at distance b, at energy √s • b-distribution is needed Our ansatz: b-distribution = Fourier transform of soft gluon Kt distribution LEI 2007, Hiroshima, December 2007 67 12/28/07

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