NLO multileg processes at the LHCpittau/talk_madrid.pdfNLO multileg processes at the LHC Roberto...
Transcript of NLO multileg processes at the LHCpittau/talk_madrid.pdfNLO multileg processes at the LHC Roberto...
NLO corrections at LHC pp→ttbb The calculation Results
NLO multileg processes at the LHC
Roberto Pittau
Departamento de Fısica Teorica y del CosmosUniversidad de Granada
Madrid, February 4, 2010
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
NLO multileg processes at the LHC
Roberto Pittau
Departamento de Fısica Teorica y del CosmosUniversidad de Granada
Madrid, February 4, 2010
1 Why NLO corrections at the LHC?
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
NLO multileg processes at the LHC
Roberto Pittau
Departamento de Fısica Teorica y del CosmosUniversidad de Granada
Madrid, February 4, 2010
1 Why NLO corrections at the LHC?
2 pp → ttH → ttbb and pp → ttbb
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
NLO multileg processes at the LHC
Roberto Pittau
Departamento de Fısica Teorica y del CosmosUniversidad de Granada
Madrid, February 4, 2010
1 Why NLO corrections at the LHC?
2 pp → ttH → ttbb and pp → ttbb
3 The calculation
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
NLO multileg processes at the LHC
Roberto Pittau
Departamento de Fısica Teorica y del CosmosUniversidad de Granada
Madrid, February 4, 2010
1 Why NLO corrections at the LHC?
2 pp → ttH → ttbb and pp → ttbb
3 The calculation
4 Results
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Why NLO corrections at the LHC?
NLO (1-loop) calculations at the LHC are needed for:1 computing Backgrounds for New Physics Searches2 Measurements of fundamental quantities:
αs mt
MW MH · · ·
Heavy New Physics states undergo long chain decays
SM Processes accompanied by multi-jet activity
⇒1 at LHC multileg NLO MCs needed2 for some processes the full set of the EW radiative corrections
is also needed
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The Les Houches NLO Wishlist
Priority list of processes experimentalist wish to know at NLOZ. Bern et. al., arXiv:0803.0494
NLO Wishlist 2007
• pp → W + j • pp → tt + 2j • pp → V + 3j• pp → H + 2j • pp → V V bb • pp → ttbb
• pp → V V V • pp → V V + 2j • pp → bbbb
2009 update
• pp → tttt • pp → 4j • pp → W + 4j• pp → Z + 3j • pp → Wbbj
In this talk I will concentrate on
pp → ttbb and pp → ttH → ttbb
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Available NLO calculations
pp → ttbb Background:
Bredenstein, Denner, Dittmaier, Pozzorini [arXiv:0905.0110]
Bevilacqua, Czakon, Papadopoulos, R.P., Worek [arXiv:0907.4723]
︸ ︷︷ ︸
They agree at the permil level!
pp → ttH Signal:
Beenakker, Dittmaier, Kramer, Plumper, Spira, Zerwas (2001)
Reina, Dawson (2001)
Dawson, Orr, Reina, Wackeroth (2003)
pp → ttH → ttbb Signal:
This talk (Preliminary)
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Higgs Production Mechanisms and Decays
[GeV]Hm210 310
Bra
nchi
ng R
atio
-310
-210
-110
1
ATLASbbττγγ
WWZZtt
[GeV]Hm210 310
Cro
ss-s
ectio
n [p
b]
-110
1
10
210
ATLAS H→gg
qqHWHZHttH
ATLAS TDR, arXiv:0901.0512 [hep-ex]
pp → ttH → ttbb important for measuring H Yukawacouplings for 115 GeV < MH < 140 GeV
Best experimental signature
Semileptonic channel with multiple b-tags
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Signal vs Backgrounds
M(bb) [GeV]0 50 100 150 200 250 300 350 400
Cro
ss-s
ectio
n [fb
/30G
eV]
0
1
2
3
4
5
6
M(bb) [GeV]0 50 100 150 200 250 300 350 400
Cro
ss-s
ectio
n [fb
/30G
eV]
0
1
2
3
4
5
6
ttjj ttbbEW ttbbQCD Signal Signal
ATLAS
M(bb) [GeV]0 50 100 150 200 250 300 350 400
Cro
ss-s
ectio
n [fb
/10G
eV]
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Mean=121.6GeV
RMS=21.8GeV
ATLAS
B/B∆
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
tota
l sig
nific
ance
00.20.40.60.8
11.21.41.61.8
22.2
cut-basedpairing likelihoodconstrained mass fit
ATLAS
ATLAS TDR, arXiv:0901.0512 [hep-ex]
A recently proposed selection strategy based on highlyboosted Higgs bosons gives a Statistical Significance of 4.5σPlehn, Salam, Spannowsky, arXiv:0910.5472
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
A typical 2 → m process at NLO
σNLO =
∫
m
dσB +
∫
m
(
dσV +
∫
1dσA
)
+
∫
m+1
(dσR − dσA
)
1 dσB is the Born cross section
2 dσV is the Virtual correction (loop diagrams)
3 dσR is the Real correction
4 dσA and∫
1 dσA are unintegrated and integrated counterterms(allowing to compute the Real part in 4 dimensions)
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The Virtual correction
M1−loop =∑
i
di Boxi +∑
i
ci Trianglei +∑
i
bi Bubblei
+∑
i
ai Tadpolei + R + O(ǫ)
Scalar Loop Functions ∗
Tadpolei =∫
dnq 1D0
Bubblei =∫
dnq 1D0D1
Trianglei =∫
dnq 1D0D1D2
Boxi =∫
dnq 1D0D1D2D3
∗ Known analytically
Di = (q + pi)2 − m2
i and n = 4 + ǫ
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The OPP Method (Ossola, Papadopoulos, Pittau, 2007)
Working at the integrand level
M1−loop =
∫
dnq∑
I⊂{0,1,...,m−1}
N (I)(q)∏
i∈I Di(q)︸ ︷︷ ︸
A(q)=A(q)+A(q,q,ǫ)
N (I)(q) = N (I)(q) + N (I)(q, q, ǫ)
For example, in the case of pp → ttbb
A(q) =P N
(6)i
(q)
Di0Di1
· · · Di5| {z }
+N
(5)i
(q)
Di0Di1
· · · Di4| {z }
+N
(4)i
(q)
Di0Di1
· · · Di3| {z }
+N
(3)i
(q)
Di0Di1
Di2| {z }
+ · · ·
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The function to be sampled numerically to extract the coefficients
N (m−1)(q) =m−1∑
i0<i1<i2<i3
[
d(i0i1i2i3) + d(q; i0i1i2i3)] m−1∏
i6=i0,i1,i2,i3
Di
+m−1∑
i0<i1<i2
[c(i0i1i2) + c(q; i0i1i2)]m−1∏
i6=i0,i1,i2
Di
+
m−1∑
i0<i1
[
b(i0i1) + b(q; i0i1)] m−1∏
i6=i0,i1
Di
+
m−1∑
i0
[a(i0) + a(q; i0)]
m−1∏
i6=i0
Di
+ P (q)
m−1∏
i
Di
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Solving the OPP Equation 1
The functional form of the spurious terms should be knownOssola, Papadopoulos, R. P., Nucl.Phys.B763:147-169,2007
del Aguila, R. P., JHEP 0407:017,2004
Example (p0 = 0)
d(q; 0123) = d(0123) ǫ(qp1p2p3)
∫
dnqd(q; 0123)
D0D1D2D3= d(0123)
∫
dnqǫ(qp1p2p3)
D0D1D2D3= 0
The coefficients {di, ci, bi, ai} and {di, ci, bi, ai} are extractedby solving linear systems of equations
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Solving the OPP Equation 2
The use of special values of q helps
D0(q±) = D1(q
±) = D2(q±) = D3(q
±) = 0
N (m−1)(q±) =[
d(0123) + d(q±; 0123)] m−1∏
i6=0,1,2,3
Di(q±)
d(0123) =1
2
[
N (m−1)(q+)∏m−1
i6=0,1,2,3 Di(q+)+
N (m−1)(q−)∏m−1
i6=0,1,2,3 Di(q−)
]
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
A classical example
∫
dnq1
D0D1D2D3D4D5D6
N(q) = 1
D0(q±) = D1(q
±) = D2(q±) = D3(q
±) = 0
d(0123) =1
2
[1
D4(q+)D5(q+)D6(q+)+
1
D4(q+)D5(q+)D6(q+)
]
· · ·
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
What about R (= R1 + R2)?
The origin of R1
1
Di
=1
Di
(
1 −q2
Di
)
⇒ predicted within OPP
The origin of R2
R2 =
∫
dnqN (I)(q, q, ǫ)
D0 · · · Dm−1⇒ effective tree-level Feynman Rules∗
∗ QCD: Draggiotis, Garzelli, Papadopoulos, R. P., JHEP 0904:072,2009
EW: Garzelli, Malamos, R. P., JHEP 1001:040,2010
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The Real correction
Recursion Relations at tree level
(figure by A. van Hameren)
Feynman Diagrams avoided
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The counterterms
The Catani-Seymour dipoles
• Catani, Seymour, Nucl. Phys. B485, 291 (1997)
• Catani, Dittmaier, Seymour, Trocsanyi, Nucl. Phys. B627, 189 (2002)
• Czakon, Papadopoulos, Worek, JHEP 0908 (2009) 085
• Massless
• Massive
• Polarized
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Recursion Relations at 1-loop
OPP + hard-cut allow to use the same tree-level Recursion
Relations for m + 2 tree-like structures
=
1
2
16
1
2
4 8
16
321
2
16
1
2
4 8
16
32f
128f f
_
64
The color can be treated as at the tree level
1 32
4 8
2 16
1 32
4 8
2 16
128 64
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The Helac-NLO System
HELAC1LOOP
CutTools
HELACDIPOLES OneLOop
(figure by G. Bevilacqua)
1 CutTools
{di, ci, bi, ai} and R1
2 HELAC-1LOOP
N(q) and R2
3 OneLOop
scalar 1-loop integrals
4 HELAC-DIPOLES
Real correction and CS dipoles
Ossola, Papadopoulos, R. P., JHEP 0803 (2008) 042
van Hameren, Papadopoulos, R. P., JHEP 0909 (2009) 106
Czakon, Papadopoulos, Worek, JHEP 0908 (2009) 085
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Other NLO Tools
Analytic formulae
MCFM [Campbell et al.]
Feynman Diagrams
HAWK · · · [Denner, Dittmaier et al.]
FormCalc/LoopTools/FeynCalc [Hahn et al.]
GOLEM [Binoth et al.]
OPP/Unitarity
BlackHat/SHERPA [Berger et al.]
Rocket/MCFM [Ellis et al.]
C++ [Lazopoulos]
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
A Les Houches Accord to merge Real (R) and Virtual (V) parts
Monte Carlo (R) One Loop Program (V)
Contract
⇔
A proposal for⇔ can be found in
Binoth et al. arXiv:1001.1307
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Cross sections at NLO
pp → ttbb + X
σBLO [fb] σB
NLO [fb] K-factor
1489.2 ± 0.9 2642 ± 3 1.77
µR = µF = µ0 = mt (CTEQ6)
pp → ttH + X → ttbb + X
σSLO [fb] σS
NLO [fb] K-factor
150.375 ± 0.077 207.268 ± 0.150 1.38
µR = µF = µ0 = mt + mH/2 (CTEQ6)
pT (b) > 20 GeV , ∆R(b, b) > 0.8 , |ηb| < 2.5
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Distributions at NLO
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Scale dependence of the Background
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Scale dependence of the Signal
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
The effect of a jet veto on the Signal/Background ratio
The extra radiation is mainly at low pT and in the central region
Signal
With pT (j) < 50 GeV:
RLO = 0.10 → RNLO = 0.079 → RNLO−veto = 0.064
Tuning necessary(e.g. Bredenstein, Denner, Dittmaier, Pozzorini, [arXiv:1001.4727])
Roberto Pittau NLO multileg processes at the LHC
NLO corrections at LHC pp→ttbb The calculation Results
Conclusions
1 We discussed NLO multileg calculations for LHC physics
2 We described the HELAC-NLO system, based on the recentlyintroduced OPP method
3 As an example, we presented a few results on the Higgsproduction process
pp → ttH → ttbb
and on its main QCD background
pp → ttbb
4 In the future, we plan to compute more processes contained inthe NLO Les Houches Wish List
5 Public NLO code in preparation
Roberto Pittau NLO multileg processes at the LHC