High order corrections in theory of heavy quarkonium

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1 High order corrections in theory of heavy quarkonium Alexander Penin TTP Karlsruhe & INR Moscow ECT Workshop in Heavy Quarkonium Trento, Italy, August 17-31, 2006 A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.1/42

2 Topics discussed Modern (perturbation) theory of nonrelativistic bound states Status of high order perturbative calculations Phenomenology of top, bottom and charm Nonrelativistic renormalization group Theoretical and experimental challenges A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.2/42

3 Do we need high order PT? A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.3/42

4 Do we need high order PT? Theory: Complicated multiscale dynamics First principle QCD predictions A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.3/42

5 Do we need high order PT? Theory: Complicated multiscale dynamics First principle QCD predictions Phenomenology: Heavy quark masses A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.3/42

6 Do we need high order PT? Theory: Complicated multiscale dynamics First principle QCD predictions Phenomenology: Heavy quark masses Yes, we do! A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.3/42

7 Heavy Quarkonium at NNLO Spectrum Leptonic/photonic width Threshold production (Pineda, Yndurain) (Melnikov, Yelkhovsky; Penin, Pivovarov) (Czarnecki, Melnikov; Beneke, Smirnov, Signer; Kühn, Penin, Pivovarov; Hoang, Teubner) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.4/42

8 Heavy Quarkonium at NNLO Spectrum Leptonic/photonic width Threshold production (Pineda, Yndurain) (Melnikov, Yelkhovsky; Penin, Pivovarov) (Czarnecki, Melnikov; Beneke, Smirnov, Signer; Kühn, Penin, Pivovarov; Hoang, Teubner) Apparent slow convergence: Γ(Υ(1S) l + l ) = Γ LO (1 0.5 NLO NNLO +...) M(Υ(1S)) = M LO (1 0.1 NLO 0.05 NNLO +...) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.4/42

9 Bottom quark mass at NNLO Pole mass short-distance mass (Beneke; Hoang; Melnikov, Yelkhovsky; Pineda) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.5/42

10 Bottom quark mass at NNLO Pole mass short-distance mass (Beneke; Hoang; Melnikov, Yelkhovsky; Pineda) Method Order m b (m b ) (GeV) Penin, Pivovarov 98 nonrelativistic Υ sum rules NNLO 4.21 ± 0.11 Melnikov, Yelkhovsky 99 " " 4.20 ± 0.10 Beneke, Signer 99 " " 4.25 ± 0.08 Hoang 00 " " 4.17 ± 0.05 Kühn, Steinhauser 01 low moments sum rules " ± Pineda 01 spectrum, Υ(1S) resonance " ± m b (m b ) = 4.2 ± 0.1 GeV A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.5/42

11 e + e t t threshold production at NNLO NNLO LO NLO Born µ = 50, 75, 100 GeV E (GeV) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.6/42

12 Precision b-physics (CKM,...): δm b < 50 MeV Precision t-physics at ILC: δr(e + e t t) < 3% General structure of PT: renormalons,... Full N 3 LO analysis is necessary A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.7/42

13 Historical Overview s. Quantum mechanics, time-independent perturbation theory, Dirac s theory of radiation s. Early days of quantum field theory, noncovariant perturbation theory Covariant perturbation theory....there is a moral here for us. The artificial separation of high and low frequencies, which are handled in different ways, must be avoided (Schwinger, Particles, sources and fields, Vol.2) Beginning of the nonrelativistic effective theory era (Caswell, Lepage). Late 1990s. Dimensional regularization & threshold expansions push the effective theory to a new level. A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.8/42

14 Nonrelativistic Effective Theory Characteristic momentum regions: Hard Soft (static quarks) Potential (static gluons) Ultrasoft p 0 m q, p 0 vm q, p 0 v 2 m q, p 0 v 2 m q, p m q p vm q p vm q p v 2 m q A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.9/42

15 Nonrelativistic Effective Theory Characteristic momentum regions: Hard Soft (static quarks) Potential (static gluons) Ultrasoft p 0 m q, p 0 vm q, p 0 v 2 m q, p 0 v 2 m q, p m q p vm q p vm q p v 2 m q Schrödinger theory & multipole radiation A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.9/42

16 Nonrelativistic Effective Theory Characteristic momentum regions: Hard Soft (static quarks) Potential (static gluons) Ultrasoft p 0 m q, p 0 vm q, p 0 v 2 m q, p 0 v 2 m q, p m q p vm q p vm q p v 2 m q Schrödinger theory & multipole radiation Dynamical degrees of freedom A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.9/42

17 QCD NQCD pnrqcd (Caswell, Lepage; Bodwin, Braaten, Lepage; Pineda, Soto) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.10/42

18 QCD NQCD pnrqcd (Caswell, Lepage; Bodwin, Braaten, Lepage; Pineda, Soto) q (iγ µ D µ m q ) q A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.10/42

19 QCD NQCD pnrqcd (Caswell, Lepage; Bodwin, Braaten, Lepage; Pineda, Soto) q (iγ µ D µ m q ) q ( ) ψ id 0 + D2 ψ + 1 2m q 8m 3 q hard modes integrated out ψ D 4 ψ c F g s 2m q ψ σ Bψ +... A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.10/42

20 QCD NQCD pnrqcd (Caswell, Lepage; Bodwin, Braaten, Lepage; Pineda, Soto) q (iγ µ D µ m q ) q ( ) ψ id 0 + D2 ψ + 1 2m q 8m 3 q hard modes integrated out ψ D 4 ψ c F g s 2m q ψ σ Bψ +... soft modes integrated out ( ) ψ i g s r E ψ m q A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.10/42

21 Potential NRQCD Schrödinger equation ( Pineda, Soto; Brambilla, Pineda, Soto, Vairo; Kniehl, Penin) (H E) (r,r,e) = δ(r r ) Effective Hamiltonian H = 2 m q + V Coulomb (r) + δh Multipole interaction to ultrasoft gluons g s (r 1 r 2 ) E + g s (σ 1 σ 2 )B +... A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.11/42

22 Nonperturbative effects } {{ } Λ QCD v 2 m q vm q m q Top Local condensate expansion (Voloshin, Leutwyler) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.12/42

23 Nonperturbative effects v 2 m q vm q m q } {{ } Λ QCD Bottom Time-nonlocal condensates (Brambilla, Pineda, Soto, Vairo) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.12/42

24 Nonperturbative effects v 2 m q vm q m q } {{ } Λ QCD Charm NRQCD matrix elements (Bodwin, Braaten, Lepage) or nonperturbative potentials A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.12/42

25 Loops in the Effective Theory Problem: Separation of regions in virtual momentum space A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.13/42

26 Loops in the Effective Theory Problem: Separation of regions in virtual momentum space Regions are separated in dimensional regularization! Effective theory in dimensional regularization (Pineda, Soto; Czarnecki, Melnikov, Yelkhovsky; Beneke, Signer, Smirnov; Kniehl, Penin, Smirnov, Steinhauser) gauge, Lorenz invariance + automatic matching ideal for high-order calculations A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.13/42

27 Loops in the Effective Theory Problem: Separation of regions in virtual momentum space Regions are separated in dimensional regularization! Effective theory in dimensional regularization (Pineda, Soto; Czarnecki, Melnikov, Yelkhovsky; Beneke, Signer, Smirnov; Kniehl, Penin, Smirnov, Steinhauser) gauge, Lorenz invariance + automatic matching ideal for high-order calculations Threshold Expansion (Beneke, Smirnov) Expansion of the Feynman integrals in v Effective Theory Expansion of the QCD Lagrangian in v A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.13/42

28 Loops in the Effective Theory Threshold expansion ➊ In every region expand the integrand in Taylor series with respect to the small parameters ➋ Integrate the expanded integrand over the whole integration domain of the loop momenta ➌ Put to zero any scaleless integral A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.14/42

29 Loops in the Effective Theory Threshold expansion ➊ In every region expand the integrand in Taylor series with respect to the small parameters ➋ Integrate the expanded integrand over the whole integration domain of the loop momenta ➌ Put to zero any scaleless integral After step ➊ the effective theory vertices & propagators are recovered A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.14/42

30 Loops in the Effective Theory Threshold expansion ➊ In every region expand the integrand in Taylor series with respect to the small parameters ➋ Integrate the expanded integrand over the whole integration domain of the loop momenta ➌ Put to zero any scaleless integral After step ➊ the effective theory vertices & propagators are recovered QCD, NRQCD and pnrqcd can be used for the perturbative calculations without matching! A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.14/42

31 Loops in the Effective Theory THRESHOLD EXPANSION pnrqcd Hard region Wilson coefficients Soft region Potentials Potential region Quantum Mechanical PT Ultrasoft region Multipole radiation A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.15/42

32 NLO corrections to HFS Spin-flip potential: V S (q 2 ) = 4πC F α s S 2 3m 2 q A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.16/42

33 NLO corrections to HFS Spin-flip potential: ( V S (q 2 ) = 4πC F α s S 2 3m 2 q 1+ α π» ǫ ««µ2 + ln m 2 C A 1 q 2 C F ln 2+i3π T 4 F hard contribution QCD on-shell on-threshold amplitude A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.16/42

34 NLO corrections to HFS Spin-flip potential: ( V S (q 2 ) = 4πC F α s S 2 3m 2 q hard contribution QCD on-shell on-threshold amplitude 1+ α π + α π» ǫ h ǫ ««µ2 + ln m 2 C A 1 q 2 C F + + ln µ2 q 2 C A 5 9 T F n l i ) 6 6 ln 2+i3π T 4 F soft contribution NQCD, static heavy quark propagator Coulomb potential: V C (q 2 ) = 4πC F α s (q 2 ) q 2» 1 + α s π `31 36 C A 5 9 T F n l A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.16/42

35 NLO corrections to HFS Quantum Mechanical PT (potential contribution) δg = G C V 1 loop S G C + 2G C V tree S G C V 1 loop C G C A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.17/42

36 NLO corrections to HFS Quantum Mechanical PT (potential contribution) δg = G C V 1 loop S G C + 2G C V tree S G C V 1 loop C G C Result for general n E NLO hfs (n) = 1 3 C 4 F α4 s n 3 j 1 + α s π» 7 CA 4 «CF α s ln n C F n + 12 n2 Ψ 2 (n) 9 n n f T F n γ E n nψ 1 (n) 264 n 2 ff Ψ 2 (n) C A 72 n (Penin, Steinhauser) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.17/42

37 Heavy Quarkonium Spectrum at O(α 5 sm q ) Perturbative bound state energy E p.t. n = E C n + δe (1) n + δe (2) n + δe (3) n +..., δe (3) n consists of: ➊ matrix elements of the N 3 LO effective Hamiltonian ➋ iterations of the NLO and NNLO effective Hamiltonian ➌ ultrasoft contribution A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.18/42

38 Typical N 3 LO contributions O(v 2 ) O(v) O(1) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.19/42

39 Effective Hamiltonian to N 3 LO H = (2π) 3 δ(q) p 2 m q p4 4m 3 q! + V C ( q ) + V 1/m ( q ) + V 1/m 2( q, S, L) +... Static potential V C ( q ) = 4πC F α s ( q ) q 2 ( 1 + α s( q ) 4π a 1 + «αs ( q ) 2 αs ( q ) a 2 + 4π 4π «3»a ) 3 + 8π 2 3A µ2 C ln q 2 Nonabelian potential V 1/m ( q ) = π2 C F α 2 s( q ) m q q j b 1 + α s( q ) π» b µ `C2 2 ff A + 2C A C F ln q 2 Breit potential V 1/m 2( q, S, L) = πc F α s ( q ) m 2 q j d 0 + α s(µ) π»d 1 (m 2q /q2 ) + 43 (C A 2C F )ln µ2 q 2 ff +... A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.20/42

40 Effective Hamiltonian to N 3 LO Static potential a 1 a 2 a 3 (Fischler; Billoire) (Peter; Schröder; Kniehl, Penin, Smirnov, Steinhauser) Padé only (Chishtie, Elias) Nonabelian potential b 1 b 2 (Gupta, Radford; Titard, Yndurain) (Kniehl, Penin, Smirnov, Steinhauser) Breit potential d 1,... (Titard, Yndurain; Manohar, Stewart; Kniehl, Penin, Smirnov, Steinhauser) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.21/42

41 Ultrasoft contribution (Kniehl, Penin; Kniehl, Penin, Smirnov, Steinhauser) G s C G o C G s C X Z G s,o (r, r, E) = n ψn s,o (r)ψn s,o (r ) E n E Instanteneous contribution! δ us H = 5 18 ln ln µ 6 C 3 A C F α 4 s 2 `EC 1 q 4 q Retarded contribution a.k.a. Bethe Log δe (3) n 1 α 2 sc 2 F EC n Z 0 d 3 k (2π) 3 r kn 2 E C n k 2 /m q 3 ln E C 1 E C n k 2 /m q A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.22/42

42 N 3 LO ground state energy δe (3) 1 E C 1 = α 3 s n l = nl = a 3 + (Penin, Steinhauser) ln(α s ) n l = nl =5 Renormalon contribution Padé estimate (Chishtie, Elias) 0.001a 3 = { nl = nl =5 A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.23/42

43 Top and bottom masses Υ(1S) mass: M Υ(1S) = 2m b + E p.t. 1 + δ n.p. E 1 δ n.p. E 1 = m q D α s G a µν Gaµν E (C F α s m q ) 4 = 60 ± 30 MeV (Voloshin, Leutwyler) Toponium resonance energy: E res = 2m t + E p.t. 1 + δ Γ t E res δ Γ te res = 100 ± 10 MeV A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.24/42

44 Bottom quark mass from Υ(1S) NLO NNLO N 3 LO m b (GeV) µ (GeV) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.25/42

45 Bottom quark mass from Υ(1S) m _ b (m_ b ) (GeV) NLO NNLO N 3 LO µ (GeV) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.26/42

46 e + e t t resonance energy NLO NNLO N 3 LO S=1 E p.t. t (GeV) µ (GeV) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.27/42

47 Top and bottom masses at N 3 LO Bottom quark mass from Υ(1S): m b (m b ) = 4.34 ± 0.07 GeV (Penin, Steinhauser) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.28/42

48 Top and bottom masses at N 3 LO Bottom quark mass from Υ(1S): m b (m b ) = 4.34 ± 0.07 GeV (Penin, Steinhauser) Toponium resonance energy: E res = ( m t GeV GeV ) ± m t Top quark mass with 80 MeV accuracy A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.28/42

49 Excited states How large are the nonperturbative effects? Gluon condensate δ n.p. E n n 6 A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.29/42

50 Excited states How large are the nonperturbative effects? Gluon condensate δ n.p. E n n 6 ρ n = E n E 1 2m b +E 1 Υ(2S) Υ(3S) 10 2 ρ C n ρ exp n A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.29/42

51 Excited states How large are the nonperturbative effects? Gluon condensate δ n.p. E n n 6 ρ n = E n E 1 2m b +E 1 Υ(2S) Υ(3S) 10 2 ρ C n ρ (1) n ρ exp n A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.29/42

52 Excited states How large are the nonperturbative effects? Gluon condensate δ n.p. E n n 6 ρ n = E n E 1 2m b +E 1 Υ(2S) Υ(3S) 10 2 ρ C n ρ (1) n ρ (2) n ρ exp n A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.29/42

53 Excited states How large are the nonperturbative effects? Gluon condensate δ n.p. E n n 6 ρ n = E n E 1 2m b +E 1 Υ(2S) Υ(3S) 10 2 ρ C n ρ (1) n ρ (2) n ρ (3) n ρ exp n A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.29/42

54 Heavy Quarkonium at N 3 LO Spectrum O(α 3 s) (n = 1, Penin, Steinhauser) (n > 1, Penin, Smirnov, Steinhauser; Beneke, Kiyo,Schuller) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.30/42

55 Heavy Quarkonium at N 3 LO Spectrum O(α 3 s) (n = 1, Penin, Steinhauser) (n > 1, Penin, Smirnov, Steinhauser; Beneke, Kiyo,Schuller) Leptonic/photonic width and resonance production O(αs 3 ln 2 α s ) O(αs 3 ln α s ) O(β0 3α3 s), (Kniehl, Penin) (Kniehl, Penin, Smirnov, Steinhauser; Hoang) (Penin, Smirnov, Steinhauser; Beneke, Kiyo,Schuller) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.30/42

56 Heavy Quarkonium at N 3 LO Spectrum O(α 3 s) (n = 1, Penin, Steinhauser) (n > 1, Penin, Smirnov, Steinhauser; Beneke, Kiyo,Schuller) Leptonic/photonic width and resonance production O(αs 3 ln 2 α s ) O(αs 3 ln α s ) O(β0 3α3 s), (Kniehl, Penin) (Kniehl, Penin, Smirnov, Steinhauser; Hoang) (Penin, Smirnov, Steinhauser; Beneke, Kiyo,Schuller) Threshold production N 3 LO ln 2 v N 3 LO lnv O(β0 3α3 s) (Pineda) (Manohar, Hoang, Stewart, Teubner) (Beneke, Kiyo, Schuller) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.30/42

57 Υ(1S) leptonic width Γ 1 /Γ µ (GeV) N 3 LO EXP NNLO NLO LO A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.31/42

58 e + e t t resonance production R 1 /R µ (GeV) N 3 LO NNLO NLO LO A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.32/42

59 Nonrelativistic Renormalization Group Several scales: m q, m q v, m q v 2 Logarithmic integrals between the scales ln v ln α s A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.33/42

60 Nonrelativistic Renormalization Group Several scales: m q, m q v, m q v 2 Logarithmic integrals between the scales ln v ln α s Logarithmic corrections Renormalization of pnrqcd Singularities of effective theory NRG equations Solution of NRG equations Resummation of log corrections A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.33/42

61 Bottomonium HFS in NLL approximation j M Υ(1S) M ηb = C4 F α4 s(ν)m b y y 25 + α» s(m b ) π π «1024 π2 y π y π y π y 25 3 π y «88057 π2 + y π y π2 629 π y 2873 π y F 1, 1; ; y «2873 π y 1 2F 1 1, 1; 82 « ; «42 y 25 7 «µ π2 ln + C F α s (µ)m b y 1 ln y y y «1250 y π 2 l y = α s(µ) α s (m b ) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.34/42

62 Nonrelativistic Renormalization Group Spectrum: NNLL, αs n ln n 2 α s NLL HFS, αs n ln n 1 α s (Pineda; Manohar, Hoang, Stewart) (Kniehl, Penin, Pineda, Smirnov, Steinhauser) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.35/42

63 Nonrelativistic Renormalization Group Spectrum: NNLL, αs n ln n 2 α s NLL HFS, αs n ln n 1 α s (Pineda; Manohar, Hoang, Stewart) (Kniehl, Penin, Pineda, Smirnov, Steinhauser) Threshold production: NLL, αs n ln n 1 v partial NNLL, αs n ln n 2 v (Pineda; Manohar, Hoang, Stewart, Teubner) (Manohar, Hoang, Stewart, Teubner; Pineda, Signer) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.35/42

64 Nonrelativistic Renormalization Group Spectrum: NNLL, αs n ln n 2 α s NLL HFS, αs n ln n 1 α s (Pineda; Manohar, Hoang, Stewart) (Kniehl, Penin, Pineda, Smirnov, Steinhauser) Threshold production: NLL, αs n ln n 1 v partial NNLL, αs n ln n 2 v (Pineda; Manohar, Hoang, Stewart, Teubner) (Manohar, Hoang, Stewart, Teubner; Pineda, Signer) Leptonic/photonic width and resonance production: NNLL spin dependence, α n s ln n 2 α s (Penin, Pineda, Smirnov, Steinhauser) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.35/42

65 Nonrelativistic Renormalization Group WARNING! Resummation parameter ln v 1 NRG can reduce scale dependence NRG cannot cure slow convergence A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.36/42

66 Nonrelativistic Renormalization Group WARNING! Resummation parameter ln v 1 NRG can reduce scale dependence NRG cannot cure slow convergence Theoretical error estimate in (partial) NNLL analysis of e + e t t threshold production (Manohar, Hoang, Stewart, Teubner) 2% (2000) 3% (2001) 6% (2004) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.36/42

67 Nonrelativistic Renormalization Group WARNING! Resummation parameter ln v 1 NRG can reduce scale dependence NRG cannot cure slow convergence Theoretical error estimate in (partial) NNLL analysis of e + e t t threshold production (Manohar, Hoang, Stewart, Teubner) 2% (2000) 3% (2001) 6% (2004) More realistic 10% (Pineda, Signer, 2006) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.36/42

68 Nonrelativistic Renormalization Group WARNING! Resummation parameter ln v 1 NRG can reduce scale dependence NRG cannot cure slow convergence Theoretical error estimate in (partial) NNLL analysis of e + e t t threshold production (Manohar, Hoang, Stewart, Teubner) 2% (2000) 3% (2001) 6% (2004) More realistic 10% (Pineda, Signer, 2006) Most realistic 15% (has not been changed since 1998) (my personal) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.36/42

69 HFS in charmonium E hfs (MeV) EXP µ (GeV) ւ NLL ւ NLL տ NLO տ NLO LO տ LL տ LL A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.37/42

70 HFS in bottomonium E hfs (MeV) µ (GeV) ւ NLL ւ NLL տ NLO տ NLO LO տ LO տ LL A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.38/42

71 Γ Υ(1S) /Γ ηb ratio ւ NLO ւ NLO տ NNL տ NLL ւ NNLL ւ NNLL LO Γ(Υ(1S) e + e ) Γ(η b γγ) R b տ NNLO տ NNLO µ (GeV) A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.39/42

72 NRG analysis of η b η b mass from M(Υ(1S)) M(η b ) in NLL: M(η b ) = 9421 ± 11 (th) +9 8 (δα s) MeV A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.40/42

73 NRG analysis of η b η b mass from M(Υ(1S)) M(η b ) in NLL: M(η b ) = 9421 ± 11 (th) +9 8 (δα s) MeV η b photonic width from Γ(Υ(1S) e+ e ) Γ(η b γγ) in NNLL: Γ(η b γγ) = ± 0.089(th) (δα s) ± 0.015(exp) kev A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.40/42

74 NRG analysis of η b η b mass from M(Υ(1S)) M(η b ) in NLL: M(η b ) = 9421 ± 11 (th) +9 8 (δα s) MeV η b photonic width from Γ(Υ(1S) e+ e ) Γ(η b γγ) in NNLL: Γ(η b γγ) = ± 0.089(th) (δα s) ± 0.015(exp) kev α s (M Z ) with the accuracy ±0.003 best among the analyses based on low-energy data A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.40/42

75 Summary A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.41/42

76 Summary Effective theory: Scale separation, power counting, NRG Perturbative calculation through threshold expansion First N 3 LO, NNLL results on the market. Promising! A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.41/42

77 Summary Effective theory: Scale separation, power counting, NRG Perturbative calculation through threshold expansion First N 3 LO, NNLL results on the market. Promising! Phenomenology: m b, m t from N 3 LO spectrum η b properties from NRG α s from bottomonium HFS A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.41/42

78 Challenging problems A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.42/42

79 Challenging problems Theory: Tree-loop static potental N 3 LO Υ-sum rules N 3 LO threshold production pnrqcd + Lattice A. Penin, TTP Karlsruhe & INR Moscow ECT Workshop, Trento, 2006 p.42/42

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