modifications: an overview
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1 pp elastic scattering with infrared modifications: an overview Werner K. Sauter Grupo de Fenomenologia de Partículas de Altas Energias IF UFRGS Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.1
2 Summary Brief introduction to the IP omeron; The model: two gluon exchange; Results; Improvements; Conclusions. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.2
3 Introduction The IP omeron : Regge theory versus QCD (BFKL): different predictions for the cross sections with small momentum transfer in high energy collisions. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.3
4 Introduction The IP omeron : Regge theory versus QCD (BFKL): different predictions for the cross sections with small momentum transfer in high energy collisions. LN Model: QCD vacuum properties modified the gluon propagator in long range (soft) interactions Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.3
5 The model: Introduction Two gluon exchange: Low-Nussinov model for the IP omeron; Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.4
6 The model: Introduction Two gluon exchange: Low-Nussinov model for the IP omeron; Modeling the hadron collisions as photon-photon collisions; Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.4
7 The model: Introduction Two gluon exchange: Low-Nussinov model for the IP omeron; Modeling the hadron collisions as photon-photon collisions; Gunion & Soper (after Cheng & Wu): multiple gauge boson exchange in s Channel; Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.4
8 The model: Introduction Two gluon exchange: Low-Nussinov model for the IP omeron; Modeling the hadron collisions as photon-photon collisions; Gunion & Soper (after Cheng & Wu): multiple gauge boson exchange in s Channel; pp scattering with two gluon exchange: A pp 2 = 8isα2 s dk D(k 2 )D ( ( k) 2) [E 1 ( ) E 2 (k, k)] 2. (1) Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.4
9 The model: Introduction The E s are form factors: E 1 proton s Dirac elastic form factor, E 1 (t = 2 ) = 4m 2 p 2, 79t ( ) 2. (2) (4m 2 p t) 1 t 0,71 Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.5
10 The model: Introduction The E s are form factors: E 1 proton s Dirac elastic form factor, E 1 (t = 2 ) = 4m 2 p 2, 79t ( ) 2. (3) (4m 2 p t) 1 t 0,71 E 2 has a arbritary functional form but the infrared divergences goes to zero when k s 0 E 2 (k a, k b ) = E 1 (k 2 a + k 2 b fk a k b ), (3) where f is a hadron depend parameter. First, Cudell & Ross used f = 7, later Cudell & Nguyen used f = 1 (used here). Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.5
11 The model: Introduction Rewrite the amplitude as A pp 2 (s, t) = 8isα2 s (T 1 T 2 ), (4) T 1 = T 2 = s 0 s p ± = /2 ± k, 0 dk D(p + )D(p )E 2 1 ( ), dk D(p + )D(p )E 2 (p +, p ) [ 2E 2 1 ( ) + E 2 (p +, p ) ], Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.6
12 The model: Introduction Rewrite the amplitude as A pp 2 (s, t) = 8isα2 s (T 1 T 2 ), (4) T 1 = T 2 = s 0 s p ± = /2 ± k, 0 dk D(p + )D(p )E 2 1 ( ), dk D(p + )D(p )E 2 (p +, p ) [ 2E 2 1 ( ) + E 2 (p +, p ) ], T 1 : the gluons strucks the same quark inside the proton and T 2 : different quarks inside the proton. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.6
13 The Model: Cross Sections Cross sections by optical theorem: σtot 0 = App 2 (s, 0), is (4) dσ 0 = App 2 (s, t) 2 dt 16πs 2. (5) Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.7
14 The Model: Cross Sections Cross sections by optical theorem: σtot 0 = App 2 (s, 0), is (6) dσ 0 = App 2 (s, t) 2 dt 16πs 2. (6) Note that the cross sections are independent of energy Too simple approx. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.7
15 The Model: Cross Sections Cross sections by optical theorem: σtot 0 = App 2 (s, 0), is (5) dσ 0 = App 2 (s, t) 2 dt 16πs 2. (5) Note that the cross sections are independent of energy Too simple approx. In low momentum transfer: dσ dt = A ebt A = σ2 tot 16π, B = d dt ( ln dσ ). (4) dt t=0 Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.7
16 The model: Pros and cons Problems: Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.8
17 The model: Pros and cons Problems: no energy dependence Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.8
18 The model: Pros and cons Problems: no energy dependence B(t = 0) for D(k 2 ) = 1/k 2 Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.8
19 The model: Pros and cons Problems: no energy dependence B(t = 0) for D(k 2 ) = 1/k 2 Possible solution: Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.8
20 The model: Pros and cons Problems: no energy dependence B(t = 0) for D(k 2 ) = 1/k 2 Possible solution: ad hoc Regge energy term. σ tot = dσ dt = ( s m 2 p ( s m 2 p ) 0,08 σ 0 tot, (3) ) 0,168 dσ 0 dt. (3) Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.8
21 The model: Previous results LN model (pp pp at s = 53 GeV) Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.9
22 The model: Previous results LN model (pp pp at s = 53 GeV) Cudell & Ross EDS solutions; Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.9
23 The model: Previous results LN model (pp pp at s = 53 GeV) Cudell & Ross EDS solutions; Halzen, Krein & Natale Cornwall s solution; Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.9
24 The model: Previous results LN model (pp pp at s = 53 GeV) Cudell & Ross EDS solutions; Halzen, Krein & Natale Cornwall s solution; UKQCD Coll. Lattice solution; Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.9
25 The model: Previous results LN model (pp pp at s = 53 GeV) Cudell & Ross EDS solutions; Halzen, Krein & Natale Cornwall s solution; UKQCD Coll. Lattice solution; Aguilar, Mihara & Natale Comparison of propagators. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.9
26 The model: Our approach Our approach: using IR modified gluon props but not fixing parameters with LN formulae. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.10
27 The model: Our approach Our approach: using IR modified gluon props but not fixing parameters with LN formulae. Cornwall propagator: D 1 C (q2 ) = [ q 2 + m 2 (q 2 ) ] b g 2 ln [ ] q m 2 (q 2 ) Λ 2 QCD m 2 (q 2 ) = m 2 g ( ) ln q2+4 m2 g Λ 2 QCD ( ) 4 m 2 ln g Λ 2 QCD 12/11 Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.10
28 The model: Propagators Cornwall modified propagator: D C (q 2 ) = 1 q 2 + m 2 (q 2 ) Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.11
29 The model: Propagators Cornwall modified propagator: D C (q 2 ) = 1 q 2 + m 2 (q 2 ) Massive: D M (q 2 ) = 1 q 2 + m 2 g Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.11
30 The model: Propagators Cornwall modified propagator: D C (q 2 ) = 1 q 2 + m 2 (q 2 ) Massive: D M (q 2 1 ) = q 2 + m 2 g Häbel/Gribov propagator: D HG (q 2 ) = q2 q 4 + b 4 Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.11
31 The model: Propagators Gorbar/Natale propagator D GN (q 2 ) = 1 q 2 + m 2 GN (q2 ), m 2 GN(q 2 ) = µ 2 gθ(χµ 2 g q 2 ) + µ2 g q 2 Θ(q2 χµ 2 g) Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.12
32 The model: Coupling Constant α s fixed: α s = 0, 9 and α s = α s (0). Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.13
33 The model: Coupling Constant α s fixed: α s = 0, 9 and α s = α s (0). α s running: α s (k 2 ) = 4π β 0 ln ( k2 +4m 2 D Λ 2 QCD ), Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.13
34 The model: Coupling Constant α s fixed: α s = 0, 9 and α s = α s (0). α s running: α s (k 2 ) = 4π β 0 ln ( k2 +4m 2 D Λ 2 QCD ), The scale of the coupling is the momentum of the gluon. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.13
35 Results dσ/dt (mb/gev 2 ) α s = 0.9 Cornwall Cornwall (var) Massivo (m g =0.8 GeV 2 ) Habel/Gribov Gorbar/Natale α s = α s (0) t (GeV 2 ) t (GeV 2 ) Differential cross section. s = 53 GeV. Fixed coupling. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.14
36 Results dσ/dt (mb/gev 2 ) α s = 0.9 Cornwall Cornwall (var) Massivo (m g =0.8 GeV 2 ) HabelGribov Gorbar/Natale α s = α s (0) t (GeV 2 ) t (GeV 2 ) Differential cross section. s = 1.8 TeV. Fixed coupling. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.15
37 Results dσ/dt (mb/gev 2 ) α s = 0.9 Cornwall Cornwall (var) Massivo (m g =0.8 GeV 2 ) HabelGribov Gorbar/Natale α s = α s (0) t (GeV 2 ) t (GeV 2 ) Differential elastic cross section. s = 53 GeV. Fixed coupling. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.16
38 Results α s = 0.9 Cornwall Cornwall (var) Massivo (m g =0.8 GeV 2 ) HabelGribov Gorbar/Natale α s = α s (0) dσ/dt (mb/gev 2 ) t (GeV 2 ) t (GeV 2 ) Differential elastic cross section. s = 1.8 TeV. Fixed coupling. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.17
39 Results 10 3 sqrt(s) = 53 GeV 10 3 sqrt(s)= 1.8 TeV dσ/dt (mb/gev 2 ) Cornwall Cornwall (var.) Massivo (m g = 0.8 GeV) HabelGribov Gorbar/Natale t (GeV 2 ) t (GeV 2 ) Differential elastic cross section. s = 1.8 TeV. Running coupling. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.18
40 Conclusions Good (or poor) agreement with the data in particular cases (with same parameters of previous analisis). Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.19
41 Conclusions Good (or poor) agreement with the data in particular cases (with same parameters of previous analisis). The model with running coupling have a good agreement with the data. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.19
42 Conclusions Good (or poor) agreement with the data in particular cases (with same parameters of previous analisis). The model with running coupling have a good agreement with the data. Strong dependence of the running coupling. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.19
43 Improvements Cudell & Nguyen: next leading order (but not BFKL). Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.20
44 Improvements Cudell & Nguyen: next leading order (but not BFKL). BFKL with non perturbative propagators: Hancock & Ross, Vacca & Venturi, Nikolaev, Zakharov & Zoller, Forshaw & Harriman. Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.20
45 References Cudell, Ross Nucl. Phys B 359 (1991) 247 Cudell, Nguyen Nucl. Phys. B 420 (1994) 669 UKQCD Coll. Phys. Lett. B 369 (1996) 130 Halzen et al. Phys. Rev. D 47 (1993) 295 Aguilar et al. Phys. Rev. D 65 (2002) , hep-ph/ NNZ JETP Lett. 60 (1994) 694, Phys. Lett. B 328 (1994) 486 Jenkovszky et al. Sov. J. Nucl. Phys. 53 (1991) 329, Z. Phys. C 63 (1994) 131 Ross J. Phys. G 15 (1989) 1175 Hancock, Ross Nucl. Phys. B 383 (1992) 575, Nucl. Phys. B 394 (1993) 200 Vacca, Venturi Il Nuovo Cim. A 108 (1995) 77 Forshaw & Harriman Phys. Rev. D 46 (1992) 3778 Seminários de Fenomenologia de Partículas de Altas Energias 2003/1 p.21
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