theory progress in top‐antop threshold physics at the ilc€¦ · 15.05.2012 maximilian...
TRANSCRIPT
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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐3
[Hoang,MS:1111.4486[hep‐ph],1102.0269[hep‐ph]]
e+e!! t t̄
resonance@LinearColider:t̄t
Top‐an8topthreshold:QCDeffects
• 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)
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐4
resonance@LinearColider:t̄t
incomplete!!!
Theorystatus:2010
!mt ! 100 MeV !
!"tot/"tot ! 6 % <3%neededforprecise
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐5
Top‐an8topthreshold:QCDeffects
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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐6
Top‐an8topthreshold:QCDeffects
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]
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐7
Top‐an8topthreshold:QCDeffects
ln(E2/m2), ln(p2/m2), ln(E2/p2) ! ln v
modifiedRG:
“ultrasoh”
!
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐8
Top‐an8topthreshold:QCDeffects
!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 ")
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐9
Top‐an8topthreshold:QCDeffects
!!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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐10
Top‐an8topthreshold:QCDeffects
!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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐11
Top‐an8topthreshold:QCDeffects
!"
"!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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐12
Top‐an8topthreshold:QCDeffects
[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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐13
Top‐an8topthreshold:QCDeffects
[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)
!
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐14
Top‐an8topthreshold:QCDeffects
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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐15
Top‐an8topthreshold:QCDeffects
340 342 344 346 3480.0
0.5
1.0
1.50.1 < ! < 0.4
LLNNLL(old)
NLL
!s (GeV)
!(p
b)
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐16
Top‐an8topthreshold:QCDeffects
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]
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐17
Top‐an8topthreshold:QCDeffects
decreasestoabout2‐3%!!"th
tot
"tot
[Hoang,MS,‘11]
(preliminary)
Top‐an8topthreshold:EWeffects
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐18
e+e!! t t̄
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐19
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]
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐20
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]
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐21
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(!) !
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐22
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
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐23
e+e!! t t̄ H
• ForlightHiggs():fullphasespacenonrela8vis8c!mustsum,termsrecycleresults(vNRQCD)factor2enhancementovertreelevel(+factor2frompolarizedbeams)
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐24
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(!)
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐25
e+e!! t t̄ H
!"thtot
"totdecreasessubstan8ally! RGimprovementimportant!
Backup
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐26
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:
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐27
Top‐an8topthreshold:QCDeffects
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]
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐28
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
02.03.2012 MaximilianStahlhofen‐UniversityofVienna DPG2012‐30
Produc8on/annihila8oncurrent(3S1):
(CMS)! c1(!) · "j e!1 (x)! "# $
!†p"#(i#2)$!"p
+ . . .
LvNRQCD = Lusoft + Lpot + Lsoft
[Luke,Manohar,Rothstein;2000]
Dµ = !µ + igAµ(x)
Lusoft : !†p(x)
!iD0 ! (p!iD)2
2m + . . ."!p(x) + . . .
Lpot : ! V !†p!!p"†
!p!"!p + . . .
V ! Vck2 + Vk!
2
mk + Vr(p2+p!2)
2m2k2 + V2m2 + Vs
m2 S2 + . . . Vc,k,...
vNRQCD
02.03.2012 MaximilianStahlhofen‐UniversityofVienna DPG2012‐31
Recycleresults:,
15.05.2012 MaximilianStahlhofen‐UniversityofVienna TopQuarkPhysicsatLeptonColliders‐32
AssociatedHiggsproduc8on:
• Dominantcontribu8onsfromHiggsradia8ngofthetop/an8top
• preciseextrac8onoftopYukawacouplingpossible• Atlargeendpoint:dynamicsnonrela8vis8c
• For(ILCphase1)and:fullphasespacenonrela8vis8c!!!mustsum,!
e+e!! t t̄ H
t t̄!
s ! 500 GeV
EH
mH ! 120 GeV
t t̄ (!s/v)n (!s ln v)n
t t̄vNRQCD c1(!)/c1(1)!
d!
dEH
"
EH!EmaxH
!#c21,0(",
"s,mt,mH) + c2
1,1(","
s,mt,mH)$# Im[G(0, 0, v, ")]
G(0, 0, v, !)
NLOmatching
[Denner,Divmaier,Roth,Weber;2004]
[Farrell,Hoang;2005]