HASPECT PHOTOPRODUCTION OF π + π PAIRS. Antoni Szczurek 1,2 Piotr Lebiedowicz 1

Transcription

1 HASPECT 06 PHOTOPRODUCTION OF π + π PAIRS IN PROTONPROTON SCATTERING AS A COMPETITION FOR DIFFRACTIVE MECHANISMS Antoni Szczurek, Piotr Lebiedowicz Institute of Nuclear Physics PAN Kraków University of Rzeszów A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

2 CONTENTS Introduction Central diffractive production of π + π pairs 3 Tensor pomeron 4 Photoproduction amplitudes 5 Results 6 Conclusions A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

3 INTRODUCTION Central diffractive production pp ppπ + π is being studied by COMPASS, STAR, ATLAS, CMS and ALICE. Several analyses are underway. The main motivation is search for resonant states and exotic π + π states as glueballs or glueball candidates. For example f 0 (500) was observed long time ago be the WA experiment at CERN. Some time ago Lebiedowicz and Szczurek proposed a Regge model for a production of continuum via twopomeron exchanges (both pomeron and reggeon exchanges are possible in general). The interaction parameters were fixed by Regge fits to NN and πn total cross sections (DonnachieLandshoff) and slope parameters from elastic scatterings. The helicity conservation was assumed. The simple model was extended by including absorption effects. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

4 CENTRAL DIFFRACTIVE PRODUCTION OF π + π PAIRS p (p a) p (p ) t p (p a) p (p ) t (a) γ, IP, IR γ, IP, IR π + (p 3) π (p 4) p (p b) p (p ) ˆt γ, IP, IR t (b) γ, IP, IR π (p 4) π + (p 3) p (p t b) p (p ) RYSUNEK: The central diffractive production of π + π in protonproton collisions. Two diagrams are present û Proposed by: P. Lebiedowicz and A. Szczurek, Exclusive pp ppπ + π reaction: From the threshold to LHC", Phys. Rev. D8 (0) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

5 TENSOR POMERON Recently the concept of tensor pomeron was introduced and explored in some processes. C. Ewerz, M. Maniatis and O. Nachtmann, A model for soft highenergy scattering: Tensor pomeron and vector odderon", Ann. Phys. 34 (04) 3. P. Lebiedowicz, O. Nachtmann and A. Szczurek, Exclusive central diffractive production of scalar and pseudoscalar mesons: tensorial vs. vectorial pomeron, Ann. Phys. 344C (04) 30. P.Lebiedowicz, O. Nachtmann and A. Szczurek, "The ρ 0 and DrellSöding contributions to central exclusive production of π + π pairs in protonproton collisions at high energies", arxiv:4.3677, Phys. Rev. D9 (05) P. Lebiedowicz, O. Nachtmann and A. Szczurek, Central exclusive diffractive production of π + π continuum, scalar and tensor resonances in pp and p p scattering within tensor pomeron approach, Phys. Rev. D9 (06) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

6 TENSOR POMERON, PROPAGATOR The propagator of the tensorpomeron exchange is written as (Ewerz, Maniatis, Nachtmann) i (IP) µν,κλ (s, t) = (g µκ g νλ + g µλ g νκ ) 4s g µνg κλ ( isα IP )α IP(t) () (IP) µν,κλ (s, t) = (IP) νµ,κλ (s, t) = (IP) µν,λκ (s, t) = (IP) κλ,µν (s, t), g µν (IP) µν,κλ (s, t) = 0, gκλ (IP) µν,κλ (s, t) = 0. () A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

7 TENSOR POMERON, COUPLING TO PROTON The corresponding coupling of tensor pomeron to protons (antiprotons) including a vertex form factor, taken here to be the Dirac electromagnetic form factor of the proton F (t) for simplicity, is written as: iγ (IPpp) µν (p, p) = iγ (IP p p) µν (p, p) = i3β IPNN F `(p p) j hγ µ(p + p) ν + γ ν(p i + p) µ ff 4 gµν(p/ + p/), (3) where p/ = γ κ p κ and β IPNN =.87 GeV. A sufficiently good representation of the Dirac form factor F (t) is given by the dipole formula 4mp.79 t F (t) = (4mp t)( t/md, (4) ) where m p is the proton mass and m D = 0.7 GeV is the dipole mass squared. For the f IR reggeon exchange a similar form of the propagator and the f IR pp effective vertex is assumed, with the Regge parameters: α IR+ (t) = α IR+ (0) + α IR + t, α IR+ (0) = , α IR + = 0.9 GeV A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY (5) 7 / 45

8 IS PHOTOPRODUCTION POSSIBLE? It is often believed that doublepomeron exchange is the dominant mechanism. Other mechanisms? Is photoproduction possible? Here we consider both resonant ρ 0 and continuum (DrellSöding) production and discuss their role. In many experimental situations protons are not measured. What it means as far as photoproduction contribution is considered? A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

9 PHOTOPRODUCTION, RESONANCE CONTRIBUTION p (pa) p (p) p (pa) p (p) (a) p (pb) γ ρ 0 [ω] ρ 0 IP, fir [air] p (p) π + (p3) π (p4) (b) IP, fir [air] ρ 0 RYSUNEK: The central exclusive ρ 0 production and its subsequent decay into Pwave π + π in protonproton collisions. p (pb) γ ρ 0 [ω] p (p) π + (p3) π (p4) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

10 PHOTOPRODUCTION OF ρ 0 MESON ρ 0 (p ρ,λ ρ ), p(p,λ ) T γ(q,λ γ ), p(p b,λ b ) M λγλ b λ ρλ = ( i)(ǫ (ρ) µ ) iγ (IPρρ) µναβ (p ρ, q) i (ρ) νκ (q) iγ κσ (γ ρ) We use standard kinematic variables (q)ǫ (γ) σ i (IP) αβ,δη (s, t) ū(p,λ )iγ (IPpp) δη (p, p b )u(p b,λ b ), (6) s = W γp = (p b + q) = (p + p ρ ), t = (p p b ) = (p ρ q). (7) The f IR pp vertex is obtained by replacing 3β IPNN by g fir pp/m 0 with M 0 = GeV and g fir pp =.04. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

11 PHOTOPRODUCTION, RESONANCE CONTRIBUTION In the highenergy smallangle approximation we get: M λγλ b λ ρλ (s, t) = ie m ρ γ ρ (ρ) T (0)(ǫ(ρ) µ ) ǫ (γ) ν V µνκλ (s, t, q, p ρ ) (p + p b ) κ (p + p b ) λ δ λ λ b F (t)f M (t). (8) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

12 PHOTOPRODUCTION, RESONANCE CONTRIBUTION M λγλ b λ ρλ (s, t) = ie m ρ γ ρ (ρ) T (0)(ǫ(ρ) µ ) ǫ (γ) ν V µνκλ (s, t, q, p ρ ) (p + p b ) κ (p + p b ) λ δ λ λ b F (t)f M (t). (9) Here 4π/γρ = 0.496, ( (ρ) T (0)) = mρ A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

13 PHOTOPRODUCTION, RESONANCE CONTRIBUTION The function V µνκλ (s, t, q, p ρ ) has the form V µνκλ (s, t, q, p ρ ) = { 4s [ Γ (0) µνκλ (p ρ, q) 3β IPNN a IPρρ ( isα IP) αip(t) + M 0 g f IR pp a fir ρρ( isα IR + ) α IR + [ Γ () µνκλ (p ρ, q) 3β IPNN b IPρρ ( isα IP )α IP(t) + M 0 g f IR pp b fir ρρ( isα IR + ) α IR + (t) where the explicit tensorial functions Γ (i) µνκλ (p ρ, q), i = 0,, are given by Ewerz, Maniatis and Nachtmann. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

14 PHOTOPRODUCTION, RESONANCE CONTRIBUTION F M (t), the pion electromagnetic form factor in a parametrization valid for t < 0, F M (t) = t/λ, () 0 where Λ 0 = 0.5 GeV. ( (IP) F (IP) B ρp t ρp (t) = exp ) ( ) (f, F (f IR) B IR ) ρp t ρp (t) = exp, () for the pomeron and f IR exchanges with the slope parameters = 7.7 GeV and B (f IR) ρp = 4.0 GeV, respectively. B (IP) ρp m ρ a IPρρ + b IPρρ = 4β IPππ = 7.04 GeV, (3) m ρ a f IR ρρ + b fir ρρ = M 0 g f IR ππ = 9.30 GeV ; (4) A. SZCZUREK (INP PAS KRAKÓW) 3 HASPECT WEEK 06 3 KRAKOW, MAY / 45

15 PHOTOPRODUCTION, ρ 0 CONTRIBUTION set A : a IPρρ = 0.7 GeV 3, a fir ρρ = 0 GeV 3, b IPρρ = 6. GeV, b fir ρρ = 9.3 GeV, ( set B : a IPρρ = a fir ρρ = 0 GeV 3, b IPρρ = 7.04 GeV, b fir ρρ = 9.3 GeV( A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

16 PHOTOPRODUCTION, ρ 0 CONTRIBUTION p) (µb) 0 σ (γp ρ low energy data H 93 ZEUS 9 ZEUS 93 ZEUS 94 set B set A ) dσ/d t (µb/gev 0 γ p ρ p s = 80 GeV = ± λ ρ ZEUS data 5 0 W γp total IP f IR (GeV) 3 3 = 0 λ ρ t (GeV ) RYSUNEK: A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

17 PHOTOPRODUCTION OF π + π, KINEMATICS We shall study exclusive production of π + π in protonproton collisions at high energies p(p a,λ a ) + p(p b,λ b ) p(p,λ ) + π + (p 3 ) + π (p 4 ) + p(p,λ ), (9) where p a,b, p, and λ a,b, λ, = ± denote the fourmomenta and helicities of the protons, and p 3,4 denote the fourmomenta of the charged pions, respectively. The kinematic variables for reaction (9) are p 34 = p 3 + p 4, q = p a p, q = p b p, s = (p a + p b ) = (p + p + p 34 ), M ππ = p 34, s = (p a + q ) = (p + p 34 ), s = (p b + q ) = (p + p 34 ), t = q, t = q ; (0) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

18 PHOTOPRODUCTION, ρ 0 CONTRIBUTION The Born amplitude for exclusive photoproduction of π + π can be written as the following sum: M Born pp ppπ + π = M (γip) + M (IPγ) + M (γf IR) + M (f IRγ). () If we want to treat p pcollisions (Tevatron) we must be careful since then there is no symmetry any more for the amplitude under p(p a ) p(p b ), p(p ) p(p ), etc. Using the charge conjugation (C) properties of the γ, IP and f IR exchanges we get for p p scattering from () M Born p p p pπ + π = M (γip) M (IPγ) + M (γf IR) M (f IRγ). () Note that these sign changes are automatically obtained using the Feynman rules for the tensor pomeron and f IR exchanges but have to be implemented by hand for the vectorial pomeron and f IR exchanges. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

19 PHOTOPRODUCTION, ρ 0 CONTRIBUTION The bare amplitude (excluding rescattering effects) for the γipexchange, see diagram (a), can be written in terms of our building blocks as follows: M (γip) λ aλ b λ λ π + π = ( i)ū(p, λ )iγ µ (γpp) (p, p a )u(p a, λ a ) i (γ) µσ (q ) iγ σν (γ ρ) (q ) i (ρ) νρ (q ) i (ρ) ρκ (p 34 ) iγ κ (ρππ) (p 3, p 4 ) iγ (IPρρ) ρ ρ αβ (p 34, q ) i (IP) αβ,δη (s, t ) ū(p, λ )iγ (IPpp) δη (p, p b )u(p b, λ(3) b ). For the IPγexchange the amplitude has the same structure with p(p a ), p(p ) p(p b ), p(p ), t t and s s. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

20 PHOTOPRODUCTION, ρ 0 CONTRIBUTION In a similar way we can write down the γf IR and f IR γ amplitudes. For simplicity, in the following we shall consider the amplitude (3) in the highenergy smallangle limit. Including both, pomeron and f IR exchanges, we obtain in this way M (γip+ γf IR) λ aλ b λ λ π + π ie(p + p a ) µ F (t )δ λ λ a e m ρ γ ρ t (ρ) µρ (q ) (ρ) ρ κ (p 34) g ρππ (p 3 p 4 ) κ F(ρ) (q ) F (ρ) (p 34 ) V ρ ρ αβ (s, t, q, p 34 )F M (t ) (p + p b ) α (p + p b ) β F (t )δ λ λ b (4), A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

21 PHOTOPRODUCTION, ρ 0 CONTRIBUTION where the ρ 0 propagator is given as follows ( i µν (ρ) (k) = i g µν + k ) µk ν k (ρ) + iǫ T (k k µ k ν ) i k + iǫ (ρ) L (k ) (5) with the invariant transverse (ρ) T (k ) and longitudinal (ρ) L (k ) functions. The function V ρ ρ αβ (s, t, q, p 34 ) is as defined in () and includes two tensorial functions Γ (i) ρ ρ αβ (p 34, q ) for i = 0,. From (3.) and (3.) of [?] we have q ρ Γ(i) ρ ρ αβ (p 34, q ) = 0, p ρ 34 Γ(i) ρ ρ αβ (p 34, q ) = 0, g αβ Γ (i) ρ ρ αβ (p 34, q ) = 0, i = 0,. (6) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

22 PHOTOPRODUCTION, ρ 0 CONTRIBUTION Form factor for internal part of the diagram: F (ρ) (k ) = Similar formulas for ρ 0 (450). [ + k (k m ρ ) Λ 4 ρ ] nρ (7) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY 5 06 / 45

23 PHOTOPRODUCTION, CONTINUUM CONTRIBUTION p (pa) p (p) p (pa) p (p) p (pa) p (p) π (pt) γ π + (p3) π (p4) π (pu) γ π (p4) π + (p3) γ π + (p3) π (p4) IP, fir IP, fir IP, fir (a) p (pb) p (p) (b) p (pb) RYSUNEK: The diagrams for photoninduced central exclusive continuum π + π production in protonproton collisions. There are also 3 additional diagrams with the role of (p(p a ), p(p )) and (p(p b ), p(p )) exchanged. p (p) (c) p (pb) p (p) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

24 DRELLSÖDING CONTRIBUTION M (a) λaλ b λ λ π + π = ( i)ū(p, λ )iγ (γpp) µ (p, p a)u(p a, λ a) i (γ) µν (q ) iγ (γππ) ν (p t, p 3 ) i (π) (p t ) iγ (IPππ) (p αβ 4, p t ) i (IP) αβ,δη (s, t ) ū(p, λ )iγ (IPpp) δη (p, p b )u(p b, λ b ), M (b) λaλ b λ λ π + π = ( i)ū(p, λ )iγ (γpp) µ (p, p a)u(p a, λ a) i (γ) µν (q ) iγ (γππ) ν (p 4, p u) i (π) (p u) iγ (IPππ) (p αβ u, p 3 ) i (IP) αβ,δη (s, t ) ū(p, λ )iγ (IPpp) δη (p, p b )u(p b, λ b ), M (c) λaλ b λ λ π + π = ( i)ū(p, λ )iγ (γpp) µ (p, p a)u(p a, λ a) i (γ) µν (q ) iγ (IPγππ) ν,αβ (q, p 4, p 3 ) i (IP) αβ,δη (s, t ) ū(p, λ )iγ (IPpp) δη (p, p b )u(p b, λ b ). (30) (8) (9) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

25 DRELLSÖDING CONTRIBUTION In the highenergy approximation we can write for the tensorpomeron exchange M (a) λaλ b λ λ π + π ie (p + p a) µ δ λ λa F (t )F M (t ) (p t p 3 ) µ t p t mπ β IPππ (p 4 + p t ) α (p 4 + p t ) β 4s ( is α IP )α IP (t ) 3β IPNN (p + p b ) α(p + p b ) β δ λ λ b F (t )F M (t ), (3) M (b) λaλ b λ λ π + π ie (p + p a) µ δ λ λa F (t )F M (t ) t (p 4 + p u) µ p u m π β IPππ (p u p 3 ) α (p u p 3 ) β 4s ( is α IP )α IP (t ) 3β IPNN (p + p b ) α(p + p b ) β δ λ λ b F (t )F M (t ), (3) M (c) λaλ b λ λ π + π ie (p + p a) ν δ λ λa F (t )F M (t ) t β IPππ ˆgαν(p 4 p 3 ) β + g βν (p 4 p 3 ) α 4s ( is α IP )α IP (t ) 3β IPNN (p + p b ) α (p + p b ) β δ λ λ b F (t )F M (t ). (33) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

26 DRELLSÖDING CONTRIBUTION So far for the amplitude for pointlike pions. A possible way to include form factors for the inner subprocesses is to multiply the amplitude for the pointlike particles with a common factor (Poppe, SzczurekKlusekGawenda), M (γip) = (M (a) + M (b) + M (c) ) F(pt, p u, p 34 ). (34) A common form factor for all three diagrams is chosen in order to maintain gauge invariance, and a convenient form is F(p t, p u, p 34 ) = F (p t ) + F (p u ) + F ( p 34 ). (35) Here we take the monopole form factor which is normalized to unity at the onshell point F(m π ) = : F(p ) = Λ π m π Λ π p. (36) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

27 ABSORPTION CORRECTIONS We should add the absorptive corrections to the Born amplitude to give the full physical amplitude for the pp ppπ + π reaction. M pp ppπ + π = MBorn pp ppπ + π + M pp rescattering pp ppπ + π. (37) Here (and above) we have for simplicity omitted the dependence of the amplitude on kinematic variables. The details how to conveniently reduce the number of kinematic integration variables are discussed by Lebiedowicz and Szczurek. The amplitude including pprescattering corrections in the fourbody reaction discussed here is given by M pp rescattering pp ppπ + π (s, p, p ) = i 8π s d k M pp pp (s, k )M Born pp ppπ + π where p = p k and p = p + k. Here, in the overall c.m. system, p and p are the transverse components of the momenta of the finalstate protons and k is the transverse momentum carried A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

28 RESULTS RYSUNEK: Twodimensional distribution in ξ = log (p / GeV) and ξ = log (p / GeV) for the photoproduction mechanism at s = 7 TeV. In the calculation we have used the parameter set A and we have taken Λ ρ = GeV and n ρ = 0.5. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45 PROTON TRANSVERSE MOMENTA ξ 0 dσ/dξ dξ (µb) pp pp π + π s = 7 TeV ξ

29 RESULTS RYSUNEK: The distributions in ξ at s = 0.5 and 7 TeV for the kinematical range of ρ 0 mass window m π M ππ.5 GeV. Here Λ ρ = GeV and n ρ = 0.5. The solid line pomeron and f IR exchanges included. The blue dotted lines represent results for the exponential type of form factors both for the A. SZCZUREK pomeron (INP PAS and KRAKÓW) f IR exchangeshaspect with the WEEK slope 06 parameters KRAKOW, MAY / 45 PROTON TRANSVERSE MOEMENTA (µb) dσ/dξ pp pp π + π s = 500 GeV (µb) dσ/dξ pp pp π + π s = 7 TeV IP γ + f γ IR γ IP + γ f IR ξ ξ

30 RESULTS RYSUNEK: Twopion continuum (DrellSöding) contributions at s = 0.5 TeV (lower lines) and 7 TeV (upper lines). The results for the form factors (4) and () in the amplitudes (3) (33) and no extra multiplicative form factors for A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45 INVARIANT MASS DISTRIBUTION OF THE DRELLSÖDING CONTINUUM dσ/dm ππ (µb/gev) s = 7 TeV pp pp π + π ππ continuum s = 0.5 TeV M ππ (GeV)

31 RESULTS RYSUNEK: Twopion invariant mass distributions at s = 7 TeV for two different scenarios. The ρ(770) (red line), ρ(450) (violet line), continuum (blue line) and total (black line) contributions are shown. The top panels correspond to a hard form factor and the form factor F(pt, p u, p34 ) = for the inner processes. The result for the exponential type of form factors and the hard form factor for Λ ρ = GeV and n ρ = 0.5 is shown by the blue dotted line in the top left panel only. In the top right panel, for the ρ(450) contribution, the thin and thick lines represent results for g ρ ππ = 0.5 and, respectively. The ρ(450) contribution is included only in this panel. The bottom A. SZCZUREK panel (INP PAS corresponds KRAKÓW) to a soft HASPECT form WEEKfactor 06 and a nontrivial KRAKOW, MAY 5 form06 factor 3 / 45 DIPION INVARIANT MASS DISTRIBUTION (µb/gev) dσ/dm ππ ρ(770) pp pp π + π s = 7 TeV Λ ρ Λ ρ Λ ρ = GeV, n ρ = GeV, n ρ = GeV, n ρ continuum total = 0.4 = 0.5 = 0.6 (µb/gev) dσ/dm ππ ρ(770) total pp pp π + π s = 7 TeV Λ ρ = Λ ρ = GeV n ρ = n ρ = 0.5 ρ(450) continuum (µb/gev) dσ/dm ππ pp pp π + π s = 7 TeV Λ ρ Λ ρ Λπ = GeV, n ρ = GeV, n ρ = 0.8 GeV = 0.6 = M ππ (GeV) M ππ (GeV) M ππ (GeV)

32 RESULTS INTERFERENCE EFFECTS (µb/gev) dσ/dm ππ pp pp π + π s = 7 TeV total 0 ρ (770) continuum interference M ππ (GeV) RYSUNEK: Twopion invariant mass distribution at s = 7 TeV for the resonant and nonresonant contributions as well as their coherent sum. The interference term of ρ 0 with the π + π continuum is also shown. Here Λ ρ = GeV and n ρ = 0.5. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

33 RESULTS PION TRANSVERSE MOMENTUM DISTRIBUTION (µb/gev) pp pp π + π s = 7 TeV dσ/dp T, π p (GeV) T, π RYSUNEK: The distributions in pion transverse momentum for the central exclusive ρ 0 π + π and continuum π + π production at s = 7 TeV. The meaning of the lines is the same as for the invariant mass distribution. The blue dotted line represents result for the exponential type of form factors. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

34 RESULTS RAPIDITY AND PSEUDORAPIDITY DISTRIBUTIONS (µb) π dσ/dy pp pp π + π s = 500 GeV (µb) π dσ/dy pp pp π + π s = 7 TeV y π y π (µb) π dσ/dη pp pp π + π s = 500 GeV (µb) π dσ/dη pp pp π + π s = 7 TeV A. SZCZUREK (INP PAS KRAKÓW) HASPECT η WEEK 06 KRAKOW, MAY η / 45 π π

35 RESULTS RAPIDITY CORRELATIONS π y 5 pp pp π + π s = 7 TeV dσ/dy dy (µb) π + π y π + RYSUNEK: The correlation between the rapidities y π + and y π for the photoproduction mechanism at s = 7 TeV. Plotted is dσ/dy π +dy π in µb. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

36 RESULTS RYSUNEK: The distribution in azimuthal angle between the outgoing protons (left panel) and between the outgoing pions (right panel) for the central exclusive photoproduction at s = 7 TeV for the kinematical range of ρ 0 mass window m π M ππ.5 GeV. The solid lines correspond to the pomeron A. SZCZUREK and (INP PAS f IR KRAKÓW) exchanges in the HASPECT amplitudes WEEK 06 while thekrakow, longdashed MAY 5 06 lines 36 / 45 AZIMUTHAL CORRELATIONS (µb) pp dσ/dφ total γ IP + IP γ pp pp π + π s = 7 TeV (µb) ππ dσ/dφ 8 6 pp pp π + π s = 7 TeV 4.5 γ IP + γ f (IP γ + f γ ) IR IR φ (deg) pp φ ππ (deg)

37 RESULTS RYSUNEK: Twopion invariant mass distributions at s = 7 TeV with kinematical cuts specified in the figure. We show results for the doublepomeron/reggeon contribution calculated in the simple LebiedowiczSzczurek Reggelike model and from the photonpomeron/reggeon A. SZCZUREK (INP PAS KRAKÓW) contribution HASPECTas WEEKdiscussed 06 in the KRAKOW, present MAY 5 paper, / 45 INVARIANT MASS DISTRIBUTION (µb/gev) dσ/dm ππ IP/IRIP/IR pp pp π + π s = 7 TeV η < 0.9 π p > 0. GeV T, π (µb/gev) dσ/dm ππ IP/IRIP/IR pp pp π + π s = 7 TeV y <.5 π p > 0. GeV T, π γip/ir + IP/IRγ γip/ir + IP/IRγ M ππ (GeV) M ππ (GeV)

38 RESULTS INTEGRATED CROSS SECTION TABLICA: The integrated cross sections in µb for the exclusive π + π production via the photoproduction mechanism without and with some typical experimental cuts. The line with s =.96 TeV corresponds to the p p collision. In the calculations for the last three lines the following cuts were imposed: η π <.0, η ππ <.0, p,π > 0.5 GeV, < t, t < 0.03 GeV at s = 00 GeV (STAR cuts) while at the LHC energies y π <.5, p,π > 0. GeV (CMS cuts) and η π < 0.9, p,π > 0. GeV (ALICE cuts). s, TeV IP and fir IP (STAR cuts) (ALICE cuts) (CMS cuts).6.53 A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

39 RESULTS DOUBLEPOMERON VERSUS PHOTOPRODUCTION Recently we have not only continuum but also resonant contributions. I will show a few examples of competition of the photoproduction and diffractive contributions. A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

40 RESULTS Data not yet available A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45 DOUBLEPOMERON VERSUS PHOTOPRODUCTION real experimental cuts of ATLAS (measurement of protons) (µb/gev) dσ/dm ππ 5 5 pp pp π s = 8 TeV + π total η π <.5, p > 0. GeV t,π ππcontinuum < t < 0.38 GeV f 0 (500) f 0 (980) f (70) photoproduction Ratio s = 8 TeV η π <.5, p > 0. GeV t,π < t < 0.38 GeV pp pp π + π diffractive diff. continuum photoproduction M ππ (GeV) M ππ (GeV) RYSUNEK:

41 RESULTS DOUBLEPOMERON VERSUS PHOTOPRODUCTION real experimental cuts of STAR (measurement of protons) dσ/dm ππ (µb/gev) pp pp π + π s = 00 GeV η <, η <, p > 0.5 GeV π ππ t, π < t, t < 0.03 GeV STAR preliminary data M ππ (GeV) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

42 RESULTS DOUBLEPOMERON VERSUS PHOTOPRODUCTION real experimental cuts of CMS (no measurement of protons) (µb/gev) pp pp π + π y <, p > 0. GeV π t, π CMS preliminary data s = 7 TeV (µb/gev) pp pp π + π y <, p > 0. GeV π t, π CMS preliminary data s = 7 TeV dσ/dm ππ 0 dσ/dm ππ M ππ (GeV) M ππ (GeV) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

43 RESULTS DOUBLEPOMERON VERSUS PHOTOPRODUCTION real experimental cuts of ALICE (no measurement of protons) (µb/gev) dσ/dm ππ pp pp π + π s = 7 TeV η < 0.9, p > 0. GeV π t, π M ππ (GeV) A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45

44 RESULTS Before our work only diffractive contributions were discussed for the pp ppπ + π reaction. First estimates of the contributions from the resonances ρ(770), ρ(450). First estimate of the DrellSöding (continuum) contribution. The ρ 0 photoproduction and purely diffractive contributions have different dependences on the proton transverse momenta. Transverse proton momentum cuts change the relative size of the photoproduction and doublepomeron/reggeon contributions. Also azimuthal angle correlations between protons are quite different. One could separate: φ pp < 90 o and φ pp > 90 o. The contribution of ρ 0 in the first region should be strongly enhanced for ppcollisions (this is not true for p pcollisions). We have also discussed the role of soft pprescattering corrections which lead to a shape deformation of differential distributions in contrast to the commonly used uniform factor A. SZCZUREK known (INPas PAS KRAKÓW) gap survival factor. HASPECT WEEK 06 KRAKOW, MAY / 45 CONCLUSIONS

45 RESULTS CONCLUSIONS Thank You A. SZCZUREK (INP PAS KRAKÓW) HASPECT WEEK 06 KRAKOW, MAY / 45