Nonperturbative QCD in pp scattering at the LHC

Transcription

1 Nonperturbative QCD in pp scattering at the LHC IX Simpósio Latino Americano de Física de Altas Energias SILAFAE Jochen Bartels, Hamburg University and Universidad Tecnica Federico Santa Maria Introduction: the transverse distance scale Total cross section, elastic scattering BFKL and recent developments multiple interactions saturation diffraction Not covered: heavy ion collisions (AAS or pa)

2 Introduction At the LHC we are looking for new physics (mostly) at large momentum scales which allows to use hard QCD : parton densities, partonic subprocesses, jets... But: there is another class of final states which Gavin Salam s talk 1) has large cross section: total cross section is about 100 mb For comparison: cross sections of hard processes are smaller: Typical jet cross section at the LHC: Higgs cross section: O(pb) 2) are fully or partly nonperturbative µb this talk

3 Perturbative vs. nonperturbative QCD: relevant scale is the transverse distance time, longitudinal direction transverse plane long extension along incoming direction Z T (s, t) is d 2 be i~q ~b A(s, ~ b), t = ~q 2 tot = 1 Z s ImT (s, 0) d 2 ba(s, ~ b) wee parton cloud r B A A B z r A b B b long formation time A nonperturbative R 2 (s) =R 2 A + R 2 B + 0 ln s

4 short distance - long distance: static potential: V (~r) q string q short distance: coulomb potential large distance: linear potential, string tension gluon cloud A wee parton cloud r B A b r A A b B b short distance: dipole-dipole: BFKL no finite radius, cloud grows with power of energy long distance: hadron-hadron: Pomeron hadron size r A,B, Pomeron slope

5 hard processes confined to small regions total cross section, elastic scattering probes all distances most processes lie in between; in particular: BFKL searches start in small regions, but are sensitive to large distances multiple interactions and saturation explore the interface hard diffraction is sensitive to small and large distances each final state has its own way to exhibit large distance effects Total cross section, elastic scattering BFKL and recent developments multiple interactions saturation diffraction

6 Total cross section, elastic scattering Sizes of soft cross section: 2 total cross section: 98 mb elastic cross section 24.8 mb 2 single diffractive cross section mb 2 2 double diffractive cross section 8,8 mb 2 inelastic cross section 70 mb Forward direction has large cross sections: theory wanted!

7 Totem results:

8 Theory/models for total cross section: Exp : tot = 98.3mb Block, Halzen: Fit of formula (95.4) tot = (ln m ) ln m ( m ) 0.5 Donnachie, Landshoff: Regge pole, soft plus hard (soft alone: tot 91mb ) tot = c 1 s P,soft(0) 1 + c 2 s P,hard(0) 1 (98) soft : P,soft (t) = t hard : P,hard (t) = t Eikonal ansatz for elastic cross section Tel Aviv (Gotsman, Levin, Maor) Durham (Martin, Khoze, Ryskin) (98.6) (96.4) Pomeron graphs

9 Elastic cross section: dip structure

10 Comparison with p p (although at different energies): signal for the Odderon? model-dependent analysis, before Totem Jenkovsky et al Simplest explanation: three gluon exchange (Donnachie, Landshoff: ISR data) = beginning of Odderon (analogue of BFKL)

11 Small-size dipole scattering: BFKL Elastic scattering of two small dipoles * * Balitsky,Fadin,Kuraev, Lipatov 1975/76 Im T = sum over gluon production * * Important properties: growth with energy: tot s! 4N BF KL c ln 2,! BFKL = s z + O( 2 s) strong growth in transverse direction gluon cloud A b transverse

12 More remarkable properties of the BFKL Pomeron: 1) unitarity: nonlinear equations bootstrap equation ImT 2!2 = X n Z d n T 2!n 2 = 2) Beginning of a 2+1 dim field theory, with reggeized gluons as d.o.f. 3) In LO: two-dimensional conformal invariance (Moebius invariance): connection with N=4 SYM (=most symmetric gauge theory), integrability, theory might be solvable 4) Electroweak theory, gravity: high energy behavior vs. renormalizibility

13 How to test this calculation: 1) collisions in electron-positron scattering (LEP) 2) Mueller-Navelet jets in pp-scattering (Tevatron, LHC) e + e * * Q 2 k t * k t k t e e + e HERA, forward jets LHC, Mueller-Navelet ok, not fully convincing ok wait for data

14 Comments on BFKL-related activities for the LHC: k t 1) NLO available: BFKL, jet vertex, numerical analysis 2) Angular decorrelation as BFKL signal Colferai et al. Papa et al. k t Sabio Vera, Schwennsen; Colferai et al. Papa et al: 3) BFKL energy dependence: use different machine energies

15 Jet-gap-jet (hard color singlet exchange) Cox,Forshaw,Lonnblad; Enberg,Ingelman, Motyka; Royon BFKL needs all conformal spins BFKL d pp dx 1 dx 2 de 2 T = Sf(x 1,E T )f(x 2,e T ) d qq JJ (,E T ) de 2 T Survival factor S: (other chains, radiation?) Modelled by Monte Carlo

16 New formulation of BFKL (HERA): discrete Regge poles Kowalski, Ross, Lipatov BFKL equation is often written as (y, k) = Z d 2 k 0 K BFKL (k, k 0 ) (y, k 0 ) where kernel has continuous eigenvalue spectrum. Instead: boundary conditions at infrared plus asymptotic freedom lead to discrete spectrum. Quasiclassical picture: Lipatov 1986 Eigenvalues and wave functions are sensitive to changes at turning points in UV region... ln k 2 t 2 QCD Fit to HERA data. Signal of new physics?

17 Multi-Parton Interactions (MPI) Inclusive cross section vs.underlying event: Inclusive cross section event structure in pp collisions: number of chains grows with energy remnant j i partons (quarks, gluons) +final state radiation hadronization remnant Pictures have slightly different meaning: event cross section involves summation Cancellations (collinear factorization, AGK) Mostly based uopn eikonal formula Important consisteny check!

18 Important question: where is diffraction (rapidity gaps)? Soft diffraction: remnant contains diffraction soft gap remnant contains diffraction soft gap BUT: second, third... chain may fill the gap, less diffraction Sum over chains and all rescattering effects: lowers the probability of rapidity gaps

19 (semi)hard diffraction: add new contribution gap required by AGK As in soft diffraction: additional chains fill the gap. Leaves the eikonal approximation!

20 Double parton cross sections: d = X i 1 i 2 Z dx 1 dx 2 f i1 (x 1,µ)dˆi1 i 2!2 jet(x 1,x 2,µ; p 1,Y 1,p 2,Y 2 )f i2 (x 2,µ) single parton (no rescattering) d DP = m eff X Z dx 1 dy 1 dx 2 dy 2 H i1 j 1 (x 1,y 1,µ a,µ b ) i 1,j 1,i 2,j 2 dˆi1 i 2! jet(x 1,y 1,µ a ; p 1,Y 1 )dˆj1 j 2!jet(y 2,y 2,µ b ; p 2,Y 2 )H i2 j 2 (x 2,y 2,µ a,µ b ) correction: double parton (no rescattering) AGK

21 Cross sections have been calculated (e.g. double J/Psi) Theoretical questions being addressed: Evolution of double parton densities: double DGLAP misses transverse dependence corrections: correlations, splitting double DGLAP k 1 k 3 x 1 y 1 k 3 q 12 k 1 1 x 2 y 2 b k 2 k 4 q 34 k 4 k a Higher twist suppression: only after integration over jet momenta b

22 Saturation Saturation was first discussed in the context of small-x gluon densities at HERA, later on it started to play a major role in ion collisions (color glass condensate) several chains recombinations high gluon density saturation scale nonlinear BK-equation Saturation scale Q 2 s = Q x Q s 1GeV at x = 10 5 Evidence in ep scattering : geometric scaling successful models for F_2 ratio of diffractive to total cross section

23 Saturation at the LHC (in pp): larger kinematic region Potential signals: <pt>, <n>? Ridge effect? Drell Yan in forward region much more in AA and pa: larger saturation scale

24 Ridge effect in pp and pa collisions: two particle correlation, azimuthal correlations single chain double chain Saturation is a strong candidate: strong field: high density low p T : saturation momentum x = 10 5 Q s 1GeV angular correlation: need extra ingredient

25 Dusling, Venugopalan k q k k p k k p y p q y q p k k q k form factor effect s p =q saturation form factor effect Difference between pp and pa is in the details of saturation

26 Diffractive/rapidity gap processes Central exclusive production (CEP): forward spectrometer Topic of intense discussion (Bialas,Landshoff;... ;Durham group) H or SUSY; candles Sudakov Needed: NLO calculation of hard subprocess Survival probability Experimental aspects: clean signal, precise mass determination Theoretical ingredients: parton densities, Sudakov factor, suppression rules survival probability

27 Khoze

28 Recent developments: Diphoton seen at Tevatron double meson states, resonances production c } Learn about CEP dynamics Two photon physics: W 1.8 T ev anomalous quartic coupling W L W L = VV-scattering : unitarity problem W L W L

29 Conclusions Fundamental problem in nonperturbative high energy QCD : understand the transition and the large distance region small large transverse distance region Small: BFKL, DGLAP Large: total, elastic cross section (Pomeron) most final states sensitive to both, e.g. multiple interactions saturation diffraction their study provides the necessary theoretical help