Top quark pair production cross section in e + e and hadronic collisions

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1 Top quark pair producion cross scion in + and hadronic collisions M. Bnk (TU Münchn) LC13: Exploring QCD from h infrard rgim o... LHC and Linar Collidrs Trno, Ialy, Sp 16-20, 2013 Oulin Top producion a h LHC NNLL rsummd MB, P. Falgari, S. Klin, C. Schwinn, [hp-ph]; MB, P. Falgari, S. Klin, J. Piclum, C. Schwinn, M. Uiali, F. Yan, [hp-ph] (TOPIXS program) Top producion nar hrshold in + collisions MB, Kiyo, Schullr, hp-ph/ ; MB, Kiyo, [hp-ph]; MB, Kiyo, Schullr, in prparaion. Effciv fild hory of unsal paricl producion and non-rsonan ffcs MB, Janzn, Ruiz-Fmnia [hp-ph]; Janzn, Ruiz-Fmnia [hp-ph] M. Bnk (TU Münchn) Trno, 17 Spmr / 28

2 Th op quark could lik any ohr quark, jus happns o a i mor massiv. SM simpl, prhaps unxciing = Prcision sudis of op quark propris (mass, widh) hrough inclusiv producion, FB and charg asymmris, invarian mass, p T (momnum) spcra c.... inracs srongly wih h Higgs and migh provid a window o ESB or o a srongly coupld scor (parial composinss) hav nw flavour-changing inracions drmin h fa of h Univrs Sarch for anomalous couplings, anomalis in producion and dcay. This is no a rviw... focus on rcn progrss in inclusiv producion. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

3 Th op quark could lik any ohr quark, jus happns o a i mor massiv. SM simpl, prhaps unxciing = Prcision sudis of op quark propris (mass, widh) hrough inclusiv producion, FB and charg asymmris, invarian mass, p T (momnum) spcra c.... inracs srongly wih h Higgs and migh provid a window o ESB or o a srongly coupld scor (parial composinss) hav nw flavour-changing inracions drmin h fa of h Univrs Sarch for anomalous couplings, anomalis in producion and dcay. This is no a rviw... focus on rcn progrss in inclusiv producion. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

4 Th op quark could lik any ohr quark, jus happns o a i mor massiv. SM simpl, prhaps unxciing = Prcision sudis of op quark propris (mass, widh) hrough inclusiv producion, FB and charg asymmris, invarian mass, p T (momnum) spcra c.... inracs srongly wih h Higgs and migh provid a window o ESB or o a srongly coupld scor (parial composinss) hav nw flavour-changing inracions drmin h fa of h Univrs Sarch for anomalous couplings, anomalis in producion and dcay. This is no a rviw... focus on rcn progrss in inclusiv producion. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

5 Toal op-pair producion cross scion Hadronic producion (LHC) Bnchmark for QCD calculaions of hadronic procsss. Now h mos prcisly prdicd purly hadronic cross scion. Thorically clan u no vry prcis mass drminaion. Tmpla for sarchs for unknown paricls wih missing ransvrs momnum. Consrain on gluon disriuion in h proon in a momnum fracion rgion rlvan o Higgs producion. + Vry prcis and clan mass masurmn and widh masurmn a hrshold Couplings aov hrshold M. Bnk (TU Münchn) Trno, 17 Spmr / 28

6 Toal op-pair producion cross scion Hadronic producion (LHC) Bnchmark for QCD calculaions of hadronic procsss. Now h mos prcisly prdicd purly hadronic cross scion. Thorically clan u no vry prcis mass drminaion. Tmpla for sarchs for unknown paricls wih missing ransvrs momnum. Consrain on gluon disriuion in h proon in a momnum fracion rgion rlvan o Higgs producion. + Vry prcis and clan mass masurmn and widh masurmn a hrshold Couplings aov hrshold M. Bnk (TU Münchn) Trno, 17 Spmr / 28

7 I. Hadronic producion M. Bnk (TU Münchn) Trno, 17 Spmr / 28

8 Daa vs. NLO dominan a Tvaron dominan a LHC NLO corrcion is larg (50% a LHC) [NLO QCD: Nason, Dawson, Ellis (1988), Bnakkr al. (1989)] Daa rquirs prcision yond NLO Tvaron NLO CDF D NLO ATLAS CMS LHC (7 TV) LHC (8 TV) ± ± ± 2 ± 11 ± ± 2 ± 31 ± ± 3 ± 11 ± 10 σ (in p). NLO: m = GV. MST2008NLO, PDF+α s rror a 68% CL; indpndn µ r and µ f variaions. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

9 Thorical progrss yond NLO σ had ( s, m ) = i,j=q, q,g β = 1 4m 2 /ŝ dx i dx j f i (x i )f j (x j ) ˆσ ij ( ŝ, m ) ŝ = x i x j s NLO [NLO QCD: Nason, Dawson, Ellis, 1988, Bnakkr al., 1989] NLL rsummd [Caani al.; Brgr, Conopanagos; Kidonakis, Smih, Vog, 1996; Bonciani al., 1998] NNLO approx [MB, Czakon, Falgari, Miov, Schwinn, 2009; MB, Falgari, Klin, Schwinn, 2010; Aliv al., 2010; from 1PI/1PM disriuions: Ahrns al., 2010/11; Kidonakis, 2010] NNLL rsummd [MB, Falgari, Klin, Schwinn, 2011 (sof and Coulom); Cacciari, Czakon, Mangano, Miov, Nason, 2011 (sof) (Top++); MB, Falgari, Klin, Piclum, Schwinn, Uiali, Yan, 2012 (TOPIXS); from 1PI/1PM disriuions: Ahrns al., 2010/11] NNLO [Bärnruhr, Czakon, Miov, 2012 (q q); Czakon, Fidlr, Miov, 2013 (gg)] NNLO + NNLL [2013 v2 vrsions of (Top++) and (TOPIXS)] M. Bnk (TU Münchn) Trno, 17 Spmr / 28

10 Thorical progrss yond NLO σ had ( s, m ) = i,j=q, q,g β = 1 4m 2 /ŝ dx i dx j f i (x i )f j (x j ) ˆσ ij ( ŝ, m ) ŝ = x i x j s NLO [NLO QCD: Nason, Dawson, Ellis, 1988, Bnakkr al., 1989] NLL rsummd [Caani al.; Brgr, Conopanagos; Kidonakis, Smih, Vog, 1996; Bonciani al., 1998] NNLO approx [MB, Czakon, Falgari, Miov, Schwinn, 2009; MB, Falgari, Klin, Schwinn, 2010; Aliv al., 2010; from 1PI/1PM disriuions: Ahrns al., 2010/11; Kidonakis, 2010] NNLL rsummd [MB, Falgari, Klin, Schwinn, 2011 (sof and Coulom); Cacciari, Czakon, Mangano, Miov, Nason, 2011 (sof) (Top++); MB, Falgari, Klin, Piclum, Schwinn, Uiali, Yan, 2012 (TOPIXS); from 1PI/1PM disriuions: Ahrns al., 2010/11] NNLO [Bärnruhr, Czakon, Miov, 2012 (q q); Czakon, Fidlr, Miov, 2013 (gg)] NNLO + NNLL [2013 v2 vrsions of (Top++) and (TOPIXS)] M. Bnk (TU Münchn) Trno, 17 Spmr / 28

11 Rsummaion: rakdown of pruraion hory a small β Fixd-ordr PT no applical for hrshold producion (non-rlaivisic) Coulom forc A A 0 g2 β Inhiid (sof) radiaion A A 0 g 2 ln 2 β Pruraion hory raks down du o h mrgnc of small scals Mβ, Mβ 2 M, ŝ. Sum h sris of nhancd quanum flucuaions o all ordrs: { } { σ = σ 0 [1 + g 2 1 β, ln2,1 β + g 4 1 β 2, ln } ] 2,1 β, ln 4,3,2,1 β +... β ( ) αs k [ ] = σ 0 xp ln β g 0 (α s ln β) + g 1 (α s ln β) + α sg 2 (α s ln β) +... β k=0 }{{}}{{}}{{} (LL) (NLL) (NNLL) { 1 (LL,NLL); α s, β (NNLL); α 2 } s, αsβ, β2 (NNNLL);... M. Bnk (TU Münchn) Trno, 17 Spmr / 28

12 Rsummaion: rakdown of pruraion hory a small β Fixd-ordr PT no applical for hrshold producion (non-rlaivisic) Coulom forc A A 0 g2 β Inhiid (sof) radiaion A A 0 g 2 ln 2 β Pruraion hory raks down du o h mrgnc of small scals Mβ, Mβ 2 M, ŝ. Sum h sris of nhancd quanum flucuaions o all ordrs: { } { σ = σ 0 [1 + g 2 1 β, ln2,1 β + g 4 1 β 2, ln } ] 2,1 β, ln 4,3,2,1 β +... β ( ) αs k [ ] = σ 0 xp ln β g 0 (α s ln β) + g 1 (α s ln β) + α sg 2 (α s ln β) +... β k=0 }{{}}{{}}{{} (LL) (NLL) (NNLL) { 1 (LL,NLL); α s, β (NNLL); α 2 } s, αsβ, β2 (NNNLL);... M. Bnk (TU Münchn) Trno, 17 Spmr / 28

Join sof-gluon and Coulom rsummaion [MB, Falgari, Schwinn (2009, 2010)] ˆσ(β, µ) = i H i (M, µ) dω R α J Rα (E ω 2 ) Rα i (ω, µ) Facorizaion and rsummaion wih non-rlaivisic and sof-collinar EFT.

13 Join sof-gluon and Coulom rsummaion [MB, Falgari, Schwinn (2009, 2010)] ˆσ(β, µ) = i H i (M, µ) dω R α J Rα (E ω 2 ) Rα i (ω, µ) Facorizaion and rsummaion wih non-rlaivisic and sof-collinar EFT. Summaion of ln β rms y SCET RGE quaion in x-spac, no momn spac. [Bchr, Nur (2006); Bchr, Nur, Xu (2007)] Mach o fixd-ordr rsul o dscri h rgion β 1 ˆσ NNLL machd = [ˆσNNLL ˆσ NNLL xp. o NNLO ] + ˆσNNLO M. Bnk (TU Münchn) Trno, 17 Spmr / 28

14 Impac of NNLO and rsummaion [TOPIXS] σ [p] Tvaron LHC ( s =7 TV) LHC ( s =8 TV) NLO NNLO app NNLO NNLL m = GV, α s(m Z ) = , (N)NLO MST08 PDFs, firs rror horical uncrainy, scond PDF+α s a 68% CL. Thorical rror: indpndn sof/hard/coulom scal variaions, rsummaion amiguiis. Tvaron (q q) significan rsummaion/nnlo ffc [+8%], rducion of horical uncrainy [8% 3%] (xcluding PDF + α s rror), hrshold approximaion workd wll. LHC (gg) small rsummaion [+1%]/significan NNLO ffc [+4%], significan rducion of horical uncrainy [13% 4.5%], hrshold xpansion did no work ha wll. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

15 Comparison of NNLL rsuls Σ p 8.5 Σ p lf of dashd: NNLO app + NNLL MB, Falgari, Klin, Schwinn 2011; TOPIXS 1.0 (m = GV) Cacciari, Czakon, Mangano, Miov, Nason 2011 (m = GV) Ahrns, Frroglia, Nur, Pcjak, Yang 2011 (1PI, m = GV) Ahrns, Frroglia, Nur, Pcjak, Yang 2011 (PIM, m = GV) righ of dashd: NNLO + NNLL Piclum; 2013 upda of MB, Falgari, Klin, Piclum, Schwinn, Uiali, Yan 2012; TOPIXS 2.0 (m = GV) Czakon, Fidlr, Miov, 2013 op++2.0 (m = GV) Exprimns: CDF/D comind; CMS/ATLAS-CONF Error ars: solid hory, dashd PDF (+α s) addd PDF s: MST 2008 NNLO M. Bnk (TU Münchn) Trno, 17 Spmr / 28

16 Top mass from oal cross scion [upda of and ] Exprimnal cross scion dpnds on assumd m. Σ m p 10 9 Σ m p Maximiz join liklihood f (m ) = dσ f h (σ m ) f xp(σ m ). m = ( ) GV (Tvaron daa) m = ( ) GV (CMS daa [ ]) Consisn wih op dcay mass rconsrucion! (m = ± 0.8 GV) S also Langnfld al. (2009), D0, CDF,... M. Bnk (TU Münchn) Trno, 17 Spmr / 28

17 II. Thrshold producion in + M. Bnk (TU Münchn) Trno, 17 Spmr / 28

18 Pair producion hrshold Coulom forc and ak Dcay Ulra-prcis mass masurmn Uniqu QCD dyanmics Sal op quark, no srong inracion 0.6 Σ M. Bnk (TU Münchn) Trno, 17 Spmr / 28

19 Pair producion hrshold Coulom forc and ak Dcay Ulra-prcis mass masurmn Uniqu QCD dyanmics Sal op quark, wih srong Coulom forc 0.6 Σ M. Bnk (TU Münchn) Trno, 17 Spmr / 28

20 Pair producion hrshold Coulom forc and ak Dcay Ulra-prcis mass masurmn Uniqu QCD dyanmics Unsal op quark, wih srong Coulom forc 0.6 Σ Smalls srucur in paricl physics known o xis (10 17 m). Dirc spcroscopic widh masurmn. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

21 Thrshold scan a ILC Addiional smaring of h rsonanc du o am luminosiy spcrum (collidr-spcific) and ISR Mos rcn sudy for ILC/CLIC [Sidl, Simon, Tsai, Poss, 2013] assums 10 f 1 a 10 poins. [δm ] hr = 27 MV [simulanous fi of α s] M. Bnk (TU Münchn) Trno, 17 Spmr / 28

22 Ky ims for horical prcision All-ordr summaion sinc α s/v can larg. ll-dfind framwork (EFT) o comin rlaivisic and oundsa ffcs. Mass dfiniion: aandon h pol mass! Ponial-suracd mass [MB, 1998] m PS (µ f ) m pol q <µ f Cancllaion of larg pruraiv conriuions from h IR. d 3 q (2π) 3 ṼCoulom( q ) High ordrs: NNLO calculaions find larg uncrainy [up ±25%] in h cross scion in h rsonanc pak rgion (MB, Signr, Smrinov; Hoang, Tunr; Mlnikov,Ylkovsky; Yakovlv; Nagano al.; Pnin, Pivovarov, 1998/99). May lss afr log(v) rsummaion [±3%] (Hoang al., 2002; Hoang, Sahlhofn, 2011) Basic chniqus workd ou nd of 1990s u h nx ordr is hard! M. Bnk (TU Münchn) Trno, 17 Spmr / 28

23 Non-rlaivisic EFT In h asnc of lcrowak corrcions (q µq ν q 2 g µν) Π(q 2 ) = i d 4 x iq x 0 T(j µ(x)j ν(0)) 0, j µ (x) = [ γ µ ](x) R σ X σ 0 = 12π 2 Im Π(s) Rlvan scals: m 175 GV (hard), m α s 30 GV (sof, ponial) and h ulrasof scal (us) m α 2 s 2 GV. L QCD [Q(h, s, p), g(h, s, p, us)] L PNRQCD [Q(p), g(us)] µ > m µ < m v Th ulrasof scal appars xplicily only a NNNLO. A compl calculaion of h (nonlogarihmic) NNNLO corrcion is hrfor ndd. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

24 Maching/ffciv Lagrangian a NNNLO Maching of currns and inracions (ponials and ulrasof) j i = c v ψ σ i χ + dv 6m 2 ψ σ i D 2 χ +... L QCD L PNRQCD L PNRQCD = ψ ( id 0 + i Γ m + 4 ) 8m 3 ψ + χ ( id 0 i Γ 2 2 2m 4 ) 8m 3 χ [ ] ( + d d 1 r ψ ψ (x + r) αsc ) [ ] F + δv(r, ) χ χ (x) r g sψ (x)xe(, 0)ψ(x) g sχ (x)xe(, 0)χ(x) Thr-loop maching rquird for h hard vrx c v [Marquard, Piclum, Sidl, Sinhausr, unpulishd] and h Coulom ponial [Anzai, Kiyo, Sumino, 2009; Smirnov, Smirnov, Sinhausr, 2009]. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

25 NNNLO cross scion calculaion [MB, Kiyo, 2008; MB, Kiyo, Schullr, in prparaion] whr G (1,8) c (r, r, E) = my ( ) ) 2π y(r+r (2l + 1)(2yr) l (2yr ) l r r s!l s (2l+1) (2yr)L s (2l+1) (2yr ) P l rr l=0 (s + 2l + 1)!(s + l + 1 λ) s=0 Th ulrasof conriuion is (D = d 1) y = m(e + iɛ), λ = mαs {C F (singl); C F C A /2 (oc)} 2y δg us = ( i)(ig s) 2 d d ( ) k i k i k j 6 C F (2π) d k 2 k 0 2 δ ij d D p n (2π) n=1 D i G (1) (p 1, p 2 ; E)i G (8) (p 3, p 4 ; E + k 0 )i G (1) (p 5, p 6 ; E) [ 2p i i 3 (2π) D δ (D) (p 3 p 2 ) + (ig s) 2 C A 2(p 2 p 3 ) i ] [ m 2 (p 2 p 3 ) 4 i 2pj 4 (2π) D δ (D) (p 4 p 5 ) + (ig s) 2 C A 2(p 4 p 5 ) j ] m 2 (p 4 p 5 ) 4 Difficuly is h xracion of h divrgnc in dim. rg. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

26 Cross scion nar hrshold, from 2nd o 3rd ordr m,ps (20 GV) = 170 GV, Γ = 1.4 GV 1.4 NNLO 1.4 NNNLO R 0.8 R Μ GV 0.4 No h final rsul! Μ GV [MB, Signr, Smirnov, 1999] [MB, Kiyo, Schullr, in progrss] M. Bnk (TU Münchn) Trno, 17 Spmr / 28

27 III. Non-rsonan ffcs M. Bnk (TU Münchn) Trno, 17 Spmr / 28

28 Fin-widh divrgncs and lcrowak ffcs Th QCD-only rsul usually discussd is far from raliy Fini-widh divrgncs (ovrall divrgnc, alrady a NNLO): [δg(e)] ovrall αs ɛ E Sinc E = s 2m + iγ, h divrgnc survivs in h imaginary par: Im [δg(e)] ovrall m αsαw ɛ Elcrowak ffc. Mus considr + +. Significan non-rsonan ackground from off-shll op dcay (unlss igh invarian mass cus ar applid), no dscrid y NRQCD. Sars a NLO [MB, Janzn, Ruiz-Fmnia, 2010; Pnin, Piclum, 2011] QED ffcs [Pinda, Signr, 2006; MB, Janzn, Ruiz-Fmnia, 2010], lcrowak asorpiv pars [Hoang, Rissr, 2004], iniial sa radiaion (formalism in [MB, Falgari, Schwinn, Signr, Zandrighi]). M. Bnk (TU Münchn) Trno, 17 Spmr / 28

29 Unsal paricl ffciv hory [MB, Chapovsky, Signr, Zandrighi, 2003] Unsal paricl EFT provids a sysmaic xpansion of h ampliud in powrs of Γ/m. Rsonan conriuions Producion of an on-shll, non-rlaivisic pair and susqun dcay +. Non-rsonan conriuions Off-shll lins. Full hory diagrams xpandd around s = 4m 2. ia = k,l C (k) p C p (l) d 4 x + T[iO (k) p (0) io p (l) (x)] + + k C (k) 4 + io (k) 4 (0) + O (v) p O (a) p = ē c2 γ i c1 ψ σ i χ = ē c2 γ i γ 5 c1 ψ σ i χ σ non-rs = 1 [ ] Im C (k) 4 s k + io (k) 4 (0) + O (k) 4 = ē c1 Γ 1 c2 ē c2 Γ 2 c1, M. Bnk (TU Münchn) Trno, 17 Spmr / 28

30 Unsal paricl ffciv hory [MB, Chapovsky, Signr, Zandrighi, 2003] Unsal paricl EFT provids a sysmaic xpansion of h ampliud in powrs of Γ/m. Rsonan conriuions Producion of an on-shll, non-rlaivisic pair and susqun dcay +. Non-rsonan conriuions Off-shll lins. Full hory diagrams xpandd around s = 4m 2. ia = k,l C (k) p C p (l) d 4 x + T[iO (k) p (0) io p (l) (x)] + + k C (k) 4 + io (k) 4 (0) + O (v) p O (a) p = ē c2 γ i c1 ψ σ i χ = ē c2 γ i γ 5 c1 ψ σ i χ σ non-rs = 1 [ ] Im C (k) 4 s k + io (k) 4 (0) + O (k) 4 = ē c1 Γ 1 c2 ē c2 Γ 2 c1, M. Bnk (TU Münchn) Trno, 17 Spmr / 28

31 Non-rsonan corrcions a NLO h1 h2 h3 ν h4 ν ν ν ν h5 h6 h7 h8 h9 h10 Equivaln o h dimnsionally rgulad + + procss wih Γ = 0, xpandd in h hard rgion around s = 4m 2. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

32 Non-rsonan corrcions a NLO ν h1 h3 ν ν ν h5 h6 h7 h8 h9 Equivaln o h dimnsionally rgulad + + procss wih Γ = 0, xpandd in h hard rgion around s = 4m 2. ν h4 h2 h10 0 Σ Σ [MB, Janzn, Ruiz-Fmnia, 2010] s GV QED and non-rsonan corrcions rlaiv o h LO cross scion in prcn: σ (1) QED /σ(0) (uppr solid lu), σ (1) non-rs /σ(0) for h oal cross scion (lowr solid rd) and M = 15 GV (lowr dashd rd). Th rlaiv siz of h sum of h QED and non-rsonan corrcions is rprsnd y h middl (lack) lins, for M,max (solid) and M = 15 GV (dashd) Larg corrcion low hrshold. Invarian mass cus can applid wihin h EFT framwork. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

33 + + nar s = 4m 2 NLO + NNLO singular rms [Janzn, Ruiz-Fmnia, 2013] Ralisic cross scion calculaions almos compld. ISR corrcions should applid in h horical prdicion, no h xprimnal simulaion. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

34 Summary I Hadronic cross scion now compud a NNLO+NNLL (sof + Coulom) Thorical uncrainy: 3% (Tvaron), 4.5% (LHC) PDF + α s uncrainy (68% CL): 5% Bs prdicd purly hadronic cross scion. PDF rror dominas. Solid consrain on ligh nw physics. ll-dfind drminaion of m wih a prsn rror of (4 5) GV, consisn wih h op mass rconsrucion from dcay producs. Oulook: diffrnial NNLO; NNNLL rsummaion. II + X cross scion nar hrshold now compud a NNNLO. Sizal 3rd ordr corrcions and rducion of horical uncrainy. Ulra-prcis mass masurmn. Ralisic prdicions for + + nar op-pair hrshold availal wih sufficin accuracy, including cus. Oulook: NNNLO cod; compl NNLO non-rsonan. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

35 Summary I Hadronic cross scion now compud a NNLO+NNLL (sof + Coulom) Thorical uncrainy: 3% (Tvaron), 4.5% (LHC) PDF + α s uncrainy (68% CL): 5% Bs prdicd purly hadronic cross scion. PDF rror dominas. Solid consrain on ligh nw physics. ll-dfind drminaion of m wih a prsn rror of (4 5) GV, consisn wih h op mass rconsrucion from dcay producs. Oulook: diffrnial NNLO; NNNLL rsummaion. II + X cross scion nar hrshold now compud a NNNLO. Sizal 3rd ordr corrcions and rducion of horical uncrainy. Ulra-prcis mass masurmn. Ralisic prdicions for + + nar op-pair hrshold availal wih sufficin accuracy, including cus. Oulook: NNNLO cod; compl NNLO non-rsonan. M. Bnk (TU Münchn) Trno, 17 Spmr / 28

The Top Pair Threshold: Status & New Developments

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