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Q2 2 2 1 Q2 1 s(Q2) s(Q2) Q2 Q2 s (Q2) Q2 2 Q2 1 n s > 0 dns n n An = s = An.

s[L] L =ln(Q2/2) s[L] f(s[L]) ln(Q2/2) s[L] Lm p2 2 p2 2 1 Q2 s L = ln(Q2/2) Ls =ln(s/2) (Q2) A(Q2) A(Q2) s [L] A[L] A[Ls] s Q2 2 Q2 30 2 Q2 =1 - 10 2 Q2 3 2 Q2 =3-10 Q2 AAV bb H0 bb 2 2 2 Q2 =1 - 10 2 O(s) b b Q2 2 O(s) O(A2) e+e- H0 bb 3 O(s) O(A3) 2 R 2 F F(Q2) 2 1 - 10 O(s) sLD(Q2) 0 F(Q2) O(A2) 2 O(s) (l)() n A(l)(Q2) = d ; n + Q2 0 (l)() n A(l)(s) = d. n s D R Q2 a[L] L B(Q2) = Z(Q2)/Z(2) B(2) Z[L] a[L] = 0/(2b0) a[L] ln(a[L]) Nf A[L] A[L] A[L] F(z, ) A[L] A-m[L] =Lm a-m[L] = Lm L 2 L =0 A(0) ( - 1) () =.

A(0) 2-1 A1[L] A1[L] (L, ) (L, ) A[L] - (A1[L]) A[L] - (A1[L]) (L, ) = ; (L, ) =. A[L] A[L] (L, ) (L, ) 2 (L, 0.62) (L, 0.62) Q2, s 1 L 2.4 = 300 | (L, 1.62)| | (L, 1.62)| L 5.1 2 Q2, s 15.2 | (L, 2.62)| > 0.23 2 | (L, 2.62)| > 0.31 L 5.1 Q2, s 15.2 >1 0.1 0.1 M[L,] E[L, ] 0.05 0.05 0 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.15 -0.2 -0.2 L L 2 4 6 8 10 2 4 6 8 10 (L, ) L =ln(s/2) (L, ) L =ln(Q2/2) =0.62 =1.62 =2.62 A(2) A(2) 1 1 O(c2) 1 L =0 |L| > 2 a(2) a(2) L L [-10, +10] [1, 2] O(c4) 1 Nf A ;(l)[Ls] Nf = 6 Nf A1+[L - t] P(t) 1 t du P(t) P 1 - u1/ 1 - u1/ 0 P(t) dn = d1 P(t) tn-1dt.





0 P (t) =(t-2) d n =2n-1 P (t) =te-t d n = n! L k1[t] k =4, 5, 6 P (t) f =4 f =5 f =6 L 5 L 12 H0 bb H0 b b ( b R b) b 2 R (MH) ( b =b(m2), b) 0 b 3 m2 b b(m2) =3 GF MH m2/4 2 mb M b 0 b b mb(Q2) b 2 2 2 R (MH) = m2(MH) R (MH) b D R R (s) =3m2(s) 1+ rn an(s).

b n1 rn 2 D R R dn Nf =5 b 0 1 ( [L])n+ (1 + s) B(2); [L] n+0 (2) (2) B [L; {, }] (2)[L] 1+s [L].

B(3); [L] n+0 l B(l); (s) n+0 (l) R (s) =3 m2 B(l); (s) + dn(5), (l) 0 n n1 (l) DS dn (l);5 D B(l); n+0 2 R Nf (l); B(l); n+0 Bn+0{...} dn(Nf) (l) Bn+0{...} B(l); n+0;dn l n+0;dn (l) (s) =3 m2 B(l); (s) + B(l); (s) R .

(l) 0 n n1 Nf Nf =5 34 34 R (M ) [ 2] R (M ) [ 2] 32 32 30 30 28 28 26 26 24 24 22 22 M [ ] M [ ] 60 80 100 120 140 60 80 100 120 140 R (M2) R (1);Z = Nf =5 111 A(1); (m2 ) =0.120 1 Z (4) = 231 Nf =5 dn(Nf) dn(5) (4) = Nf =5 261 A(3); (m2 ) =0.120 1 Z Nf M =50 M = 150 L dn(Nf) :=dn(5) Nf =5 Nf dn(Nf) H (M ) 0 bb dn(5) n =1, 2, 3, 4 (n +1) + (n) d n = cn-1, 1+ c =2.4 = -0.52 + t/c P (t) = e-t/c. c ( +1) dn(5) n = 1, 2, 3, 4 d5(5) P (t) R [L] L [11.7, 13.6] 80 - 180 f N =3 = 201 A 1 (m2 ) = 0.122 Z 3.5 Hbb [MeV] 0.025 2[L] 0.02 3.0 FAPT H bb 0.015 2.5 0.01 3[L] 2.0 0.005 4[L] L MH [GeV] 1.5 12 12.5 13 13.5 80 100 120 140 160 180 N[L] N = 2, 3 4 H [L] 0 bb L =ln(M2/2) Hbb M N N = 1 N = 2 N =3 L5



2 2 F (Q2) 2 2 =1 =1 (Q2 (Q2 (Q2 Q2F ) Q2F ) Q2F ) 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 Q2 [ 2] Q2 [ 2] Q2 [ 2] 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 Q2F 2 2 2 =1 2 =5.76 2 2 = 10 7.5% 5% 2 2 2 =1 2 =10 1% 2 2 2 =1 2 =50 2% b0 Nf Nf 2 = Q2 2 Nf 0.26 Q2F (Q2) Q2F (Q2) 0.4 0.24 0.3 0.22 0.2 0.2 0.18 0.16 0.1 0.14 Q2 [ 2] Q2 [ 2] 0 10 20 30 40 50 0 10 20 30 40 50 Q2F 2 = Q2 Nf 2 2 =5.76 2 = Q2 2 = Q2 A(s) A(s) + + R(s) =e e- (s)/e e-+-(s) A (-s) F(Q2) O(s) 0.8 0.8 Q2F(Q2) [GeV2] 0.6 0.6 0.4 0.4 0.2 0.2 Q2 [GeV2] 2 4 6 8 10 2 4 6 8 10 Q2F(Q2) 2 2 =0.4 q 2 Q2 7 qAq(Q2, M2) 2 Q2 4 sLD(Q2) Q2 Q2 0 2 42f sLD(Q2) =, 0 1+s(Q2)/ 2 2 0.67 Q2 10 2 2 sLD(Q2 =10 ) =0.87 0 2 sLD Q2 =10 20 0 2 O(s) 2 2 Q2 2 Q2 7 l (z, -, 1) F (z, ) D b b

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