Theory Progress in Top‐Antop Threshold Physics at the ILC€¦ · 15.05.2012 Maximilian...

MaximilianStahlhofen

TheoryProgressinTop‐An8topThresholdPhysicsattheILC

Incollabora8onwithAndréHoang

•  Top‐an8topthreshold:QCDeffects

•  Top‐an8topthreshold:EWeffects

•  AssociatedHiggsproduc8on:

•  Summary/Outlook

Outline

15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐2

e+e! ! t t̄ H

[Hoang,MS:1111.4486[hep‐ph],1102.0269[hep‐ph]]

Top‐an8topthreshold:QCDeffects


[Hoang,MS:1111.4486[hep‐ph],1102.0269[hep‐ph]]

e+e!! t t̄

resonance@LinearColider:t̄t


•  Nonpert.effectssuppressed [Fadin,Khoze,‘87]

•  Nosharpresonancepeaks

!t ! 1.5GeV" "QCD

340 342 344 346 3480.0

0.5

1.0

1.5

v! 1

LLNNLL

NLL

!s (GeV)

!(p

b)


resonance@LinearColider:t̄t

incomplete!!!

Theorystatus:2010

!mt ! 100 MeV !

!"tot/"tot ! 6 % <3%neededforprecise



340 342 344 346 3480.0

0.5

1.0

1.5

v! 1

LLNNLL

NLL

!s (GeV)

!(p

b)

!t, yt, !s

QCDnearthreshold: v ! !s " 1

(! !t " "QCD)mt ! !p " mtv ! Ekin " mtv23scales:“hard” “soh” “ultrasoh”

•  “Coulombsingulari8es”

•  Largelogs:

vNRQCD



ln(E2/m2), ln(p2/m2), ln(E2/p2) ! ln v

QCDnearthreshold: v ! !s " 1

(! !t " "QCD)mt ! !p " mtv ! Ekin " mtv23scales:“hard” “soh”

•  “Coulombsingulari8es”

•  Largelogs:

vNRQCD

! “subtrac8onvelocity”

RGE’sresumlogs: [!s ln v]n , !s [!s ln v]n , !2s [!s ln v]n ...

LL NLL NNLL

[Luke,Manohar,Rothstein‘00]



ln(E2/m2), ln(p2/m2), ln(E2/p2) ! ln v

modifiedRG:

“ultrasoh”

!



!tot ! Im!

+ + +...

+ + +...

V V V

V V V V

c1 c1 c1 c1 c1 c1

c1 c1 c1 c1

vNRQCD

sohgluon:kµ!mv kµ!mv2ultrasohgluon: poten8al:

+O(v)Vceffec8vecurrent:

kµ!(mv2,mv)c1

powercoun8ngin v ! !s

GNNLL known ! [Hoang,Manohar,Stewart,Teubner,‘02]

GNNNLO known! [Beneke,Kiyo,Schuller,‘07]

[Pineda,Signer,‘06]

!! !2

!rm + Vc(r)! E

"G(!r,!r ",E) = "(3)(!r !!r ")



!!tot ! Im

!+ + +...

+ + +...

V V V

V V V V

c1 c1 c1 c1 c1 c1

c1 c1 c1 c1

! Im!c1(!)2 · G(0, 0,E, !)

"

(LL)

currentrenormaliza8on NLLLL

V V

[Hoang,‘03][Luke,Manohar,Rothstein,‘00][Pineda,‘02][Hoang,Stewart,‘03]

ln!

c1(!)c1(1)

"= ! LL

#$%&0

+ ! NLL + ! NNLLmix + ! NNLL

nonmix

missing



!tot ! Im!c1(")2 · G(0, 0,E, ")

"

!"

"!ln[c1(!)] = !Vc(!)

16#2

!Vc(!)

4+ V2(!) + Vr(!) + S2 Vs(!)

"+

1

2Vk(!)NLL:

soh ultrasoh

correc8ons

•  dominant:

•  largecontribu8onto

!s(mv2)>!s(mv)

! NNLLnonmix

[Hoang,‘03]

•  knownsohcontribu8onssmall



!"

"!ln[c1(!)] = !Vc(!)

16#2

!Vc(!)

4+ V2(!) + Vr(!) + S2 Vs(!)

"+

1

2Vk(!)NLL:

renormalize

! !V2 loopr,2

RGE""# VNLLr,2 (")

[Hoang,MS,‘06]

•  Feynmangauge

•  ,dim.reg.

•  O(103)diagrams

MS



[Pineda,‘11]

!"

"!ln[c1(!)] = !Vc(!)

16#2

!Vc(!)

4+ V2(!) + Vr(!) + S2 Vs(!)

"+

1

2Vk(!)NLL:

renormalize

! !V2 loopk

RGE""# VNLLk (")

[Hoang,MS,‘11]

•  3loops:2xusoh1xpoten8al(finite)•  Feynmangauge•  ,dim.reg.•  O(104)diagrams•  Genera8on:ownMathema'cacode•  IntegraIs:IBP&par8alfrac.

MS



[Pineda,‘11]

0.1 0.2 0.3 0.4 0.51.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

NLL

NLL+NNLLnonmix

c1(!)c1(1)

!



0.1 0.2 0.3 0.4 0.51.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

NLL+NNLLnonmix+NNLLmix,usoh

•  largeusohNNLLcontribu8onscompensateeachother!

•  goodconvergence:•  knownsoh(nonmixing)contribu8onsatNNLLare8ny!

[Hoang,MS,‘11]

c1(!)c1(1)

!

[c1(! =0.15)]2 = 1! 0.096|NLL ! 0.029|NNLL

NLL

NLL+NNLLnonmix



340 342 344 346 3480.0

0.5

1.0

1.50.1 < ! < 0.4

LLNNLL(old)

NLL

!s (GeV)

!(p

b)



340 342 344 346 3480.0

0.5

1.0

1.50.1 < ! < 0.4

LL

NNLL(new)

NLL

!s (GeV)

!(p

b)

•  LOEWeffectsincludedby

•  Combina8onwithNNLLEWeffectsanddetailederroranalysis W.I.P

GLL(0, 0,E, !)! GLL(0, 0,E + i!, !) [Fadin,Khoze,‘87]



decreasestoabout2‐3%!!"th

tot

"tot

[Hoang,MS,‘11]

(preliminary)

Top‐an8topthreshold:EWeffects


e+e!! t t̄


Top‐an8topthreshold:EWeffects

•  Powercoun8ng:

•  Physicalfinalstate:

•  Applylooseinvariantmasscutsonreconstructedtops/an8tops:noeffectonresonantcontribu8ons!non‐resonantbackgroundsuppressed:

!t/mt ! !EW ! !2s ! v2 " 1

e+e!!W+W!bb̄

p2t,̄t = (mt ±!Mt)2 = m2

t + "2 mt!t ! "2 ! m2t

E =!

s" 2mt # E + i!tLO: (replacementrule)

unstabletoppropagator:i

E/2 + p0 ! p2/(2m) + i!t/2 [Fadin,Khoze,‘87]


Top‐an8topthreshold:EWeffectsBeyondLO:

•  QED:“Coulombphoton”trivialextensionofQCDcorrec8ons

•  GluonexchangewithfinalstatenegligibleatNLOandNNLO

•  Correc8onstocurrentmatching:

[Fadin,Khoze,Mar8n‘94][Melnikov,Yakovlev‘94]

[Hoang,Reisser‘05][Beneke,Jantzen,Ruiz‐Femenia‘10]

complexmatching

c1(1) = cborn1,LL + cQCD

1,NLL + cQCD1,NNLL + i cbW,abs

1,NNLL + cEW1,NNLL + . . .

[Hoang,Reisser‘06]

[Kuhn,Guth‘92]


Top‐an8topthreshold:EWeffectsBeyondLO:

•  QED:“Coulombphoton”trivialextensionofQCDcorrec8ons

•  GluonexchangewithfinalstatenegligibleatNLOandNNLO

•  Correc8onstocurrentmatching:

•  “Phasespacematching”fortoallowforcuts:NLO,NNLO,N3LO✔

[Fadin,Khoze,Mar8n‘94][Melnikov,Yakovlev‘94]

[Hoang,Reisser‘05][Beneke,Jantzen,Ruiz‐Femenia‘10]

c1(1) = cborn1,LL + cQCD

1,NLL + cQCD1,NNLL + i cbW,abs

1,NNLL + cEW1,NNLL + . . .

phasespacedivergence

sumsphasespacelogsinatNLL✔C(!)

[Hoang,Reisser,Ruiz‐Femenia‘10]

!tot ! Im!c1(")2 G(0, 0,E + i!t, ")

"! #s!t

$+ finite

i C(!) ·

C(!) !


Top‐an8topthreshold:EWeffects dashedline:NNLLpureQCDpredic8on

(addstepbystep)+NNLLQEDeffects+NNLLEWcurrentmatching(real)+NNLLEWcurrentmatching(absorb8ve)+NLL+NNLL+N3LLphasespacematchingcontribu8ons(psm)

!Mt = 15 GeV

!Mt = 35 GeV

psm ! 50%

psm ! 5"10%

Shihinpeakposi8on:30‐50MeV

largepsmcorrec8onduetounphysicalphasespaceinpureQCDpredic8on

[Hoang,Reisser,Ruiz‐Femenia‘10]

AssociatedHiggsproduc8on


e+e!! t t̄ H

•  ForlightHiggs():fullphasespacenonrela8vis8c!mustsum,termsrecycleresults(vNRQCD)factor2enhancementovertreelevel(+factor2frompolarizedbeams)


AssociatedHiggsproduc8on:e+e!! t t̄ H

[Farrell,Hoang;2006]

LO

NLO

resummedNLL(QCD)

•  realis8cstudies:?

(!s/v)n (!s ln v)n

(!yt/yt)ILC500GeV ! 30% " 10# 15% [Juste,’02,’06]

mH ! 120 GeV t t̄t t̄

!s " 500 GeV

(ILCphase1)

Summary/Outlook•  precisefromthresholdphysics• 

•  knownuptoNNLL✔

•  NewatNNLL✔•  EWconribu8onsuptoNNLL✔

•  (ILCphase1)atNLL(EWeffectsmissing)

•  Outlook:-  Detailederroranalysisfor :EW+QCD

-  scalar(stop)pairproduc8onatthreshold

G(0, 0,E, !)

!tot(e+e!! t t̄ )

mt, yt,!s, !t t t̄

W.I.P

!tot ! Im!c1(")2 · G(0, 0,E, ")

"+ . . .

c1(!)


e+e!! t t̄ H

!"thtot

"totdecreasessubstan8ally! RGimprovementimportant!

Backup


GLL(0, 0,E, !) =m2

4"

!iv ! CF#s

"ln

#!iv

!

$! 1

2+ ln 2 + $E + !

#1! iCF#s

2v

$%&+

m2CF#s

16"%

!tot ! Im!

! |c1(")|2 · Im!" i

"d4x eiq̂x #0| T#j e! !

1 (x)#j e!1 (0) |0$

#+ . . .

! |c1(")|2 · Im$G(0, 0,E, ")

%+ . . .

!

GNNLL known ! [Hoang,Manohar,Stewart,Teubner;2002]

GNNNLO known! [Beneke,Kiyo,Schuller;2007]

[Pineda,Signer;2006]

!! !2

!rm + Vc(r)! E

"G(!r,!r ",E) = "(3)(!r !!r ")LOSG:



Results

RGE’s+matchingathardscale give:(! = 1)

!Vr(!)

"NLL

usoft= 8"#s(m!)

#! 4!

"0Ar ln #s(m$2)

#s(m$) +$

"1

"20Ar !

!#s(m!2)!#s(m!)

"8!"0

Br

%&

!V2(!)

"NLL

usoft= 4"#s(m!)

#! 4!

"0A2ln #s(m$2)

#s(m$) +$

"1

"20A2 !

!#s(m!2)!#s(m!)

"8!"0

B2

%&LL NLL

!Vk(!)

"NLL

usoft= 2"2

s (m!)#! 4!

"0Ak ln #s(m$2)

#s(m$) +$

"1

"20Ak !

!"s(m!2)!"s(m!)

"8!"0

Bk

%&

!A2

B2

"= CF(CA ! 2CF)

!AB

"

!Ar

Br

"= !CACF

!AB

"

!Ak

Bk

"= !CACF(CA ! 2CF)

!AB

"

A =1

3!

B =CA(47 + 6!2)! 10nfT

108!2

[Hoang,MS;2011][Pineda;2011]


vNRQCD

“poten8al”gluon

02.03.2012 MaximilianStahlhofen‐UniversityofVienna DPG2012‐29

LvNRQCD = Lusoft + Lpot + Lsoft

[Luke,Manohar,Rothstein;2000]

Dµ = !µ + igAµ(x)

Lusoft : !†p(x)

!iD0 ! (p!iD)2

2m + . . ."!p(x) + . . .

Lpot : ! V !†p!!p"†

!p!"!p + . . .

V ! Vck2 + Vk!

2

mk + Vr(p2+p!2)

2m2k2 + V2m2 + Vs

m2 S2 + . . . Vc,k,...

Lsoft :

vNRQCD


Produc8on/annihila8oncurrent(3S1):

(CMS)! c1(!) · "j e!1 (x)! "# $

!†p"#(i#2)$!"p

+ . . .

LvNRQCD = Lusoft + Lpot + Lsoft

[Luke,Manohar,Rothstein;2000]

Dµ = !µ + igAµ(x)

Lusoft : !†p(x)

!iD0 ! (p!iD)2

2m + . . ."!p(x) + . . .

Lpot : ! V !†p!!p"†

!p!"!p + . . .

V ! Vck2 + Vk!

2

mk + Vr(p2+p!2)

2m2k2 + V2m2 + Vs

m2 S2 + . . . Vc,k,...

vNRQCD


Recycleresults:,


AssociatedHiggsproduc8on:

•  Dominantcontribu8onsfromHiggsradia8ngofthetop/an8top

•  preciseextrac8onoftopYukawacouplingpossible•  Atlargeendpoint:dynamicsnonrela8vis8c

•  For(ILCphase1)and:fullphasespacenonrela8vis8c!!!mustsum,!

e+e!! t t̄ H

t t̄!

s ! 500 GeV

EH

mH ! 120 GeV

t t̄ (!s/v)n (!s ln v)n

t t̄vNRQCD c1(!)/c1(1)!

d!

dEH

"

EH!EmaxH

!#c21,0(",

"s,mt,mH) + c2

1,1(","

s,mt,mH)$# Im[G(0, 0, v, ")]

G(0, 0, v, !)

NLOmatching

[Denner,Divmaier,Roth,Weber;2004]

[Farrell,Hoang;2005]

Theory Progress in Top‐Antop Threshold Physics at the ILC€¦ · 15.05.2012 Maximilian...

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