features of ds/dt at small t at lhc (elastic scattering)
DESCRIPTION
Features of ds/dt at small t at LHC (elastic scattering). O.V. Selyugin (JINR Dubna ). With the construction of large accelarators , it is hoped that the mysteries of high-energy scattering will unfold in the near future. Hung Cheng, Tsai Tsun Wu Phys.Rev.Lett . ( 1970 ). - PowerPoint PPT PresentationTRANSCRIPT
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Features of ds/dt at small t at LHC(elastic scattering)
O.V. SelyuginO.V. Selyugin (JINR Dubna)(JINR Dubna)
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With the construction of large accelarators, it is hoped With the construction of large accelarators, it is hoped that the mysteries of high-energy scattering will unfold that the mysteries of high-energy scattering will unfold
in the near futurein the near future..
Hung Cheng, Tsai Tsun WuHung Cheng, Tsai Tsun WuPhys.Rev.Lett. (Phys.Rev.Lett. (19701970))
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linked to tot via dispersion relations
sensitive to tot beyond the energy
at which is measured
predictions of tot beyond LHC energies
Or, are dispersion relations still valid at LHC energies?
The The parameter parameter
33
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0.24 0.04 ( 4 . . .)UA Coll M Bozzo et al
0.135 0.015 ( 4 / 2 ., . .)UA Coll C Augier et al
ProblemsProblems 540CERN pp pp s GeV
. . , . . 55, 841)1992 0.24 0.0. 03 (19 O V Selyugin Yad Fiz
Comment
. . , . . 198, 5831995 0.135 0.. 2 )0 0 (17 O V Selyugin Phys Lett B
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1800FNAL pp pp s GeV
72.1 3.3 710 .tot E Coll
80.03 2.24 . ( . .)tot E Coll Abeet all
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Model el/ t=0) B t=0)
COMPETE 111 0.11
Marseilles 103 0.28 0.12 19
Dubna 128 0.33 0.19 21.
Pomer.(s+h) 150 0.29 0.24 21.4
Serpukhov 230 0.67
PredictionsPredictions 14s TeV
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Usual assumptionsUsual assumptions/2Im ( , ) / (0.389 4 ) Bt
N totF s t e /2Re ( , ) / (0.389 4 ) Bt
N totF s t e Re Im( , ) ( , )B s t B s t
exp.( ) ( )tot js f s
( ) . exptot js fix from other eriment
( ) . expjs fix from other eriments
oror
oror
UA4/2UA4/2
TOTEMTOTEM.or fix from theory
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22 2 1/2
2 2 2 2
( ) ( ) 1 1 ( , )Im ( , ) [ ( )]
1 (1 ) 1N C C C
d s tF s t F F F
dt
2 2 21 ( , )( ( ) (1 ( , ) Im ( , ) 2( ( , ) ( , )) Im )C N N C
d s tF t s t F s t s t s t F F
dt
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Proton-proton
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Proton-antiproton
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( , ) ( , ) | |N nf sfF s t F s t t h
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Dependence of the slope B(s,t) from the size of the examined interval t for UA4/2 experiment
triangles – exponential form of FCircles - + additional term sqrt(-t) k F
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Soft and hard PomeronSoft and hard Pomeron
Donnachie-Landshoff model;
Schuler-Sjostrand model
1 01 ln( / )1
0
( , ) [ ( ) t s ssT s t h e
s
2 02 ln( / ) 22
0
( ) ] ( )t s ssh e F t
s
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Dubna Dynamical ModelDubna Dynamical Model
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( , ) (1 exp[ ( , )])b s s b
Impact parameter representation and unitarization schemes
0
0
( , ) ( ) ( , )T s t is b db J bq b s
EikonalEikonal
K-matrixK-matrix( , ) ( , )
( , ) ; ( , ) ( , )1 ( , ) 1 ( , )
s b iK s bs b K s b i s b
s b i K s b
( [1 ]) (1 );dN
Ln N Ndy
(1 );dN
N Ndy
U-matrixU-matrix (1 / );u
dNN N c
dy
2uc
R.Arnold (1964). N.Nikolaev, E.Predazzi (1993R.Arnold (1964). N.Nikolaev, E.Predazzi (1993))
R.Blankenberger, M.Goldberger(1962); S.Troshin, N.Tyurin (1993) ; L.Jenkovszky et. all. R.Blankenberger, M.Goldberger(1962); S.Troshin, N.Tyurin (1993) ; L.Jenkovszky et. all.
( , ) ( , )( , ) 2 ; ( , ) ( , ) / 2
1 ( , ) / 2 1 ( , )
s b iU s bs t U s b i s b
s b iU s b
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Ratio - Im T(s,t)/Re(s,t) (Soft+hard Pomeron)Ratio - Im T(s,t)/Re(s,t) (Soft+hard Pomeron)
500s GeV
5s TeV
Eikonal represantation
14s TeV
100s GeV
2s TeV
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Slope of the differential cross sectionsSlope of the differential cross sections
Eikonal represantation
5s TeV
14s TeV
500s GeV100s GeV
( , ) ( [ ( , )];d d
B s t Ln s tdt dt
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N=90N=90
[0.0005 0.1] t
Simulation of the experimental data by the Simulation of the experimental data by the model with model with non-exponentialnon-exponential behavior of behavior of
B(s,t) and B(s,t) and s,t)s,t)
LHCLHC 14 TeV14 TeV
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14s TeV
2s TeV
J.-R. Cudell, O.V. Selyugin, Phys.Rev.Lett. , 102 (2009) 0320003
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tot = 152.5 mb;
B(t=0) = 21.4 GeV-2; = 0.24 (t=0);
14s TeV Non-exponetial t-dependenceNon-exponetial t-dependence
2 133i 2 120i
2 109i 2 108i
tot = 155.3+/-0. 5;fix = 0.15; B = 23.1+/-0.15; nfix = 1;
tot = 180+/- 2.1; fix = 0.15;B = 23.2+/-0.15; n = 0.74+/0.07;
tot = 153.4+/- 0.7;
= 0.26; B = 23.5+/-0.17; nfix = 1;
tot = 142.3+/- 2.8;
= 0.29; B = 23.6+/-0.19; nfix = 1.15+/0.04;
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FeaturesFeatures - - RR
2( , ) [ ( ) Re ( , )] 0th
R i C i N is t F t F s t
min( , ) 0th
R s t
min minRe ( , ) ( )pp ppN CF s t F t
exp exp 2( , ) 1 / / ( ) ( ( ) ( ) Im ( , ))R i C i N
s t d dt t t F t F s t exp exp 2( , ) 1 / / ( ) ( ( ) ( ) Im ( , ))R i C i N
s t d dt t t F t F s t
2( , ) [ ( ) Re ( , )] 0th
R i C i N is t F t F s t
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Experiment ISRExperiment ISR
52.8 GeVs
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48.38tot mb 212.87B GeV
Polynomial fit
6 parameters
Experiment ISRExperiment ISR
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Proton-proton elastic scattering at LHCProton-proton elastic scattering at LHC
111.5tot mb 222B GeV
Re ( , )( , ) 0.15
Im ( , )N
N
F s ts t
F s t
2min 0.0044ppt GeV
COMPETE values
/ 2Im ( , ) /(0.389 4 ) BtN totF s t e
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AKM theorem (G.Anderson, T. Kinoshita, A. Martin)
The regime of the maximal axiomatic growth of F(s,t)
[Im F(s,t) ~ Re F(s,t) ~ Ln2(s)]
Allowed by asymptotic theorem
( , ) / ( , 0) ( );F s t F s g
0 0/ ln( / ) ;t t s s
The scattering amplitude must have infinity many zerous in a very nerow region of t
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Statistical independent choicesStatistical independent choices
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2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1
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Proron-antiproton Proron-antiproton UA4/2 - parametersUA4/2 - parameters
tot = 62.2 mb;
B = 15.5 GeV-2;
= 0.135;
20.9085 10 .q GeV
33 1.2 0.35;L
25 1.7 0.4;L
99 0.74 0.2;L
540s GeV
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2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1
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New parameters New parameters (model fit)(model fit)
tot = 63.54 mb;
B = 15.485 GeV-2;
= 0.158;
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ENDEND
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SummarySummary
The experiments on the proton elastic scattering occupy the important place in the reserch program at LHC.
Non-linear equations correspound to the different form of the unitarization schemes. They have the same assymptotic regime. They lead to the non-exponential behavior of the scattering amplitude..
The additional researches is needed.
Very likely that BDL regime will be reached at LHC energies. It will be reflected in the behavior of B(t) and (t).
The effects have to be account in the fitting procedure of all 4
values – L, B, simulteniously.
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SummarySummary
The new method of the determination of the real part
of the elastic hadron amplitude give the possibility to find
the special features in its behavior
The non-fitting (statistical) method can shows the existance some oscillations in the differential cross sections and help to check up the
values of L, B,
To reserch of the non-lenear behavior of the parameters of the scattering amplitude it is neeed to develop new methods.