Bogoliubov Readings Bogoliubov Readings Extra dimensions and - PowerPoint PPT Presentation

Joint Institut for Nuclear Research Moscow Moscow- -Dubna Dubna 22- -25 September 25 September 22 2010 International Workshop 2010 International Workshop “ Bogoliubov Readings Bogoliubov Readings” ” “ Extra dimensions and Gravitation Potential with taking into account the hadron form-factor O.V. Selyugin (JINR Dubna) (JINR Dubna) O.V. Selyugin

� 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 → → pp pp pp pp σ d = π Φ 2 + Φ 2 + Φ 2 + Φ 2 + Φ 2 2 [| | | | | | | | 4 | | ] 1 2 3 4 5 dt t e αϕ Φ = Φ +Φ h e i ( , ) ( , ) ( ) st st i i i ϕ = γ + + ν + ν m ( , ) [ log (B (s,t) | t | / 2 ) ] s t 1 2 γ = ν ν 0,577... ( ) the Euler constant and are small correction terms 1 2 3 3

( , )) log B s t + ν ϕ = + γ + ν ( , ) [ ( ] s t 1 2 i | | t ν 1 − 2 second Born approximation (2 photon diagram) O.V. Selyugin Mod.Phys.Lett. A11, 2317 (1996) ν 2 − 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)

ρ parameter The ρ parameter The Re ( , ) F s t ρ = N ( , ) ; s t Im ( , ) F s t N linked to σ tot via dispersion relations sensitive to σ tot beyond the energy at which is measured σ d ρ + αϕ ฀ | Im ( ( , ) ) F F s t Interference C h dt ∞ ′ σ ′ σ ( ) ( ) E C E E ∫ ′ ′ ρ σ = + ± − m ( ) ( ) [ ]. E E dE P ± ± ′ ′ ′ ′ π − + ( ) ( ) P P E E E E E E m predictions of σ tot beyond LHC energies J.-R. Cudell, O.Selyugin Or, are dispersion relations still valid at LHC Phys.Rev.Lett. 102, 032003, (2009) energies?

If the additional amplitude is almost REAL σ + + 2 ฀ ( / )( , ) [Re ( ) Re ( , ) Re ( , )] d dt s t F t F s t F s t C N osc 2 ; + + [Im ( ) Im ( , ) Im ( , )] F t F s t F s t C N osc Δ σ ≈ ( / ) ( , ) d dt s t ad ρ + α ϕ + ϕ {2Re Im ( ( , ) sin[ ( ( ) ( , ))]} F F s t t s t C N em c CN α ϕ + ϕ + + 2Im ( , )[Re ( )sin[ ( ( ) ( , ))] Im ( , )] F s t F t t s t F s t osc C em c CN N α ϕ + ϕ + ρ 2Re ( , )[[Re ( )cos[ ( ( ) ( , ))] ( , )Im ( , )] F s t F t t s t s t F s t ; osc C em c CN N Δ σ ฀ ( / ) ( , ) d dt s t ad ρ + α ϕ + ϕ + {2Re Im ( ( , ) sin[ ( ( ) ( , ))]} F F s t t s t C N em c CN + ρ 2Re ( , )[Re ( ) ( , )Im ( , )] F s t F t s t F s t ; ad C N

Extra dim ensions Extra dim ensions {x 1 ,x 2 ,x 3 }+1(circle with small radius R)

Large extra dim ensions Large extra dim ensions

Kaluza - - Klein tow er Klein tow er Kaluza

Arkani- - Ham ed, Dim opoulos, Dvali Ham ed, Dim opoulos, Dvali Arkani 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) ; • T. Han, J.Lykken, and R.-J. Zhng, Phys.Rev 59 (1999) 105006. • R. Emparan, Phys.Rev. D64 (2001); • R. Emparan, M. Masir, R. Ratttazzi , Phys.Rev. D65 (2002); I. Ya, Aref’eva, arXiv: 1007.4777.

+ = 2 2 d d M r M + (4) (4 ) d d 2/ d ⎛ ⎞ M − − = × 1 ⎜ ⎟ 32/ 17 d Pl ฀ 10 10 r M cm ⎜ ⎟ + (4 ) d d M ⎝ ⎠ + (4 ) d + = d = 1 M TeV 2 4 2 r 2 = 0. 1mm

Virtual graviton exchange Virtual graviton exchange d continuous ∞ ⌠ − π π 1 d 1 q dq − = 1 / 2 d ฀ T T A ⎮ ( ) csc( ) d grav. + ⌡ 2 2 2 2 2 q q q T o q ⌠ − 1 2 max d d 1 q dq M d d M = + − ฀ T T s s A ⎮ [1, , 1 , ] F grav. 2 1 + 2 2 2 2 ⌡ 2 2 q q d q q 0 T

Born am plitude Born am plitude O.V. Selyugin, O.V. Teryaev , Phys.Rev. D 85, (2009) π 2 2 M s = + Born s A ln (1 ) d = 2 grav. 4 2 M q + 4 2 2 S s M q M − Born = 2 − d A d ( s ) [1 ( )] ArcTan d = 3 grav. 4 M M M q + + 4 4 d d s 2 2 2 S s M q M − = − + Born 2 d A d ( s ) [1 ln(1 s )] d = 4 grav. 4 2 2 M M M q + + 4 4 d d s π / 2 d 2 = Γ S d ( / 2) d

Born as a function of the upper limit – k M s A g Extra dimensions d = 2, 3, 4

I m pact param eter representation ( d= 2 ) I m pact param eter representation ( d= 2 ) 1 ∞ ∫ − χ = − ( , ) s b ( , ) ( ) [1 ] T s t b J b q e db 0 π 2 0 ∞ ∫ χ = π ( , ) 2 ( ) ( , ) s b q J bq T s q dq 0 B 0 (d= 2) (d= 2) S χ − 2 ฀ ( , ) (1 ( )] / s b b M K b M b 1 4 s s M d

Gravi- - potential ( d= 2 ) potential ( d= 2 ) Gravi χ 2 ( , ) d b s b ∞ ∫ = − ( ) V r db π − r dr 2 2 r b r 1 − − − M r M r ฀ ( ) (1 ) V r e M re s s s 3 r

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

I.Ya. Aref’eva - arXiv:1007.4777 ∞ ∫ − n = − − ix ( ) ( ) [ 1] F y i x J xy e dx 0 n 0 = = ; / ; y b q x b b c c 1/ n ⎡ ⎤ − π Γ n /2 1 (4 ) ( / 2) s n = ⎢ b ⎥ + c n 2 ⎣ 2 ⎦ M d

Screening long range potential – – Screening long range potential ( rigid string) ( rigid string) ∞ ∫ = χ − χ ( , ) ( ) ( , ) exp[ ( , )]) T s t is b db J bq s b s b osc 0 osc 0 ( ) 2 2 h s − − χ = − /( ) h b r ( , ) [1 ]; osc s b e scr χ = osc ( , ) ; s b osc 2 − 2 2 ( ) r b scr 1 iq = ( , ) ( ); T s t K i r q 1 osc scr 2 r scr

Nucleon-Gravitation Interaction (Gravitation form-factors) O.V. Selyugin, O.V. Teryaev , Phys.Rev. D 85, (2009) − 2 (1 ) x ( ) q ฀ H , ( )ex p[ ] ; x t q x a t + 0.4 x − 2 (1 ) x ( ) ε q q ฀ , ( )exp[ ]; E x t x a t − 0.4 x 1 1 = ∫ = ∫ ( ) ( ) ξ ξ q q q q ( ) , , ; ( ) , , ; F t dx H x t F t dx E x t 1 2 − − 1 1 1 ∫ ( ) ( ) ξ + ξ = Δ + Δ 2 2 q q [ , , , , ] ( ) ( ) ; dx x H x t E x t A B q q − 1

Nucleon-Gravitation Interaction O.V. Selyugin, O.V. Teryaev , Found.Phys. V.40(7),(2010) = − Λ 2 2 Λ = 2 2 ( ) 1 / [1 / ] ; 1.8 . G t t GeV π 2 2 s M % = + Born 2 A ln (1 s ) ( ) G t grav. 4 2 M q + 4 2 ⎛ Λ ⎞ 1 r % − Λ = − + + Λ + Λ Born r ( ) ⎜ 1 (1 (18 (9 ))) ⎟ . V r r r e . grav 3 ⎝ ⎠ 18 r

∞ Λ 2 2 M ∫ χ 2 = Λ 3 3 Λ 2 ( ) ~ ( ) log( s ) ( ) ( ) log( ); b q J qb G t b K b M grav . 0 3 s 2 48 q 0 ⎡ ⎤ 2 Λ 5 3 + 4 log( ) 1 5 1 s M b b χ = Λ + + % s ( ) ( ) (1 ) . b ⎢ K b ⎥ . 3 grav ⋅ + + 4 4 1.5 ⎣ 1.4 48 2.2 10 2(1 ) ⎦ M b b s

Impact gravitation contribution (d=2) on spin correlation parameter σ ↑ − σ ↓ d d = A N σ ↑ + σ ↓ d d σ π 4 d = Φ + Φ + Φ − Φ Φ * Im[( ( , ) ( , ) ( , ) ( , )) ( , )] A s t s t s t s t s t 1 2 3 4 5 N 2 dt s σ π 4 d = * Im [ ] A F F N 2 nfl fl dt s σ π 4 d = * ϕ − ϕ | || | sin( ) A F F N nfl fl 1 2 2 dt s

SUMMARY SUMMARY * The additional dimension d=2 do not contradict the existence experimental data. * The gravitatin hadron form-factor can be obtained from GPDs of 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) 1 m m m m = = 1 2 1 2 ( ) . F r G N 2 2 2 r M r Pl G N ´ = 10 ´-39 GeV hc = = × − 19 1.22 10 M GeV Planck mass Pl G N 5 h c − = − 1/ 2 33 ฀ [ ] 10 l cm Planck length Pl π 8 G N