When Higgs Production QCD Dressed, Met EW

Transcription

1 Outlines When Higgs Production QCD Dressed, Met EW Decay Giampiero PASSARINO Dipartimento di Fisica Teorica, Università di Torino, Italy INFN, Sezione di Torino, Italy HEPTOOLS Network Workshop on Higgs Boson Phenomenology,Zürich, Switzerland 7-9 January 2009

2 Outlines Based on work done in collaboration with Stefano Actis,Christian Sturm and Sandro Uccirati Thanks: M. Grazzini, M. Spira, P. Kant

3 Outlines Outlines (1, 2,) 1 From the analytical structure of EW NNLOs 2 to their numerical evaluation and their interplay with QCD, what else, but the inevitable!

4 Outlines Outlines (1, 2,) 1 From the analytical structure of EW NNLOs 2 to their numerical evaluation and their interplay with QCD, what else, but the inevitable!

5 Outlines Outlines (1, 2,) 1 From the analytical structure of EW NNLOs 2 to their numerical evaluation and their interplay with QCD, what else, but the inevitable!

6 Introduction Part I Preludio

7 Introduction & Motivation Calculation & Techniques Results & Discussion Summary & Conclusion QCD Introduction & Motivation Higgs production σ [fb] qq qqh bb h qb qth SM Higgs production qq Wh TeV4LHC Higgs working group gg h gg,qq tth qq Zh LHC m h [GeV] Dominant production mechanism: Gluon fusion NLO QCD Heavy top-quark limit: Dawson; Djouadi, Spira, Zerwas Entire Higgs-mass range: Djouadi, Graudenz, Spira, Zerwas; Harlander, Kant; Anastasiou, Beerli, Bucherer, Daleo, Kunszt; Aglietti, Bonciani, Degrassi, Vincini NNLO QCD Harlander; Catani, Florian, Grazzini; Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, Smith, Neerven; Anastasiou, Melnikov, Petriello; Catani, Grazzini C. Sturm Brookhaven Forum, Terra Incognita: from LHC to Cosmology, November 7th, 2008 Two-loop electroweak corrections to Higgs production and decay at LHC 3

8 Introduction QCD K - factor(s) The bulk From LO to NNLO and NNLL

9 Introduction EW What about EW? NLO for [%] δ δ complex W-boson mass EW δ real W-boson mass EW M h [GeV]

10 W 3 0! Introduction Introduction & Motivation EW Introduction Globally & Motivation Higgs decay 6 78 X YZ 4+, [ \[ ] ^ _^ ^ ` " #. / - - a ba a a c U V V Calculation & Techniques Results & Discussion Summary & Conclusion ) * ' ( $ &% 9 : ; < = R S T O P Q M N K L LB C D I J J G H H E F F F H d WW e ZZ dominant process for heavy Higgs boson H f g h bb dominant process for light Higgs, but huge QCD background. 3 H i j k rare process Brl 10m n, but experimentally clean NLO EW corrections of o p G f mt 2 q Liao,Li; Fugel, Kniehl, Steinhauser corrections of r s G f m t h 2u Korner, Melnikov, Yakovlev exact light-fermion contribution Aglietti, Bonciani, Degrassi, Vincini Contributions involving top-quark and yz weak bosons exp. in M h 2 v w 4Mwx 2 Degrassi, Maltoni Djouadi, Graudenz, Spira, Zerwas { full EW corrections: in this talk Actis, Passarino, C.S., Uccirati C. Sturm Brookhaven Forum, Terra Incognita: from LHC to Cosmology, November 7th, 2008 } ~ Two-loop electroweak corrections to Higgs production and decay at LHC 4

11 Introduction Status Synopsis From PO to RO from gg H to pp gg ƒ H X QCD, light Higgs NLO K-fact. ˆ NNLO K-fact. ˆ EW Š 2008 approximate incomplete divergent Uncertainty Remaining sources of large corrections?

12 Introduction Status Synopsis From PO to RO from gg H to pp gg ƒ H X QCD, light Higgs NLO K-fact. ˆ NNLO K-fact. ˆ EW Š 2008 approximate incomplete divergent Uncertainty Remaining sources of large corrections?

13 Introduction Status Synopsis From PO to RO from gg H to pp gg ƒ H X QCD, light Higgs NLO K-fact. ˆ NNLO K-fact. ˆ EW Š 2008 approximate incomplete divergent Uncertainty Remaining sources of large corrections? Œ

14 Introduction Status Synopsis From PO to RO from gg H to pp gg ƒ H X QCD, light Higgs NLO K-fact. ˆ NNLO K-fact. ˆ EW Š 2008 approximate incomplete divergent Uncertainty Remaining sources of large corrections?

15 Tools Part II Intermezzo Ž

16 Tools Introduction & Motivation Calculation & Techniques Results & Discussion Summary & Conclusion Calculation GraphShot& package Techniques I...some diagrams contributing to the EW 2-loop corrections gg H: LO t NLO t Z W t t W, H : LO t W NLO t W fermionic bosonic W Z, š W t, œ C. Sturm Brookhaven Forum, Terra Incognita: from LHC to Cosmology, November 7th, 2008 } ~ ž Two-loop electroweak corrections to Higgs production and decay at LHC 5

17 Tools Introduction & Motivation Calculation & Techniques Results & Discussion Summary & Conclusion Calculation GraphShot& package Techniques II 2-loop contributions are computed numerically: Diagrams: GraphShot S. Actis, A. Ferroglia, G. Passarino, M. Passera, C.S., S. Uccirati Form3 based package for automatic generation and manipulation of 1- and 2-loop Feynman diagrams: insert Feynman-rules, perform traces, remove reducible scalar products, symmetrize integrals, reduction, counter terms, renormalization,... UV-finite integrals classified into: s calar, vector and tensor type integrals mapped on form factors Form factors are evaluated numerically in parametric space Before num. integration: Cancel collinear sing. + StudyŸ threshold For a moment consider H without loss of generality ª «C. Sturm Brookhaven Forum, Terra Incognita: from LHC to Cosmology, November 7th, 2008 Two-loop electroweak corrections to Higgs production and decay at LHC 6

18 Tools µ µ µ µ µ µ µ à À à à µ µ µ µ µ µ µ µ µ µ µ À À Reduction Generating the Amplitude: reduction ²± ³ ƒ µ º¹ ²» ¼¾½ µ º¹ º¹ ¼ÂÁ ÄÅÁ º¹ ÆÈÇÊÉÌËÎ̓ϲÐÒÑÓÇÔÆÇÊÕÖËÎÉØ ÙÐÒÚÓÛ ÜÎÝßÞàÝâáÒãåäÖäçæƒã èåéëêçìîíïìîè ìîðîãåýâñòìôóêêõæàý öîøëíïùúáçýßþûêüêçìîíïìîè ìîðôýûþ ÿ æàý ûý è ã é²ãåùôðîáßù ÞàÝ ö ãåñüìùêâùúã ÞƒÝÂéûý áõý ì ûã Þƒð ìôþàýöè ã ÞàÝÎìôóØêçæƒÝ ö ø é²ãåùôðîáßù ûêõæàýîñòýâäâìîþƒé è ã ÞƒÝÎäÂìôÞûêßùôã ÞàñÓêçæƒÝ äõæƒã èåéëêçìîíïìîè ìîðîãåýâñòìôó ö ö ùôþƒé "!âþ ÿüæƒýöêõæƒã áçéëè ã ÞàÝ äâìôþûêßùôã ÞàñÓêõæàÝ êßìôí ìôèåìîðîãåýâñ#%$&')( ùúþàé*,+-ƒìùêâùúã ÞàÝâéûý áçý. ì ûã Þƒð ìôþàýöè ã ÞƒÝ ó áõì/ êçæàýîé²ãåùôðîáßù ñüù ì0 ûýôþ ÿ æàý ùúáõáõì01 ñòã Þàé²ã ä¾ù¾êßý êçæƒý äâìîáòáçýâñòí ìôþàé²ýâþàäâýâñ2 Ýßê31 ÝâÝâÞ íïùúáçýâþåê ùúþàé äçæƒã èåéëêçìîíïìîè ìîðîãåýâñâþ

19 Tools Permutations Generating the Ampitude Strategy group diagrams into families, paying attention to permutation of external legs p 3 p 3 p 3 5 p1 p 3 p 2 p 1 p 1 p 1 p 1 p 1 p 2 4 p 2 p 2 p 2 p 2 p 3 p 3

20 Tools =< Loops Rooting Strategy mapping onto a standard rooting for loop momenta 7 P p 2 q 2 q 1 7 q q 2 28 p : P q 2; P p 2 q 1 : q 2 q 2; p 1 q 18 P q 18 p 2 p 1 q 1 q 1; p 1 p 1 q q 1 9 P q q 2 9 P?> 6

21 Tools =< Identities Symmetry Strategy apply symmetries to identify identical objects : P p m 1 1 m m : P m 4 m 5 p 2 q q 2 9 P q q 1 9 P?> m 5 p 2 m 3 m 4 m 2 m 1 p

22 Tools MI List-of-diagrams: all what is needed T A T B S A S C S E S D V E V I V G V M V K V H A

23 Tools Poles C Logs All-you-can-do-analytic rule-of-the-game Adelante Numerics, cum judicio UV UV poles, of course beware, overlapping divergencies IR/Coll IR poles, of course Collinear logs, of course upshot Cancellations, if any, enforced analytically B

24 Tools Poles C Logs All-you-can-do-analytic rule-of-the-game Adelante Numerics, cum judicio UV UV poles, of course beware, overlapping divergencies IR/Coll IR poles, of course Collinear logs, of course upshot Cancellations, if any, enforced analytically D

25 Tools J J M J Coll I Collinear Example double divergency F double subtraction 1 1 L L ; L ; H L 5 L E 1 dxdy dxdy 0 xyag xh yikj BG xh yi'm 0 xyag xh yikj 1 1 xyag xh 0IOJ BG xh 0I xyag 0H yioj BG 0H yi 1 xyag 0H 0IOJ BG 0H 0I 0 First term 5 set L 0 Second (third) term 5 integrate in y(x) P ln L Last term 5 integrate in x and y P ln 2 L 1 L BG xh yi ;N;

26 Tools M R J Coll II Extracting Collinear divergencies Theorem Coefficients of collinear logarithms are integrals of one-loop functions m m p 2 p 2 : P M 5 M 4 M 3 m m ln m2 s 0 1 dy : P M 5 M 3 M 4 Q finite part p 1 1: ys p 1 yp 1

27 Tools M Coll III Extracting Collinear divergencies Example Sometimes the answer is explicit : P mu m M mu m p 2 p 1 ln m2 s ln mv 2 s Li 2 Li 3 s s J M 2 2 S 12 M 2 9 ln M2 s Li 2 s J M 2 ln m2 s J ln mv 2 s s M 2 J finite part T

28 Tools M Theorem I General results I Coll. behavior of arbitrary two-loop q -scalar, UV-finite diagrams q m zp p q X p m 1 m qy a Z[Z[Z qy a ln m2 s 0 1 dz \ 1] z^ p qy 1 a Z[Z_Z qy m a J coll. fin. W

29 Tools M f Theorem II General results II Generalization to tensor integrals q m p q X p r 1 m qa 1Z[Z_Z qa qy a Z[Z[Z qy a m ln m2 s 1 9cb 2d zp m2 UVG si 9eb ln 4 s 0 1 dz G 9 zi r \ 1] z^ p 1 m qy a Z[Z[Z qy a pg 1hihih ` r pg J c. f.

30 Tools z M M l Theorem III General results III 9 P 2{ M 2 H l V H dc k P 2 M 2l 2P 2 q 1m p 1n 4o q 1m p 1p k 2 1 n lng 1 9 z I 2 q P p 1 1 lts s lu L Lv l 2 1 l 1 lts s lu lu n 1 l Li 2 o s M M m mr m mr p 2 p o L l Lv p p 2y zp 1 n dz o 1n zp P 2 L l o P 2 l 2 q m p 2p Lv q P M M j 0 w 1 q zx p 1

31 Tools M M M H R R R UV Extracting Ultraviolet divergencies V I : P m 5 m 1 m 2 m 3 m 4 p 2 p 1 1 ~ 4 1 d n q 1 d n q 2 x ƒ q1; 2 m1 2 2ƒ q 1 : q 2 S 2 ; m2 2 3ƒ q2; 2 m3 2 4ƒ q 2; p 1 S 2 ; m4 2 5ƒ q 2; PS 2 ; m5 2 C 0 1 dx ds 3 G y 1 H y 2 H y 3 I y 1 y 2 y 3 x G 1 9 xi : 2 G 1 9 y 1 I. 2: 1 V : 1: The single pole can always be expressed in terms of 1L. V I M m 1 m3 2 m3 2 m 2 f : P p 2 m 5 J finite part h m 4 m 3 p 1 }

32 Tools J J Š J J Š M M WSTI Checks Off-shell WSTIs involving special sources contracted sources 5 black circles physical ones 5 gray boxes H H H 0 Y A Y Z H X ˆ W X 0 0

33 Tools M M Numerics I Tasting numerical evaluation Finite par Œ ts Write the finite part of a FD in one of the following forms: 1 dx QR R xs V xs VG xiž 0; 2 dx QG xi ln n VG xi ; 3 dx QR R xs R V V xs f R xs P xs fg xi ln n G 1J xi&h Li n G xi&h S n pg xi Typical integrand with k Feynman variables: 1 i i z n k V #G k z 1H hihih H z k I ln m VG z 1 H hihih H z k I&H 9 1H 9 k 2H z 0H 1 z n 1 V quadratic with respect to a subset of z in which each z 2 i proportional to one squared external momentum. is

34 Tools Numerics II bite-and-run strategy I Multivariate Polylogs V is not complete k n 1 and m k 0 (m 0 similar) 1 a x l b k š 1 x a ln 1 l a b x k n 2 and m k 0 (m 0 similar) 1 o a x y l b x l c y l 2 dp k n ln 1 l o a d n b cp x b o axy l bx l cy l dp š x š y a d n b c

35 Tools M M M M M ž M Numerics III bite-and-run strategy II Multivariate PolyLogs V is complete VG zi z t H z J 2 K t z J L G z t 9 Z t I H G z 9 ZINJ B M QG zij BH Z 9 K t H : 1 H B L 9 K t H : 1 K H ž t Ÿ M M z QG zi 9 QG zi&h 9 G z 9 Z I { 2H 1 V G zi 9 ž t Ÿ dy y : 1 QG zi y J B œ e.g. V : ž t Ÿ z z 0 1 Q ln 1 J Q B

36 EW thresholds Part III Andante

37 EW thresholds Around threshold H W W u d u u H W W u d u u H Z Z u u u u H W W u d u u

38 EW thresholds s Singularities FD have a complicated analytical structure A frequently encountered singular behavior is associated with the so-called normal thresholds: the leading Landau singularities of self-energy-like diagrams which can appear, in more complicated diagrams, as sub-leading singularities.

39 EW thresholds M J f Bubbles 1 -behavior H m m m 9 - m 2 m H m m m reg. part at M 0

40 EW thresholds Bubbles II Origin of 1 (1-loop «diagrams) (H wave-function FR) W (1-loop diagrams) W H Pure 2-loop diagrams H H (W mass FR) W W W ª

41 EW thresholds ² ² ² Coulomb Logarithmic singularities H W³_ W³_ W³_ W³_ W³[ Remnant of Coulomb singularity W³_ W³_ H ² W³_ ± W³_ µ ln W µ 1 W

42 EW thresholds ² ² ² Complex for Coulomb Cure for logarithmic singularities H W³_ W³_ W³_ W³_ W³[ Complex W Mass V K ] Re[s Γ W W Γ¹ W Γ W = GeV = 2.093/2 GeV = 2.093/10 GeV = 0 GeV s [GeV]

43 ¼ ¼ Γ W Γ W Γ W Γ W = GeV = 2.093/2 GeV = 2.093/10 GeV = 0 GeV º s [GeV]

44 Complex poles Part IV Impetuoso ½

45 Complex poles Solutions RM scheme - none where masses are the real on-shell ones; it gives the extension of the generalized minimal subtraction scheme up to two loop level. MCM scheme - minimal start by removing the Re label in those terms that, coming from finite renormalization, violate WSTIs. split the amplitude ¾ À NLO M i W Z A SR i i J A LOG ln 9 2 W 9 i0 J A REM H

46 Complex poles Solutions RM scheme - none where masses are the real on-shell ones; it gives the extension of the generalized minimal subtraction scheme up to two loop level. MCM scheme - minimal start by removing the Re label in those terms that, coming from finite renormalization, violate WSTIs. split the amplitude Á À NLO M i W Z A SR i i J A LOG ln 9 2 W 9 i0 J A REM H

47 Complex poles M M MCM Solutions MCM scheme - minimal After proving that all coefficients, gauge-parameter independent by construction, satisfy the WST identities, we minimally modify the amplitude introducing the complex-mass scheme of for the divergent terms. m 2 i m 2 i M 2 i s i 1 J 1 J G F M 2 W 2Ã 2 ~ ReÄ R 2 G F s W 2Ã 2 ~ Ä R 2 1S i G s i I H 1S i G Mi 2 I Å Â

48 Complex poles MCM II Solutions pitfalls A nice feature of the MCM scheme is its simplicity MCM scheme - minimal The MCM, however, does not deal with cusps associated with the crossing of normal thresholds. MCM scheme - minimal The large and artificial effects arising around normal thresholds in the MCM scheme (or in RM scheme) are aesthetically unattractive. In addition, they represent a concrete problem in assessing the impact of two-loop EW corrections on processes Æ

49 Complex poles MCM II Solutions pitfalls A nice feature of the MCM scheme is its simplicity MCM scheme - minimal The MCM, however, does not deal with cusps associated with the crossing of normal thresholds. MCM scheme - minimal The large and artificial effects arising around normal thresholds in the MCM scheme (or in RM scheme) are aesthetically unattractive. In addition, they represent a concrete problem in assessing the impact of two-loop EW corrections on processes Ç

50 Complex poles CM Solutions CM scheme - complete The procedure described for the divergent terms has been extended to the remainder A REM. In particular, all two-loop diagrams have been computed with complex masses for the internal vector bosons. CM scheme - complete In the full CM setup, the real parts of the W and Z self-energies induced by one-loop renormalization of the masses and the couplings have to be traded for the associated complex expressions. È

51 Complex poles CM Solutions CM scheme - complete The procedure described for the divergent terms has been extended to the remainder A REM. In particular, all two-loop diagrams have been computed with complex masses for the internal vector bosons. CM scheme - complete In the full CM setup, the real parts of the W and Z self-energies induced by one-loop renormalization of the masses and the couplings have to be traded for the associated complex expressions. É

52 Results Part V Allegro Ê

53 Results Ó Ì Ó Ô EW on gluon-gluon fusion Ñ 8 Ð 6 WW ZZ tt Ò δ EW, total 4 δ EW [%] Ï 2 Î 0 WW 5 ZZ tt -2 Ë M H [GeV] Ì 350 Í

54 Results Decay EW on decay (Ö Ö ) Í 5 Ø 4 Ì 3 2 δù δú δù EW, CM QCD QCD δ EW, MCM EW, CM +δ Ú [%] δ 1 Î Õ M H [GeV]

55 CM Û

56 Results Ý Comparison I Comparing δ EW [%] 10 WW ZZ tt Ñ 8 Ð 6 Ø 4 2 Î 0-2 δ EW, light ferm. δ EW, light ferm., Fig.2 of first paper of Ref.[27] δ EW, total, CM Ü -4 Ì M H [GeV] Ì

57 10 Þ WW ß ZZ 8 6 δ EW, light ferm. δ EW, light ferm., Fig.2 of first δ EW, total, CM 4 2

58 Results è è Comparison II Comparing δ EW [%] 10 æ 8 å 6 ä 4 ã 2 â 0-2 WW ZZ è δ EW, total, CM δ EW, total, MCM δ EW, total, obtained from Table 2 of Ref.[28] á M H [GeV]

59 ï ò ü ý êresults Corrections to g ë g ì H í Method for NLO EW Comparison II Threshold behaviour for H Complex Summary î Threshold behaviour Results Conclusions Comparison of EW corrections to H ó ô õ ö around the WW threshold, ø ù obtained using different schemes for treating unstable particles ð ñ [%] δ 4 û2 ú real masses MCM (div.) CM (all) WW M H [GeV] þ Result obtained with real masses divergent at WW ; good approx. below; completely off above threshold, since no cancellation mechanism occurs ÿ Result in MCM setup finite, shows cusp; result in CM setup is smooth At threshold, result in MCM setup 3 5 ; result in CM setup 2 7 prediction at the level requires complete CMS implementation é

60 ï ò ü ý êcorrections to g ë g H M ethod for NLO EW Threshold behaviour for H î Threshold behaviour Results Conclusions Comparison of EW corrections to H ö around the WW threshold, ø ù obtained using different schemes for treating unstable particles [%] δ 4 û2 ú real masses MCM (div.) CM (all) WW M H [GeV] Result obtained with real masses divergent at WW ; good approx. below; completely off above threshold, since no cancellation mechanism occurs Result in MCM setup finite, shows cusp; result in CM setup is smooth At threshold, result in MCM setup 3 5 ; result in CM setup 2 7 prediction at the level requires complete CMS implementation

61 More Results Part VI Allegro Con Brio

62 More Results EW on K-factors - uncertainty We introduce two options for including NLO electroweak corrections CF (Complete Factorization): 0 G ij Û 0 1!#" EW$ M 2 H % G ij & PF (Partial Factorization): 0 G ij Û 0 G ij!#' 2 S$)( 2 R % " EW$ M 2 H % G 0 ij * Can we do it better? Babis, Radja and Frank say yes

63 More Results, LHC EW on K-factors - LHC K factor pp H + X MRST 2002 s = 14 TeV NNLO QCD NNLO QCD + NLO EW M H [GeV] +

64 . More Introduction Results & Motivation Calculation & Techniques Results & Discussion Summary & Conclusion 5 LHC Another Result: view The hadronic process pp / H 0 X Use Fortran program HiggsNNLO by M. Grazzini K-factor: Ratio cross section with higher orders over LO result pp H + X s=14 TeV MRST K factor NNLO QCD NNLO QCD + NLO EW M H [GeV] Uncertainty band: Variation of 1 R, 2 F, PF, CF Central value for cross section is shifted by 2-5% ( - 3 M H GeV) 6 7 C. Sturm Brookhaven Forum, Terra Incognita: from LHC to Cosmology, November 7th, Two-loop electroweak corrections to Higgs production and decay at LHC 11

65 More Results, Tevatron EW on K-factors - Tevatron K factor pp H + X MRST 2002 s = 1.96 TeV NNLO QCD NNLO QCD + NLO EW M H [GeV] :

66 êmore Corrections Resultsto g ry ã ä é ë g < H M = ê ethod for NLO EW Threshold behaviour Results Conclusions Í Ô Ï Í Tevatron NLO EW corrections at the Tevatron Tevatron summary stu z{ vwx }~ Impact of NLO EW effects at Tevatron II, > s? 1@ A 96 TeV, 100 GeV B M H C D 200 GeV (using HIGGSNNLO, by M.Grazzini) q n op k lm h ij e fg ² ² ³ µ ± ¹ º» ¼ ½ M H [GeV] ¾ CF À Á Â Ã Ä PF Å Æ Ç 120 È É 4 Ê A 9 Ë 1Ì Î Ï 5 Ð Ñ 7 Ò 1Ó Õ 4Ö 8 Ø 1Ù Ú Û 0 Ü Ï 5 Ý Û 0 Þ ß 2à 1 á Û 0 â 6 a bcd ^ _` E F G H I J J I [ \] K L M N O P Q R S T UV W X Y Z ƒ ˆ Š Œ Ž š œ ž Ÿ ª «Uncertainty band shows stronger sensitivity on the Higgs mass, once NLO EW effects are included å æ ; 12ç for M H è 120 GeV) Impact of NLO EW corrections smaller respect to NNLL resummation Catani,de Florian,Grazzini,Nason 03 ( 95 ê ò CL exclusion of a SM Higgs for M H ë 170 GeV, ì í effects relevant; CM result employed by Anastasiou,Boughezal,Petriello 08, prediction î is 7 ï 10ð larger than ñ ò used by TEVNPH WG

67 ômore Corrections Resultsto g "! # ƒ õ g ö H M ô ethod for NLO EW Threshold behaviour Results Conclusions v ` p u { p Tevatron NLO EW corrections at the LHC LHC summary '() $%& Impact of NLO EW effects at LHC, ø s ù 14 TeV, 100 GeV ú M H û Ï 500 GeV (using HIGGSNNLO, by M.Grazzini) N T N T O U P V Q W R X S Y Z [ \ ] ^ _ M H [GeV] F a b c d PF e f g 120 h 4i A 9 j 2k l Ï 5 m A 9 n 2o q 2r 1 s 1t w 1x 7 y u 0 z } u 0 ~ p 8 u 0 8 ü ý þ ÿ * + +, -. / : : ; < = G AH BI CJ DK EL FM Uncertainty band shows stronger sensitivity on the Higgs mass, once NLO EW effects are included WW and tt thresholds visible, but smooth having introducedó everywhere CMs Impact of NLO EW corrections comparable to that of NNLL resummation Catani,de Florian,Grazzini,Nason 03 ( 6 for M H 120 GeV); for large M H NLO EW corrections turn negative, screening effect with NNLL resummation C

68 Factorization Conclusions Part VII Crescendo

69 Factorization Š Conclusions Factorization I yes is thre loops at M H 0: effective theory Operator expansion plus matching or brute force tadpoles H H H Š H ˆ

70 Factorization Š Conclusions Factorization II Building with Effective theory m t m H 0 H Š H H H

71 Factorization Conclusions Factorize or not Factorize? Missing the real McCoy I Define M the mixed three-loop EW the two-loop EW How good is. MŽ 0? wrt MŽ M H What is usually done: MŽ M H the difference is MŽ 0 ; MŽ M H? Assume it is MŽ 0 E with Esmall EWŽ M H MŽ 0 EWŽ 0 EWŽ 0 MŽ M H EWŽ M H EWŽ 0 Œ

72 Factorization Conclusions Factorize or not Factorize? Missing the real McCoy II If E is almost zero this difference is MŽ 0 EWŽ 0 EWŽ M H EWŽ 0 so, the effective error is in MŽ M H š with e EWŽ M H EWŽ 0 MŽ 0 Ž 1 1 e at M H 170 GeV this difference is not tiny at all which, contradicts the assumption that E is small.

73 Factorization Conclusions Factorize or not Factorize? M H 0 versus finite M H However the altrenative is MŽ x š EWŽ x Ž 1 where doesn t depend on x. How zero is EWŽ M H Ž 0 ž Ÿ Ž M H? impossible to prove it with just one point, x 0; plausible, soft gluon dominance; œ more difficult than before, if the top triangle is almost point-like, here there is a structure with openings of thresholds etc.

74 Factorization Conclusions Factorize or not Factorize? Facts or Misfits? Example How good is heavy-top NLO QCD wrt complete NLO QCD? from literature: excellent, From the Lion s Mouth (Spira): the deviations of the heavy top mass limit from the fully massive result is in the range of 6 for 170 GeV Higgs mass at the Tevatron. less than 15 for Higgs masses below 700 GeV from Harlander Kant Ž 170 GeV Ž 0 ž

75 Factorization Conclusions Factorize or not Factorize? Difficult to say at NNLO Example Approximation is fair enough if it remains «10 of our 6 The main source of difference could come from diagrams without top: is M H m t M W a good approximation? H Z Z q ª

76 Factorization Conclusions Conclusions Recapitulation No matter what, NLO EW corrections to gg H are under control without incongruent large effects around EW thresholds Refrain Next update of Tevatron analysis with higher luminosity should appear in February/March,, it looks like the old times with the two communities busy to fill a gap Or, if I create a negative Higgs field and bombard the rest of the community with a stream of Higgs anti-bosons, it might disintegrate (free adaptation from Stephen Soderbergh s Solaris, 2002).

77 Factorization Conclusions Conclusions Recapitulation No matter what, NLO EW corrections to gg H are under control without incongruent large effects around EW thresholds Refrain Next update of Tevatron analysis with higher luminosity should appear in February/March,, it looks like the old times with the two communities busy to fill a gap Or, if I create a negative Higgs field and bombard the rest of the community with a stream of Higgs anti-bosons, it might disintegrate (free adaptation from Stephen Soderbergh s Solaris, 2002).