Electroweak corrections to tri-boson production at the ILC
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- Osborne Golden
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1 Elctrowak corrctions to tri-boson production at th ILC Duc Ninh LE ork in collaboration with Fawzi BOUDJEMA, Hao SUN and Marcus EBER Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.1/23
2 Outlin Motivation Calculation: +, Prliminary rsults Conclusions Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.2/23
3 Th LCs Th Intrnational Linar Collidr (ILC, s Bhnk s lctur): CM nrgy: GV. Luminosity: of th ordr cm 2 s 1. Th Compact LInar Collidr (CLIC, s Tssmlis s talk): CM nrgy: 0.5 3TV. Luminosity: also of th ordr cm 2 s 1. + collidrs ar high prcision machins. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.3/23
4 SM trilinar and quartic gaug couplings Trilinar couplings: chcking th non-ablian gaug structur. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.4/23
5 SM trilinar and quartic gaug couplings Trilinar couplings: chcking th non-ablian gaug structur. Quartic couplings: also giv a window on th spontanous symmtry braking (SSB) mchanism. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.4/23
6 SM trilinar and quartic gaug couplings Trilinar couplings: chcking th non-ablian gaug structur. Quartic couplings: also giv a window on th spontanous symmtry braking (SSB) mchanism. SM: unitarity constraints and th prturbativ condition (and xprimntal facts) indicat th xistnc of a small-mass Higgs and nw physics at TV scal. H = this suggsts som connction btwn th Higgs, nw physics and quartic gaug couplings (contact intractions). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.4/23
7 production at LEP 20 LEP 02/03/2001 Prliminary σ [pb] Racoon / YFS 1.14 no vrtx (Gntl 2.1) only ν xchang (Gntl 2.1) E cm [GV] SM trilinar couplings: wll tstd at LEP. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.5/23
8 production at LEP 20 LEP 02/03/2001 Prliminary σ [pb] Racoon / YFS 1.14 no vrtx (Gntl 2.1) only ν xchang (Gntl 2.1) E cm [GV] SM trilinar couplings: wll tstd at LEP. hat about th quartic gaug couplings? Not wll tstd. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.5/23
9 Quartic couplings and Higgs mchanism? (γ) Th thrshold for is about 250GV ( s LEP = 209GV). nd th LCs (LHC upgrad???). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.6/23
10 Quartic couplings and Higgs mchanism? (γ) Th thrshold for is about 250GV ( s LEP = 209GV). nd th LCs (LHC upgrad???). V H V V =, ; a Higgs strahlung contribution. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.6/23
11 Quartic couplings and Higgs mchanism? (γ) Th thrshold for is about 250GV ( s LEP = 209GV). nd th LCs (LHC upgrad???). V H V V =, ; a Higgs strahlung contribution. At th LCs th radiativ E corrctions must b takn into account (obvious from LEP s rsults: th famous Higgs blu band, top mass prdiction,...). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.6/23
12 1-loop multi-lg calculation: thortical challngs Qustion: hy do w hav to do this? Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.7/23
13 1-loop multi-lg calculation: thortical challngs Qustion: hy do w hav to do this? Answr: hav to liv with prturbativ QFT, as a mattr of fact. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.7/23
14 1-loop multi-lg calculation: thortical challngs Qustion: hy do w hav to do this? Answr: hav to liv with prturbativ QFT, as a mattr of fact. In som rspct, E radiativ corrctions ar mor difficult thn QCD corrctions du to th prsnc of many mass scals (Passarino). In practic, this mans that thr ar a lot of scalar intgrals with diffrnt mass configurations. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.7/23
15 1-loop multi-lg calculation: thortical challngs Qustion: hy do w hav to do this? Answr: hav to liv with prturbativ QFT, as a mattr of fact. In som rspct, E radiativ corrctions ar mor difficult thn QCD corrctions du to th prsnc of many mass scals (Passarino). In practic, this mans that thr ar a lot of scalar intgrals with diffrnt mass configurations. At prsnt, th frontir of on-loop multi-lg calculation ar 2 3 and a fw 2 4 procsss (mor dtails in Bvilacqua s talk). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.7/23
16 1-loop multi-lg calculation: thortical challngs Qustion: hy do w hav to do this? Answr: hav to liv with prturbativ QFT, as a mattr of fact. In som rspct, E radiativ corrctions ar mor difficult thn QCD corrctions du to th prsnc of many mass scals (Passarino). In practic, this mans that thr ar a lot of scalar intgrals with diffrnt mass configurations. At prsnt, th frontir of on-loop multi-lg calculation ar 2 3 and a fw 2 4 procsss (mor dtails in Bvilacqua s talk). Among th long list, gaug boson production is an important topic and attracts a lot of intrst: 1-loop QCD corrction to pp V V V at th LHC: ÒÓØ Ç ÓÐ È Ô ÓÔÓÙÐÓ Ò ¾¼¼ µ À Ò Ð Ò ÔÔ Ò Ð ¾¼¼ µ Ä ÞÓÔÓÙÐÓ Å ÐÒ ÓÚ Ò È ØÖ ÐÐÓ ¾¼¼ µ ººº È ØØ Ù 1-loop E corrction to + ËÙ Å Ò Ï Ò Ò ÙÓ : ¾¼¼ µ. + + : mor intrsting but also much mor difficult. This has not bn calculatd. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.7/23
17 + V V : tr diagrams : 9 diagrams, no trilinar and quartic couplings in SM : 20 diagrams, trilinar and quartic couplings contribut in SM V V H V f V (γ) (γ) (γ) Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.8/23
18 + + : on-loop diagrams t Hooft-Fynman guag, nglcting < S > couplings: ν γ() ν ν γ ν ν ν ν ν ν ν ν ν ν ν ν ν γ G Topology (1767) (2736) Loop Amp. (FormCalc-6.0) 6.4MB 6.9MB 4-point point Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.9/23
19 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
20 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. IR-divrgncs cancl out. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
21 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. IR-divrgncs cancl out. Initial Stat Collinar (ISC) contribution is subtractd to gt th pur wak corrction. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
22 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. IR-divrgncs cancl out. Initial Stat Collinar (ISC) contribution is subtractd to gt th pur wak corrction. FynArts-3.4, FormCalc-6.0(Mathmatica+ FORM) to gnrat Fynman diagrams and to gt th hlicity amplitud xprssions [s Hahn s talk]. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
23 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. IR-divrgncs cancl out. Initial Stat Collinar (ISC) contribution is subtractd to gt th pur wak corrction. FynArts-3.4, FormCalc-6.0(Mathmatica+ FORM) to gnrat Fynman diagrams and to gt th hlicity amplitud xprssions [s Hahn s talk]. SloopS( ÖÓ ÓÙ Ñ Ò Ë Ñ ÒÓÚ) to mak sur that th amplituds ar corrct by chcking gaug invarianc (using NLG Fynman ruls). Mor latr. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
24 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. IR-divrgncs cancl out. Initial Stat Collinar (ISC) contribution is subtractd to gt th pur wak corrction. FynArts-3.4, FormCalc-6.0(Mathmatica+ FORM) to gnrat Fynman diagrams and to gt th hlicity amplitud xprssions [s Hahn s talk]. SloopS( ÖÓ ÓÙ Ñ Ò Ë Ñ ÒÓÚ) to mak sur that th amplituds ar corrct by chcking gaug invarianc (using NLG Fynman ruls). Mor latr. LoopTools(FF+ Tnsor rduction +...) to calculat all on-loop intgrals. [À Ò Ú Ò ÇÐ Ò ÓÖ Ò Î ÖÑ Ö Ò] Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
25 calculation framwork dσ + V V 1 loop = dσ + V V virt + dσ + V V γ ral UV-divrgnc is rgularisd by using on-shll rnormalisation. IR-divrgncs cancl out. Initial Stat Collinar (ISC) contribution is subtractd to gt th pur wak corrction. FynArts-3.4, FormCalc-6.0(Mathmatica+ FORM) to gnrat Fynman diagrams and to gt th hlicity amplitud xprssions [s Hahn s talk]. SloopS( ÖÓ ÓÙ Ñ Ò Ë Ñ ÒÓÚ) to mak sur that th amplituds ar corrct by chcking gaug invarianc (using NLG Fynman ruls). Mor latr. LoopTools(FF+ Tnsor rduction +...) to calculat all on-loop [À Ò Ú Ò intgrals. Ò Î ÖÑ Ö Ò] ÇÐ Ò ÓÖ BASES(Ã Û Ø ) and VEGAS to do phas spac intgration and to gt distributions. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.10/23
26 Loop intgrals and numrical instabilitis k i = P i 1 j=1 p j, i = 1, 2,3,... dt(g) = dt(2k i k j ): Gram dtrminant dt(y ) = dt(m 2 i +m2 j (k i k j ) 2 ): modifid Cayly dtrminant Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.11/23
27 Loop intgrals and numrical instabilitis k i = P i 1 j=1 p j, i = 1, 2,3,... dt(g) = dt(2k i k j ): Gram dtrminant dt(y ) = dt(m 2 i +m2 j (k i k j ) 2 ): modifid Cayly dtrminant 5pt intgrals ar rducd to 4pts ÒÒ Ö Ò ØØÑ Ö ¾¼¼¾ E 0 = P 5 i=1 dt(y i ) dt(y ) D 0(i) Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.11/23
28 Loop intgrals and numrical instabilitis k i = P i 1 j=1 p j, i = 1, 2,3,... dt(g) = dt(2k i k j ): Gram dtrminant dt(y ) = dt(m 2 i +m2 j (k i k j ) 2 ): modifid Cayly dtrminant 5pt intgrals ar rducd to 4pts ÒÒ Ö Ò ØØÑ Ö ¾¼¼¾ E 0 = P 5 i=1 dt(y i ) dt(y ) D 0(i) Tnsor 4pt intgrals up to rank 4: Passarino-Vltman rduction D ijkl = f(p i, m i )/ dt(g) 4 = numrical instabilitis occur whn dt(g) is small (clos to PS boundary). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.11/23
29 Loop intgrals and numrical instabilitis k i = P i 1 j=1 p j, i = 1, 2,3,... dt(g) = dt(2k i k j ): Gram dtrminant dt(y ) = dt(m 2 i +m2 j (k i k j ) 2 ): modifid Cayly dtrminant 5pt intgrals ar rducd to 4pts ÒÒ Ö Ò ØØÑ Ö ¾¼¼¾ E 0 = P 5 i=1 dt(y i ) dt(y ) D 0(i) Tnsor 4pt intgrals up to rank 4: Passarino-Vltman rduction D ijkl = f(p i, m i )/ dt(g) 4 = numrical instabilitis occur whn dt(g) is small (clos to PS boundary). Scalar 4pt intgrals: can b tricky sinc thr ar a lot of configurations with diffrnt mass scals m, M and s. In practic th log- and Spnc- argumnts can b vry clos to 0 and 1, lading to numrical cancllation (obsrvd in ). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.11/23
30 Loop intgrals and numrical instabilitis k i = P i 1 j=1 p j, i = 1, 2,3,... dt(g) = dt(2k i k j ): Gram dtrminant dt(y ) = dt(m 2 i +m2 j (k i k j ) 2 ): modifid Cayly dtrminant 5pt intgrals ar rducd to 4pts ÒÒ Ö Ò ØØÑ Ö ¾¼¼¾ E 0 = P 5 i=1 dt(y i ) dt(y ) D 0(i) Tnsor 4pt intgrals up to rank 4: Passarino-Vltman rduction D ijkl = f(p i, m i )/ dt(g) 4 = numrical instabilitis occur whn dt(g) is small (clos to PS boundary). Scalar 4pt intgrals: can b tricky sinc thr ar a lot of configurations with diffrnt mass scals m, M and s. In practic th log- and Spnc- argumnts can b vry clos to 0 and 1, lading to numrical cancllation (obsrvd in ). Solutions: small DtG xpansion or using quadrupl prcision (loop library only, th rsults bcom stabl, 5 tims slowr). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.11/23
31 Ral corrction (I) 1) Two cutoff phas spac slicing approach: asy to implmnt but tim consuming ral = dσ + + γ soft (δ s ) + dσ + + γ hard (δ s ), dσ + + γ hard (δ s ) = dσ + + γ coll (δ s, δ c ) + dσ + + γ fin (δ s, δ c ) dσ + + γ Soft part: E γ < δ s s/2 = E, dσ soft = dσ Born α 2π 2 4X i,j=1 k < E d 3 k 2ω k ±p i p j Q i Q j (p i.k)(p j.k). Collinar part: {E γ E, cos θ γf > 1 δ c }, ŝ = xs, dσ coll = 2X i=1 α 2π Q2 i 1 δs 0 dxdσ Born (ŝ)» 1 + x 2 1 x ln ŝδ c 2m 2 i x 2x 1 x Finit part: {E γ E, cos θ γf 1 δ c }, numrical intgration using Mont Carlo BASES. 2) Dipol subtraction approach: to cross chck, in progrss. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.12/23
32 Ral corrction (II) Ral corrction is cutoff-indpndnt. Factorization condition: δ s and δ c ar sufficintly small. And δ c 2m 2 /s to us th collinar intgration formula. σ[fb] σ hard s=500gv M H =120GV -4 δ c =7 10 σ virt+soft σ virt+soft+hard log δ 10 s σ[fb] σ coll σ fin σ hard s=500gv M H =120GV -3 δ s = log δ 10 c Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.13/23
33 Gnuin wak corrction Th univrsal QED contribution from ISR: δ QED V +S = 2α π»(l 1)ln δ s + 34 L + π2 6 1, L = ln(s/m 2 ). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.14/23
34 Gnuin wak corrction Th univrsal QED contribution from ISR: δ QED V +S = 2α π»(l 1)ln δ s + 34 L + π2 6 1, L = ln(s/m 2 ). For + : δ is obtaind by subtracting th abov QED corrction from th Virt+Soft on. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.14/23
35 Gnuin wak corrction Th univrsal QED contribution from ISR: δ QED V +S = 2α π»(l 1)ln δ s + 34 L + π2 6 1, L = ln(s/m 2 ). For + : δ is obtaind by subtracting th abov QED corrction from th Virt+Soft on. For + + : aftr subtracting th abov QED corrction from th Virt+Soft, th rsult is still δ s dpndnt du to th final stat radiation, in th form a + bln δ s. By taking two diffrnt valus of δ s (10 3 and 10 4 ) w can solv for b. Continu to subtract this bln δ s contribution, w gt th rsult which dos not dpnd on δ s. This is dfind as th gnuin wak corrction (δ ). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.14/23
36 Gnuin wak corrction Th univrsal QED contribution from ISR: δ QED V +S = 2α π»(l 1)ln δ s + 34 L + π2 6 1, L = ln(s/m 2 ). For + : δ is obtaind by subtracting th abov QED corrction from th Virt+Soft on. For + + : aftr subtracting th abov QED corrction from th Virt+Soft, th rsult is still δ s dpndnt du to th final stat radiation, in th form a + bln δ s. By taking two diffrnt valus of δ s (10 3 and 10 4 ) w can solv for b. Continu to subtract this bln δ s contribution, w gt th rsult which dos not dpnd on δ s. This is dfind as th gnuin wak corrction (δ ). Larg QED corrctions rquir highr ordr tratmnt. Th abov procdur pavs th way to rsummation. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.14/23
37 Non-Linar gaug chck Gnral Non-Linar gaug (NLG) fixing Lagrangian ( ÓÙ Ñ ÓÔ Ò ½ ): L GF = 1 ξ ( µ i αa µ igc βµ ) µ+ + ξ g 2 (v + δh + i κχ 3 )χ ξ (. + ξ g (v + εh)χ 3 ) 2 1 (.A) 2. 2c 2ξ A Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.15/23
38 Non-Linar gaug chck Gnral Non-Linar gaug (NLG) fixing Lagrangian ( ÓÙ Ñ ÓÔ Ò ½ ): L GF = 1 ξ ( µ i αa µ igc βµ ) µ+ + ξ g 2 (v + δh + i κχ 3 )χ ξ (. + ξ g (v + εh)χ 3 ) 2 1 (.A) 2. 2c 2ξ A Choos ξ = ξ = ξ A = 1: propagators ar th sam as in th linar t Hooft-Fynman gaug, loop tnsor structur is simplst. 1 k 2 M 2 " # k µ k ν g µν (1 ξ ) k 2 ξ M 2 Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.15/23
39 Non-Linar gaug chck Gnral Non-Linar gaug (NLG) fixing Lagrangian ( ÓÙ Ñ ÓÔ Ò ½ ): L GF = 1 ξ ( µ i αa µ igc βµ ) µ+ + ξ g 2 (v + δh + i κχ 3 )χ ξ (. + ξ g (v + εh)χ 3 ) 2 1 (.A) 2. 2c 2ξ A Choos ξ = ξ = ξ A = 1: propagators ar th sam as in th linar t Hooft-Fynman gaug, loop tnsor structur is simplst. 1 k 2 M 2 " # k µ k ν g µν (1 ξ ) k 2 ξ M 2 Nw on-loop Fynman ruls: trilinar and quartic gaug-higgs couplings dpnd on 5 non-linar gaug paramtrs ( α, β, δ, κ, ε). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.15/23
40 Non-Linar gaug chck Gnral Non-Linar gaug (NLG) fixing Lagrangian ( ÓÙ Ñ ÓÔ Ò ½ ): L GF = 1 ξ ( µ i αa µ igc βµ ) µ+ + ξ g 2 (v + δh + i κχ 3 )χ ξ (. + ξ g (v + εh)χ 3 ) 2 1 (.A) 2. 2c 2ξ A Choos ξ = ξ = ξ A = 1: propagators ar th sam as in th linar t Hooft-Fynman gaug, loop tnsor structur is simplst. 1 k 2 M 2 " # k µ k ν g µν (1 ξ ) k 2 ξ M 2 Nw on-loop Fynman ruls: trilinar and quartic gaug-higgs couplings dpnd on 5 non-linar gaug paramtrs ( α, β, δ, κ, ε). Squard amplitud: indpndnt of thos paramtrs (gaug invariant). Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.15/23
41 NLG Chck and numrical instability ( α, β) ÏÏ ½µ ÏÏ ¾µ ¼ ¼µ ¹ º ¼ ¼ ¾ ¼ ½ ¹ ¹ º ¾½ ¾¾¼ ¹¾ º ¼ ¾ ½½½½¾ ¼ ½ ¾¼ ¼ ¾ ¾½ ¹¾ ½ ¼µ ¹ º ¼ ¼ ¾ ¼ ½ ¹ ¹ º ¼ ½ ¹¾ º ¼ ¾ ½½½½½¼ ½½ ¾ ¼ ¼½ ¾ ¹¾ ¼ ½µ ¹ º ¼ ¼ ½ ¾ ¹ ¹ º ¾¾ ½½ ¼ ¹¾ º ¼ ¾ ½½½½ ¼ ½¼½ ½¼ ¾ ¾ ½ ¹¾ : at last 10 digit agrmnt at a random point with doubl prcision. : for a DP random point, got only 4 digit agrmnt. By using QP, got 12 digits. Gaug invarianc chck is much wors for. This is an indication of numrical instability. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.16/23
42 Chcks on th rsults gaug invarianc chck: tr and on-loop squard amplitud lvl. UV and IR finitnss: on-loop squard amplitud lvl and for th virtual + soft corrctions. Two indpndnt calculations: diffrnt loop intgral libraris, diffrnt intgrators (BASES and VEGAS). This final chck is in progrss. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.17/23
43 All rsults ar prliminary Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.18/23
44 + : Total Xsction σ[fb] LO Full NLO ak M H =120GV s[gv] δ[%] Full NLO ak M H =120GV s[gv] Total Xsction pak about 1fb is at s 550GV. Th wak corrction gos from 3.5% to 10% whn s incrass from 500GV to 1TV. Comparisons with Su t al. arxiv: : Low nrgis (350, 500GV) quit good agrmnt (lss than 0.2%), at 1TV about 0.5%. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.19/23
45 + + : Total Xsction ak 40 0 σ[fb] LO Full NLO ak M H =120GV δ[%] Full NLO M H =120GV s[gv] s[gv] Total Xsction pak about 50fb (50 tims largr than σ ) is at s 900GV. Th wak corrction gos from 1.6% to 8.9% whn s incrass from 500GV to 1.5TV. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.20/23
46 + + : Distributions (I) [fb/gv] dσ/dp T s=500gv M H =120GV LO NLO dσ/dm()[fb/gv] s=500gv M H =120GV LO NLO p [GV] T M()[GV] Quit small corrctions (lss than 5%) at small GV. At larg GV, larg corrctions ( 30%) du to th hard photon ffct [dominant contribution coms from th low-nrgy photon rgion (s th δ s -plot) which corrsponds to larg p T and larg M.] Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.21/23
47 + + : Distributions (II) [fb] dσ/dy LO NLO s=500gv M H =120GV dσ/dy()[fb] s=500gv M H =120GV LO NLO y y() small corrctions ( 4 10%), shap unchangd. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.22/23
48 Conclusions Tri-boson production ( and ) at th ILC is a vry important procss to tst th quartic gaug couplings and th Higss mchanism. This is th first stp towards th undrstanding of SSB mchanism if th LHC cannot find th Higgs. Th prliminary rsults of our calculation indicat that E corrctions ar significant and hav to b takn into account whn doing analysis. Final rsults will b publishd soon. Corfu, 2009 Sp 4th Duc Ninh LE, Gaug boson production at th ILC p.23/23
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