Bogoliubov Readings Bogoliubov Readings Extra dimensions and - - PowerPoint PPT Presentation

Extra dimensions and Gravitation Potential with taking into account the hadron form-factor

International Workshop International Workshop

“ “Bogoliubov Readings Bogoliubov Readings” ”

Moscow Moscow-

• Dubna

Dubna 22 22-

• 25 September

25 September 2010 2010 O.V. Selyugin O.V. Selyugin (JINR Dubna) (JINR Dubna)

Joint Institut for Nuclear Research

Introduction Coulomb-hadron interference Extra-dimensional gravity (ADD-scenario) Born amplitude and eikonalization Properties of the “oscillation” GPDs and Hadron gravtation form-

factor

Gravitational potential Summary

Elastic scattering am plitude Elastic scattering am plitude

2 2 2 2 2 1 2 3 4 5

2 [| | | | | | | | 4 | | ] d dt σ π = Φ + Φ + Φ + Φ + Φ

1 2

( , ) [ log (B (s,t) | t | / 2 ) ] s t ϕ γ ν ν = + + + m

( , ) ( , ) ( )

h e i i i i

st st t e αϕ Φ = Φ +Φ

pp pp →

pp pp →

( )

0,577...

the Euler constant

γ =

1 2

and are small correction terms

ν ν

3 3

1 2

( , ) [ ( ]

( , )) | |

i

s t log B s t

t

ϕ γ ν

ν

= + +

+

ν1 − 2 second Born approximation (2 photon diagram)

O.V. Selyugin Mod.Phys.Lett. A11, 2317 (1996)

ν2 − 2 second Born approximation (photon-Pomeron

interference with taking into account dipole form-factor of the nucleons)

O.V. Selyugin, Mod.Phys.Lett., A12, 1379, (1997); Phys.Rev. D60, 074028 (1999)

Re ( , ) ( , ) ; Im ( , )

N N

F s t s t F s t ρ =

| Im ( ( , ) )

Interference C h

d F F s t dt σ ρ αϕ + ฀

( ) ( ) ( ) ( ) [ ]. ( ) ( )

m

E E C E E E dE P P P E E E E E E σ σ ρ σ π

∞ ± ± ±

′ ′ ′ ′ = + − ′ ′ ′ ′ − +

∫

m

The The ρ ρ parameter parameter J.-R. Cudell, O.Selyugin

Phys.Rev.Lett. 102, 032003, (2009) linked to σtot via dispersion relations sensitive to σtot beyond the energy at which is measured

predictions of σtot beyond LHC energies Or, are dispersion relations still valid at LHC energies?

2 2 ;

( / )( , ) [Re ( ) Re ( , ) Re ( , )] [Im ( ) Im ( , ) Im ( , )]

C N

• sc

C N

• sc

d dt s t F t F s t F s t F t F s t F s t σ + + + + ฀

If the additional amplitude is almost REAL

;

( / ) ( , ) {2Re Im ( ( , ) sin[ ( ( ) ( , ))]} 2Re ( , )[Re ( ) ( , )Im ( , )]

ad C N em c ad C N CN

d dt s t F F s t t s F s t F t s t F s t t σ ρ α ϕ ϕ ρ + Δ + + + ฀

;

( / ) ( , ) {2Re Im ( ( , ) sin[ ( ( ) ( , ))]} 2Im ( , )[Re ( )sin[ ( ( ) ( , ))] Im ( , )] 2Re ( , )[[Re ( )cos[ ( ( ) ( , ))] ( , )Im ( , )]

ad C N em c CN

• sc

C em c CN N

• sc

C em c CN N

d dt s t F F s t t s t F s t F t t s t F s t F s t F t t s t s t F s t σ ρ α ϕ ϕ α ϕ ϕ α ϕ ϕ ρ Δ ≈ + + + + + + +

Extra dim ensions Extra dim ensions {x1,x2,x3}+1(circle with small radius R)

Large extra dim ensions Large extra dim ensions

Kaluza Kaluza -

• Klein tow er

Klein tow er

Arkani Arkani-

• Ham ed, Dim opoulos, Dvali

Ham ed, Dim opoulos, Dvali

ADD scenario

[Cylinder homogeneous and metric flat neglect tension of brane]

• N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys.Lett., B 429 (998) 263;

Phys.Rev., 59 (1999) 0860004.

• G.F. Giudice, R.Rattazzi and J.D.Wells Nucl.Phys., B 544 (1999) ;
• Nucl.Phys., B 630 (2002) ;
• R. Emparan, Phys.Rev. D64 (2001);
• R. Emparan, M. Masir, R. Ratttazzi , Phys.Rev. D65 (2002);
• I. Ya, Aref’eva, arXiv: 1007.4777.
• T. Han, J.Lykken, and R.-J. Zhng, Phys.Rev 59 (1999) 105006.

2/ 1 32/ 17 (4 ) (4 )

10 10

d d Pl d d d

M r M cm M

− − + +

⎛ ⎞ = × ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ฀

2 2 (4) (4 ) d d d d

M r M

+ +

=

2 d =

4 2

1 M TeV

+ =

r2 = 0. 1mm

Virtual graviton exchange Virtual graviton exchange

1 1 / 2 grav. 2 2 2

1 A ( ) csc( ) 2 2

d d T T T

• q

dq d q q q π π

∞ − −

= + ⌠ ⎮ ⌡ ฀

max

2 1 grav. 2 1 2 2 2 2

1 A [1, , 1 , ] 2 2

q d d s s T T T

M M q dq d d F q q d q q

−

= + − + ⌠ ⎮ ⌡ ฀

d continuous

Born am plitude Born am plitude d = 2

2 2 2 Born 2 grav. 4 2 2 4 4

A ( ) [1 ln(1 )]

d d s s d d s

S s M q M M M M q

− + +

= − +

d = 4

2 Born 2 grav. 4 4 4

A ( ) [1 ( )]

d d s d d s

S s M q M ArcTan M M M q

− + +

= −

d = 3

2 2 Born grav. 4 2 4 2

A ln (1 )

s

M s M q π

+

= +

/ 2

2 ( / 2)

d d

S d π = Γ O.V. Selyugin, O.V. Teryaev, Phys.Rev. D 85, (2009)

Ag

Born as a function of the upper limit – k Ms

Extra dimensions d = 2, 3, 4

I m pact param eter representation ( d= 2 ) I m pact param eter representation ( d= 2 )

( , ) 2 ( ) ( , )

B

s b q J bq T s q dq χ π

∞

=

∫

(d= 2) (d= 2)

2 1 4

( , ) (1 ( )] /

s s d

S s b b M K b M b M χ − ฀

( , )

1 ( , ) ( ) [1 ] 2

s b

T s t b J b q e db

χ

π

∞ −

= −

∫

Gravi Gravi-

• potential ( d= 2 )

potential ( d= 2 )

3

1 ( ) (1 )

s s

M r M r s

V r e M re r

−

− − ฀

2 2

2 ( , ) ( )

r

d b s b V r db r dr b r χ π

∞

= − −

∫

Experim ental data UA4 / 2 Experim ental data UA4 / 2

I.Ya. Aref’eva - arXiv:1007.4777

( ) ( ) [ 1]

n

ix n

F y i x J xy e dx

−

∞

= − −

∫

1/ /2 1 2

(4 ) ( / 2) 2

n n c n d

s n b M π

− +

⎡ ⎤ Γ = ⎢ ⎥ ⎣ ⎦ ;

c

y b q = / ;

c

x b b =

Screening long range potential Screening long range potential – – ( rigid string) ( rigid string)

( , ) ( ) ( , ) exp[ ( , )])

• sc
• sc

T s t is b db J bq s b s b χ χ

∞

= −

∫

1

1 ( , ) ( ); 2

• sc

scr scr

iq T s t K i r q r =

2 2

/( )

( , ) [1 ];

scr

h b r

• sc s b

e χ

− −

= −

2 2 2

( ) ( , ) ; ( )

• sc
• sc

scr

h s s b r b χ = −

Nucleon-Gravitation Interaction (Gravitation form-factors)

( )

2 0.4

(1 ) , ( )ex ; p[ ]

q

x x t q x a t x

+

− ฀ H

O.V. Selyugin, O.V. Teryaev, Phys.Rev. D 85, (2009)

( )

2 0.4

(1 ) , ( )exp[ ];

q q

x E x t x a t x ε

−

− ฀

( ) ( )

1 2 2 1

[ , , , , ] ( ) ( ) ;

q q q q

dx x H x t E x t A B ξ ξ

−

+ = Δ + Δ

∫

( )

1 1 1

( ) , , ;

q q

F t dx H x t ξ

−

=∫

( )

1 2 1

( ) , , ;

q q

F t dx E x t ξ

−

=∫

Nucleon-Gravitation Interaction

2 2 2 2

( ) 1 / [1 / ] ; 1.8 . G t t GeV = − Λ Λ =

2 2 Born 2 grav. 4 2 4 2

A ln (1 ) ( )

s

s M G t M q π

+

= + %

. 3

1 ( ) 1 (1 (18 (9 ))) . 18

Born r grav

r V r r r e r

− Λ

Λ ⎛ ⎞ = − + + Λ + Λ ⎜ ⎟ ⎝ ⎠ %

O.V. Selyugin, O.V. Teryaev, Found.Phys. V.40(7),(2010)

2 2 2 3 3 2 . 3 2

( ) ~ ( ) log( ) ( ) ( ) log( ); 48

s grav s

M b q J qb G t b K b M q χ

∞

Λ = Λ Λ

∫

2 5 3 4 . 3 4 4 1.5

log( ) 1 5 1 ( ) ( ) (1 ) . 1.4 48 2.2 10 2(1 )

s grav s

s M b b b K b M b b χ ⎡ ⎤ Λ + = Λ + + ⎢ ⎥ ⋅ + + ⎣ ⎦ %

Impact gravitation contribution (d=2)

• n spin correlation parameter

* 1 2 3 4 5 2

4 Im[( ( , ) ( , ) ( , ) ( , )) ( , )]

N

d A s t s t s t s t s t dt s σ π = Φ + Φ + Φ − Φ Φ

* 2

4 Im [ ]

N nfl fl

d A F F dt s σ π =

* 1 2 2

4 | || | sin( )

N nfl fl

d A F F dt s σ π ϕ ϕ = −

N

d d A d d σ σ σ σ ↑ − ↓ = ↑ + ↓

SUMMARY SUMMARY

* The additional dimension d=2 do not contradict the existence

experimental data.

* The gravitatin hadron form-factor can be obtained from GPDs

• f hadron. It leads to changing of gravitation potential on the

distances order the hadron size. It is need take into account when the Black Hole production is examined.

SUMMARY SUMMARY

* The long range potential can be leads to the some

periodic structure in the hadron differential cross sections.

* We find that with d=2 in the framework of ADD scenario there

is the manifestation of the additional dimensions as the specific behaviour of the analyzing power of the hadron-hadron scattering.

* It is need research these and other effects in the universal

scenario where the all filds can be live in the extra dimentions.

THE END THE END Thanks for your Thanks for your attention attention

Proton - Del = (F1_em – A_gr)

Newton case (N= 4) Newton case (N= 4)

5 1/ 2 33

[ ] 10 8

Pl N

c l cm Planck length G π

−

= − h ฀

1 2 1 2 2 2 2

1 ( ) .

N Pl

m m m m F r G r M r = =

19

1.22 10

Pl N

hc M GeV Planck mass G = = × −

GN ´= 10 ´-39 GeV

4. N-dimensional gravipotential (ADD-model) Oscillations”- I. Aref’eva [1007.4777:arXiv-hep-ph]

• 2. a) Van-der-Waals potential Vad ~

h/r4

• 3. S-L interaction

( , ) 2

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

c s b

C ad LS

F s t F s t is b db J bq e s b

χ

χ

∞

+ = − +

∫

• K. Chadan, A. Martin: “Scattering theory and dispersion relations for a class
• f long-range oscillating potentials”, CERN (1979)

2 2

( ) sin[exp( )]/ (1 ) ; V r r r µ + ฀

2

( , ) ;

ad d

s F s t M ฀

b) F. Ferrer, M. Nowakowski (1998) (Golstoun boson – long range forces) Vad ~ h/r3

Universal scenario?

• A. De Rujula , arXiv:1008.3861

3 1/3 (2)

[ ] 3.32 0.22 ; .

p

r fm = ±

critic: I. Cloet, G.A. Miller arXiv: 1008.4345

Literature Literature

1. T.Kaluza, Sitz. Preuss. Akad. K1, 966 (1921); O.Klein, Zeit. F.Phys, 37, 895 (1926); 2. M.J.Duff, B.E.W. Nilsson and C.N.Pope, Phys.Rep. 130,1 (1986); T.Appelquist, A. Chodos and P.G.O. Freund (Ed.), Modern Kaluza-Klein Theories, Addison-Wesley (1987) 3. E.Witten, Nucl.Phys. B186, 412 (1981); A.Salam and J. Strathdee, Ann.Phys.(N.Y.) 141, 316(1982) 7.

• N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys.Lett., B 429 (998) 263;

Phys.Rev., 59 (1999) 0860004. . L. Randal, and R. Sandrum, Phys. Lett., 83 (1999) 3370, 4690. 8. V.A. Rubakov, Phys. Usp. 44 (20001) 871. . V.A. Perez-Lorenzana, hep-ph/0503177

• G.F. Giudice, R.Rattazzi and J.D.Wells Nucl.Phys., 544 (1999) 3.
• . D59 (1999) 105002
• T. Han, J.Lykken, and R.-J. Zhng, Phys.Rev 59 (1999) 105006.

1 2 (4 ) (4 ) 2

( ) .

d N d d

m m F r G r

+ + +

=

(4 ) 3

4

d N d N d

V G G S π

+ +

=

is the volume of compactified dimensions

Vd

2 2 (4 ) (4) / d d

M M V

+

=

(4 ) (2 ) 3 (4 )

1

N d d d d

G S M

+ + + +

=

1. The N-dimensional word manifests itself as a difference in the inverts power of the radius 1/r^d

Kaluza Kaluza -

• Klein picture

Klein picture

From 4-n point o view - (4+d) g (q1, q2, …qd ) looks like a massive particle of mass |q| + Yukawa potentials mediated by all the massive modes

for r >> L

(4) 1 1 2

( ) ( ) (2 )

N d d d d

G V S d V r m m r π

+

Γ = = ( )d

KK d

N s r ฀

2 .

1

grav d Pl KK

A G M N s

−

฀ ฀

2 2 2 2 4 4

( ) ( )

d d Pl d d d Pl d

s M s M M M

+ + + +

= =