Parametrización del comportamiento de la sección eficaz total en colisiones Hadrónicas
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(2) PARAMETRIZACIÓN DEL COMPORTAMIENTO DE LA SECCIÓN EFICAZ TOTAL EN COLISIONES HADRÓNICAS. CARLOS ALBERTO SANABRIA. Monografía para optar al título de Físico. Director CARLOS ARTURO ÁVILA, PhD.. UNIVERSIDAD DE LOS ANDES FACULTAD DE CIENCIAS DEPARTAMENTO DE FÍSICA BOGOTÁ 2004.
(3) a D.M.G.L, por su fe en mí.
(4) "Science has 'explained' nothing; the more we know the more fantastic the world becomes and the profounder the surrounding darkness." — Aldous Huxley.
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(9) . . . 2 0 % K + p K − p > =" √s > 8 GeV 2 2 % π+ p π − p > =" √s > 8 GeV 2 , % pp pp √s > 8 GeV 2 < % K + p K −p √s > 8 GeV 2 . % π+ p π− p √s > 8 GeV 2 / ' 2 )1 % 8? ? √? ? 9 s > 8 GeV ; ' 2 )) ' pp pp > $.)) √s > 8 GeV 2 )- ' K +p K − p > $.)) √s > 8 GeV 2 )( ' π+ p π − p > $.)) √s > 8 GeV 2 )0 ' pp pp √s > 8 GeV 2 )2 ' K + p K −p √s > 8 GeV 2 ), ' π+ p π− p √s > 8 GeV 2 )< $ √s > 5 GeV @ . 2. (. (/ 01 0) 002. 0< 21 2) 22( 20 22. 2..
(10) . . . ,. 2 ). ' pp pp > =" √s > 8 GeV 2/.
(11) 2 ) A > 2 - A > 2 ( % & 2 0 % & 2 2 % & 2 , % & $<)1B$.)) 2 < χ2 /d.o.f. % 2 . % σtot & % 2 / % ρ & % 2 )1 ' & ; 2 )) ' & ; 2 )- ' & ; 2 )( ' & ; $<)1B$.)) 2 )0 χ2 /d.o.f. ' 2 )2 % σtot & ' 2 ), % ρ & ' <. -/ (1 (( (( (0 (0 (2 0( 0( 0, 0. 0. 0/ 0/ 2, 2<.
(12) % 4 ; + > > + + C D E + + C+ D = C D ' @ 5 + + 5 + + $ ; ? ; 8 9F + 8 9F + ; @ 8 α 9 $ + ; + ..
(13) . . . . 8pp9 G 8Kp) 8πp9 . /.
(14) . . . + ; 8 > 9 $ & α ; $ + ; + + H(I 8 9 + H-I $ G ; $ 5 ; ; )1.
(15) . . . . . . . . . 8 9 " : ' 8" 9 /.1 !A ) . *A $ ; '7 8 9 $ : $ '7 5 . ,2* < *A ; )0 *A % & -< G '$% > $ '$% @ ; > + 3×105 $ '7 ; $ 5 > ' 5 - ) $ '7 + )-/, 2)1 J '$% ; ) ( *A * 5 '7 ))0. *A J :> ' 8:'9 4 ' 84' 9 E 4 " : ' ; 8" 9 ' K ' : ' 8'':'9 ' K #G : ' 8'#:'9 7 $ ' 8L$L9 $ :' @ 1 2 *A ; ) 2 *AF + (1 L + . )).
(16) . . . . . . . . . " - )? 4 + '7. )-.
(17) . . . . . . . . . 8 9 8 - -9 $ + = $ 8$ 4' > ( L :' + )2 L 9 8 - (9 E G (11 6M (11 :' % - 0 . " - (? % . " - 0? $ 8 4' 9 $ 8 9 . )(.
(18) . . . . . . . " - -? $ :'. . . )0.
(19) . . . . . . . . . > $ 5 . )2.
(20) . $ + 8θ9 8b9 8 ( )9 $ + + + % + dσ + + dΩ 8 ( -9 $ + + dσ + + + dΩ . " ( )? % + b + θ + ),.
(21) . . . " ( -? ' + dΩ D(θ). )<. . dσ . + . ? D(θ) ≡. dσ dΩ. $ 5 + b + θ ? b db D(θ) = sin(θ) dθ . $ 4 D D + + C D N = + + dΩ ? σtot =. D(θ)dΩ. ' C D 8 ; 9 C DF ½ ½ .
(22) . . . ).. . " ( (? = 5 . . . 3 5 z 8 ( (9 ' + 5 . . ψi (z) = Aeikz 5 + ' + ? eikr ikr ψ(r) = A e + f (θ) r. N ¾? S=. 1 [ψ ∗ ψ − (ψ ∗ )ψ] 2im. ?. 2. S = (A). 2. kẑ |f (θ)| k + m r2 m. . ẑ ; > = ¾ . .
(23) . . . . )/. ? dσ. =. D(θ). =. D(θ)dΩ = f (0)2 . S(θ)r2 dΩ S(θ) · dA = |S(0)| |S(0)|. f (θ) ; + θ . . . 8A899 5 5 4O ? ψ(r, θ, φ) = R(r)Ylm (θ, φ). Ylm (θ, φ) 5 u(r) = rR(r) ? 2 −. 1 d u 1 l(l + 1) + V (r) + u = Eu 2 2m dr 2m r2. 5 ? d2 u ≈ −k 2 u dr2. > +? u(r). =. Ceikr. R(r). ≈. eikr r. . $ 5 ? d2 u l(l + 1) − u = −k 2 u dr2 r2.
(24) . . . -1. . +? (1). R(r) = Chl (kr). h(1) 7G ¿ = l ⎡. ⎤ (1). ψ(r, θ, φ) = A ⎣eikz + l,m. Cl,m hl (kr)Ylm (θ, φ)⎦. P ψ(r, θ) = A e. ikz. ∞. . + l=0. 2l + 1 (1) Cl hl (kr)Pl (cos θ) 4π. +? 1 f (θ) = k. . ∞. l+1. (−i) l=0. ? σ=. 1 k2. ∞. 2l + 1 Cl Pl (cos θ) 4π. 2. |Cl | l=0. 4 . ' 89 . ?. $ −α |f (z)| ≤ O |z| |z| → ∞ & α>0 f (z ∗ ) = f ∗ (z). 89 > jl nl . ¿ h(1) ≡ j (x) + in (x) l l l.
(25) . . . -). . 89 + z = R + iε z = −R + iε ? 1 f (z) = 2πi. c. f (z )dz z − z. E z = x + iε f (x + iε) =. 1 2πi. . R. −R. 1 f (x + iε)dx + x − x − iε 2πi. S(R). f (z )dz z − x − iε. 48 9 r → ∞ $ f (x) =. 1 2πi. . ∞. −∞. f (x + iε)dx x − x − iε. $ 89 ' 89 f (polos) (z) = n. Xn z − xn. xn Xn E P 1 = ∓ iπδ(x − x) x − x ± iε x −x. f (x). =. 1 −iπ 2πi. = n. Xn + iπf (x) + P x n−x n ∞ Xn f (x )dx 1 + P x − xn πi −∞ x − x. . ∞. −∞. f (x )dx x − x. " > ? e{f (x)} m{f (x)}. 1 Xn m{f (x )}dx + P x − xn π x − x cortes n ∞ m{f (x )}dx 1 = − P π x − x −∞. =. .
(26) . . . . --. $ 89 . ' s → ∞ 5 + & (). s → ∞ ; ; σ̄tot (s) →1 σtot (s). ' * . $ s → ∞ + σtot (s) ≤ mπ . π ln2 (s) ≤ (60mb) ln2 (s) m2π. )(/ 2< !A . . H),I σtot (s) =. m{Ah1 h2 (s)} 2mE. s → ∞ ? σtot (s) =. m{Ah1 h2 (s)} s.
(27) . . = ; ? ) $ √s + . . - ' ; ( $ ; lnγ (s) " 8γ ≤ 29 . . . $ > 5 > 8 C D 9 + + > + ; + -(.
(28) . . . . . -0. " 0 )? = > + + + 5 $ > + 0 - $ ? χ2 =. . yi − f (xi ) ξi. 2. $ yi > f (xi ) + + ξi ' χ2 5 χ2 H2 <2/I yi f (xi ) ξi = f (xi ) > + aj 8 ; + 9 + % + ? ∂χ2 =0 ∂aj. $ 5 .
(29) . . . . -2. . Sección eficaz total σ Bajas energias. σ (mb). Rayos cosmicos. Tevatron. 100. pp pp-. Altas energias. 0. 10. 1. 10. 2. 10. 3. 10 √s (GeV). 4. 10. 5. 10. 6. 10. " 0 -? 6 > σtot. 0 ) "J * : <<½ ' 5 χ2 + 63:E3* 8 /0 )9 = $ : $ H0I ": "J * : << $ 0 ( @ > 0 0 @ ½ !"#"$% & .
(30) . . . . . " 0 (? $ . " 0 0? $ . -,.
(31) . . . . -<. . % 8σtot 9 ? m{Ah1 h2 (s)} s. σtot (s) =. % ρ ? ρ(s) ≡. e{Ah1 h2 (s)} m{Ah1 h2 (s)}. $ s Ah h (s) h1 h2 = σtot ρ +? 1. 2. ∂σtot (s) 1 ∂ {Ah1 h2 (s)} = · ∂aj s ∂aj . 1. ∂ρ(s) = ∂aj. {Ah1 h2 (s)}. ∂ {Ah1 h2 (s)} − ∂aj. {Ah1 h2 (s)} ∂ {Ah1 h2 (s)} · {Ah1 h2 (s)} ∂aj. . * σtot ρ + χ2 + ? χ2 =. ∂χ2 =2 ∂aj. . . σexp i − σtot (si ) ξ(σexp i ). . 2 +. σexp i − σtot (si ) ∂σtot (si ) + ξ(σexp i )2 ∂aj. ρexp i − ρtot (si ) ξ(ρexp i ). 2. ρexp i − ρtot (si ) ∂ρtot (si ) ξ(ρexp i )2 ∂aj. . ' ' ? (V −1 )ij =. 1 ∂ 2χ 2 ∂ai ∂aj. = Vij = cov(ai , aj ).
(32) . . . . . -.. ' χ2 & 8 9 & > & aj ' & > ) + & 1 > > + .
(33) . . . . . * > %=! 8% = !9 = ' 8 0 - √s > σtot 9 ; H(I : G H-I 8 2 )9 √ s [GeV ]. ,),0 .)-, )1<))0)-) ).,)2 -02(/. σtot [mb]; 7 /( ± )0 )1) ± ), ))< ± ). )10 ± -, /( ± -< )-0 ± (0. 2 )? A . √ s [GeV ]. ,)<.)-< )1<1< )0)1( ).,(-020(. σtot [mb]; : G )-1 ± )2 )(1 ± ). )20 ± )< )(2 ± -/ )-/ ± (1 ),- ± (.. . > . $> 5 * =" $<)1H))I $.))H<I 2 - -/.
(34) . . . √ s [GeV ]. ).11. (1. . √. σtot [mb]; =" .1 1(1 ± - -0. 2 -? A . s [GeV ]. ).11 ).11. σtot [mb];. $<)1B$.)) <) 0- ± - 0) <- . ± ( ). > . . = > 5 ? 7? = 7 =" 7$? = 7 $<)1B$.)) :? = : G =" :$? = : G $<)1B$.)) 6+ . ! " 3 + % H,I % ? σtot =. m{Ah1 h2 (s)} = X h1 h2 sε + Y1h1 h2 s−η1 ∓ Y2h1 h2 s−η2 s. $ 5 Y2 + h1 h2 ; 8 9 ; 8 9 ' 8Q R9 ? e{Ah1 h2 (s)} s. = −X. h1 h2 ε. s cot. . 1+ε 1 − η1 h1 h2 −η1 π − Y1 π s cot 2 2.
(35) . . . (). . ∓Y2h1 h2 s−η2 tan. . 1 − η2 π 2. . ' + + ' ; > 2 ) = √s > 5 GeV χ2 > √s > 8GeV + χ2 /d.o.f. = 1,09 $ Y1 .
(36) . . . (-. . 0.40. ε. η1. 0.6. η2. 0.1 0.35 0.55 0.09 5 20. 10. Xpp. 5 70. 10. Y1pp. 5. 10. 5. 10. 5. 10. 5. 10. Y2pp 40. 18 60 5. 30. 10. 5. 11 X Κp. 20. 10. 15. 10. Y1Κp. Y2Κp 15. 12 5. 12. 10. Xπp. 5. 10. Y1πp. 10 5. 8. 25. 6. 10. 5 2. 2. Y2πp. 30. χ. 10 800. Numero de puntos. 1.5 400 1 5. 10. " 2 )? . 5. % . 10. . $ 2 ( 2 0 2 2 2 , 7 7$ : :$ .
(37) . . . ((. . 7 ; =" ε η1 η2 X pp Y1pp Y2pp. 1 1/20 ± 1 11-2 1 (,2 ± 1 1)0 1 2,, ± 1 1)0 ). 2- ± 1 2) ,, - ± - 1 (< 1 ± - ,. 2 (? . X Kp Y1Kp Y2Kp X πp Y1πp Y2πp. )1 2. ± 1 -0 )2 01 ± 1 0/ )0 / ± ) 1 )) ./ ± 1 (1 -. 1) ± 1 ,< < 0< ± 1 2,. % & . 7 ; $<)1B$.)) ε η1 η2 X pp Y1pp Y2pp. 1 1/)0 ± 1 11-( 1 (.) ± 1 1)0 1 2,, ± 1 1)0 )/ (1 ± 1 0/ ,< - ± - ) (< ) ± - ,. 2 0? . X Kp Y1Kp Y2Kp X πp Y1πp Y2πp. )1 /0 ± 1 -)2 12 ± 1 2) )2 1 ± ) 1 )- (0 ± 1 -. -. 1, ± 1 ,/ < 2- ± 1 2,. % & .
(38) . . . (0. . : G ; =" ε η1 η2 X pp Y1pp Y2pp. 1 1/./ ± 1 11-< 1 (2- ± 1 1)0 1 2,2 ± 1 1)0 )< ., ± 1 20 ,2 ) ± - 1 (< 1 ± - ,. 2 2? . X Kp Y1Kp Y2Kp X πp Y1πp Y2πp. )1 -< ± 1 -2 )2 ,1 ± 1 0< )0 / ± ) 1 )) 2) ± 1 () -< ., ± 1 ,0 < 00 ± 1 2,. % & . : G ; $<)1B$.)) ε η1 η2 X pp Y1pp Y2pp. 1 1/0) ± 1 11-2 1 (,/ ± 1 1)0 1 2,, ± 1 1)0 ). <, ± 1 2,, ( ± - ) (< ) ± - ,. 2 ,? $<)1B$.)). X Kp Y1Kp Y2Kp X πp Y1πp Y2πp. )1 ,/ ± 1 -0 )2 -0 ± 1 0/ )0 / ± ) 1 )- 1 (± 1 (1 -< /( ± 1 ,. < 0/ ± 1 2<. % & . χ2 /d.o.f. 2 < J 7 H<I ; + : 5 : G H-I % .
(39) . . . (2. . . . . χ2 /d.o.f.. ) 1,< ) 1<. ) 1/) ))0. 2 <? χ2 /d.o.f. %. ;. $ 2 - ; : > ; > =" $<)1B$.)) > 7 : G .
(40) η1. 0.58. ne. nc. ne. nc. hc. he. 70. Y1pp. 40. ne. 0.56. 0.35. Xpp. η2. nc. 0.40. he. ε. 0.09. 20. (,. . hc. . he. 0.10. . hc. . Y2pp. 19 65 18. nc. ne. nc. ne. nc. ne. 16. he. hc. ne. nc. Y1Κp. he. 16. he. hc. ne. nc. XΚp. he. 11.0. he. hc. 35. Y2Κp. 10.5 15 14. hc. ne. nc. he. hc. ne. nc. he. hc. 10.0 13 Xπp. 29. Y1πp. Y2πp 8. 28. 12. 7. 27. hc. ne. nc. he. hc. ne. nc. he. hc. 11. " 2 -? % 8? ? √ ? ? 9 s > 8 GeV % $ 7 2 ( 2 0 2 2 pp Kp πp $ 2 , 2 < 2 . .
(41) . . . (<. . Sección eficaz total σ. 100. pp pp 0. 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 pp pp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 (? % pp √ pp > =" s > 8 GeV.
(42) . . . (.. . Sección eficaz total σ. 100. +. Κp Κp 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 +. Κp Κp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 0? % K +p − K √ p > =" s > 8 GeV.
(43) . . . (/. . Sección eficaz total σ. 100. +. πp πp 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 +. πp πp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 2? % π+ p √π− p > =" s > 8 GeV.
(44) . . . 01. . Sección eficaz total σ. 100 hc he nc ne 0. 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1. hc he nc ne. -0.2 1. 10. 100 √s (GeV). 1000. " 2 ,? √ pp pp s > 8 GeV. 10000. % .
(45) . . . 0). . Sección eficaz total σ. 100. hc he nc ne 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1. hc he nc ne. -0.2 1. 10. 100 √s (GeV). 1000. " 2 <? √ K + p K − p s > 8 GeV. 10000. % .
(46) . . . 0-. . Sección eficaz total σ. 100. hc he nc ne 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1. hc he nc ne. -0.2 1. 10. 100 √s (GeV). 1000. " 2 .? π+ p π− p √s > 8 GeV. 10000. % .
(47) . . . 0(. . " 2 / 2 . σtot ρ pp pp̄ ; % $ J6%$*$ 8J 6 % $ * $> 9H.I ' +> ; 7$ : - 2 + - 211 !A pp ,) (( ± 1 01 ,) 01 ± 1 01 pp̄ pp ,1 ,, ± 1 (. pp̄ ,1 <( ± 1 (. pp ,) .0 ± 1 0) pp̄ ,) /) ± 1 0) pp ,) 1. ± 1 01 pp̄ ,) )2 ± 1 01 2 .? % . σtot [mb]. . E 0 * '7 20, !A ) . *A )0 *A ,- (- ± 1 0( << <( ± 1 /- ))0 , ± - 2 ,- (. ± 1 0- << <2 ± 1 /- ))0 , ± - 2 ,) ,1 ± 1 0) <, ). ± 1 ., ))1 , ± - ,) ,, ± 1 0) <, )/ ± 1 ., ))1 , ± - ,- .< ± 1 00 <. /. ± 1 /< )). ) ± - < ,- /( ± 1 00 </ 11 ± 1 /< )). ) ± - < ,- 12 ± 1 0- << )< ± 1 /) ))( - ± - 0 ,- )) ± 1 0- << )/ ± 1 /) ))( - ± - 0 σtot & . A'7 )11 *A )(. 0 ± ( < )(. 0 ± ( < )(- 0 ± ( ( )(- 0 ± ( ( )0( 2 ± 0 1 )0( 2 ± 0 1 )(, ( ± ( , )(, ( ± ( , %. - E 0 * '7 211 !A 20, !A ) . *A )0 *A 1 )0)2 ± 1 )0-( ± 1 )0.) ± 1 )21, ± pp 1 11(1 11(( 1 11(. 1 1101 pp̄ 1 )0-- ± 1 )0-/ ± 1 )0.( ± 1 )21, ± 1 11(1 11(( 1 11(. 1 1101) 1 )(,- ± 1 )(,. ± 1 )0-) ± 1 )00- ± 1 11(1 1 11() 1 11(2 1 11(< pp pp̄ 1 )(,/ ± 1 )(<2 ± 1 )(-- ± 1 )00- ± 1 11(1 1 11() 1 11(2 1 11(< 1 )0,1 ± 1 )0,. ± 1 )2(( ± 1 )2,) ± 1 11(0 1 11(2 1 1101 1 110( pp pp̄ 1 )0,/ ± 1 )0<0 ± 1 )2(0 ± 1 )2,) ± 1 11(0 1 11(2 1 1101 1 110( 1 )(/< ± 1 )010 ± 1 )0,) ± 1 )0.2 ± 1 11(1 11(( 1 11(< 1 1101 pp pp̄ 1 )010 ± 1 )0)) ± 1 )0,( ± 1 )0.2 ± 1 11(1 11(( 1 11(< 1 1101 2 /? % ρ & % ρ. A'7 )11 *A 1 )21/ ± 1 1101 1 )21/ ± 1 1101 1 )000 ± 1 11(< 1 )000 ± 1 11(< 1 )2,0 ± 1 1100 1 )2,0 ± 1 1100 1 )0.. ± 1 1101 1 )0.. ± 1 1101.
(48) . . . 00. . ! # = & ; & 4 " ;6 4 & = 5 5 H/I ? σtot =. m{Ah1 h2 (s)} = λh1 h2 [A + B lnγ (s)] + Y1h1 h2 s−η1 ∓ Y2h1 h2 s−η2 s. e{Ah1 h2 (s)} s. = πλh1 h2 B ln(s) − ∓Y2h1 h2 s−η2 tan. Y1h1 h2 s−η1. . 1 − η2 π 2. cot . . 1 − η1 π 2. . γ = 2H) / .I + " ; 6 γ ≤ 2 + λpp ) + 8 > Aλpp Bλpp A B λpp 9 ' √s ≥ 3 GeV √s ≥ 10 GeV 2 / % √s ≥ 8 GeV .
(49) . 2.1. . . 02. . γ. 0.40. η1. 0.6. η2. 2 0.55. 0.30 1.9. 5. 10. 5. A. 10. Y1pp. 25. 60. 40. 20. 50. 30. 5 0.6. 10. λΚp. 5. 15. 15. 10. 5. 10. 5. 10. 5. 10. Y2pp. 10. Y1Κp. 5. Y2Κp. 0.58 10 12. 0.56 5 0.66. 10. 5. λπp. 10 8. Y1πp. Y2πp. 25 6. 0.64 20 5. 0.28. 10. Β. 5 2. 10. 2. χ. 800. puntos. 400. 0.24. 1 5. 10. 5. 10. " 2 /? . 5. ' . 10. . $ 5 > =" $<)1B$.)) + 7 .
(50) . . . 0,. . : G F γ < 2 " ;6 8 2 /9F +> γ : γ = 1,9778 ± 0,0080 8 2 )-9 7 ; =" γ. η1. η2. ) /<-< ± 1 11.-. 1 (</ ± 1 1-2. 1 220 ± 1 1)0. A(mb). B(mb). χ2 /d.o.f. -2 .. ± 1 /0. 1 -0)2 ± 1 11<-. ) 10. 01-. pp. Kp. πp. λpp Y1pp (mb) Y2pp (mb). ) 89 2/ 1 ± - < (2 - ± - 2. 1 2,.2 ± 1 11,1 1 ,(/) ± 1 1101 )1 -1 ± 1 ,, -- /2 ± 1 <( )0 )) ± 1 // , /- ± 1 20. 2 )1? ' & ; .
(51) . 0<. . γ. η1. 1.98. η2. 0.4. 1.96. 0.56. 0.35. λΚp. 0.57. ne. nc. ne. nc. he. Y2Κp. 14. he. nc. ne. he. nc. ne. ne. nc. he. ne. nc. he. hc. 9. 8. λπp. 24. Y1πp. Y2πp. 0.64. 7 22. 0.63. ne. nc. ne ne. he. nc nc. hc. he he. 6. hc 0.26. hc. ne 16. Y1Κp. 10. 0.56. hc. ne. nc nc. 32. hc 11. Y2pp 36. hc. 0.58. ne. 55. nc. 24. he. 60. hc. 26. 40 Y1pp. he. 65. A. he. hc. ne. nc. he. hc 28. he. 0.54. 1.94. hc. 2. . hc. . Β. 0.24. hc. 0.22. " 2 )1? % 8? ? √ ? ? 9 s > 8 GeV '.
(52) . . . 0.. . 7 ; $<)1B$.)) γ. η1. η2. ) /,01 ± 1 11.2. 1 0)( ± 1 1-(. 1 22( ± 1 1)0. A(mb). B(mb). χ2 /d.o.f. -< -1 ± 1 <-. 1 -((- ± 1 11,0. ) 10. 01(. pp. Kp. πp. λpp Y1pp (mb) Y2pp (mb). ) 89 ,) , ± - / (2 1 ± - 2. 2 ))? ;. 1 2,)1 ± 1 110. 1 ,(0) ± 1 11(( / 01 ± 1 ,2 -( -, ± 1 .( )0 1( ± 1 /. , .. ± 1 20 ' & . . : G ; =" γ. η1. η2. ) /<<. ± 1 11.1. 1 (2< ± 1 1-,. 1 222 ± 1 1)0. A(mb). B(mb). χ2 /d.o.f. -0 /) ± ) 1/. 1 -0/) ± 1 11<.. ) 1/. 01-. pp. Kp. πp. λpp Y1pp (mb) Y2pp (mb). ) 89 2< 0 ± - 0 (2 0 ± - 2. 1 2<0) ± 1 11,/ 1 ,0-< ± 1 110, )1 <- ± 1 ,. -- .) ± 1 ,0 )0 ), ± 1 // , /0 ± 1 20. 2 )-? ' & ; .
(53) . . . 0/. . : G ; $<)1B$.)) γ. η1. η2. ) /,.2 ± 1 11.0. 1 (/, ± 1 1-2. 1 22( ± 1 1)0. A(mb). B(mb). χ2 /d.o.f. -, 2/ ± 1 .(. 1 -(,/ ± 1 11,.. ) 1/. 01(. pp. Kp. πp. λpp Y1pp (mb) Y2pp (mb). ) 89 ,1 ) ± - / (2 ) ± - 2. 1 2,0, ± 1 1120 1 ,(,2 ± 1 11(< / <, ± 1 ,2 -( 10 ± 1 </ )0 1. ± 1 /. , /1 ± 1 20. 2 )(? ' & ; $<)1B$.)) 8 2 )09 7$ . . 2 )0? '. χ2 /d.o.f.. χ2 /d.o.f.. ) 10) 101 ) 1.< ) 1/(. . . $ 2 )) 2 )- 2 )( ; > 7$ √s ≥ 8 GeV $ 2 )0 2 )2 2 ), ' 2 )2 2 ), ; 8 γ 9 ').
(54) . . . 21. . Sección eficaz total σ. 100. pp pp 0. 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 pp pp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 ))? ' pp pp > $.)) √ s > 8 GeV.
(55) . . . 2). . Sección eficaz total σ. 100. +. Κp Κp 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 +. Κp Κp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 )-? ' K + p K − p > $.)) √s > 8 GeV.
(56) . . . 2-. . Sección eficaz total σ. 100. +. πp πp 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 +. πp πp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 )(? ' π+ p π− p > $.)) √ s > 8 GeV.
(57) . . . 2(. . Sección eficaz total σ. 100 hc he nc ne 0. 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1. hc he nc ne. -0.2 1. 10. 100 √s (GeV). 1000. " 2 )0? √ pp pp s > 8 GeV. 10000. ' .
(58) . . . 20. . Sección eficaz total σ. 100. hc he nc ne 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1. hc he nc ne. -0.2 1. 10. 100 √s (GeV). 1000. " 2 )2? K + p K − p √s > 8 GeV. 10000. ' .
(59) . . . 22. . Sección eficaz total σ. 100. hc he nc ne 10 0 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1. hc he nc ne. -0.2 1. 10. 100 √s (GeV). 1000. " 2 ),? √ π+ p π− p s > 8 GeV. 10000. ' .
(60) . . . - 211 !A pp ,) -) ± 1 0, pp̄ ,) -. ± 1 0, pp ,1 0( ± 1 0( ,1 21 ± 1 0( pp̄ pp ,) ,, ± 1 0< pp̄ ,) <( ± 1 0< pp ,1 .1 ± 1 00 pp̄ ,1 .< ± 1 00 2 )2? % . σtot [mb]. . 2,. . E 0 * 20, !A ) . *A ,- ), ± 1 0/ <, 0. ± 1 /, ,- -- ± 1 0/ <, 21 ± 1 /, ,) (( ± 1 0, <0 ., ± 1 .< ,) 01 ± 1 02 <0 .. ± 1 .< ,- ,0 ± 1 21 << 0. ± ) 11 ,- <) ± 1 21 << 21 ± ) 11 ,) <- ± 1 0< <2 ,( ± 1 /,) <. ± 1 0< <2 ,2 ± 1 / σtot . '7 )0 *A )1< - ± - ) )1< - ± - ) )1( < ± ) / )1( < ± ) / )1/ 0 ± - )1/ 0 ± - )12 ( ± - 1 )12 ( ± - 1 & . A'7 )11 *A )-0 2 ± - . )-0 2 ± - . )-1 1 ± - 0 )-1 1 ± - 0 )-< 2 ± - / )-< 2 ± - / )-- ) ± - , )-- ) ± - , '. 8γ = 19 '- 8γ = 29 ' +> σtot 7$ : ) / + . ! . . + # H)(I -11- $ ' ? m{Ah1 h2 (E)} = Ah1 1 h2 E −N1 ∓ Ah2 1 h2 E −N2 + C0h1 h2 + C2h1 h2 lnγ (s) s Bh1 h2 e{Ah1 h2 (E)} E = + s plab πplab. . ∞. m. plab. . σh1 h̄2 (E ) σh1 h2 (E ) − E (E − E) E (E + E). . dE . ' & 5 σF ? plab. =. E. =. s − m2a − m2p 2mp. plab + m2a. 2 − m2a.
(61) . . . - 211 !A 1 )0<< ± pp 1 11(( pp̄ 1 )0., ± 1 11(( 1 )02, ± 1 11( pp 1 )0,2 ± pp̄ 1 11(1 )0/) ± 1 11(0 pp pp̄ 1 )0// ± 1 11(0 1 )0,2 ± 1 11( pp pp̄ 1 )0<0 ± 1 11(( 2 ),? % ρ. 2<. . E 0 * '7 20, !A ) . *A )0 *A 1 )0.1 ± 1 )0,. ± 1 )(0/ ± 1 11(( 1 11(1 11-. 1 )0.. ± 1 )0<1 ± 1 )(0/ ± 1 11(( 1 11(1 11-. 1 )0,1 ± 1 )02( ± 1 )(0. ± 1 11(1 11() 1 11-/ 1 )0,< ± 1 )022 ± 1 )(0. ± 1 11(1 11() 1 11-/ 1 )0/0 ± 1 )0.1 ± 1 )(2- ± 1 11(0 1 11(1 11-. 1 )21) ± 1 )0.) ± 1 )(2- ± 1 11(0 1 11(1 11-. 1 )0,. ± 1 )02/ ± 1 )(0< ± 1 11(1 11() 1 11-. 1 )0<, ± 1 )0,) ± ) )-0< ± 1 11(( 1 11() 1 11-. ρ & . A'7 )11 *A 1 )-.- ± 1 11-< 1 )-.- ± 1 11-< 1 )-., ± 1 11-. 1 )-., ± 1 11-. 1 )-.- ± 1 11-, 1 )-.- ± 1 11-, 1 )-.( ± 1 11-< 1 )-.( ± 1 11-. '. = ma mp ; $ ? ). F + ; + + 3 # H)(I χ2 + ' > & Bpp = 0 $ ; 2 )< 2 ). 2 ). σ ρ $ & E > Bpp C0 = 0 .
(62) . . . 80. γ. A1pp. AKp. 40. 60. 2 10. η1. 5 25. 20. 10. 40 5. 10. A2pp. 5 10. 0.6. 10. 0.4. 5. 5. A2Kp. 10. A2πp. 4 8. 10. 5. 10. 5. 10. 1. η2. Bpp. 50. 0.55. 80. BKp. 5. 10. -1. 2. χ. 35. 5. 10. 10. 10. C0Kp. 20. 14 5. 10. 10. C0πp. 16 5. 0.1. Χ2ππ. puntos. 5. Bπp. 16. 30 5. 5. C0pp. 1.5 1. 10. 0. 0. 0.5. 5. 40. 0. 1000 900 800 700 600 500 400 300. 5. 9 20. 2. Aπp. 20. 2.5. 0.8. 2.. . 10. 5. 10. 0.2 C2Kp. 0.15. 0.1. C2πp. 0.1. 0.05. 0.05 5. 10. 0. 5. 10. 5. 10. 0. 5. 10. " 2 )<? $ √s > 5 GeV @ .
(63) . . . 2/. . Sección eficaz total σ. 100. pp pp 0. 10. 1. 2. 10. 10. 3. 10 √s (GeV) Valor de ρ. 4. 5. 10. 6. 10. 10. 0.2 0.1 0 -0.1 pp pp. -0.2 1. 10. 100 √s (GeV). 1000. 10000. " 2 ).? ' pp √ pp > =" s > 8 GeV.
(64) . . $ ; H)(I > + + ; ; )1111 ' 7 H(I ; : G H-I $ : G * ; =" $<)1 $.))F & $<)1B$.)) + ; . : γ ,1. > 2.
(65) . . . . ,). " ; 6 * # H)(I " ;6 + γ + >; $ χ2 /d.o.f 1 .
(66) . . . * > $ •. • •. ? $ % ; + ; ? 3 ? ! + + ; . % + • •. ? ' > > ? ' + ' & & 8 )9 & 8 -9 $ + √s ≥ sqmin1 5 + ) √s ≥ sqmin1 + √ 1 s ≥ sqmin2 ,-.
(67) . •. . . . ,(. S ? $ + 8 + 9 $>; > + TUV UV CD CLD C%3D . •. •. •. B ? + % > TU>VTUV ? !+ UV8 L %39 U>V ? !+ .
(68) . . ! ! ! . !! ! . . !" ! # . # ! ! $ "% ! & ' & ' $ (% & ' . ,0.
(69) . . . )&)& $ (% )& " ! " ! !*%+,- . -" * /+% "+% # * " 0 1234 /%"1. . . 5' ! " ! 0 ( 6 ! " 6 ! " 0 ( 6 ! 6 ! ! * ! " 5 ! * ! " ! "+% 7 ! + + ! 8 0 ( 6 9: ! 5'5 !; ) 0 ( 6 7 ! 6 ! ! * ! < "+% 55. 6 !. : 5 ===================================================================. :929 5' ! " ! ! " ! ! ! $ "% ! / . ! # . ,2.
(70) . . . # !" . . !# !# ) ) & ' & ' $ ( $ ( !# ) $ (% & ' ( ! *6+ 63*63 > ? 6 5 ( 5 *"# 5 ( ! 55 5 ( ! " 5 ( ! : ( . -%% <. /%% -%". <. 0 ( 6 @ 4 & + +++6 * " .*/%% ! *6& + 63*63 > ? 6 5 .6 ((-(% 6 5*-%" !# ) & ' * < " -%% 0 ( 6$3# 3 # 4 A & + 6 0 ( 67 4 3 4 & + 6 * = " 0 ( 6 3! 4 B 6 : . 9 5. ===================================================================. :929 5'4. ,,.
(71) . . . . . ! ! ! & ' & ' $ (% & ' !# !# $ ( !# $ ( . 4 !!. . : &; 345 4 ) 4 4 ! ! @ 4 "%%% "%%% "%%% # ! 4 4 C ! )3 4 4 4 3! 4 4 3 "%%%" "%%%" "%%%" ! 3! 4 4 C ! 4 ) 4 ! 3! 3 " ! ! " . !" !-4 . 4 $ (% & ' 3 D 4. . . . 4 3 4 4 4 . ,<.
(72) . . + " / ( . , "% "" " . $4 # # E< E< E= E= < < = =. . ,.. . 34 )! A )! A )! A )! A )! A )! A. 4 4 3 4 3 4 5 !%+,- . -"%+,- . -"%+,- . -"%+,- . -" < %+/-,(..%+/-,(..%+/-,(..%+/-,(.. < %+"-, (,,%+"-, (,,%+"-, (,,%+"-, (,, 4 *% 5 *" . . A 4 4 4 3 4 "+4 +4 +. < <. 4 . . !#. 0 & ' 36 / 6 64 '6 !# "B 58 !# 6 6 =" 6'6 "B 58 6 6 =" 6+46 0 6 @ 4 A 6 & ' 0 6:4 )& 6 & ' 3. <. 5'7 ! & ' & ' 3 5 D*" D * D D * D D * D 55 3 * 4 * 4 < 0 6 3! 4 4 6 6 B 6 55.
(73) . . . 9 5 =================================================================== :929 5'7 !& . ! & ' 3. . ! ! !!. # @ "%%% "%%% "%%% 43!!@ ! ! ! $ (% & ! & ' 3 'A '4 . 0 !!. 3 . #. A. 4. )& 4. 4 & ' 3. %. 'A '4 *+ 9+ 9 * 7*& ' 3 : 9:*6 06 ::*6 * % " 'A '4 *+7:+. ". 9 *,* %%7*& ! : 9:*656 . <. . *%. . 3! . 4. 3 . 3. . 4. 4. 5 ,, & ! "" . ,. 3 4 A # * ! ! ! 4 * )! * 4 @ * ! "%% <. # . 5 ,* %% 5* %" 43!!@# 43!!@43!!@ 43!!@ @. 56. ,/.
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(77) . . . ) # 3 4 3 E< E= D ! + 3 3 ) )3 " @ 3 ) ="+ 79 . ! 4). ) 4 # . . . 4 ). <. : : 4 : % ! * / " < = = ) ( = - : " ! * / "< " : ! * = "= : - ! * ) ( "= - : / ! * "< " : ! * "= : ( ! * =) "= - : 579 0 1! A #4. 3 #. . 1. 5 : 9 5 ===================================================================== 4 4 @ 3 4 4 3 4 4 &3 4 . <(.
(78) . . &3 " - / ( . #. . . 4 ! 4. . 4 ). 11. =I =I " =I =I 8 =I H" =I H . 79 . 4). . . 4 ) : :. < <. : : 4 : % * = / " "< " = = "= = ) ( = - "= - . <. : " * / "< " : "< " = "< " . <. : * "= = : "= < "= . <. : - * ) ( "= - : "= - < "= - : / * =" "< " "< " : * =" "= "= : ( . <0.
(79) . . . . * =) "= - "= - . : 579 0 1. A #4. 3 #. . 1. 5 :. 9 5 ===================================================================== 3 4 &; )! @ 3 4 4 79 . )! 4). . !! ! . 4 ) . !. 7 4+F+% . $. G: : :+++ J5 5 5 : : K )!* / :F =! )! * ! %). . : . 4')!* /4' 4 :F =! )! * ! 4) 57 9. . <2.
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