Features of ds/dt at small t at LHC(elastic scattering)

O.V. SelyuginO.V. Selyugin (JINR Dubna)(JINR Dubna)

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))

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

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

1800FNAL pp pp s GeV

72.1 3.3 710 .tot E Coll

80.03 2.24 . ( . .)tot E Coll Abeet all

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

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

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

Proton-proton

Proton-antiproton

( , ) ( , ) | |N nf sfF s t F s t t h

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

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

Dubna Dynamical ModelDubna Dynamical Model

( , ) (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

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

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

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

14s TeV

2s TeV

J.-R. Cudell, O.V. Selyugin, Phys.Rev.Lett. , 102 (2009) 0320003

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;

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

Experiment ISRExperiment ISR

52.8 GeVs

48.38tot mb 212.87B GeV

Polynomial fit

6 parameters

Experiment ISRExperiment ISR

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

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

Statistical independent choicesStatistical independent choices

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

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

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

New parameters New parameters (model fit)(model fit)

tot = 63.54 mb;

B = 15.485 GeV-2;

= 0.158;

ENDEND

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.

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.