Top Quarks, Unstable Particles... and NRQCD

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1 Top Quarks, Unstable Particles... and NRQCD André H. Hoang Max-Planck-Institute for Physics Munich (Thanks to A. Manohar, I. Stewart, T. Teubner, C. Farrell, C. Reisser, M. Stahlhofen ) INT Workshop, May 5, 2005 A. H. Hoang p.1

2 Outline Top Physics at the Threshold vnrqcd (stable top): action, fields, scales, renormalization, RGE s,... - scale correlation - Applications: σ(e + e t t) m t, Γ t, λ tth σ(e + e t th) λ tth vnrqcd (unstable top): top decay, non-factorizable corrections, Conclusions, (many) Open Issues summing ln n (m t /Γ t ) INT Workshop, May 5, 2005 A. H. Hoang p.2

3 Top Physics at the Threshold Q 2 t t GeV = v top = 1 4m2 t s E m t 1 σ(e + e γ, Z t t) [pb] (δm t ) exp+theo thr.mass 100 MeV (δλ tth /λ tth ) exp 15 50% (δα s (M Z )) exp (δγ t ) exp 50 MeV δσ t t/σ t t 3% INT Workshop, May 5, 2005 A. H. Hoang p.3

4 Top Physics at the Threshold σ(e + e t th) 2.5 Σ e e tt H fb m H = 120 GeV s GeV δλ t /λ t 5% (m H = 120 GeV) ILC-1 ( s < 500 GeV) ILC-2 ( s > 500 GeV) region of large Higgs energy e + e - t t t t collinear QCD effects localized in t t system t t dynamics non-relativistic H INT Workshop, May 5, 2005 A. H. Hoang p.3

5 Top Physics at the Threshold perturbation theory in α s breaks down γ t g t 1 αs/ v ( αs/ v ) 2 ( αs/ v ) 3 Coulombsingularities Schrödinger Equation INT Workshop, May 5, 2005 A. H. Hoang p.4

6 Top Physics at the Threshold perturbation theory in α s breaks down γ t g t 1 αs/ v ( αs/ v ) 2 ( αs/ v ) 3 Coulombsingularities Schrödinger Equation perturbation theory in α s breaks down large logs (α s ln v) n ( m 2 ) m t = 175 GeV, p 25 GeV, E 4 GeV ln t = 8 E 2 RGE s INT Workshop, May 5, 2005 A. H. Hoang p.4

7 Top Physics at the Threshold perturbation theory in α s breaks down γ t g t 1 αs/ v ( αs/ v ) 2 ( αs/ v ) 3 Coulombsingularities Schrödinger Equation perturbation theory in α s breaks down large logs (α s ln v) n ( m 2 ) m t = 175 GeV, p 25 GeV, E 4 GeV ln t = 8 E 2 RGE s Γ t 1.5 GeV Λ QCD v = E m v eff = E+iΓ t m (Fadin,Khoze) m p = mv eff E = mv 2 eff Λ QCD always true! top threshold entirely perturbative! Schrödinger theory INT Workshop, May 5, 2005 A. H. Hoang p.4

8 EFT - Shopping List σ t t v n,m ( ) n ) [ ] m α s v (α s ln v 1, {v, α s }, {v 2, α s v, αs}, 2... LL NLL NNLL Action from Lagrangian in terms of field operators Manifest power counting in v at all times consistently obeye E p m and E p 2 /m Symmetries: gauge, spin,... Regulator independence matching in different schemes Renormalization of the theory Dimensional regularization anomalous dimensions, summation of (α s ln v) m INT Workshop, May 5, 2005 A. H. Hoang p.5

9 Different Effective Theories Classic "NRQCD": ( 92-95) Separate p > m from p < m "NRQCD-pNRQCD" ( 97-99) Separate also p > mv from p < mv Bodwin, Braaten, Lepage [Production, Decays, Lattice] Pineda, Soto, Brambilla, Vairo [ cc, bb] Combined 1- and 2-step matching, running Pineda ( 01) Power counting not uniform in different parts of the theory "vnrqcd" ( 99) Luke, Manohar, Rothstein, Stewart, A.H. Separation of all degrees of freedom at m [t t] 1-step matching and running, uniform power counting Correlation of mv and mv 2 (needed in general for Λ QCD mv 2 : e. g. c 1, also in QED) INT Workshop, May 5, 2005 A. H. Hoang p.6

10 vnrqcd Action = fields for degrees of freedom that can resonate in the regions hard, soft, potential, ultrasoft. potential quarks ψ p, χ p : (k 0, k) (mv 2, mv) soft gluons A µ q,s: (k 0, k) (mv, mv) ultrasoft gluons A µ us: (k 0, k) (mv 2, mv 2 ) Momentum Regions Beneke, Smirnov; Labelle;... hard soft potential ultrasoft k 0 m mv mv 2 mv 2 k m mv mv mv 2 INT Workshop, May 5, 2005 A. H. Hoang p.7

11 vnrqcd Action = fields for degrees of freedom that can resonate in the regions hard, soft, potential, ultrasoft. potential quarks ψ p, χ p : (k 0, k) (mv 2, mv) soft gluons A µ q,s: (k 0, k) (mv, mv) ultrasoft gluons A µ us: (k 0, k) (mv 2, mv 2 ) In dimensional regularization d D x L(x) is dimension-0, kinetic terms are O(v 0 ): ψ p (mv) 3/2 ɛ, A µ q,s (mv) 1 ɛ, A µ us (mv 2 ) 1 ɛ 2 renormalization scales are needed: µ S mv, µ U mv 2 powers of µ ɛ U, µɛ S of all operators unambiguously fixed Renormalization scales are correlated: µ U µ 2 S /m µ U mν 2, µ S mν all couplings are functions of ν INT Workshop, May 5, 2005 A. H. Hoang p.7

12 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. INT Workshop, May 5, 2005 A. H. Hoang p.8

13 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. L usoft = j ψ p»id 0 (p id)2 2m ff + ψ p4 8m p 1 4 Gµν u G u µν +... D µ = µ + iµ ɛ Ug u A µ us renormalization gives g 2 u 4π = α s(µ U ) = α s (mν 2 ) INT Workshop, May 5, 2005 A. H. Hoang p.8

14 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. j 1 L soft = L QCD (ϕ q, A q, c q ) µ 2ɛ S gs 2 2 ψ p [A µ q, A ν q ]U µν (σ) ψ p ψ p {Aµ q, A ν q }W µν (σ) ψ p ff +ψ p [ c q, c q ]Y (σ) ψ p + (ψ p T B Z µ (σ) ψ p ) ( ϕ q γ µ T B ϕ q ), renormalization gives g2 s 4π = α s(µ S ) = α s (mν), U (σ), W (σ), Y (σ), Z (σ) contain HQET couplings (c F, c S,...) INT Workshop, May 5, 2005 A. H. Hoang p.8

15 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. = C(ν = 1) = 0 C(ν < 1) 0 INT Workshop, May 5, 2005 A. H. Hoang p.8

16 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. L potential = µ 2ɛ S V ψ p ψ p χ p χ p +..., (k = p p ) V =» V (s) c k 2 + V (s) k π2 m k + V (s) r (p 2 +p 2 ) 2m 2 k 2 + V (s) 2 m 2 + V s (s) m 2 S2 + V (s) Λ m Λ + V (s) t 2 m 2 T INT Workshop, May 5, 2005 A. H. Hoang p.8

17 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. L mass = ψ p ψ p δm t +..., pole mass: δm t = 0 1S mass: δm t = m t» C 2 F α 2 s Ligeti, Manohar, AHH Teubner, AHH cancellation of O(Λ QCD ) renormalon from L mass + T[L soft, L soft ] PS mass, kinetic mass,... Beneke; Bigi etal. INT Workshop, May 5, 2005 A. H. Hoang p.8

18 vnrqcd Action L = L usoft + L soft + L potential, (multipole expansion everywhere) + L mass + L electroweak Luke, Manohar, Rothstein, Stewart, A.H. L electroweak = ψ p ψ p i Γ t , gives rule of thumb E E + i Γ t valid to NLO Fadin, Khoze Melnikov, Yakovlev complete NNLO (NNLL) finite width effects and electroweak corrections are still unknown (partial results see part II) works only for inclusive treatment of top decay INT Workshop, May 5, 2005 A. H. Hoang p.8

19 Velocity Renormalization Group (1) Match vnrqcd to full QCD at ν = 1 (µ S = µ U = m) (2) Determine anomalous dimensions in terms of ν (LL example) d µ S C = γ S (α s (µ S )) dµ S potential, soft loops d µ U C = γ U (α s (µ U )) dµ U ultrasoft loops ν d dν C(ν) = γ S(α s (mν)) + 2γ U (α s (mν 2 )) (3) Run Wilson coefficient from ν = 1 to ν = v α s sum all large logs: ln( m mν ), ln( m mν 2 ) (4) Calculate matrix elements with L vnrqcd (ν = v) no large logs: ln( p mν ) ln( v ν ), ln( E mν 2 ) ln( v2 ν 2 ) INT Workshop, May 5, 2005 A. H. Hoang p.9

20 Cross Section at NNLL Order Schematic: σ t t c(ν) 2 Im G(0, 0, s) +... ) ( 2 m 4 4m 3 + V (r) ( s 2m 2δm) iγ t G(r, r ) = δ (3) (r r ) G(0, 0, s) d 4 x e iq.x 0 T J(x)J (0) 0, J = ψ pσχ p INT Workshop, May 5, 2005 A. H. Hoang p.10

21 Cross Section at NNLL Order Schematic: σ t t c(ν) 2 Im G(0, 0, s) +... ) ( 2 m 4 4m 3 + V (r) ( s 2m 2δm) iγ t G(r, r ) = δ (3) (r r ) Running couplings of 1/k 2 potentials: V c (ν) 3 loops Pineda, Soto ( 00) Manohar, Stewart, A.H. ( 01) Stewart, A.H. ( 02) 1/m k potentials: V k (ν) 2 loops Manohar, Stewart, A.H. ( 00, 01) Stewart, A.H. ( 02) 1/m 2 potentials: V 2 (ν), V r (ν), V s (ν) 1 loop Manohar, Stewart ( 99) Pineda ( 01) Stewart, A.H. ( 02) only non-trivial divergences are 1/ɛ divergences ( LL ) INT Workshop, May 5, 2005 A. H. Hoang p.10

22 Cross Section at NNLL Order Schematic: σ t t c(ν) 2 Im G(0, 0, s) +... ) ( 2 m 4 4m 3 + V (r) ( s 2m 2δm) iγ t G(r, r ) = δ (3) (r r ) NLL Running of production current [ ln ν ln c(ν) = V c(ν) Vc (ν) 16π 2 4 ] + V 2 (ν) + V r (ν) + S 2 V s (ν) V k,eff(ν) Luke, Manohar, Rothstein INT Workshop, May 5, 2005 A. H. Hoang p.10

23 Cross Section at NNLL Order Schematic: σ t t c(ν) 2 Im G(0, 0, s) +... ) ( 2 m 4 4m 3 + V (r) ( s 2m 2δm) iγ t G(r, r ) = δ (3) (r r ) NLL Running of production current [ ln ν ln c(ν) = V c(ν) Vc (ν) 16π 2 4 ] + V 2 (ν) + V r (ν) + S 2 V s (ν) V k,eff(ν) Luke, Manohar, Rothstein NNLL running checks conceptual structure and renormalizability of the EFT important for phenomenology INT Workshop, May 5, 2005 A. H. Hoang p.10

24 NNLL Anomalous Dimension of J AHH, Phys.Rev. D69, (2004) 3-loop subdivergences of current correlators at 4 loops, NNLL non-mixing contributions (a) (b) (c) (a) σ+σ =2 (b) σ+σ =0 ν 2,r,s (c) σ+σ =0 (d) (e) (f) (d) σ+σ =0 (e) σ+σ =0 (f) C 2ϕ,2A,2c (g) (h) (i) (g) (j) (k) (l) (m) (a) δν 2,r,s (b) δν c ν 2,r,s (c) δν k1,k2 (d) δν k (e) δν c (f) δν c (g) δν c (h) δc 2 (i) δc 1 INT Workshop, May 5, 2005 A. H. Hoang p.11

25 NNLL Anomalous Dimension of J AHH, Phys.Rev. D69, (2004) 3-loop subdivergences of current correlators at 4 loops, NNLL non-mixing contributions NLL prediction of NNLL 1/ɛ 2 term confirmed INT Workshop, May 5, 2005 A. H. Hoang p.11

26 NNLL Anomalous Dimension of J AHH, Phys.Rev. D69, (2004) 3-loop subdivergences of current correlators at 4 loops, NNLL non-mixing contributions NLL prediction of NNLL 1/ɛ 2 term confirmed correlation of scales µ U = µ 2 S /m needed by consistency δz NNLL,1 c ɛ = couplings ɛ + couplings ɛ ( m µu ln µ 2 S ) INT Workshop, May 5, 2005 A. H. Hoang p.11

27 NNLL Anomalous Dimension of J AHH, Phys.Rev. D69, (2004) 3-loop subdivergences of current correlators at 4 loops, NNLL non-mixing contributions NLL prediction of NNLL 1/ɛ 2 term confirmed correlation of scales µ U = µ 2 S /m needed by consistency δz NNLL,1 c ɛ = couplings ɛ + couplings ɛ ( m µu ln µ 2 S ) NNLL non-mixing logs confirmed by 3-loop perturbation theory (Kniehl, Penin, Smirnov, Steinhauser) NNLL mixing contributions still missing w.i.p. (M. Stahlhofen) INT Workshop, May 5, 2005 A. H. Hoang p.11

28 Cross Section: e + e t t 1S mass - fixed order A.H. Q t 2 R v m 1S t = 175 GeV LO, NLO, NNLO s GeV ν = INT Workshop, May 5, 2005 A. H. Hoang p.12

29 Cross Section: e + e t t 1S mass - RG-improved, with NNLL non-mixing terms A.H. 1.6 Q t 2 R v m 1S t = 175 GeV LL, NLL, NNLL s GeV expansion shows better convergence scale uncertainties: ± 3% ν = theory error estimate: δσ t t/σ t t ±6% [aim: ±3%] INT Workshop, May 5, 2005 A. H. Hoang p.12

30 Cross Section: e + e t th dσ de H «E H E max H h C0 2 (µ, s, m t, m H ) + C1 2 (µ, i s, m t, m H ) Im[G(0, 0, v, µ)] t t e + e - + hard QCD corrections H γ t g soft & ultrasoft QCD corrections t 1 α s / v ( α s / v ) 2 ( α s / v ) 3 INT Workshop, May 5, 2005 A. H. Hoang p.13

31 Cross Section: e + e t th dσ deh fb GeV m t 1 S 180 GeV, m H 140 GeV s 600 GeV Born Α s LL NLL E H GeV good matching of NLL vnrqcd and O(α s ) full theory results matching at v 0.2 INT Workshop, May 5, 2005 A. H. Hoang p.14

32 Cross Section: e + e t th dσ deh fb GeV m t 1 S 180 GeV, m H 140 GeV s 550 GeV E H GeV good matching of NLL vnrqcd and O(α s ) full theory results matching at v 0.2 INT Workshop, May 5, 2005 A. H. Hoang p.14

33 Cross Section: e + e t th m t = 180 GeV s [GeV] mh [GeV] σ(born) [fb] σ(nll) [fb] σ(nll) σ(born) (20) (37) (30) (13) (5) (6) non-relativistic effects relevant up to s < 700 GeV INT Workshop, May 5, 2005 A. H. Hoang p.15

34 5 seconds break... INT Workshop, May 5, 2005 A. H. Hoang p.16

35 vnrqcd (unstable quarks) Optical Theory: effective complex indices of refraction for absorptive processes vnrqcd: contributions from real W b final states included in EFT matching conditions to QCD+ew. theory (=SM) complex matching conditions effective Lagrangian non-hermitian total rates through the optical theorem powercounting from stable theory still valid (gauge) symmetries constrain effective interactions INT Workshop, May 5, 2005 A. H. Hoang p.17

36 vnrqcd (unstable quarks) quark bilinears: ( L usoft ) t W b t ImΣ t = 1 2 Γ t = iσ t = δl = ψ p [ i Γ t 2 ( 1 p2 2m 2 t ) ] ψ p power counting: Γ t m t g 2 m t v 2 g g v α s finite lifetime is LL order, E E + iγ t Fadin,Khoze NNLL time dilatiation effect E E + iγ t prescription does not work beyond LL order INT Workshop, May 5, 2005 A. H. Hoang p.17

37 vnrqcd (unstable quarks) Currents: non-bw-cuts not included bw-cuts gauge invariant t e + t γ,z e - ( ) t e + ] [ + C LL + C NLL + C NNLL + ic abs NNLL Op = t e - Re[C ew NNLL ] (Kühn, Guth 1992) INT Workshop, May 5, 2005 A. H. Hoang p.17

38 vnrqcd (unstable quarks) soft & ultrasoft interactions: ( L usoft, L soft ) (LL), NLL and NNLL for stable quarks electroweak matching conditions (g 2 v 2 ) are beyond NNLL no interference (=non-factorizable) effects from ultrasoft gluon exchange at NLL (Khoze etal., Melnikov etal.) and NNLL e + e - γ,z t - t W - b - W + g b e + e - γ,z t - t W - W + b - g b q=0 q=0 Σ + = 0 e + e - γ,z t - t W - b - W + g b e + e - γ,z t - t W - W + b - g b Watch the power of powercounting and gauge invariance! INT Workshop, May 5, 2005 A. H. Hoang p.17

39 vnrqcd (unstable quarks) soft & ultrasoft interactions: ( L usoft, L soft ) (LL), NLL and NNLL for stable quarks electroweak matching conditions (g 2 v 2 ) are beyond NNLL no interference (=non-factorizable) effects from ultrasoft gluon exchange at NLL (Khoze etal., Melnikov etal.) and NNLL potentials: ( L potential ) q=0 q=0 Σ + = 0 V Coulomb is the only LL interaction but no electroweak corrections due to gauge invariance INT Workshop, May 5, 2005 A. H. Hoang p.17

40 Total Cross Section σ Γ,1 tot [ ] = 2N c Im 2 C LL i Cabs NNLL G coul + (C LL ) 2 δg coul INT Workshop, May 5, 2005 A. H. Hoang p.18

41 Total Cross Section ] [ 2 C LL i C abs NNLL Gcoul + (C LL ) 2 δgcoul σ Γ,1 tot = 2Nc Im accounts for interferences: irreducible resonant vs. non-resonant W + W b b final states INT Workshop, May 5, 2005 A. H. Hoang p.18

42 Total Cross Section σ Γ,1 tot [ ] = 2N c Im 2 C LL i Cabs NNLL G coul + (C LL ) 2 δg coul ( σtot) Γ 1 α s Γ t ɛ logarithmic phase space UV divergences ( ) e + e - anom. dim. for (e + e )(e + e ) operator i C(µ) e - e + additional correction: σ Γ,2 tot C(µ) (optical theorem) G LL coul = m2 t 4π { i v C F α s [ ( ) 1 4ɛ + ln i mt v µ + ψ ( 1 i C F α s 2 v ) ] } INT Workshop, May 5, 2005 A. H. Hoang p.18

43 Total Cross Section σ Γ,1 tot [ ] = 2N c Im 2 C LL i Cabs NNLL G coul + (C LL ) 2 δg coul ( σtot) Γ 1 α s Γ t ɛ logarithmic phase space UV divergences ( ) e + e - anom. dim. for (e + e )(e + e ) operator i C(µ) e - e + additional correction: σ Γ,2 tot C(µ) (optical theorem) s-independent µ-dependent, parametrically NLL order (!) C(m t ) unknown phase space corrections (work i.p.) non-resonant background INT Workshop, May 5, 2005 A. H. Hoang p.18

44 Total Cross Section: e + e t t Γ,Z pb Σ tot % 3% 2% s GeV finite lifetime corrections comparable to NNLL QCD corrections shift in the peak position: MeV (δm ex t 50 MeV) INT Workshop, May 5, 2005 A. H. Hoang p.19

45 What s left to do... NNLL Total Cross Section: (A) electroweak corrections NNLL phase space matching corrections C eeee (µ = m t )< 0 NNLL running of C eeee (µ) O(α s ) corrections to ic eett abs (µ = m t) due to mixing (B) QCD corrections (RGE-improved) Current uncertainty: (δσ t t/σ t t) QCD ±6% full NLL running of potentials Differential Cross Sections, (multi-quark final states): efficiencies more involved treatment of unstable particles INT Workshop, May 5, 2005 A. H. Hoang p.20

46 Colors This is blue This is red This is brown This is magenta This is Dark Green This is Dark Blue This is Green This is Cyan Test how this color looks Test how this color looks Test how this color looks Test how this color looks Test how this color looks INT Workshop, May 5, 2005 A. H. Hoang p.21

47 Fields in vnrqcd potential quark (P 0, P) (m v 2, mv) Luke, Manohar, Rothstein 1999 = P 0 = k 0, P = p + k mv k k = (k 0, k) mv 2 p m v (index) (dynamic) p Ψ QCD (x) ψ p (x us ) χ p (x us ) similar to HQET (Georgi, 1990) mv 2 reparametrization invariance: k k + k, p p k INT Workshop, May 5, 2005 A. H. Hoang p.22

48 Fields in vnrqcd Luke, Manohar, Rothstein 1999 soft gluon (P 0, P) (m v, mv) = P 0 = p 0 + k 0, P = p + k A µ QCD,soft (x) Aµ p (x us ) ultrasoft gluon (P 0, P) (m v 2, mv 2 ) A µ QCD,usoft (x) Aµ (x us ) INT Workshop, May 5, 2005 A. H. Hoang p.22

49 Fields in vnrqcd Luke, Manohar, Rothstein 1999 INT Workshop, May 5, 2005 A. H. Hoang p.22

Recent Results in NRQCD

Max-Planck-Institute für Physik (Werner-Heisenberg-Institut) Recent Results in NRQCD Pedro D. Ruiz-Femenía Continuous Advances in QCD 2006 Continuous Advances in QCD 2006 May 11-14, University of Minnesota