(Universal Characteristic )

Transcription

1 Tishreen University Journal for Research and Scientific Studies - Basic Sciences Series Vol. No. (Trimer) He Efimov (Universal Characteristic ) (renormalization ) ١٩٥

2 Tishreen University Journal for Research and Scientific Studies - Basic Sciences Series Vol. No. Studying the Three-Body Problem in the Effective Quantum Field Theory by using the Monte Carlo Method Dr. Hasan Salman * Dr. Taiseir Moala * Samer Sayid (Received ٢٥ / ٣ / ٢٠٠٨. Accepted ١٩/٥/٢٠٠٨) ABSTRACT This research is concerned with Efimov states of helium trimer He ; these states have universal characteristics displaying the interaction of three bodies at low energy, where the scattering length is greater than the range of interaction. The mathematical theory used in this study is the effective quantum field theory, which physically says that we do not need to know the physics of high energy in order to study low energy physics. This theory enables us to get rid of the infinites by introducing the renormalization function. The numerical solution to integral equations has been carried out by using the Monte Carlo method. Keywords: effective quantum field theory, renormalization, Monte Carlo method, random variable, integral equation. * Professor, Physics Department, Faculty of Science, Tishreen University, Lattakia, Syria. **Professor, Physics Department, Faculty of Science, Tishreen University, Lattakia, Syria. ***Postgraduate Student, Physics Department, Faculty of Science, Tishreen University, Lattakia, Syria. ١٩٦

3 Tishreen University Journal. Bas Sciences Series (Effective Quantum Field Theory ) QCD (Chromodynamic) QCD QCD (underlying theory ) (next to leading order) (Leading order ) QCD R R r m A a ( Shallow bound state ) He ١٩٧

4 Λ r s A (Path Integrales) ( He ) a A (S Wave bound sates) Bedaque, Hammer, and Kolck Wilson NLO LO (Dimensional Analysis ) ( He ) Efimov ١٩٨

5 Tishreen University Journal. Bas Sciences Series g g B Λ v v v, g B ١٩٩

6 ٢٠٠

7 Tishreen University Journal. Bas Sciences Series ri ( r1, r2, r3 ), pi ( p1, p2, p3 ) P 1 P2 P3 0 ٢٠١

8 . 3 I 1 P 0 ٢٠٢

9 Sciences Series Tishreen University Journal. Bas ٢٠٣ ( p ) ),, ( p p p ),, ( p p p p q q 2 1 D E q q U q d g E D ) ( ) ( p q q

10 1 U,U (Perturbative Uniform Expansion p q pqz Λ Method ) ٢٠٤

11 Tishreen University Journal. Bas Sciences Series p /Λ, η/p, η/λ, p/λ p ~ η «Λ f l (p,η,λ) f h (p,η,λ) η/p, η/λ η «p «Λ 2 O( 2 ) η «Λ~p f d (p,η,λ) η/λ 3 3 ٢٠٥

12 η/q, O(η /Λ ) (η/p)(p/q)=(η/q), (q/λ) (η/p) O(η /Λ ) (q/λ) (η/p) p q η/λ η/λ, p/λ (η/p)(p/q)(q/λ)=(q/λ) p=q ٢٠٦

13 Tishreen University Journal. Bas Sciences Series (Next (Leading order ) D(P) O(( ) ) η to-leading order ) O D h (p) D L (p) 1 O(( ) ) p D (p) n (n) p G n ٢٠٧

14 G 2 3 2, G2, D( 3 p ), D1 ( p) 2 D(p) u,, p, q, ) dq ( 2 3 ٢٠٨

15 Tishreen University Journal. Bas Sciences Series ( ) D NLO LO ٢٠٩

16 D (P) u ٢١٠

17 Tishreen University Journal. Bas Sciences Series NLO LO ٢١١

18 Q ٢١٢

19 Tishreen University Journal. Bas Sciences Series NLO LO f l O O η/λ D l /D l ٢١٣

20 cos( 0 ln( p )) f d f l p»(η, η ) f d f h p«λ B,B Λ f d f h θ l δ Λ Λ, δ θ h l0 δ ho n n δ θ G B f h f l ٢١٤

21 Tishreen University Journal. Bas Sciences Series J ε J 1 n (... ) 1 2 n J ( ) r n x0.5 n x = 1 Pr n J rn 2 D(ε) r n =σ(ε) Pr Neumann Series ( I ( J) J ) Importance Separation for Integrals G l M G[a,b] f F( t) dt ٢١٥

22 θ* N (j) E G i V(G i ) (Shallowest bound state ) Λ B B ٢١٦

23 Tishreen University Journal. Bas Sciences Series mk mk Bedaque Eric Braaten and H.W. Hammer mk= μev Bedaque He and Hammer - WEINBERG, S. The Quantum Theory Of Fields, Cambridge University Press, United States Of America,. - WALECK, A, DRIK, J. Theortical Nuclear and Subnuclear Physics. World Scientific.. - WEINBERG, S. Nucleon Nucleon potential from an effective chiral lagrangian. Phys. Lett B. Vol.,, pp.. - Aitchison, I, Gauge Theories In Particle Physics, University Press, Lodon,. - FRIES, D.C. Quarks and nuclear forces. Springer-Verlag, Berlin,. - MARTINE, J. Effective Field Theory For Nuclear Physics. Nuclear Physics A,, pp-. - ROUDNEV, V. Investigation Of He Trimer On The Base Of Faddeev Equation Equation In Configuration Space, Chemical Physics Letters,,, pp-. - PROCEEDUNGS OF THE NINTH EUROPEAN CONFERENCE. Few Body Problem in Physics., Tbilisi, Georgia. - BEDAQUE, P. The Three Boson System With Short Range Interactions, Nuclear Physics A,,, PP.. - KAZAKER, D. Particle Physics Beyond The Standard Model, Elsevier, Amesterdam,. - COTTINGHAM, W. An Introduction To Standard Model Of Paricle Physics, University Press,. - Parameswarna, V. Quantum Field Theory, Springer,. ٢١٧

24 - ARFKEN, G. Mathematical Methods For Physicists, Harcourt Press USA,. - TAO, P. An Introduction To Computational Physics. Cambridge university Press.. - SCHWEIZER, W. Numerical quantum dynamics. Kluwear academic publishers.. - LANDAU, R. Computational Physics. John Wiley,. - PRESS, W. Numerical Recipes in C. Cambridge university Press.. - HAMMER, H. The Four Boson System With Short Range Interaction, Phys.Rev A,, Issue,. ٢١٨

25 Tishreen University Journal. Bas Sciences Series ٢١٩