The Top Pair Threshold: Status & New Developments

Transcription

1 Th Top Pair Thrshold: Saus & Nw Dvlopmns André H. Hoang Max-Planck-Insiu for Physics Munich hanks o T. Tubnr, A. Manohar, I. Swar, P. Ruiz-Fmnia C. Rissr, C. Farrll, M. Sahlhofn Loopfs V, SLAC, Jun A. H. Hoang p.1

2 Oulin Brif inroducions masurmns & rquirmns hory issus Saus of QCD corrcions Elcrowak ffcs hard lcrowak corrcions fini lifim ffcs & phas spac maching Ohr Applicaion: H, m b from σ( hadrons) Loopfs V, SLAC, Jun A. H. Hoang p.2

3 Thrshold Masurmns Thrshold Scan: s 350 V (Phas I) coun numbr of vns color singl sa background is non-rsonan physics wll undrsood (rnormalons, summaions) δm xp 50 MV δm h 100 MV ha mass? sris 2m hr + pr.sris (shor disanc mass: 1S MS) Loopfs V, SLAC, Jun A. H. Hoang p.3

4 Thrshold Masurmns Thrshold Scan: s 350 V (Phas I) coun numbr of vns color singl sa background is non-rsonan physics wll undrsood (rnormalons, summaions) δm xp 50 MV δm h 100 MV ha mass? sris 2m hr + pr.sris (shor disanc mass: 1S MS) Simulaions L = 300 fb 1, scan poins Prala, Marinz, Miqul (δm ) sa 20 MV (δλ /λ ) sa = 15 50% (δα s (M )) sa = (δγ ) sa = 50 MV Loopfs V, SLAC, Jun A. H. Hoang p.4

5 Thrshold Masurmns Thrshold Scan: s 350 V (Phas I) coun numbr of vns color singl sa background is non-rsonan physics wll undrsood (rnormalons, summaions) δm xp 50 MV δm h 100 MV ha mass? sris 2m hr + pr.sris (shor disanc mass: 1S MS) Simulaions Influnc of Luminosiy spcrum (LO QED ffc!) Boogr vns Bam sprad Bamsrahlung ISR σ(s) = 1R 0 dxl(x)σ 0 (x 2 s) [pb] σ dfaul +bam sprad +bamsrahlung +ISR x shap of L(x) ssnial babbah accolinariy s [V] Loopfs V, SLAC, Jun A. H. Hoang p.4

6 Thrshold Masurmns Thrshold Scan: s 350 V (Phas I) coun numbr of vns color singl sa background is non-rsonan physics wll undrsood (rnormalons, summaions) δm xp 50 MV δm h 100 MV ha mass? sris 2m hr + pr.sris (shor disanc mass: 1S MS) Simulaions & hory goal: (δσ/σ) ho 3 % (δm ) sa 20 MV (δλ /λ ) sa = 15 50% (δα s (M )) sa = (δγ ) sa = 50 MV (δm ) sys 50 MV (δλ /λ ) sys =? (δα s (M )) sys = (δγ ) sys = 15 MV (δm ) ho 100 MV (δλ /λ ) ho? (δα s (M )) ho? (δγ ) ho? Loopfs V, SLAC, Jun A. H. Hoang p.4

7 Thory Issus m (hard) p m v (sof) E m v 2 (ulrasof) prurbaion hory in α s braks down (α s /v) n g 1 αs/ v ( αs/ v ) 2 ( αs/ v ) 3 Coulombsingulariis Schrödingr Equaion prurbaion hory in α s braks down larg logs (α s ln v) n ( m 2 ) m = 175 V, p 25 V, E 4 V ln E 2 = 8 RE s muli-scal problm 8 < : vnrqcd: 1-sp maching pnrqcd A. Signr s alk Loopfs V, SLAC, Jun A. H. Hoang p.5

8 Thory Issus Γ 1.5 V Λ QCD v = E m v ff = E+iΓ m (Fadin,Khoz) m p = mv ff E = mv 2 ff > Λ QCD always ru! op hrshold nirly prurbaiv! Schrödingr hory E Γ : op quarks ar always producd off-shll! mhods for on-shll producion do no apply for horical compuaions xprimnal analysis hory for unsabl paricls Loopfs V, SLAC, Jun A. H. Hoang p.5

9 vnrqcd (sabl quarks) L = L usof + L ponial + L sof Luk, Manohar, Rohsin, Swar, A.H. D µ = µ + iµ ɛ U g s(mν 2 )A µ L usof : ψ p(x) {id 0 (p id)2 2m δm } ψ p (x) L ponial : µ 2ɛ S V (ν) ψ p ψ p χ p χ p L sof : µ 2ɛ S U µν(ν) ψ p A µ q A ν q ψ p µ U µ 2 S /m V =» Vc (ν) k 2 + V k(ν)π 2 m k + V r(ν)(p 2 +p 2 ) 2m 2 k 2 + V 2(ν) m 2 + V s(ν) m 2 S2 + V Λ(ν) m 2 Λ + V (ν) m 2 T k p p Loopfs V, SLAC, Jun A. H. Hoang p.6

10 vnrqcd (sabl quarks) L = L usof + L ponial + L sof Luk, Manohar, Rohsin, Swar, A.H. D µ = µ + iµ ɛ U g s(mν 2 )A µ L usof : ψ p(x) {id 0 (p id)2 2m δm } ψ p (x) L ponial : µ 2ɛ S V (ν) ψ p ψ p χ p χ p L sof : µ 2ɛ S U µν(ν) ψ p A µ q A ν q ψ p µ U µ 2 S /m xrnal currns: (producion & annihilaion) O p = C V,A (ν) [ē i ( 5 )][ψ p σ i χ p ] + ( 3 S 1 ) Loopfs V, SLAC, Jun A. H. Hoang p.6

11 Cross Scion a NNLL Ordr Schmaic: [ σ o Im d 4 x iˆqx 0 T O ] p (0) O p (x) 0 Im [ (C A (ν) 2 + C V (ν) 2 ) (0, 0, s) ] ) ( 2 m 4 4m + V (r) ( s 2m 2δm) iγ 3 (r, r ) = δ (3) (r r ) Loopfs V, SLAC, Jun A. H. Hoang p.7

12 Cross Scion a NNLL Ordr Schmaic: [ σ o Im d 4 x iˆqx 0 T O ] p (0) O p (x) 0 Im [ (C A (ν) 2 + C V (ν) 2 ) (0, 0, s) ] ( 2 m 4 4m + V (r) ( s 2m 2δm) iγ 3 ) (r, r ) = δ (3) (r r ) fully known a NNLL ordr Manohar,Swar; AH Pinda,Soo Pr 94, Schrödr 98 NLL Luk al. 99 NNLL (maching) Bnk al; Czarncki al 99 NNLL (non-mixing) AH 03 NNLL (mixing) ss. unknown spin-dpndn (sof) Pnin al. 04 usof n f Sahlhofn, AH 05 Loopfs V, SLAC, Jun A. H. Hoang p.7

13 Cross Scion a NNLL Ordr 1S mass - R-improvd, wih NNLL non-mixing rms Q 2 R v m 1S = 175 V Manohar,Swar,Tubnr,AH LL, NLL, NNLL s V RI xpansion shows br convrgnc hory rror: δσ /σ ±6% goal: 3% ν = full NNLL (mixing) running of C(ν) rquird Sahlhofn, AH (usof w.i.p.) Loopfs V, SLAC, Jun A. H. Hoang p.8

14 Cross Scion a NNLL Ordr 1S mass - fixd ordr approach Q 2 R v m 1S = 175 V Tubnr,AH; Mlnikov, Ylkovski;Yakovlv; Bnk,Signr,Smirnov; Sumino, Kiyo LO, NLO, NNLO s V pak posiion sabl (hrshold masss: 1S, PS,... ) larg snsiiviy o facorizaion/rnormalizaion scal sing ν = NNNLO parial rsuls: Pnin al , Bnk al. 05, Eiras al. 05 Loopfs V, SLAC, Jun A. H. Hoang p.8

15 NRQCD (unsabl quarks) inclusiv ramn Opical Thory: ffciv complx indics of rfracion for absorpiv procsss NRQCD: conribuions from ral b final sas includd in EFT maching condiions o QCD+w. hory (=SM) complx maching condiions & anomalous dimnsions ffciv Lagrangian non-hrmiian oal ras hrough h opical horm phas spac maching powr couning mainaind xpansion around mass-shll (Bnk al. 04) auomaic in NRQCD Chrisoph Rissr, AH; Phys. Rv. D 71, (2005) Chrisoph Rissr, AH; hp-ph/ Loopfs V, SLAC, Jun A. H. Hoang p.9

16 Elcrowak Effcs 3 classs: Hard lcrowak AHH, hp-ph/ Elcromagnic Fini lifim No gnral hory for all cass and obsrvabls! EFT for crain obsrvabls and givn powrcouning. Γ m α m α 2 s v α s α 1/2 saus for σ o : LL NLL NNLL Hard.w. El. mag. ( )? Fin. lif. w.i.p. w.i.p. Loopfs V, SLAC, Jun A. H. Hoang p.10

17 NRQCD (unsabl quarks) quark bilinars: ( L usof ) b ImΣ = 1 2 Γ = iσ = δl = ψ p [ i Γ 2 im dilaaion corrcion ) ] (1 p2 ψ p 2m 2 powr couning: Γ m g 2 m v 2 g g v α s fini lifim is LL ordr, E E + iγ Fadin,Khoz NNLL im dilaiaion ffc E E + iγ prscripion dos no work byond LL ordr Loopfs V, SLAC, Jun A. H. Hoang p.11

18 NRQCD (unsabl quarks) quark bilinars: ( L usof ) b ImΣ = 1 2 Γ = iσ = δl = ψ p [ i Γ 2 im dilaaion corrcion ) ] (1 p2 ψ p 2m 2 gluon inracions & ponials: lcrowak corrcions ihr byond NNLL ordr or vanish du o gaug cancllaions ulrasof gluon inrfrnc ffcs vanish a NLL and NNLL ordr (nw!) q=0 q=0 [Khoz al., Mlnikov al.] Σ + = 0 Loopfs V, SLAC, Jun A. H. Hoang p.11

19 NRQCD (unsabl quarks) quark bilinars: ( L usof ) b ImΣ = 1 2 Γ = iσ = δl = ψ p [ i Γ 2 im dilaaion corrcion ) ] (1 p2 ψ p 2m 2 gluon inracions & ponials: lcrowak corrcions ihr byond NNLL ordr or vanish du o gaug cancllaions,, b b - + g g b b,, b - g b b - g b ulrasof gluon inrfrnc ffcs vanish a NLL and NNLL ordr (nw!) [Khoz al., Mlnikov al.] Loopfs V, SLAC, Jun A. H. Hoang p.11

20 NRQCD (unsabl quarks) Currns: only b-cus includd b-cus gaug invarian rad as sabl paricl, ( ) ] [ + C LL + C NLL + C NNLL + ic abs NNLL Op = R[C w NNLL ] wak conribuions: C. Rissr, AH, hp-ph/ Loopfs V, SLAC, Jun A. H. Hoang p.12

21 Hard Elcrowak Effcs ral shor-disanc lcrowak corrcions: O(α m ) NNLL only maching condiions o ( )( ) opraors xis! H 0 b b H 0 b b b b b b b b H H b b ν ν ν ν ν b i i ui ui di di i i ui ui di di i i ui ui di di νi νi i i ui ui di di H 0 u u u+ u+ u u u+ u+ u u u+ u+ u u u+ u+ H H 0 QED corrcions (+ ral radiaion, ISR) no y drmind w.i.p. rzadkowski, Kühn, al. (1987) uh, Kühn (1992) updad: Rissr, AH hp-ph/ Loopfs V, SLAC, Jun A. H. Hoang p.13

22 Hard Elcrowak Effcs ral shor-disanc lcrowak corrcions: O(α m ) NNLL global normalizaion corrcion: w R[2c(1) NNLL w ] w α = 1/ α MS (m ) = 1/ m H V al. schm for α QED : α MS,n f =8 (µ = m ) m = 175 V Loopfs V, SLAC, Jun A. H. Hoang p.13

23 Fini Lifim Effcs b + and b cus Currns: Hard lcrowak & QCD maching corrcions ( ) Op = ] + [ C LL + C NLL + C NNLL + ic abs NNLL Loopfs V, SLAC, Jun A. H. Hoang p.14

24 Fini Lifim Effcs ( ) ] Currns: [ + C LL + C NLL + C NNLL + ic abs NNLL Op = σo Im [ C(ν) 2 (0, 0, s + iγ) ] accouns for irrducibl inrfrnc conribuions: rsonan non-rsonan + b b final sas Loopfs V, SLAC, Jun A. H. Hoang p.14

25 Fini Lifim Effcs Currns: [ ] O p = C LL + C NLL + C NNLL + icabs NNLL ( ) + σ o Im [ C(ν) 2 (0, 0, s + iγ ) ] ( σ Γ o ) α sγ 1 ɛ NNLL logarihmic phas spac UV divrgncs «NLL anom. dim. for ( )( ) opraor ic(µ) maching for ic(µ): physical + b b phas spac Phas Spac Maching w.i.p. + b b final sa wihou ops inpu: Riman,Kolodzj 05 Loopfs V, SLAC, Jun A. H. Hoang p.14

26 Toal Cross Scion Γ, pb Σ o % 3% 2% s V Rissr, AHH also includd summaion of phas spac logs (α s ln v) n fini lifim corrcions comparabl o NNLL QCD corrcions shif in h pak posiion: MV (δm x 50 MV) Loopfs V, SLAC, Jun A. H. Hoang p.15

27 Phas Spac Maching rquird for σ o from opical horm in EFT Rissr, Ruiz-Fmnia, AH fini imaginary maching condiions for all EFT opraors rmoval of unphysical EFT phas spac conribuions σ o [ ] k + dk d k k 0 k2 2m 2 k 2 Γ 2 + iγ 2 k 0 k2 2m 2 + iγ 2 k 0 k Loopfs V, SLAC, Jun A. H. Hoang p.16

28 Phas Spac Maching rquird for σ o from opical horm in EFT Rissr, Ruiz-Fmnia, AH fini imaginary maching condiions for all EFT opraors rmoval of unphysical EFT phas spac conribuions σ o [ ] k + dk d k k 0 k2 2m 2 k 2 Γ 2 + iγ 2 k 0 k2 2m 2 + iγ 2 (q 2 m 2 ) m2 nonrl. xp. valid doubl rsonan k 0 unphysical rgion of EFT singl/non-rsonan subracd in local xp. k Loopfs V, SLAC, Jun A. H. Hoang p.16

29 Phas Spac Maching rquird for σ o from opical horm in EFT Rissr, Ruiz-Fmnia, AH fini imaginary maching condiions for all EFT opraors rmoval of unphysical EFT phas spac conribuions σ o [ ] [ + Im ic(ν) D2 i C(ν) m 2 ] (q 2 m 2 ) m2 nonrl. xp. valid doubl rsonan k 0 unphysical rgion of EFT singl/non-rsonan subracd in local xp. k C(1), C(1),... (mach. cond. for 4 ops.) Loopfs V, SLAC, Jun A. H. Hoang p.16

30 Phas Spac Maching rquird for σ o from opical horm in EFT Rissr, Ruiz-Fmnia, AH fini imaginary maching condiions (counrrms) for all EFT opraors rmoval of unphysical EFT phas spac conribuions imaginary (fini) rnormalizaion sparaion of hard and sof phas spac conribuions maks summaion of phas spac logs maningful no fully diffrnial prdicions pracical issu: mild powr couning braking ffcs dpndnc on xprimnal cus S-wav producion: conribus a NLL ordr P-, D-,... wav sas: mandaory for consisn prdicion a LL ordr (.g. ) Loopfs V, SLAC, Jun A. H. Hoang p.17

31 ha s lf o do... a lo! NNLL Toal Cross Scion: (A) lcrowak corrcions NLL + NNLL phas spac maching C (µ = m ) NNLL running of C (µ) O(α s ) corr. s o ic abs (µ = m ) for NNLL mixing ffcs QED ffcs: ISR, bamsrahlung, Coulomb singulariis (B) QCD corrcions (RE-improvd) Currn uncrainy: (δσ /σ ) QCD ±6% full NLL running of ponials Fully Diffrnial Cross Scions: fficincis? rally ndd? inrsing horically? mor involvd ramn of unsabl paricls Loopfs V, SLAC, Jun A. H. Hoang p.18

32 Ohr Applicaions H op-yukawa coupling Thory Saus: σ( H) Born [amrs al., Djouadi al.] 1-loop w. [Dnnr al., Blangr al., You al.] O(α s ) fixd-ordr [Dimair al., Dawson al.] NLL larg-e H QCD ndpoin corrcions [C. Farrll, AHH] Σ H fb s V iny cross scion for s = 500 V masurmn of Yukawa coupling difficul δy /Y 30% fasibl a s = 500 V [A. Jus, 2002] Loopfs V, SLAC, Jun A. H. Hoang p.19

33 Ohr Applicaions H rgion of larg Higgs nrgy collinar QCD ffcs localizd in sysm dynamics non-rlaivisic H Loopfs V, SLAC, Jun A. H. Hoang p.19

34 Ohr Applicaions H rgion of larg Higgs nrgy collinar QCD ffcs localizd in sysm dynamics non-rlaivisic dσ deh fb V H m 1 S 180 V, m H 140 V s 600 V Α s 2 sing Born Α s E H V g 1 α s / v ( α s / v ) 2 ( α s / v ) 3 singulariis: (α s /v) n, (α s ln v) n fixd ordr xpansion braks down summaion of singular rms Loopfs V, SLAC, Jun A. H. Hoang p.19

35 Ohr Applicaions H facorizaion formula dσ de H «E H E max H C 2 (µ, s, m, m H ) Im[(0, 0, v, µ)] H + hard QCD corrcions g sof & ulrasof QCD corrcions 1 α s / v ( α s / v ) 2 ( αs/ v ) 3 NLL formalism: Cailiin Farrll, AH; Phys.Rv.D72, (2005) Cailin Farrll, AH; hp-ph/ Loopfs V, SLAC, Jun A. H. Hoang p.20

36 Ohr Applicaions H NLL Higgs nrgy spcrum dσ deh fb V s 700 V m 1 S 180 V, m H 140 V E H V Farrll, AH 05 larg E H ndpoin rgions incrass for smallr s / largr m H NLL maching: full hory rsuls from Dnnr, Dimair, Roh, br 04 Loopfs V, SLAC, Jun A. H. Hoang p.20

37 Ohr Applicaions H NLL Higgs nrgy spcrum dσ deh fb V m 1 S 180 V, m H 140 V s 600 V Born Α s LL NLL Farrll, AH E H V larg E H ndpoin rgions incrass for smallr s / largr m H NLL maching: full hory rsuls from Dnnr, Dimair, Roh, br 04 Loopfs V, SLAC, Jun A. H. Hoang p.20

38 Ohr Applicaions H NLL Higgs nrgy spcrum dσ deh fb V m 1 S 180 V, m H 120 V s 500 V Farrll, AH E H V larg E H ndpoin rgions incrass for smallr s / largr m H NLL maching: full hory rsuls from Dnnr, Dimair, Roh, br 04 s = 500 V: xnsion of facorizaion formula for low-e H ndpoin Loopfs V, SLAC, Jun A. H. Hoang p.20

39 Ohr Applicaion H oal cross scion Σ H fb m 1 S 175 V, m H 120 V Σ Born Σ NLL 0.8, , s V E2 s H V 2 Σ H fb Σ NLL Σ Α s Σ Born m 1 S 180 V, m H 120 V 500 V: facor 2 nhancmn ovr r lvl from summaion of (α s /v) n, (α s ln v) n rms anohr facor of 2 nhancmn for P = 80%, P + = +60% ssnial for ralisic sudis for ILC (phas I) Jus 02, 06 (δλ /λ ) ILC 500 V 30% 10 15% Loopfs V, SLAC, Jun A. H. Hoang p.21

40 Conclusion Top pair oal ra prdicions bcom mor and mor ralisic missing NNLL QCD corrcions w.i.p. dσ/σ < ±6% full s of lcrowak corrcions ( hard, QED?) op quark fini lifim: imaginary ilson cofficins b final sas phas spac maching raching goals δm 100 MV is no oally fr lunch sill considrabl work has o b invsd o g final numbr Many inrsing applicaions of hrshold physics xis. Loopfs V, SLAC, Jun A. H. Hoang p.22

41 Colors This is blu This is rd This is brown This is magna This is Dark rn This is Dark Blu This is rn This is Cyan Ts how his color looks Ts how his color looks Ts how his color looks Ts how his color looks Ts how his color looks Loopfs V, SLAC, Jun A. H. Hoang p.23