pp elasticscatteringwithinfrared modications: anoverviesauter/semo5.pdf · pp...
TRANSCRIPT
pp elastic scattering with infraredmodifications: an overview
Werner K. Sauter
Grupo de Fenomenologia de Partıculas de Altas Energias
IF–UFRGS
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.1
Summary• Brief introduction to the IPomeron;• The model: two gluon exchange;• Results;• Improvements;• Conclusions.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.2
Introduction• The IPomeron : Regge theory versus QCD
(BFKL): different predictions for the crosssections with small momentum transfer inhigh energy collisions.
• LN Model: QCD vacuum properties modifiedthe gluon propagator in long range (soft)interactions
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.3
Introduction• The IPomeron : Regge theory versus QCD
(BFKL): different predictions for the crosssections with small momentum transfer inhigh energy collisions.
• LN Model: QCD vacuum properties modifiedthe gluon propagator in long range (soft)interactions
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.3
The model: Introduction• Two gluon exchange: Low-Nussinov model
for the IPomeron;
• Modeling the hadron collisions asphoton-photon collisions;
• Gunion & Soper (after Cheng & Wu): multiplegauge boson exchange in s Channel;
• pp scattering with two gluon exchange:
App2 = 8isα2
s
∫
dkD(k2)D(
(∆− k)2)
[E1(∆) − E2(k,∆− k)]2.
(1)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.4
The model: Introduction• Two gluon exchange: Low-Nussinov model
for the IPomeron;• Modeling the hadron collisions as
photon-photon collisions;
• Gunion & Soper (after Cheng & Wu): multiplegauge boson exchange in s Channel;
• pp scattering with two gluon exchange:
App2 = 8isα2
s
∫
dkD(k2)D(
(∆− k)2)
[E1(∆) − E2(k,∆− k)]2.
(1)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.4
The model: Introduction• Two gluon exchange: Low-Nussinov model
for the IPomeron;• 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:
App2 = 8isα2
s
∫
dkD(k2)D(
(∆− k)2)
[E1(∆) − E2(k,∆− k)]2.
(1)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.4
The model: Introduction• Two gluon exchange: Low-Nussinov model
for the IPomeron;• 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:
App2 = 8isα2
s
∫
dkD(k2)D(
(∆− k)2)
[E1(∆) − E2(k,∆− k)]2.
(1)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.4
The model: Introduction• The E ’s are form factors: E1 ⇒ proton’s Dirac
elastic form factor,
E1(t = −∆2) =4m2
p − 2, 79t
(4m2p − t)
(
1 − t0,71
)2. (2)
• E2 has a arbritary functional form but theinfrared divergences goes to zero when k’s→ 0
E2(ka,kb) = E1(k2a + k2
b − fka · kb), (3)
where f is a hadron depend parameter. First,Cudell & Ross used f = 7, later Cudell &Nguyen used f = 1 (used here).
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.5
The model: Introduction• The E ’s are form factors: E1 ⇒ proton’s Dirac
elastic form factor,
E1(t = −∆2) =4m2
p − 2, 79t
(4m2p − t)
(
1 − t0,71
)2. (3)
• E2 has a arbritary functional form but theinfrared divergences goes to zero when k’s→ 0
E2(ka,kb) = E1(k2a + k2
b − fka · kb), (3)
where f is a hadron depend parameter. First,Cudell & Ross used f = 7, later Cudell &Nguyen used f = 1 (used here).
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.5
The model: Introduction• Rewrite the amplitude as
App2 (s, t) = 8isα2
s (T1 − T2) , (4)
T1 =
∫ s
0
dk D(p+)D(p−)E21 (∆),
T2 =
∫ s
0
dk D(p+)D(p−)E2(p+,p−)[
2E21 (∆) + E2(p+,p−)
]
,
p± = ∆/2 ± k,
• T1: the gluons strucks the same quark insidethe proton and T2: different quarks inside theproton.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.6
The model: Introduction• Rewrite the amplitude as
App2 (s, t) = 8isα2
s (T1 − T2) , (4)
T1 =
∫ s
0
dk D(p+)D(p−)E21 (∆),
T2 =
∫ s
0
dk D(p+)D(p−)E2(p+,p−)[
2E21 (∆) + E2(p+,p−)
]
,
p± = ∆/2 ± k,
• T1: the gluons strucks the same quark insidethe proton and T2: different quarks inside theproton.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.6
The Model: Cross Sections• Cross sections by optical theorem:
σ0tot =
App2 (s, 0)
is, (4)
dσ0
dt=
|App2 (s, t)|216πs2
. (5)
• Note that the cross sections are independentof energy ⇒ Too simple approx.
• In low momentum transfer:dσ
dt= A eBt ⇒ A =
σ2tot
16π, B =
d
dt
(
lndσ
dt
)∣
∣
∣
∣
t=0
. (6)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.7
The Model: Cross Sections• Cross sections by optical theorem:
σ0tot =
App2 (s, 0)
is, (6)
dσ0
dt=
|App2 (s, t)|216πs2
. (6)
• Note that the cross sections are independentof energy ⇒ Too simple approx.
• In low momentum transfer:dσ
dt= A eBt ⇒ A =
σ2tot
16π, B =
d
dt
(
lndσ
dt
)∣
∣
∣
∣
t=0
. (5)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.7
The Model: Cross Sections• Cross sections by optical theorem:
σ0tot =
App2 (s, 0)
is, (5)
dσ0
dt=
|App2 (s, t)|216πs2
. (5)
• Note that the cross sections are independentof energy ⇒ Too simple approx.
• In low momentum transfer:dσ
dt= A eBt ⇒ A =
σ2tot
16π, B =
d
dt
(
lndσ
dt
)∣
∣
∣
∣
t=0
. (4)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.7
The model: Pros and cons• Problems:
• no energy dependence• B(t = 0) → ∞ for D(k2) = 1/k2
• Possible solution:• ad hoc Regge energy term.
σtot =
(
s
m2p
)0,08
σ0tot, (5)
dσ
dt=
(
s
m2p
)0,168dσ0
dt. (6)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.8
The model: Pros and cons• Problems:
• no energy dependence
• B(t = 0) → ∞ for D(k2) = 1/k2
• Possible solution:• ad hoc Regge energy term.
σtot =
(
s
m2p
)0,08
σ0tot, (6)
dσ
dt=
(
s
m2p
)0,168dσ0
dt. (6)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.8
The model: Pros and cons• Problems:
• no energy dependence• B(t = 0) → ∞ for D(k2) = 1/k2
• Possible solution:• ad hoc Regge energy term.
σtot =
(
s
m2p
)0,08
σ0tot, (5)
dσ
dt=
(
s
m2p
)0,168dσ0
dt. (5)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.8
The model: Pros and cons• Problems:
• no energy dependence• B(t = 0) → ∞ for D(k2) = 1/k2
• Possible solution:
• ad hoc Regge energy term.
σtot =
(
s
m2p
)0,08
σ0tot, (4)
dσ
dt=
(
s
m2p
)0,168dσ0
dt. (4)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.8
The model: Pros and cons• Problems:
• no energy dependence• B(t = 0) → ∞ for D(k2) = 1/k2
• Possible solution:• ad hoc Regge energy term.
σtot =
(
s
m2p
)0,08
σ0tot, (3)
dσ
dt=
(
s
m2p
)0,168dσ0
dt. (3)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.8
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.
• Other approaches: Jenkovszky et al.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.9
The model: Previous results• LN model (pp → pp at
√s = 53 GeV)
• Cudell & Ross ⇒ EDS’ solutions;
• Halzen, Krein & Natale ⇒ Cornwall’ssolution;
• UKQCD Coll. ⇒ Lattice solution;• Aguilar, Mihara & Natale ⇒ Comparison of
propagators.
• Other approaches: Jenkovszky et al.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.9
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.
• Other approaches: Jenkovszky et al.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.9
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 ofpropagators.
• Other approaches: Jenkovszky et al.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.9
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.
• Other approaches: Jenkovszky et al.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.9
The model: Our approach• Our approach: using IR modified gluon props
but not fixing parameters with LN formulae.
• Cornwall propagator:
D−1C (q2) =
[
q2 + m2(q2)]
b g2 ln
[
q2 + 4 m2(q2)
Λ2QCD
]
m2(q2) = m2g
ln(
q2+4 m2g
Λ2QCD
)
ln(
4 m2g
Λ2QCD
)
−12/11
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.10
The model: Our approach• Our approach: using IR modified gluon props
but not fixing parameters with LN formulae.• Cornwall propagator:
D−1C (q2) =
[
q2 + m2(q2)]
b g2 ln
[
q2 + 4 m2(q2)
Λ2QCD
]
m2(q2) = m2g
ln(
q2+4 m2g
Λ2QCD
)
ln(
4 m2g
Λ2QCD
)
−12/11
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.10
The model: Propagators• Cornwall modified propagator:
DC ′(q2) =1
q2 + m2(q2)
• Massive:
DM(q2) =1
q2 + m2g
• Häbel/Gribov propagator:
DHG(q2) =q2
q4 + b4
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.11
The model: Propagators• Cornwall modified propagator:
DC ′(q2) =1
q2 + m2(q2)
• Massive:
DM(q2) =1
q2 + m2g
• Häbel/Gribov propagator:
DHG(q2) =q2
q4 + b4
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.11
The model: Propagators• Cornwall modified propagator:
DC ′(q2) =1
q2 + m2(q2)
• Massive:
DM(q2) =1
q2 + m2g
• Häbel/Gribov propagator:
DHG(q2) =q2
q4 + b4
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.11
The model: Propagators• Gorbar/Natale propagator
DGN(q2) =1
q2 + m2GN(q2)
,
m2GN (q2) = µ2
gΘ(χµ2g − q2) +
µ2g
q2Θ(q2 − χµ2
g)
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.12
The model: Coupling Constant• αs fixed: αs = 0, 9 and αs = αs(0).
• αs running:
αs(k2) =
4π
β0 ln(
k2+4m2D
Λ2QCD
) ,
• The scale of the coupling is the momentum ofthe gluon.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.13
The model: Coupling Constant• αs fixed: αs = 0, 9 and αs = αs(0).• αs running:
αs(k2) =
4π
β0 ln(
k2+4m2D
Λ2QCD
) ,
• The scale of the coupling is the momentum ofthe gluon.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.13
The model: Coupling Constant• αs fixed: αs = 0, 9 and αs = αs(0).• αs running:
αs(k2) =
4π
β0 ln(
k2+4m2D
Λ2QCD
) ,
• The scale of the coupling is the momentum ofthe gluon.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.13
Results
0.0 0.2 0.4 0.6 0.8 1.0|t| (GeV2)
10-3
10-2
10-1
100
101
102
103
dσ/d
t (m
b/G
eV2 )
CornwallCornwall (var)
Massivo (mg=0.8 GeV2)
Habel/GribovGorbar/Natale
αs = 0.9
0.0 0.2 0.4 0.6 0.8 1.0|t| (GeV2)
αs = αs(0)
Differential cross section.√
s = 53 GeV. Fixed coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.14
Results
0.0 0.1 0.2 0.3 0.4|t| (GeV2)
100
101
102
103
dσ/d
t (m
b/G
eV2 )
CornwallCornwall (var)
Massivo (mg=0.8 GeV2)
HabelGribovGorbar/Natale
αs = 0.9
0.0 0.1 0.2 0.3 0.4|t| (GeV2)
αs = αs(0)
Differential cross section.√
s = 1.8 TeV. Fixed coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.15
Results
0.0 0.2 0.4 0.6 0.8 1.0|t| (GeV2)
10-3
10-2
10-1
100
101
102
103
dσ/d
t (m
b/G
eV2 )
CornwallCornwall (var)
Massivo (mg=0.8 GeV2)
HabelGribovGorbar/Natale
αs = 0.9
0.0 0.2 0.4 0.6 0.8 1.0|t| (GeV2)
αs = αs(0)
Differential elastic cross section.√
s = 53 GeV. Fixed coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.16
Results
0.0 0.1 0.2 0.3 0.4|t| (GeV2)
10-1
100
101
102
103
dσ/d
t (m
b/G
eV2 )
CornwallCornwall (var)
Massivo (mg=0.8 GeV2)
HabelGribovGorbar/Natale
αs = 0.9
0.0 0.1 0.2 0.3 0.4|t| (GeV2)
αs = αs(0)
Differential elastic cross section.√
s = 1.8 TeV. Fixed coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.17
Results
0.0 0.2 0.4 0.6 0.8 1.0|t| (GeV2)
10-3
10-2
10-1
100
101
102
103
dσ/d
t (m
b/G
eV2 )
CornwallCornwall (var.)Massivo (mg = 0.8 GeV)
HabelGribovGorbar/Natale
sqrt(s) = 53 GeV
0.0 0.1 0.2 0.3 0.4|t| (GeV2)
10-1
100
101
102
103sqrt(s)= 1.8 TeV
Differential elastic cross section.√
s = 1.8 TeV. Running coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.18
Conclusions• Good (or poor) agreement with the data in
particular cases (with same parameters ofprevious analisis).
• The model with running coupling have a goodagreement with the data.
• Strong dependence of the running coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.19
Conclusions• Good (or poor) agreement with the data in
particular cases (with same parameters ofprevious analisis).
• The model with running coupling have a goodagreement with the data.
• Strong dependence of the running coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.19
Conclusions• Good (or poor) agreement with the data in
particular cases (with same parameters ofprevious analisis).
• The model with running coupling have a goodagreement with the data.
• Strong dependence of the running coupling.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.19
Improvements• Cudell & Nguyen: next leading order (but not
BFKL).
• BFKL with non perturbative propagators:Hancock & Ross, Vacca & Venturi, Nikolaev,Zakharov & Zoller, Forshaw & Harriman.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.20
Improvements• Cudell & Nguyen: next leading order (but not
BFKL).• BFKL with non perturbative propagators:
Hancock & Ross, Vacca & Venturi, Nikolaev,Zakharov & Zoller, Forshaw & Harriman.
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.20
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) 054011, hep-ph/0208095
• 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
Seminarios de Fenomenologia de Partıculas de Altas Energias – 2003/1 – p.21