Mark Strikman PSU. for Boris Blok

Transcription

1 Open charm production in Double Parton Scattering processes in forward kinematics Mark Strikman PSU for oris lok.lok M.Strikman MPI 16 arxiv:168.14; arxiv: in press

2 Hard interaction ~ 1 ~ geometrical picture ~ b 4 tegral of transverse spatial parton distributio inclusive rate does not depend on transverse size DPI rate 1/(transverse size)

3 H J/ψ ϒ γ In LT limit x1 -x << x1 p x1 x1 -x x + m V W GPD p however due to DGLAP evolution skewed GPD kinematics for large probes diagonal GPD at scale A( + p! Onium +p) / G(x 1 x 1 x t) G(x x t) G(x t) d e i G(x ) transverse spatial distribution of gluons longitudinal transverse ρ xp x d G(x ) G(x) G(x t)/g(x) F g (x t) 1/(1 t/m g (x) ) F g (x 3 ) m g total gluon density mg K 1 (m g )

4 J/ψ elastic photoproduction data 6 5 Exponential t-slope γ + p J/ψ + p 1 Exponential F g parametrization Dipole F g parametrization PYTHIA J/ψ [GeV - ] H1 5 ZEUS µ + µ - ZEUS e + e - FNAL 198 H1/ZEUS fits parametrization dσ/dt [nb/gev ] 1 FNAL E41/E458 γ + p J/ψ + p E γ 1 GeV x.5 with σeff 15 mb x t [GeV ] F g (x.3t)(1 t/m g) m g 1.1 GeV Independent particle (mean field) approximation eff 8 m g 34 mb. For m.7 GeV ~ 54 mb 1 eff Z d ( ) F 4 g( ) m g 8. Frankfurt MSWeiss 3 Puzzle - need correlations. what is ir origin? 4

5 Correlation mechanisms Generated by pcd evolution: 3 to 4 parton splits into two partons with close impact parameters in process of DGLAP evolution Correlation grows with (σeff drops) 1 Na Na Nb Nb part of to 4 In boundary condition at low washed out by pcd evolution (σeff grows) 5

6 6 D s are double GPDs

7 G and 1G are two parts of GPD calculated in two different ways. G-in mean field approach using GPD1 from charmonium photoproduction at HERA We use parametrisation due to FrankfurtStrikmanWeiss (11) 1G is calculated solving evolution equation for GPD The final answer for effective cross section is convenient to represent as Here is 4 to 4 cross section in mean field approximationwhile function R corresponds to contribution due to 3 to 4 mechanism and is calculated analytically. Note: only one unknown paramter- separating soft and hard scales so approach is practically model independent. 7

8 The total cross sections 8

9 photon + 3 jets In LHC energies at central rapidities one typically find an enhancement ~ from pcd mechanism which is consistent with data. Few examples were studied by.lok and P. Gunnellini 9

10 Challenge are LHCb double charm data: very accurate small to 4 background ( previous talk) N σeff mb x1 x - c c x4 c- c N x3 Forward kinematics -- two of x s are small. Gluon radius larger leading to larger σeff larger than for central region with smaller pcd effects which hardly can compensate this increase. Soft correlations and unfactorizable initial conditions. DFS 1.lok M. Strikman 16 1

11 atio of non-factorized (correlated) and factorized (uncor M. dingly for parton density in ladder we use: ttum is convenient to consider first non-factorized (correlated) and factorized transfer ratio : ofconsider For t ted) contributions at zero momentum transfer t : x 1 x ) ) 1 x Dnf (x1 x ) D (x x ) D (x x nfxd(x 1 ) nf 1 9 (x1 x ) ) ( DN (x1 (x D Df(x)D 1 x ) xn)(x1 )DN (x ) 1 xn ) (11) /x. atio of inelastic and elastic di raction in DIS for invariant p energy s m We can write e small x intercept of parton density is taken from GRV param riple reggeon parametrization of Zcross section we can determine normalization DN (x1 /x )DN (x /x ) (x x13 ) small dm S(M ).7 1 at ucleon gluon Numerically (.5 GeV ) meron vertex C3IP pdf in eq. from HERAx. data [4 43] for ratio of inelastic at DN (x1 )DN (x ) (1. DN (x1 /x )DN (x /x ) ) we obtain C raction at t in13 and processes ofabove vector meson production: S(M ) (1) eqs values of (.15 ± 3I P re factors xi /x take into account a smaller rapidity intervals occupied by ladders DNd (x1 )DN (x ) in. dif. and to for 1 GeV. dt di ractive states. The of transition factor GeV C!3Iinelastic.14 ±.5 GeV.5 ±.5 (15) P d t el maller rapiditydt intervals occupied by ladders in () IP we can estimate D(x x ) as 1 nf S(M ) C (M /m ) Cesult is roughly same for di ractive production of light mesons and J/ 3I P 3IP in a tates. The factor Z 1transition between soft and hard thus confirming hyposis of a smooth dxpomerons in diagram esponds to cut Pomeron that splits into two 4./x It is ) equal D(x x ) c D(x /x )D(x 1condition 1 corrsponds nf etermined from ) P! where x+.1 that (x 1 x1 3I 1 I P x xm /a duct of triple Pomeron vertex and square of proton - Pomeron residues cf. [38 4 gluon in [4 43]. Note here that to have a smooth connection with low IP () 3IP 1.1an use () to a soft Pomeron introduced additional factor ofe ective aat.1 limit integration ove of GRV x-dependence of gluon density small x in from this[41]. model. of This IP we take corresponding C (M /m ) ds relatively Pomeron in islower legstothough apriori density of f xto x hard righte ective hand side of Eq.1 equal 1 11 (13) e limit of integration over di raction masses M ) to take into account tha

12 K(x 1 x 1 ) D(x 1x 1 ) D(x 1 1 )D(x ) K K small x gluons K large x gluons p t GeV Transverse momentum dependence of K factor for GPD for regimes of small and large x in kinematics of chapter (.5 GeV ) 1

13 gram Fig. ) kinematics two+pairs Rtot Rof Rsoft of x s. pcd Rtot RpCD + Rsoft + el 8. GeV 1el /1in.8. Thus for e he cross section enhancement due to 1 mechanism Soft contribution is strongly enhanced ss section enhancement due to 1 mechanism ype contribution to R is.3r.7 For pcd ee section 3 while due to much smaller t-slope: inel << el. tion 3 while R to be larger.4while R.4 As a resul pcd + 1el 3el 1el Rsof t K1 ( + RpCD ) + + 1in 1in 3el 1el 3el 1el btainrr 1.8. leading to + RpCD ) sof t K1 ( + 1in 1in 3el due to nonperturbative correlations and interference of mb e to nonperturbative correlations and interference of n butions. ns. sources of large Rtot are presence of pcd main variation of values of RpCD with a choice of t with larger x andrtot nonperturbative enhancement for sm sources of large are presence of pcd cally completely compensated by variation of th 13

14 1.5 1/σ eff Enhancement.5 GeV R R R pcd p s 7TeV 1.5 1/σ eff Enhancement 1 GeV R pcd p s 7TeV R soft R soft R 1. R p t GeV p t GeV 1.5 1/σ eff Enhancement.5 GeV R R R pcd p s 13 TeV 1.5 1/σ eff Enhancement 1 GeV R pcd p s 13 TeV R soft R soft R 1. R p t GeV p t GeV 14

15 Rsof t whose relative contribution also increases with increase of energy. Numerical find:forsoft mechanism reduces The corresponding two LHC runs are depicted in Figs. 8. sensitivity to e Effective cross section Effective cross section 8 8 σeff mean field σeff 1 GeV σeff 1 GeV p σeff.5 GeV 6 s 7 TeV σeff mb σeff mb 6 σeff mean field 4 s 13 TeV pt GeV : p σeff.5 GeV pt GeV 16 as a function of D meson transverse momentum pt f e FIG. 8: Effective function of D meson transverse momentum p for.5 1 GeV and for 3.5x3.5 e as across t section Effective cross section 8 8 TeV and 6.5x6.5 TeV runs σ mean field σ mean field nd 6.5x6.5 TeV runs eff σeff 1 GeV eff 6 σeff.5 GeV 4 We see that e σeff mb σeff mb 6 σeff 1 GeV σeff.5 GeV 4 increases by less than 1 mb for small pt when we move from 3.5 to 6.5 TeV i.e. it e ectively remains constant with increase of energy due to increase of soft correlations e contribution compensating decrease of pcd contribution and increase of mean field M F. Int see that pt GeV increases by less than 1 mb for small p w same for -mesons pt GeV e fact of course such small changes are beyond accuracy of our model and we can only conclude e ectively remains constant 15with increase of energy d that e are approximately constant in this interval of energies for given transverse momenta pt.

16 Effect of soft term for central kinematics Soft correlations are negligible for DPS regime (typical pt> 1- GeV) but maybe important for UE (several GeV scale). Central kinematics: 16

17 Conclusions MPI model with pcd induced correlations and ~ 1 GeV starting DGLAP evolution scale and soft small x correlations agrees well with data in most cases (notable exception is double J/psi production and first steps have been done to implement it numerically in MC generators. Open questions How unknown mechanism of pt cutoff affects σeff at pt of few GeV. NLO effects for 3 to 4 17