O.V. Selyugin

BLTPh, JINR

“The dispersion relations and analysis

of the new LHC data ”

Acireale (Italy)

September, 02-08

International workshop Diffraction in High Energy Physics

(“DIFFRACTION-2016")

in collaboration with J.-R. CUDELL

FAGO, Univ. Liege

Contents

* Introduction

* Elastic hadron scattering – new data LHC

* Comparing the data with High Energy Generalized structure model (HEGS)

* Results and Summery

* The real part of the scattering amplitude from the data

* Phenomenological analysis of the new data

* Total cross sections

the new LHC data (elastic scattering)

at 7 and 8 TeV

7 TeV (TOTEM) - t [0.00515 – 0.371] 17.08.2012

7 TeV (ATLAS) - t [0.0062 – 0.3636] 25.08.2014

8 TeV (TOTEM) - t [0.028500 – 0.1947] 12.09.2015

8 TeV (ATLAS) - t [0.01050 – 0.3635] 25.06.2016

8 TeV (TOTEM) - t [0.000741 – 0.201] 11.12.2015

Total cross sections

(98.3 2.8) ;

(98.6 2.2) ;

(99.1 4.3) ;

(98.0 2.5) ;

tot mb

mb

mb

mb

96.07( 1.34)tot mb

TOTEM ATLAS

98.5( 2.9)tot mb

102.9( 2.3)tot mb

95.35( 2.0)tot mb

7000 ;s GeV

8000 ;s GeV

3.1 ;5 mb

7 ;6. mb

1 1 ˆln( )

1 2ˆ( , ) ( ) ( ) ;t sB

emF s t h G t s e 1 1 ˆ/4 ln( )2

3 3ˆ( , ) ( ) ( ) ;t sB

AF s t h G t s e

2 1 3 2ˆ ˆ ˆ ˆ ˆ( , ) ( , ) (

( ,

1 / ) ] ( , ) (1 /

;

) ]

)

B B B

B

odd

F s t F s t R s F s t R

F s

s

t

/

0

2

0

2ˆ

s 4 .

/ ;i

p

s s s

m

e

Extending of model (HEGS1) – O.V. S. Phys.Rev. D 91, (2015) 113003

1 1 ˆ/4 ln( )

2

2 ˆ(( , ) ( )) ;1

B

Odd Odd

t s

A

o

G t st

F s t hr t

e

0

1 0

ˆ ˆ( ) ( ) ln .k st ln

k qB et s

2

9 000 ;

3416; 0.00037

8

980 15| | ;

Gs

n

e

Gt

V

eV

High Energy General Structure (HEGS) model O.V.S. - Eur. Phys. J. C (2012) 72:2073

6

( , )

00

1( , ) ( ) [1 ]

2

h s bF s t b J bq e db

00

( , ) 2 ( ) ( , )h

Bs b q J bq F s q dq

2 21

( , ) [ ]2

s b dzV z bk

UNITARIZATION eikonal representation

1 10.11; 0 ;.24 ;fixed

2

9 000 ; 3416;8

. 8/ N 1 2

GeV Ns

1 2 0

2( 0.14 ;0.82; 0.31; 0.163 ;.8);Odd oh rh h k

1 253.7; 4.45; 0.05.sfR R h

High energy parameters

Low energy parameters

7 TeV (TOTEM) - t [0.00515 – 0.371]

n = 0.94

7 TeV (ATLAS) - t [0.0062 – 0.3636]

n=1.0

8 TeV (TOTEM) - t [0.0285 – 0.1947]

n=0.9

8 TeV (TOTEM) - t [0.000741 – 0.201]

n=0.9

8 TeV (ATLAS) - t [0.01050 – 0.3635]

n=1.0

4 . . .0.24 0.04 ( )UA Coll M Bozzo et al

4 / 2 ., . .0.135 0.015 ( )UA Coll C Augier et al

Problems540CERN pp pp s GeV

. . , . . )55, 8411992 0.24 0.0. 03 (19 OV Selyugin Yad Fiz

Comment

. . , . . 198, 5831995 0.135 0.. 2 )0 0 (17 OV Selyugin Phys Lett B

. , . , . , : 0905.1955( )

2009 0.009

(

0.172

A Kendi E Ferreira T Kodama arXiv hep ph

1800FNAL pp pp s GeV

(71.42 1.55) .tot mb SCINT Coll

(80.03 2.24) .tot mb CDF Coll

Problems

Comment

Very likely that this difference reflects the true errors of

the fitting procedure of the experimental data obtained

by the luminosity independent method.

ch I f

Ch II

Non-exponential behavior (origins)

1. Non-linear Regge trajectory (L. Jenkovsky et al.)

(Pion loops ) Anselm, Gribov, G. Coken-Tannoudji et.al.; Khoze, Martin;

3. Unitarization

2. Different slopes of the other contributions

(real part, odderon, spin-flip amplitude)

Dependence of the slope B(s,t) from the size of

the examined interval t for UA4/2 experiment

triangles – exponential form of F

Circles - + additional term in the slope - sqrt(-t) k

O.V.S. Phys.Lett (1994)

Ch II

2 2 2 2

1( ) 1 ( / 32 ) ( );P Pq C q h q

2 2 2 22 3/2

1 2 2

2

2

2

22

( / 4 )

( / 4

1 14( ) [ (1 ) ( ) ( )

1

8;

1 )]

qq mh q Ln L

qn

q q

2 2 2 22 3/2

1 2 2

2

2

2

22

(1 14( ) [ (1 ) ( ) (

4 / )

()

4

8

/];

1 1)

qq mh q L

qqn

qLn

A.A. Anselm, V.N. Gribov, Phys.Lett. 40B, (1972).

V.A. Khoze, A.D. Martin and M.G. Ryskin, J.Phys.G (2014)

2 2

2 2

2

4 ;

8[ ( ) ];

3

q

q mLn

( )( )( , ) ;Ln sb tF s t es

/

0

2

0

2ˆ

s 4 .

/ ;i

p

s s s

m

e

( )( )( , ) ;b n tL sF s t i es

( )( , ) ;( ) b tLn ssF s t e

Regge representation

COMPETE Collaboration Local DDR

( )( )( ) ( ) [ ].

( ) ( )m

EEC EE E dE P

P P E E E E E E

Integral dispersion relations s

2

0

0

Re ( , ) ( ) [ Im ( , ) / Im ( , 0)]Im ( , 0), , (ln( / ) .ln( / )

dF s t F s t F s t F s t as s t s s

s s d

S.M. Roy (2016)

Re ( ,0) ( ) tan[ ( 1 )]Im ( ,0) /( )2p p

E d EF E E F E

m dE m

Im ( , ) ; ( , ) ( , 0)(1. ).BtF s t he s t s t Bt

27

( , )

00

1( , ) ( ) [1 ]

2

h s bF s t b J bq e db

00

( , ) 2 ( ) ( , )h

Bs b q J bq F s q dq

2 21( , ) [ ]

2s b dzV z b

k

UNITARIZATION eikonal representation

( );( , ) ( )Born btLn sF s t s e

Pi-meson cloud

J.Pumplin, G.L. Kane, 1975, Phys.Rev. D11; pi-mezon scattering

O.V.S., S. Goloskokov, 1980, Yad.Fiz. 31, pp-scattering

2 22 2

2 2 3/21

( )( , ) (1 ) );

( 1)! ( ))

bn

n

n thT s t is b n t e

n n t

S.V. Goloskokov, O.V.S., Mod.Phys.Lett. A9 (1994)

Table rho, B 541 and 1800

Seminar in the TOTEM O.V.S. (2009) ; and

J.-R. Cudell, O.V.S. - Phys.Rev.Lett. (2009)

ch II f

/2( , ) ( )4 0.38938

h BttotF s t i e

2/2( , ) ( )4 0.38938

h Bt CttotF s t i e

2( 4 2 )] 2

.( , ) ( ) ( ) ;4 0.38938

D th totemF s t i e f t

/2 ( )( , )4 0.38938

h Bt i ttotF s t h e

2/2 ( 4 2 )]( , ) ( )

4 0.38938

Bt D th totF s t i e

ch III

20.005 | | 0.31 ; 86 .t GeV N

O.V.S., Nucl.Phys. A922 (2014) 180

TOTEM 7TeV

TOTEM 7 TeV

O.S. – J. Nucl.Phys. (Yad.Phys.) v.55 (1992)

2 2

exp.[ |( ) (Im ( ) Im ([Re ( ) Re ( ) )] / ( )] Ch С h

R td

k F t F t kd

F tt

F t

O.S. - New methods for calculating parameters of the diffraction

scattering amplitude, "VI Intern. Conf. On Diffraction...", Blois, France,(1995).

O.S. “Additional ways to determination of structure of high energy elastic scattering

amplitude” arxiv.org:[hep-ph/0104295]

P. Gauron, B. Nicolescu, O.S. “A New Method for the Determination of the Real Part of the

Hadron Elastic Scattering Amplitude at Small Angles and High Energies”

Phys.Lett. B629 (2005) 83-92

n=1. n=0.95

.

TOTEM – arXiv:1503

TOTEM – 12 (2015) CERN preprint

Ch III f

Like TOTEM analysis (N=223, 5 row)

7 8

2

7 8 8 (7) (8)

1

5 1. 1. 1. 1. 1. 0. 96.3 99.2 48212

5 0.93 0.9 0.9 0.045 95.3 98.2 2870.98 1.

1.18 1.2 106.1 1

2

5 1.14 1.1 1.1 0. 09.3025 1508

N

par T T a T b totA A

fix

tot ikn k k

b

kk

Born case:

2 31 2 32 ( /2 ) ( )

( , ) ( ) ( )B t B t B t Ln sh

totF s t h i Ln s e

2 22

1

( ( 4 2 )2 ] ) ( )(( , ) ( )

4 0.38938)

D t Ln sh t CtotF s t i Ln s f t e

2

7 8 8 (7) (8)7 8

3 1. 1. 1. 1. 1. 0.18 96.1 99.0 4774

3 0. 0.93 0.9 0.901 0.198 1 95.7 98.68 1320 7. 2

N

par T T a T b tA ot toA t in k k kk k

2 2( ( 4 2 )] ) ( )1. 24

1( , ) ( ) ( )4 0.38938

D t Ct Ln sh totF s t i Ln s f t e

1.0 1.03 0.95 0.9 0.903 0. 97.1 99.12 12 1311

; ; 22 ˆ( )2

1

( 4 2 )ˆ) (, )(Lnt th

B tot

sF s t h ets f

7 8

8 8

2

7 87(0)

0.09 0.075 1454 97 0.94 1 0.8 6.3 97 0.88.0 7.1 .0 81

par T T a T b tot totA An k k kk k

EIKONAL

2 31 2 3( /2 ) ( )

( , ) ( ) ( )B t B t B t Ln sh

B totF s t h i s e

7 8

2 7 8

7 8 8(0)

0.06 0.076 1797 0.966 1 0.9 0.91 1 96.7 98.5.01 .026 5

par T T a T b tot tA A otn k k kk k

2 determineddoes notC t

; ; 22 ˆ([ (4 2 ) )2

1

]( , ) [ (( 1 )] ;)

Ln

B

sh

t

tt

toF s t h i k t es f t

7 8

7 88 87

2

0

(0)

0.15 332 1.076 11.0.0 .14 1.127 3 95.1.02 37 9 97.fi

T T a T b totA toA

x

tk kk k k

1.0.08 97.10.14 341 1.05 1.11 1.1 0.0 9899 .8fixfix

; ; 22 ˆ( )2

1

( 4 2 )ˆ) (, )(Lnt th

B tot

sF s t h ets f

2 7 8

7 87 88(0)

0.11 3820.087 1.04 0.99 0.7 1.1 1.097 97.7 99.4599

T T a T b toA A t totk kk k k

EIKONALIZATION

2 320.47/2 8.8/2 20/2( , ) (0.9927 0.11915)h t t tF s t a i e

8 102.9tot mb TOTEM 8 TeV

2( ) [Re ( ) Re ( ;)]th h С

R t F t F t 2

exp.[ | * (Im( ) ( ) Im ( )] / ( )Ex

R

Cp hdn k F t F t k

dtt

Empty circles: n=1 Closed circles: n=0.9

dq3b1227

2 22

1

( ( 4 2 )2 ] ) ( )(( , ) ( )

4 0.38938)

D t Ln sh t CtotF s t i Ln s f t e

Final results (or) the beginning new story

* The new data bounded the different models essentially.

LHC

The problems of the determination of

• The thin structure of the slope - B(s,t), (non-exponential, oscillations)

• The term ct^2 mimic the unitarization procedure –> it is better use the

eikonal representation

• The term (or like it) play important value;

• It is need taking into account the form factors of hadrons

• The slope of Re F(s,t) exceeded the slope of Im F(s,t);

• The new LHC data show the problem with the normalization.

Wait the high precision new data at small t and 13 TeV

The new High Energy Generalized Structure model (HEGS) gives the

quantitatively description of the elastic nucleon scattering at high energy

with only 6 fitting high energy parameters. Is is shown the discrepancy

in the normalization of the TOTEM and ATLAS data.

Phenomenological analysis

It is need obtain the data in CNI region.

( ) ( , )tot s and s t

2( 4 )2D t

THANKS For your attention