Towards event generation at NNLO
Emanuele Re
Rudolf Peierls Centre for Theoretical Physics, University of Oxford
University of Sussex, 19 May 2014
Status after LHC “run I”
Scalar at 125 GeV found, study of properties begun
s = 7 TeV, L ≤ 5.1 fb-1 s = 8 TeV, L ≤ 19.6 fb-1
CMS Preliminary
Combined
µ = 0.80 ± 0.14
p
SM
s = 7 TeV, L ≤ 5.1 fb
-1
mH = 125.7 GeV
CMS Preliminary
= 0.65
κV
H → bb
µ = 1.15 ± 0.62
s = 8 TeV, L ≤ 19.6 fb
-1
68% CL
95% CL
κb
H → ττ
κτ
µ = 1.10 ± 0.41
κt
H → γγ
µ = 0.77 ± 0.27
κg
H → WW
µ = 0.68 ± 0.20
κγ
H → ZZ
BRBSM
µ = 0.92 ± 0.28
0
0.5
1
1.5
2
2.5
Best fit σ/σSM
pSM = 0.78
[ κV ≤ 1 ] pSM = 0.88
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
parameter value
1 / 35
Status after LHC “run I”
Scalar at 125 GeV found, study of properties begun
s = 7 TeV, L ≤ 5.1 fb-1 s = 8 TeV, L ≤ 19.6 fb-1
CMS Preliminary
Combined
µ = 0.80 ± 0.14
p
SM
s = 7 TeV, L ≤ 5.1 fb
-1
mH = 125.7 GeV
CMS Preliminary
κV
H → bb
µ = 1.15 ± 0.62
s = 8 TeV, L ≤ 19.6 fb
-1
68% CL
95% CL
= 0.65
κb
H → ττ
κτ
µ = 1.10 ± 0.41
κt
H → γγ
µ = 0.77 ± 0.27
κg
H → WW
µ = 0.68 ± 0.20
κγ
H → ZZ
pSM = 0.78
[ κV ≤ 1 ] pSM = 0.88
BRBSM
µ = 0.92 ± 0.28
0
0.5
1
1.5
2
2.5
Best fit σ/σSM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
parameter value
In general no smoking-gun signal of new-physics
ATLAS Exotics Searches* - 95% CL Lower Limits (Status: May 2013)
20.1
20.3
20.1
20.1
g̃
g̃
g̃
g̃
0
Yes
2b
2 e, µ (SS)
0-3 b
Yes
1-2 e, µ
Yes
1-2 b
2 e, µ
0-2 jets
Yes
2 e, µ
2 jets
Yes
0
Yes
2b
1 e, µ
Yes
1b
0
Yes
2b
mono-jet/c -tag Yes
0
2 e, µ (Z )
Yes
1b
3 e, µ (Z )
Yes
1b
20.1
20.7
4.7
20.3
20.3
20.1
20.7
20.5
20.3
20.7
20.7
b̃1
b̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃2
Yes
Yes
Yes
Yes
Yes
Yes
20.3
20.3
20.7
20.7
20.7
20.3
ℓ̃
χ̃±
1
χ̃±1
χ̃±1 , χ̃02
χ̃±1 , χ̃02
χ̃±1 , χ̃02
85-315 GeV
125-450 GeV
180-330 GeV
600 GeV
315 GeV
285 GeV
Yes
Yes
Yes
-
20.3
22.9
15.9
4.7
20.3
χ̃±1
g̃
χ̃01
χ̃01
q̃
270 GeV
2 e, µ
2 e, µ
2τ
3 e, µ
3 e, µ
1 e, µ
ℓ̃L,R ℓ̃L,R , ℓ̃→ℓχ̃1
+
−
χ̃+
1 χ̃1 , χ̃1 →ℓ̃ν(ℓν̃)
+
−
χ̃+
1 χ̃1 , χ̃1 →τ̃ν(τν̃)
χ̃±1 χ̃02 →ℓ̃L νℓ̃L ℓ(ν̃ν), ℓν̃ℓ̃L ℓ(ν̃ν)
χ̃±1 χ̃02 →W χ̃01 Z χ̃01
χ̃±1 χ̃02 →W χ̃01 h χ̃01
0
0
0
0
2b
+ −
±
1 jet
Direct χ̃1 χ̃1 prod., long-lived χ̃1 Disapp. trk
Stable, stopped g̃ R-hadron
1-5 jets
0
0
GMSB, stable τ̃, χ̃1 →τ̃(ẽ, µ̃)+τ(e, µ) 1-2 µ
0
0
2γ
GMSB, χ̃1 →γG̃ , long-lived χ̃1
0
1 µ, displ. vtx
q̃q̃ , χ̃1 →qqµ (RPV)
LFV pp→ν̃τ + X , ν̃τ →e + µ
LFV pp→ν̃τ + X , ν̃τ →e(µ) + τ
Bilinear RPV CMSSM
+
−
0 0
χ̃+
1 χ̃1 , χ̃1 →W χ̃1 , χ̃1 →eeν̃µ , eµν̃e
+
0 0
−
χ̃+
1 χ̃1 , χ̃1 →W χ̃1 , χ̃1 →ττν̃e , eτν̃τ
2 e, µ
1 e, µ + τ
1 e, µ
4 e, µ
3 e, µ + τ
0
2 e, µ (SS)
7 jets
6-7 jets
0-3 b
Yes
Yes
Yes
Yes
4.6
4.6
4.7
20.7
20.7
20.3
20.7
ν̃τ
ν̃τ
q̃, g̃
χ̃±1
χ̃±1
g̃
g̃
Scalar gluon pair, sgluon→qq̄
Scalar gluon pair, sgluon→tt̄
WIMP interaction (D5, Dirac χ)
0
2 e, µ (SS)
0
4 jets
1b
mono-jet
Yes
Yes
4.6
14.3
10.5
M* scale
g̃ →qqq
g̃ →t̃1 t , t̃1 →bs
√
s = 7 TeV
full data
√
s = 8 TeV
partial data
√
s = 8 TeV
full data
0
740 GeV
1.3 TeV
1.18 TeV
1.12 TeV
1.24 TeV
1.4 TeV
1.07 TeV
619 GeV
900 GeV
690 GeV
645 GeV
0
225-525 GeV
150-580 GeV
200-610 GeV
320-660 GeV
90-200 GeV
500 GeV
271-520 GeV
ATLAS-CONF-2013-061
1308.1841
ATLAS-CONF-2013-061
ATLAS-CONF-2013-061
0
1308.2631
ATLAS-CONF-2013-007
1208.4305, 1209.2102
0
m(χ̃1 )=0 GeV
0
±
0
m(χ̃1 )=0 GeV, m(ℓ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
0
±
0
m(χ̃1 )=0 GeV, m(τ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
±
0
0
±
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, m(ℓ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
±
0
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, sleptons decoupled
±
0
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, sleptons decoupled
±
±
0
m(χ̃1 )-m(χ̃1 )=160 MeV, τ(χ̃1 )=0.2 ns
0
m(χ̃1 )=100 GeV, 10 µs<τ(g̃)<1000 s
10<tanβ<50
832 GeV
475 GeV
0
0.4<τ(χ̃1 )<2
230 GeV
1.0 TeV
1.61 TeV
1.1 TeV
1.2 TeV
760 GeV
350 GeV
916 GeV
880 GeV
100-287 GeV
800 GeV
704 GeV
ns
0
1.5 <cτ<156 mm, BR(µ)=1, m(χ̃1 )=108 GeV
ATLAS-CONF-2013-048
ATLAS-CONF-2013-065
1308.2631
ATLAS-CONF-2013-037
ATLAS-CONF-2013-024
ATLAS-CONF-2013-068
ATLAS-CONF-2013-025
ATLAS-CONF-2013-025
ATLAS-CONF-2013-049
ATLAS-CONF-2013-049
ATLAS-CONF-2013-028
ATLAS-CONF-2013-035
ATLAS-CONF-2013-035
ATLAS-CONF-2013-093
ATLAS-CONF-2013-069
ATLAS-CONF-2013-057
ATLAS-CONF-2013-058
1304.6310
ATLAS-CONF-2013-092
λ′311 =0.10, λ132 =0.05
λ′311 =0.10, λ1(2)33 =0.05
m(q̃ )=m(g̃ ), cτLSP <1 mm
0
m(χ̃1 )>300 GeV, λ121 >0
0
m(χ̃1 )>80 GeV, λ133 >0
BR(t )=BR(b )=BR(c )=0%
1212.1272
1212.1272
ATLAS-CONF-2012-140
ATLAS-CONF-2013-036
ATLAS-CONF-2013-036
ATLAS-CONF-2013-091
ATLAS-CONF-2013-007
incl. limit from 1110.2693
1210.4826
ATLAS-CONF-2013-051
ATLAS-CONF-2012-147
m(χ)<80 GeV, limit of<687 GeV for D8
1
ATLAS-CONF-2013-047
ATLAS-CONF-2013-062
1308.1841
ATLAS-CONF-2013-047
ATLAS-CONF-2013-047
ATLAS-CONF-2013-062
ATLAS-CONF-2013-089
1208.4688
ATLAS-CONF-2013-026
1209.0753
ATLAS-CONF-2012-144
1211.1167
ATLAS-CONF-2012-152
ATLAS-CONF-2012-147
0
m(χ̃1 )<90 GeV
±
0
m(χ̃1 )=2 m(χ̃1 )
0
m(χ̃1 )=55 GeV
0
±
m(χ̃1 ) =m(t̃1 )-m(W )-50 GeV, m(t̃1 )<<m(χ̃1 )
0
m(χ̃1 )=0 GeV
0
±
0
m(χ̃1 )<200 GeV, m(χ̃1 )-m(χ̃1 )=5 GeV
0
m(χ̃1 )=0 GeV
0
m(χ̃1 )=0 GeV
0
m(t̃1 )-m(χ̃1 )<85 GeV
0
m(χ̃1 )>150 GeV
0
m(t̃1 )=m(χ̃1 )+180 GeV
100-620 GeV
275-430 GeV
110-167 GeV
130-220 GeV
10−1
m(χ̃1 )=0 GeV
0
m(χ̃1 )=0 GeV
0
±
0
m(χ̃1 )<200 GeV, m(χ̃ )=0.5(m(χ̃1 )+m(g̃ ))
0
m(χ̃1 )=0 GeV
tanβ<15
tanβ >18
m(χ̃1 )>50 GeV
0
m(χ̃1 )>50 GeV
0
m(χ̃1 )>220 GeV
m(H̃ )>200 GeV
m(g̃ )>10−4 eV
m(χ̃1 )<600 GeV
0
m(χ̃1 ) <350 GeV
0
m(χ̃1 )<400 GeV
0
m(χ̃1 )<300 GeV
1.2 TeV
1.1 TeV
1.34 TeV
1.3 TeV
sgluon
sgluon
m(q̃ )=m(g̃ )
any m(q̃ )
any m(q̃ )
Mass scale [TeV]
*Only a selection of the available mass limits on new states or phenomena is shown. All limits quoted are observed minus 1σ theoretical signal cross section uncertainty.
Extra dimensions
Yes
Yes
Yes
Yes
1.7 TeV
1.2 TeV
1.1 TeV
Large ED (ADD) : monojet + E T ,miss
Large ED (ADD) : monophoton + E T ,miss
Large ED (ADD) : diphoton & dilepton, mγ γ / ll
UED : diphoton + E T ,miss
1
S /Z 2 ED : dilepton, mll
RS1 : dilepton, mll
RS1 : WW resonance, mT ,lν lν
Bulk RS : ZZ resonance, mlljj
RS gKK→ tt (BR=0.925) : t t → l+jets, mtt
ADD BH ( M TH /M D =3) : SS dimuon, N ch. part.
ADD BH ( M TH /M D =3) : leptons + jets, Σ p
T
Quantum black hole : dijet, Fχ(mjj )
qqqq contact interaction : χ(m )
jj
qqll CI : ee & µµ, m
ll
uutt CI : SS dilepton + jets + E T ,miss
Z' (SSM) : mee/ µ µ
Z' (SSM) : mττ
Z' (leptophobic topcolor) : t t → l+jets, m
tt
W' (SSM) : mT,e/µ
W' (→ tq, g =1) : mtq
R
W'R ( → tb, LRSM) : m
tb
Scalar LQ pair (β =1) : kin. vars. in eejj, eν jj
Scalar LQ pair (β =1) : kin. vars. in µµjj, µν jj
Scalar LQ pair (β=1) : kin. vars. in ττjj, τν jj
th
4 generation : t't'→ WbWb
4th generation : b'b' → SS dilepton + jets + E
T ,miss
Vector-like quark : TT→ Ht+X
Vector-like quark : CC, mlν q
Excited quarks : γ -jet resonance, m
γ jet
Excited quarks : dijet resonance, mjj
Excited b quark : W-t resonance, mWt
Excited leptons : l-γ resonance, m
lγ
Techni-hadrons (LSTC) : dilepton,mee/ µ µ
Techni-hadrons (LSTC) : WZ resonance (lν ll), m
WZ
Major. neutr. (LRSM, no mixing) : 2-lep + jets
Heavy lepton
N± (type III seesaw) : Z-l resonance, mZl
H±L± (DY prod., BR(H±±→ll)=1) : SS ee (µµ), m
L
ll
Color octet scalar : dijet resonance, mjj
Multi-charged particles (DY prod.) : highly ionizing tracks
Magnetic monopoles (DY prod.) : highly ionizing tracks
CI
q̃, g̃
g̃
g̃
q̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
F1/2 scale
Preliminary
s = 7, 8 TeV
Reference
V'
20.3
20.3
20.3
20.3
20.3
20.3
20.3
4.7
20.7
4.8
4.8
4.8
5.8
10.5
ATLAS√
L dt = (4.6 - 22.9) fb−1
LQ
3b
7-10 jets
3b
3b
Mass limit
New
EW
direct
Long-lived
particles
RPV
0
0
0-1 e, µ
0-1 e, µ
L dt[fb−1 ]
quarks
Inclusive Searches
3rd gen.
g̃ med.
3rd gen. squarks
direct production
0
b̃1 b̃1 , b̃1 →bχ̃1
±
b̃1 b̃1 , b̃1 →tχ̃1
±
t̃1 t̃1 (light), t̃1 →bχ̃1
0
t̃1 t̃1 (light), t̃1 →Wbχ̃1
0
t̃1 t̃1 (medium), t̃1 →tχ̃1
±
t̃1 t̃1 (medium), t̃1 →bχ̃1
0
t̃1 t̃1 (heavy), t̃1 →tχ̃1
0
t̃1 t̃1 (heavy), t̃1 →tχ̃1
0
t̃1 t̃1 , t̃1 →c χ̃1
t̃1 t̃1 (natural GMSB)
t̃2 t̃2 , t̃2 →t̃1 + Z
0
Other
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
γ
0
g̃ →bb̄χ̃1
0
g̃ →tt̄ χ̃1
0
g̃ →tt̄ χ̃1
+
g̃ →bt̄ χ̃1
2 e, µ (Z )
0
2-6 jets
3-6 jets
7-10 jets
2-6 jets
2-6 jets
3-6 jets
0-3 jets
2-4 jets
0-2 jets
1b
0-3 jets
mono-jet
0
1 e, µ
0
0
0
1 e, µ
2 e, µ
2 e, µ
1-2 τ
2γ
1 e, µ + γ
MSUGRA/CMSSM
MSUGRA/CMSSM
MSUGRA/CMSSM
0
q̃q̃ , q̃→qχ̃1
0
g̃ g̃ , g̃ →qq̄χ̃1
0
±
g̃ g̃ , g̃ →qqχ̃1 →qqW ± χ̃1
0
g̃ g̃ , g̃ →qq(ℓℓ/ℓν/νν)χ̃1
GMSB (ℓ̃ NLSP)
GMSB (ℓ̃ NLSP)
GGM (bino NLSP)
GGM (wino NLSP)
GGM (higgsino-bino NLSP)
GGM (higgsino NLSP)
Gravitino LSP
R
ferm.
e, µ, τ, γ Jets Emiss
T
Model
Excit.
R
Status: SUSY 2013
Other
ATLAS SUSY Searches* - 95% CL Lower Limits
4.37 TeV M D (δ =2)
M D (δ =2)
ATLAS
4.18 TeV M S (HLZ δ =3, NLO)
Preliminary
Compact. scale R -1
-1
4.71 TeV MKK ~ R
Graviton mass (k /M Pl = 0.1)
-1
L =4.7 fb , 7 TeV [1208.2880]
1.23 TeV Graviton mass (k / M Pl = 0.1)
-1
Ldt = ( 1 - 20) fb-1
L =7.2 fb , 8 TeV [ATLAS-CONF-2012-150]
850 GeV Graviton mass (k / M Pl = 1.0)
-1
L =4.7 fb , 7 TeV [1305.2756]
2.07 TeV g mass
KK
s
=
7, 8 TeV
-1
L =1.3 fb , 7 TeV [1111.0080]
1.25 TeV M D (δ =6)
-1
L =1.0 fb , 7 TeV [1204.4646]
1.5 TeV M D (δ =6)
-1
L =4.7 fb , 7 TeV [1210.1718]
4.11 TeV M D (δ =6)
-1
L =4.8 fb , 7 TeV [1210.1718]
7.6 TeV Λ
-1
L =5.0 fb , 7 TeV [1211.1150]
13.9 TeV Λ (constructive int.)
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-051]
3.3 TeV Λ (C=1)
-1
L =20 fb , 8 TeV [ATLAS-CONF-2013-017]
2.86 TeV Z' mass
-1
L =4.7 fb , 7 TeV [1210.6604]
1.4 TeV Z' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-052]
1.8 TeV Z' mass
-1
L =4.7 fb , 7 TeV [1209.4446]
2.55 TeV W' mass
-1
L =4.7 fb , 7 TeV [1209.6593]
430 GeV W' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-050]
1.84 TeV W' mass
st
-1
L =1.0 fb , 7 TeV [1112.4828]
660 GeV 1 gen. LQ mass
nd
-1
L =1.0 fb , 7 TeV [1203.3172]
685 GeV 2 gen. LQ mass
rd
-1
L =4.7 fb , 7 TeV [1303.0526]
534 GeV 3 gen. LQ mass
-1
L =4.7 fb , 7 TeV [1210.5468]
656 GeV t' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-051]
720 GeV b' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-018]
790 GeV T mass (isospin doublet)
-1
L =4.6 fb , 7 TeV [ATLAS-CONF-2012-137]
1.12 TeV VLQ mass (charge -1/3, coupling κ qQ = ν /mQ)
-1
L =2.1 fb , 7 TeV [1112.3580]
2.46 TeV q* mass
-1
L =13.0 fb , 8 TeV [ATLAS-CONF-2012-148]
3.84 TeV q* mass
-1
L =4.7 fb , 7 TeV [1301.1583]
870 GeV b* mass (left-handed coupling)
-1
L =13.0 fb , 8 TeV [ATLAS-CONF-2012-146]
2.2 TeV l* mass ( Λ = m(l*))
-1
L =5.0 fb , 7 TeV [1209.2535]
850 GeV ρ / ωT mass ( m(ρ / ωT) - m(πT) = M )
T
T
W
-1
L =13.0 fb , 8 TeV [ATLAS-CONF-2013-015]
920 GeV ρ mass ( m(ρ ) = m(πT) + mW , m(a ) = 1.1 m(ρ ))
T
T
T
T
-1
L =2.1 fb , 7 TeV [1203.5420]
1.5 TeV N mass (m(W ) = 2 TeV)
R
-1
245 GeV N± mass (|V | = 0.055, |V | = 0.063, |V | = 0)
L =5.8 fb , 8 TeV [ATLAS-CONF-2013-019]
µ
τ
e
±±
-1
L =4.7 fb , 7 TeV [1210.5070]
409 GeV HL mass (limit at 398 GeV for µ µ )
-1
L =4.8 fb , 7 TeV [1210.1718]
1.86 TeV Scalar resonance mass
-1
L =4.4 fb , 7 TeV [1301.5272]
490 GeV mass (|q| = 4e)
-1
L =2.0 fb , 7 TeV [1207.6411]
862 GeV mass
-1
L =4.7 fb , 7 TeV [1210.4491]
-1
1.93 TeV
L =4.6 fb , 7 TeV [1209.4625]
-1
L =4.7 fb , 7 TeV [1211.1150]
-1
L =4.8 fb , 7 TeV [1209.0753]
1.40 TeV
-1
L =5.0 fb , 7 TeV [1209.2535]
-1
2.47 TeV
L =20 fb , 8 TeV [ATLAS-CONF-2013-017]
∫
10-1
*Only a selection of the available mass limits on new states or phenomena shown
1
10
102
Mass scale [TeV]
1 / 35
Status after LHC “run I”
Scalar at 125 GeV found, study of properties begun
s = 7 TeV, L ≤ 5.1 fb-1 s = 8 TeV, L ≤ 19.6 fb-1
CMS Preliminary
Combined
µ = 0.80 ± 0.14
p
SM
s = 7 TeV, L ≤ 5.1 fb
-1
mH = 125.7 GeV
CMS Preliminary
κV
H → bb
µ = 1.15 ± 0.62
s = 8 TeV, L ≤ 19.6 fb
-1
68% CL
95% CL
= 0.65
κb
H → ττ
κτ
µ = 1.10 ± 0.41
κt
H → γγ
µ = 0.77 ± 0.27
κg
H → WW
µ = 0.68 ± 0.20
κγ
H → ZZ
pSM = 0.78
[ κV ≤ 1 ] pSM = 0.88
BRBSM
µ = 0.92 ± 0.28
0
0.5
1
1.5
2
2.5
Best fit σ/σSM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
parameter value
In general no smoking-gun signal of new-physics
ATLAS Exotics Searches* - 95% CL Lower Limits (Status: May 2013)
20.1
20.3
20.1
20.1
g̃
g̃
g̃
g̃
0
Yes
2b
2 e, µ (SS)
0-3 b
Yes
1-2 e, µ
Yes
1-2 b
2 e, µ
0-2 jets
Yes
2 e, µ
2 jets
Yes
0
Yes
2b
1 e, µ
Yes
1b
0
Yes
2b
mono-jet/c -tag Yes
0
2 e, µ (Z )
Yes
1b
3 e, µ (Z )
Yes
1b
20.1
20.7
4.7
20.3
20.3
20.1
20.7
20.5
20.3
20.7
20.7
b̃1
b̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃1
t̃2
Yes
Yes
Yes
Yes
Yes
Yes
20.3
20.3
20.7
20.7
20.7
20.3
ℓ̃
χ̃±
1
χ̃±1
χ̃±1 , χ̃02
χ̃±1 , χ̃02
χ̃±1 , χ̃02
85-315 GeV
125-450 GeV
180-330 GeV
600 GeV
315 GeV
285 GeV
Yes
Yes
Yes
-
20.3
22.9
15.9
4.7
20.3
χ̃±1
g̃
χ̃01
χ̃01
q̃
270 GeV
Yes
Yes
Yes
Yes
4.6
4.6
4.7
20.7
20.7
20.3
20.7
ν̃τ
ν̃τ
q̃, g̃
χ̃±1
χ̃±1
g̃
g̃
Yes
Yes
4.6
14.3
10.5
M* scale
2 e, µ
2 e, µ
2τ
3 e, µ
3 e, µ
1 e, µ
ℓ̃L,R ℓ̃L,R , ℓ̃→ℓχ̃1
+
−
χ̃+
1 χ̃1 , χ̃1 →ℓ̃ν(ℓν̃)
+
−
χ̃+
1 χ̃1 , χ̃1 →τ̃ν(τν̃)
χ̃±1 χ̃02 →ℓ̃L νℓ̃L ℓ(ν̃ν), ℓν̃ℓ̃L ℓ(ν̃ν)
χ̃±1 χ̃02 →W χ̃01 Z χ̃01
χ̃±1 χ̃02 →W χ̃01 h χ̃01
0
0
0
0
2b
+ −
±
1 jet
Direct χ̃1 χ̃1 prod., long-lived χ̃1 Disapp. trk
Stable, stopped g̃ R-hadron
1-5 jets
0
0
GMSB, stable τ̃, χ̃1 →τ̃(ẽ, µ̃)+τ(e, µ) 1-2 µ
0
0
2γ
GMSB, χ̃1 →γG̃ , long-lived χ̃1
0
1 µ, displ. vtx
q̃q̃ , χ̃1 →qqµ (RPV)
LFV pp→ν̃τ + X , ν̃τ →e + µ
LFV pp→ν̃τ + X , ν̃τ →e(µ) + τ
Bilinear RPV CMSSM
+
−
0 0
χ̃+
1 χ̃1 , χ̃1 →W χ̃1 , χ̃1 →eeν̃µ , eµν̃e
+
0 0
−
χ̃+
1 χ̃1 , χ̃1 →W χ̃1 , χ̃1 →ττν̃e , eτν̃τ
2 e, µ
1 e, µ + τ
1 e, µ
4 e, µ
3 e, µ + τ
0
2 e, µ (SS)
7 jets
6-7 jets
0-3 b
Scalar gluon pair, sgluon→qq̄
Scalar gluon pair, sgluon→tt̄
WIMP interaction (D5, Dirac χ)
0
2 e, µ (SS)
0
4 jets
1b
mono-jet
g̃ →qqq
g̃ →t̃1 t , t̃1 →bs
√
s = 7 TeV
full data
√
s = 8 TeV
partial data
√
m(q̃ )=m(g̃ )
any m(q̃ )
any m(q̃ )
0
740 GeV
1.3 TeV
1.18 TeV
1.12 TeV
1.24 TeV
1.4 TeV
1.07 TeV
619 GeV
900 GeV
690 GeV
645 GeV
m(χ̃1 )=0 GeV
0
m(χ̃1 )=0 GeV
0
±
0
m(χ̃1 )<200 GeV, m(χ̃ )=0.5(m(χ̃1 )+m(g̃ ))
0
m(χ̃1 )=0 GeV
tanβ<15
tanβ >18
0
m(χ̃1 )>50 GeV
0
m(χ̃1 )>50 GeV
0
m(χ̃1 )>220 GeV
m(H̃ )>200 GeV
m(g̃ )>10−4 eV
0
ATLAS-CONF-2013-061
1308.1841
ATLAS-CONF-2013-061
ATLAS-CONF-2013-061
0
1308.2631
ATLAS-CONF-2013-007
1208.4305, 1209.2102
m(χ̃1 )<600 GeV
0
m(χ̃1 ) <350 GeV
0
m(χ̃1 )<400 GeV
0
m(χ̃1 )<300 GeV
1.2 TeV
1.1 TeV
1.34 TeV
1.3 TeV
m(χ̃1 )<90 GeV
±
0
m(χ̃1 )=2 m(χ̃1 )
0
m(χ̃1 )=55 GeV
0
±
m(χ̃1 ) =m(t̃1 )-m(W )-50 GeV, m(t̃1 )<<m(χ̃1 )
0
m(χ̃1 )=0 GeV
0
±
0
m(χ̃1 )<200 GeV, m(χ̃1 )-m(χ̃1 )=5 GeV
0
m(χ̃1 )=0 GeV
0
m(χ̃1 )=0 GeV
0
m(t̃1 )-m(χ̃1 )<85 GeV
0
m(χ̃1 )>150 GeV
0
m(t̃1 )=m(χ̃1 )+180 GeV
100-620 GeV
275-430 GeV
110-167 GeV
130-220 GeV
225-525 GeV
150-580 GeV
200-610 GeV
320-660 GeV
90-200 GeV
500 GeV
271-520 GeV
0
m(χ̃1 )=0 GeV
0
±
0
m(χ̃1 )=0 GeV, m(ℓ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
0
±
0
m(χ̃1 )=0 GeV, m(τ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
±
0
0
±
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, m(ℓ̃, ν̃)=0.5(m(χ̃1 )+m(χ̃1 ))
±
0
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, sleptons decoupled
±
0
0
m(χ̃1 )=m(χ̃2 ), m(χ̃1 )=0, sleptons decoupled
±
±
0
m(χ̃1 )-m(χ̃1 )=160 MeV, τ(χ̃1 )=0.2 ns
0
m(χ̃1 )=100 GeV, 10 µs<τ(g̃)<1000 s
10<tanβ<50
832 GeV
475 GeV
0
0.4<τ(χ̃1 )<2
230 GeV
1.0 TeV
1.61 TeV
1.1 TeV
1.2 TeV
760 GeV
ATLAS-CONF-2013-047
ATLAS-CONF-2013-062
1308.1841
ATLAS-CONF-2013-047
ATLAS-CONF-2013-047
ATLAS-CONF-2013-062
ATLAS-CONF-2013-089
1208.4688
ATLAS-CONF-2013-026
1209.0753
ATLAS-CONF-2012-144
1211.1167
ATLAS-CONF-2012-152
ATLAS-CONF-2012-147
ns
0
1.5 <cτ<156 mm, BR(µ)=1, m(χ̃1 )=108 GeV
ATLAS-CONF-2013-048
ATLAS-CONF-2013-065
1308.2631
ATLAS-CONF-2013-037
ATLAS-CONF-2013-024
ATLAS-CONF-2013-068
ATLAS-CONF-2013-025
ATLAS-CONF-2013-025
ATLAS-CONF-2013-049
ATLAS-CONF-2013-049
ATLAS-CONF-2013-028
ATLAS-CONF-2013-035
ATLAS-CONF-2013-035
ATLAS-CONF-2013-093
ATLAS-CONF-2013-069
ATLAS-CONF-2013-057
ATLAS-CONF-2013-058
1304.6310
ATLAS-CONF-2013-092
λ′311 =0.10, λ132 =0.05
λ′311 =0.10, λ1(2)33 =0.05
m(q̃ )=m(g̃ ), cτLSP <1 mm
0
m(χ̃1 )>300 GeV, λ121 >0
0
m(χ̃1 )>80 GeV, λ133 >0
BR(t )=BR(b )=BR(c )=0%
1212.1272
1212.1272
ATLAS-CONF-2012-140
ATLAS-CONF-2013-036
ATLAS-CONF-2013-036
ATLAS-CONF-2013-091
ATLAS-CONF-2013-007
incl. limit from 1110.2693
1210.4826
ATLAS-CONF-2013-051
ATLAS-CONF-2012-147
Extra dimensions
Yes
Yes
Yes
Yes
1.7 TeV
1.2 TeV
1.1 TeV
Large ED (ADD) : monojet + E T ,miss
Large ED (ADD) : monophoton + E T ,miss
Large ED (ADD) : diphoton & dilepton, mγ γ / ll
UED : diphoton + E T ,miss
1
S /Z 2 ED : dilepton, mll
RS1 : dilepton, mll
RS1 : WW resonance, mT ,lν lν
Bulk RS : ZZ resonance, mlljj
RS gKK→ tt (BR=0.925) : t t → l+jets, mtt
ADD BH ( M TH /M D =3) : SS dimuon, N ch. part.
ADD BH ( M TH /M D =3) : leptons + jets, Σ p
T
Quantum black hole : dijet, Fχ(mjj )
qqqq contact interaction : χ(m )
jj
qqll CI : ee & µµ, m
ll
uutt CI : SS dilepton + jets + E T ,miss
Z' (SSM) : mee/ µ µ
Z' (SSM) : mττ
Z' (leptophobic topcolor) : t t → l+jets, m
tt
W' (SSM) : mT,e/µ
W' (→ tq, g =1) : mtq
R
W'R ( → tb, LRSM) : m
tb
Scalar LQ pair (β =1) : kin. vars. in eejj, eν jj
Scalar LQ pair (β =1) : kin. vars. in µµjj, µν jj
Scalar LQ pair (β=1) : kin. vars. in ττjj, τν jj
th
4 generation : t't'→ WbWb
4th generation : b'b' → SS dilepton + jets + E
T ,miss
Vector-like quark : TT→ Ht+X
Vector-like quark : CC, mlν q
Excited quarks : γ -jet resonance, m
γ jet
Excited quarks : dijet resonance, mjj
Excited b quark : W-t resonance, mWt
Excited leptons : l-γ resonance, m
lγ
Techni-hadrons (LSTC) : dilepton,mee/ µ µ
Techni-hadrons (LSTC) : WZ resonance (lν ll), m
WZ
Major. neutr. (LRSM, no mixing) : 2-lep + jets
Heavy lepton
N± (type III seesaw) : Z-l resonance, mZl
H±L± (DY prod., BR(H±±→ll)=1) : SS ee (µµ), m
L
ll
Color octet scalar : dijet resonance, mjj
Multi-charged particles (DY prod.) : highly ionizing tracks
Magnetic monopoles (DY prod.) : highly ionizing tracks
CI
q̃, g̃
g̃
g̃
q̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
g̃
F1/2 scale
Preliminary
s = 7, 8 TeV
Reference
V'
20.3
20.3
20.3
20.3
20.3
20.3
20.3
4.7
20.7
4.8
4.8
4.8
5.8
10.5
ATLAS√
L dt = (4.6 - 22.9) fb−1
LQ
3b
7-10 jets
3b
3b
Mass limit
New
EW
direct
Long-lived
particles
RPV
0
0
0-1 e, µ
0-1 e, µ
L dt[fb−1 ]
quarks
Inclusive Searches
3rd gen.
g̃ med.
3rd gen. squarks
direct production
0
b̃1 b̃1 , b̃1 →bχ̃1
±
b̃1 b̃1 , b̃1 →tχ̃1
±
t̃1 t̃1 (light), t̃1 →bχ̃1
0
t̃1 t̃1 (light), t̃1 →Wbχ̃1
0
t̃1 t̃1 (medium), t̃1 →tχ̃1
±
t̃1 t̃1 (medium), t̃1 →bχ̃1
0
t̃1 t̃1 (heavy), t̃1 →tχ̃1
0
t̃1 t̃1 (heavy), t̃1 →tχ̃1
0
t̃1 t̃1 , t̃1 →c χ̃1
t̃1 t̃1 (natural GMSB)
t̃2 t̃2 , t̃2 →t̃1 + Z
0
Other
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
γ
0
g̃ →bb̄χ̃1
0
g̃ →tt̄ χ̃1
0
g̃ →tt̄ χ̃1
+
g̃ →bt̄ χ̃1
2 e, µ (Z )
0
2-6 jets
3-6 jets
7-10 jets
2-6 jets
2-6 jets
3-6 jets
0-3 jets
2-4 jets
0-2 jets
1b
0-3 jets
mono-jet
0
1 e, µ
0
0
0
1 e, µ
2 e, µ
2 e, µ
1-2 τ
2γ
1 e, µ + γ
MSUGRA/CMSSM
MSUGRA/CMSSM
MSUGRA/CMSSM
0
q̃q̃ , q̃→qχ̃1
0
g̃ g̃ , g̃ →qq̄χ̃1
0
±
g̃ g̃ , g̃ →qqχ̃1 →qqW ± χ̃1
0
g̃ g̃ , g̃ →qq(ℓℓ/ℓν/νν)χ̃1
GMSB (ℓ̃ NLSP)
GMSB (ℓ̃ NLSP)
GGM (bino NLSP)
GGM (wino NLSP)
GGM (higgsino-bino NLSP)
GGM (higgsino NLSP)
Gravitino LSP
R
ferm.
e, µ, τ, γ Jets Emiss
T
Model
Excit.
R
Status: SUSY 2013
Other
ATLAS SUSY Searches* - 95% CL Lower Limits
4.37 TeV M D (δ =2)
M D (δ =2)
ATLAS
4.18 TeV M S (HLZ δ =3, NLO)
Preliminary
Compact. scale R -1
-1
4.71 TeV MKK ~ R
Graviton mass (k /M Pl = 0.1)
-1
L =4.7 fb , 7 TeV [1208.2880]
1.23 TeV Graviton mass (k / M Pl = 0.1)
-1
Ldt = ( 1 - 20) fb-1
L =7.2 fb , 8 TeV [ATLAS-CONF-2012-150]
850 GeV Graviton mass (k / M Pl = 1.0)
-1
L =4.7 fb , 7 TeV [1305.2756]
2.07 TeV g mass
KK
s
=
7, 8 TeV
-1
L =1.3 fb , 7 TeV [1111.0080]
1.25 TeV M D (δ =6)
-1
L =1.0 fb , 7 TeV [1204.4646]
1.5 TeV M D (δ =6)
-1
L =4.7 fb , 7 TeV [1210.1718]
4.11 TeV M D (δ =6)
-1
L =4.8 fb , 7 TeV [1210.1718]
7.6 TeV Λ
-1
L =5.0 fb , 7 TeV [1211.1150]
13.9 TeV Λ (constructive int.)
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-051]
3.3 TeV Λ (C=1)
-1
L =20 fb , 8 TeV [ATLAS-CONF-2013-017]
2.86 TeV Z' mass
-1
L =4.7 fb , 7 TeV [1210.6604]
1.4 TeV Z' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-052]
1.8 TeV Z' mass
-1
L =4.7 fb , 7 TeV [1209.4446]
2.55 TeV W' mass
-1
L =4.7 fb , 7 TeV [1209.6593]
430 GeV W' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-050]
1.84 TeV W' mass
st
-1
L =1.0 fb , 7 TeV [1112.4828]
660 GeV 1 gen. LQ mass
nd
-1
L =1.0 fb , 7 TeV [1203.3172]
685 GeV 2 gen. LQ mass
rd
-1
L =4.7 fb , 7 TeV [1303.0526]
534 GeV 3 gen. LQ mass
-1
L =4.7 fb , 7 TeV [1210.5468]
656 GeV t' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-051]
720 GeV b' mass
-1
L =14.3 fb , 8 TeV [ATLAS-CONF-2013-018]
790 GeV T mass (isospin doublet)
-1
L =4.6 fb , 7 TeV [ATLAS-CONF-2012-137]
1.12 TeV VLQ mass (charge -1/3, coupling κ qQ = ν /mQ)
-1
L =2.1 fb , 7 TeV [1112.3580]
2.46 TeV q* mass
-1
L =13.0 fb , 8 TeV [ATLAS-CONF-2012-148]
3.84 TeV q* mass
-1
L =4.7 fb , 7 TeV [1301.1583]
870 GeV b* mass (left-handed coupling)
-1
L =13.0 fb , 8 TeV [ATLAS-CONF-2012-146]
2.2 TeV l* mass ( Λ = m(l*))
-1
L =5.0 fb , 7 TeV [1209.2535]
850 GeV ρ / ωT mass ( m(ρ / ωT) - m(πT) = M )
T
T
W
-1
L =13.0 fb , 8 TeV [ATLAS-CONF-2013-015]
920 GeV ρ mass ( m(ρ ) = m(πT) + mW , m(a ) = 1.1 m(ρ ))
T
T
T
T
-1
L =2.1 fb , 7 TeV [1203.5420]
1.5 TeV N mass (m(W ) = 2 TeV)
R
-1
245 GeV N± mass (|V | = 0.055, |V | = 0.063, |V | = 0)
L =5.8 fb , 8 TeV [ATLAS-CONF-2013-019]
µ
τ
e
±±
-1
L =4.7 fb , 7 TeV [1210.5070]
409 GeV HL mass (limit at 398 GeV for µ µ )
-1
L =4.8 fb , 7 TeV [1210.1718]
1.86 TeV Scalar resonance mass
-1
L =4.4 fb , 7 TeV [1301.5272]
490 GeV mass (|q| = 4e)
-1
L =2.0 fb , 7 TeV [1207.6411]
862 GeV mass
-1
L =4.7 fb , 7 TeV [1210.4491]
-1
1.93 TeV
L =4.6 fb , 7 TeV [1209.4625]
-1
L =4.7 fb , 7 TeV [1211.1150]
-1
L =4.8 fb , 7 TeV [1209.0753]
1.40 TeV
-1
L =5.0 fb , 7 TeV [1209.2535]
-1
2.47 TeV
L =20 fb , 8 TeV [ATLAS-CONF-2013-017]
∫
Situation will (hopefully) change at 13-14 TeV. If not, then we have
to look in small deviations wrt SM: “precision physics”.
s = 8 TeV
full data
350 GeV
916 GeV
880 GeV
sgluon
sgluon
100-287 GeV
800 GeV
704 GeV
10−1
m(χ)<80 GeV, limit of<687 GeV for D8
1
Mass scale [TeV]
*Only a selection of the available mass limits on new states or phenomena is shown. All limits quoted are observed minus 1σ theoretical signal cross section uncertainty.
10-1
*Only a selection of the available mass limits on new states or phenomena shown
1
10
102
Mass scale [TeV]
1 / 35
Search strategies and theory inputs
examples of strategies to find new-physics / isolate SM processes:
1
2
: s-channel resonance
Events / 25 GeV
µ + Emiss
T
W → µν
tt +single top
8
10
W → τν
107
DY → µ µ
106
Diboson
5
10
Multijet
104
Data
W' → µ ν M = 1.3 TeV
103
data
signal (t-channel)
s-channel
tW
tt
DY
W
diboson
QCD
stat. + syst.
CMS preliminary s = 8 TeV, L = 20 fb-1
W →lν
s = 8 TeV
106
tt
∫L dt = 19.5 fb
-1
105
: BDT output
Z→ ν ν
CMS Preliminary
106
3
: high-pt excess
107
Muon channel, 2J1T
t
QCD
105
+-
Z→ l l
104
ADD MD = 2 TeV, δ = 3
103
Unparticles d =1.7, ΛU = 2 TeV
DM Λ = 892 GeV, Mχ = 1 GeV
104
U
Data
103
102
W' → µ ν M = 2.3 TeV
102
10
10
1
10-1
10-2
10-3
500
1000
1500
2000
2500
MT (GeV)
-1
1
200
2
400
500
600
700
800
1.5
900
1000
miss
ET [GeV]
1
0.5
0
200
-0.5
0
0.5
1
BDT output
300
300
400
500
600
700
800
900
1000
(exp.-meas.)/meas.
102
Data / MC
109
overflow bin
Events / 20 GeV
CMS, 3.7 fb-1, 2012, s = 8 TeV
1010
1
0.5
0
-0.5
-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Emiss
[GeV]
T
- Higgs discovery belongs to 1 , but Higgs characterization requires theory inputs
(rates,shapes,binned x-sections,...)
- For 2 and 3 , we need to control as much as possible QCD effects (i.e. rates and
shapes, and also uncertainties!)
- Some analysis techniques (e.g. 3 ) heavily relies on using MC event generators to
separate signal and backgrounds
2 / 35
Search strategies and theory inputs
examples of strategies to find new-physics / isolate SM processes:
1
2
: s-channel resonance
Events / 25 GeV
µ + Emiss
T
W → µν
tt +single top
8
10
W → τν
107
DY → µ µ
106
Diboson
5
10
Multijet
104
Data
W' → µ ν M = 1.3 TeV
103
data
signal (t-channel)
s-channel
tW
tt
DY
W
diboson
QCD
stat. + syst.
CMS preliminary s = 8 TeV, L = 20 fb-1
W →lν
s = 8 TeV
106
tt
∫L dt = 19.5 fb
-1
105
: BDT output
Z→ ν ν
CMS Preliminary
106
3
: high-pt excess
107
Muon channel, 2J1T
t
QCD
105
+-
Z→ l l
104
ADD MD = 2 TeV, δ = 3
103
Unparticles d =1.7, ΛU = 2 TeV
DM Λ = 892 GeV, Mχ = 1 GeV
104
U
Data
103
102
W' → µ ν M = 2.3 TeV
102
10
10
1
10-1
10-2
10-3
500
1000
1500
2000
2500
MT (GeV)
-1
1
200
2
400
500
600
700
800
1.5
900
1000
miss
ET [GeV]
1
0.5
0
200
-0.5
0
0.5
1
BDT output
300
300
400
500
600
700
800
900
1000
(exp.-meas.)/meas.
102
Data / MC
109
overflow bin
Events / 20 GeV
CMS, 3.7 fb-1, 2012, s = 8 TeV
1010
1
0.5
0
-0.5
-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Emiss
[GeV]
T
- at some level, MC event generators enter in almost all experimental analyses
precise tools ⇒ smaller uncertainties on measured quantities
⇓
“small” deviations from SM accessible
2 / 35
Event generators: what they are?
ideal world: high-energy collision and detection of elementary particles
t
g
H
t
g
t
3 / 35
Event generators: what they are?
ideal world: high-energy collision and detection of elementary particles
real world:
collide non-elementary particles
we detect e, µ, γ,hadrons, “missing energy”
we want to predict final state
- realistically
- precisely
- from first principles
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[sherpa’s artistic view]
3 / 35
Event generators: what they are?
ideal world: high-energy collision and detection of elementary particles
real world:
collide non-elementary particles
we detect e, µ, γ,hadrons, “missing energy”
we want to predict final state
- realistically
- precisely
- from first principles
⇒ full event simulation needed to:
- compare theory and data
- estimate how backgrounds affect signal region
- test analysis strategies
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[sherpa’s artistic view]
3 / 35
Event generators: what’s the output?
in practice: momenta of all outgoing leptons and hadrons:
4 / 35
Plan of the talk
1. review how these tools work
- parton showers (LOPS)
- fixed-order (NLO)
2. discuss how their accuracy can be improved
- matching NLO and PS (NLOPS): POWHEG
- NLOPS merging & MiNLO
3. explain how to build an event generator that is
NNLO accurate (NNLOPS)
- Higgs production at NNLOPS
5 / 35
Plan of the talk
Why going NNLO?
6 / 35
Plan of the talk
Why going NNLO?
“just” NLO sometimes not enough:
- large NLO/LO “K-factor”
[perturbative expansion “not (yet) stable”]
- very high precision needed
NNLO is the frontier:
first 2 → 2 NNLO computations in 2012-13 !
paramount example: Higgs production
[Anastasiou et al., ’04-’05]
- the approach I’ll discuss here works for “color-singlet” production processes at the LHC
- we used it for Higgs production
[Hamilton,Nason,Zanderighi,ER ’13]
- we are currently studying Drell-Yan production
[Karlberg,Zanderighi,ER in progress]
6 / 35
parton showers and fixed order
7 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
2. quarks and gluons are color-charged
⇒ they radiate
(like photons off electrons)
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
2. quarks and gluons are color-charged
⇒ they radiate
(like photons off electrons)
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
2. quarks and gluons are color-charged
⇒ they radiate
(like photons off electrons)
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
2. quarks and gluons are color-charged
⇒ they radiate
(like photons off electrons)
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
2. quarks and gluons are color-charged
⇒ they radiate
(like photons off electrons)
3. soft-collinear emissions are ennhanced:
1
1
=
(p1 + p2 )2
2E1 E2 (1 − cos θ)
4. in soft-collinear limit, factorization properties of QCD
amplitudes
|Mn+1 |2 dΦn+1 → |Mn |2 dΦn
0
t=
n
0
0
z = k /(k + l )
o
2
2
2 2
(k + l) , lT , E θ
Pq,qg (z) = CF
1+z
αS dt
dϕ
Pq,qg (z)dz
2π t
2π
quark energy fraction
splitting hardness
2
1−z
AP splitting function
8 / 35
Parton showers I
- connect the hard scattering (µ ≈ Q) with the final state hadrons (µ ≈ ΛQCD )
- need to simulate production of many quarks and gluons
1. start from low multiplicity at high Q2
2. quarks and gluons are color-charged
⇒ they radiate
(like photons off electrons)
3. soft-collinear emissions are ennhanced:
1
1
=
(p1 + p2 )2
2E1 E2 (1 − cos θ)
4. in soft-collinear limit, factorization properties of QCD
amplitudes
|Mn+1 |2 dΦn+1 → |Mn |2 dΦn
0
t=
n
0
0
z = k /(k + l )
o
2
2
2 2
(k + l) , lT , E θ
Pq,qg (z) = CF
1+z
αS dt
dϕ
Pq,qg (z)dz
2π t
2π
quark energy fraction
splitting hardness
2
1−z
probabilistic interpretation!
AP splitting function
8 / 35
Parton showers II
5. dominant contributions for multiparticle production
due to strongly ordered emissions
t1 > t2 > t3 ...
6. at any given order, we also have virtual corrections:
for consistency we should include them with the
same approximation
- LL virtual contributions included by assigning to each internal line a Sudakov form factor:


X Z ti dt0 Z αs (t0 )

∆a (ti , ti+1 ) = exp −
Pa,bc (z) dz 
0
2π
ti+1 t
(bc)
- ∆a corresponds to the probability of having no resolved emission between ti and ti+1 off
a line of flavour a
resummation of collinear logarithms
7. At scales µ ≈ ΛQCD , hadrons form: non-perturbative effect, simulated with models fitted to
data.
9 / 35
Parton showers: summary
dσSMC = |MB |2 dΦB
|
{z
}
n
o
dσB
10 / 35
Parton showers: summary
n
dσSMC = |MB |2 dΦB ∆(tmax , t0 )
|
{z
}
o
dσB
tmax
Z
∆(tmax , t) = exp −
t
dΦ0r
αs 1
0
P
(z
)
2π t0
10 / 35
Parton showers: summary
n
dσSMC = |MB |2 dΦB ∆(tmax , t0 )+∆(tmax , t)
|
{z
}
dσB
o
dPemis (t)
| {z }
αs
2π
1 P (z)
t
dΦr
tmax
Z
∆(tmax , t) = exp −
t
dΦ0r
αs 1
0
P
(z
)
2π t0
10 / 35
Parton showers: summary
n
dσSMC = |MB |2 dΦB ∆(tmax , t0 )+∆(tmax , t)
|
{z
}
dσB
dPemis (t)
| {z }
αs
2π
1 P (z)
t
o
{∆(t, t0 ) + ∆(t, t0 )dPemis (t0 )}
|
{z
}
t0 <t
dΦr
tmax
Z
∆(tmax , t) = exp −
t
dΦ0r
αs 1
0
P
(z
)
2π t0
10 / 35
Parton showers: summary
n
dσSMC = |MB |2 dΦB ∆(tmax , t0 )+∆(tmax , t)
|
{z
}
dσB
dPemis (t)
| {z }
αs
2π
1 P (z)
t
o
{∆(t, t0 ) + ∆(t, t0 )dPemis (t0 )}
|
{z
}
t0 <t
dΦr
tmax
Z
∆(tmax , t) = exp −
t
dΦ0r
αs 1
0
P
(z
)
2π t0
10 / 35
Parton showers: summary
n
dσSMC = |MB |2 dΦB ∆(tmax , t0 )+∆(tmax , t)
|
{z
}
dσB
dPemis (t)
| {z }
αs
2π
1 P (z)
t
o
{∆(t, t0 ) + ∆(t, t0 )dPemis (t0 )}
|
{z
}
t0 <t
dΦr
tmax
Z
∆(tmax , t) = exp −
t
dΦ0r
αs 1
0
P
(z
)
2π t0
10 / 35
Parton showers: summary
n
dσSMC = |MB |2 dΦB ∆(tmax , t0 )+∆(tmax , t)
|
{z
}
dσB
dPemis (t)
| {z }
αs
2π
1 P (z)
t
o
{∆(t, t0 ) + ∆(t, t0 )dPemis (t0 )}
|
{z
}
t0 <t
dΦr
tmax
Z
∆(tmax , t) = exp −
t
dΦ0r
αs 1
0
P
(z
)
2π t0
This is “LOPS”
- A parton shower changes shapes, not the overall normalization, which stays LO (unitarity)
10 / 35
Do they work?
[Gianotti,Mangano 0504221]
! ok when observables dominated by soft-collinear radiation
% Not surprisingly, they fail when looking for hard multijet kinematics
% they are only LO+LL accurate (whereas we can compute up to (N)NLO QCD corrections)
⇒ Not enough if interested in precision (10% or less), or in multijet regions
11 / 35
Next-to-Leading Order I
αS ∼ 0.1 ⇒ to improve the accuracy, use exact perturbative expansion
LO: Leading Order
α α 2
NLO: Next-to-Leading Order
S
S
dσ = dσLO +
dσNLO
+
dσNNLO + ...
...
2π
2π
12 / 35
Next-to-Leading Order I
αS ∼ 0.1 ⇒ to improve the accuracy, use exact perturbative expansion
LO: Leading Order
α α 2
NLO: Next-to-Leading Order
S
S
dσ = dσLO +
dσNLO
+
dσNNLO + ...
...
2π
2π
Why NLO is important?
first order where rates are reliable
shapes are, in general, better described
possible to attach sensible theoretical
uncertainties
when NLO corrections large, NNLO is
desirable (as in Higgs production!)
[Anastasiou et al., ’03]
12 / 35
Next-to-Leading Order II
NLO how-to
dσ = dΦn
n
B(Φn )
| {z }
LO
+
i
αs h
V (Φn ) + R(Φn+1 ) dΦr
2π |
{z
}
o
NLO
- Inputs: tree-level n-partons (B), 1-loop n-partons (V ), tree-level n + 1 partons (R)
- truncated series ⇒ result depends on “unphysical” scales
(can be used to estimate theoretical uncertainties)
Limitations:
Results are at the parton level only (5 − 6 final-state partons is the frontier)
In regions where collinear emissions are important, they fail (no resummation)
Choice of scale is an issue when multijets in the final states
13 / 35
matching NLO and PS
I
POWHEG (POsitive Weight Hardest Emission Generator)
14 / 35
PS vs NLO
NLO
parton showers
! precision
! realistic + flexible tools
! nowadays this is the standard
! widely used by experimental coll’s
% limited multiplicity
% limited precision (LO)
% (fail when resummation needed)
% (fail when multiple hard jets)
can merge them and build an NLOPS generator?
Problem:
15 / 35
PS vs NLO
NLO
parton showers
! precision
! realistic + flexible tools
! nowadays this is the standard
! widely used by experimental coll’s
% limited multiplicity
% limited precision (LO)
% (fail when resummation needed)
% (fail when multiple hard jets)
can merge them and build an NLOPS generator?
Problem: overlapping regions!
NLO:
⊗
15 / 35
PS vs NLO
NLO
parton showers
! precision
! realistic + flexible tools
! nowadays this is the standard
! widely used by experimental coll’s
% limited multiplicity
% limited precision (LO)
% (fail when resummation needed)
% (fail when multiple hard jets)
can merge them and build an NLOPS generator?
Problem: overlapping regions!
NLO:
PS:
⊗
15 / 35
PS vs NLO
parton showers
NLO
! precision
! realistic + flexible tools
! nowadays this is the standard
! widely used by experimental coll’s
% limited multiplicity
% limited precision (LO)
% (fail when resummation needed)
% (fail when multiple hard jets)
can merge them and build an NLOPS generator?
Problem: overlapping regions!
⊗
! 2 methods available to solve this problem:
MC@NLO and POWHEG
[Frixione-Webber ’03, Nason ’04]
15 / 35
NLOPS: POWHEG I
dσPOW = dΦn B̄(Φn )
αs R(Φn , Φr )
min
∆(Φn ; kT
) + ∆(Φn ; kT )
dΦr
2π B(Φn )
16 / 35
NLOPS: POWHEG I
B(Φn ) ⇒ B̄(Φn ) = B(Φn ) +
αs h
V (Φn ) +
2π
Z
R(Φn+1 ) dΦr
i
+
dσPOW = dΦn B̄(Φn )
αs R(Φn , Φr )
min
∆(Φn ; kT
) + ∆(Φn ; kT )
dΦr
2π B(Φn )
16 / 35
NLOPS: POWHEG I
B(Φn ) ⇒ B̄(Φn ) = B(Φn ) +
αs h
V (Φn ) +
2π
Z
R(Φn+1 ) dΦr
i
+
dσPOW = dΦn B̄(Φn )
αs R(Φn , Φr )
min
∆(Φn ; kT
) + ∆(Φn ; kT )
dΦr
2π B(Φn )
↔
Z
R(Φn , Φ0r )
αs
0
∆(tm , t) ⇒ ∆(Φn ; kT ) = exp −
θ(kT
− kT ) dΦ0r
2π
B(Φn )
16 / 35
NLOPS: POWHEG II
αs R(Φn , Φr )
min
dσPOW = dΦn B̄(Φn ) ∆(Φn ; kT
) + ∆(Φn ; kT )
dΦr
2π B(Φn )
[+ pT -vetoing subsequent emissions, to avoid double-counting]
- inclusive observables: @NLO
- first hard emission: full tree level ME
This is “NLOPS”
- (N)LL resummation of collinear/soft logs
- extra jets in the shower approximation
17 / 35
NLOPS: POWHEG II
αs R(Φn , Φr )
min
dσPOW = dΦn B̄(Φn ) ∆(Φn ; kT
) + ∆(Φn ; kT )
dΦr
2π B(Φn )
[+ pT -vetoing subsequent emissions, to avoid double-counting]
- inclusive observables: @NLO
- first hard emission: full tree level ME
This is “NLOPS”
- (N)LL resummation of collinear/soft logs
- extra jets in the shower approximation
POWHEG BOX
[Alioli,Nason,Oleari,ER ’10]
large library of SM processes, (largely) automated
widely used by LHC collaborations
17 / 35
interlude: BSM with POWHEG
Recently studied DM production at the LHC, including PS effects
SM
DM
SM
DM
[Haisch,Kahlhoefer,ER ’13]
% nothing to detect ⇒ not visible !
18 / 35
interlude: BSM with POWHEG
Recently studied DM production at the LHC, including PS effects
SM
DM
SM
DM
[Haisch,Kahlhoefer,ER ’13]
! can emit extra SM particle
18 / 35
interlude: BSM with POWHEG
Recently studied DM production at the LHC, including PS effects
[Haisch,Kahlhoefer,ER ’13]
jet
SM
SM
monojet signal !
DM → missing ET
18 / 35
interlude: BSM with POWHEG
Recently studied DM production at the LHC, including PS effects
[Haisch,Kahlhoefer,ER ’13]
jet
SM
SM
monojet signal !
DM → missing ET
18 / 35
NLOPS: H+j
H+j @ NLO, H+jj @ LO are needed for inclusive H @ NNLO
,→ start from H+j @ NLOPS (POWHEG)
19 / 35
NLOPS: H+j
H+j @ NLO, H+jj @ LO are needed for inclusive H @ NNLO
,→ start from H+j @ NLOPS (POWHEG)
qT
mh
Z
h
i
B̄(Φn ) dΦn = α3S (µR ) B + αS V (µR ) + αS dΦrad R dΦn
when doing X+ jet(s) @ NLO, B̄(Φ ) is not finite !
n
,→ need of a generation cut on Φn (or variants thereof)
19 / 35
NLOPS: H+j
H+j @ NLO, H+jj @ LO are needed for inclusive H @ NNLO
,→ start from H+j @ NLOPS (POWHEG)
qT
mh
Z
h
i
B̄(Φn ) dΦn = α3S (µR ) B + αS V (µR ) + αS dΦrad R dΦn
when doing X+ jet(s) @ NLO, B̄(Φ ) is not finite !
n
,→ need of a generation cut on Φn (or variants thereof)
want to reach NNLO accuracy for e.g. y
H,
i.e. when fully inclusive over QCD radiation
- need to allow the 1st jet to become unresolved
- above approach needs to be modified
- notice: H+j is a 2-scales problem (→ choice of µ not unique! )
19 / 35
NLOPS merging
I
MiNLO (Multiscale Improved NLO)
20 / 35
MiNLO: intro
for processes with widely different scales (e.g. X+ jets close to Sudakov regions)
choice of scales is not straightforward
scale often chosen a posteriori, requiring typically
NLO corrections to be small
sensitivity upon scale choice to be minimal (→ plateau in σ(µ) vs. µ)
21 / 35
MiNLO: intro
for processes with widely different scales (e.g. X+ jets close to Sudakov regions)
choice of scales is not straightforward
scale often chosen a posteriori, requiring typically
NLO corrections to be small
sensitivity upon scale choice to be minimal (→ plateau in σ(µ) vs. µ)
MiNLO: Multiscale Improved NLO
[Hamilton,Nason,Zanderighi, 1206.3572]
- aim: method to a-priori choose scales in NLO computation
- idea: at LO, the CKKW procedure allows to take these effects into account:
modify the LO weight B(Φn ) in order to include (N)LL effects.
⇒ “Use CKKW” on top of NLO computation that potentially involves many scales
Next-to-Leading Order accuracy needs to be preserved
21 / 35
From CKKW to MiNLO
Find “most-likely” shower history (via kT -algo): Q > q3 > q2 > q1 ≡ Q0
22 / 35
From CKKW to MiNLO
Find “most-likely” shower history (via kT -algo): Q > q3 > q2 > q1 ≡ Q0
q3
q2
Q
q1
22 / 35
From CKKW to MiNLO
Find “most-likely” shower history (via kT -algo): Q > q3 > q2 > q1 ≡ Q0
q3
q2
Q
q1
Evaluate αS at nodal scales
αn
S (µR )B(Φn ) ⇒ αS (q1 )αS (q2 )...αS (qn )B(Φn )
scale compensation: use µ̄2R = (q1 q2 ...qn )2/n in V
22 / 35
From CKKW to MiNLO
Find “most-likely” shower history (via kT -algo): Q > q3 > q2 > q1 ≡ Q0
q3
q2
Q
q1
Evaluate αS at nodal scales
αn
S (µR )B(Φn ) ⇒ αS (q1 )αS (q2 )...αS (qn )B(Φn )
scale compensation: use µ̄2R = (q1 q2 ...qn )2/n in V
Sudakov FFs in internal and external lines of Born “skeleton”
B(Φn ) ⇒ B(Φn ) × {∆(Q0 , Q)∆(Q0 , qi )...}
recover NLO exactly: remove O(αn+1
) (log) terms generated upon expansion
S
(1)
B(Φn ) ⇒ B(Φn ) 1 − ∆ (Q0 , Q) − ∆(1) (Q0 , qi ) + ...
22 / 35
MiNLO: example
Example, in 1 line: H + 1 jet
Pure NLO:
Z
i
h
(NLO)
(NLO)
dΦrad R dΦn
dσ = B̄ dΦn = α3S (µR ) B + αS
V (µR ) + αS
qT
mh
23 / 35
MiNLO: example
Example, in 1 line: H + 1 jet
Pure NLO:
Z
i
h
(NLO)
(NLO)
dΦrad R dΦn
dσ = B̄ dΦn = α3S (µR ) B + αS
V (µR ) + αS
MiNLO:
Z
i
h (1)
(NLO)
(NLO)
dΦrad R
B̄ = α2S (mh )αS (qT )∆2g (qT , mh ) B 1 − 2∆g (qT , mh ) +αS
V (µ̄R )+αS
∆(qT , mh )
qT
∆(qT , qT )
mh
∆(qT , mh )
∆(qT , qT )
23 / 35
MiNLO: example
Example, in 1 line: H + 1 jet
Pure NLO:
Z
i
h
(NLO)
(NLO)
dΦrad R dΦn
dσ = B̄ dΦn = α3S (µR ) B + αS
V (µR ) + αS
MiNLO:
Z
i
h (1)
(NLO)
(NLO)
dΦrad R
B̄ = α2S (mh )αS (qT )∆2g (qT , mh ) B 1 − 2∆g (qT , mh ) +αS
V (µ̄R )+αS
∆(qT , mh )
qT
∆(qT , qT )
mh
∆(qT , mh )
* µ̄R = (m2h qT )1/3
∆(qT , qT )
Q2
i
dq 2 αS (q 2 ) h
Q2
Af log 2 + Bf
q2
2π
q
h
Q2
Q2 i
(1)
(NLO) 1 1
* ∆f (qT , Q) = −αS
A1,f log2 2 + B1,f log 2
2π 2
qT
qT
* µF = Q0 (= qT )
Z
* log ∆f (qT , Q) = −
2
qT
Sudakov FF included on Born kinematics
23 / 35
MiNLO: example
Example, in 1 line: H + 1 jet
Pure NLO:
Z
i
h
(NLO)
(NLO)
dΦrad R dΦn
dσ = B̄ dΦn = α3S (µR ) B + αS
V (µR ) + αS
MiNLO:
Z
i
h (1)
(NLO)
(NLO)
dΦrad R
B̄ = α2S (mh )αS (qT )∆2g (qT , mh ) B 1 − 2∆g (qT , mh ) +αS
V (µ̄R )+αS
∆(qT , mh )
qT
∆(qT , qT )
mh
∆(qT , mh )
∆(qT , qT )
X+ jets cross-section finite without generation cuts
,→ B̄ with MiNLO prescription: ideal starting point for NLOPS (POWHEG) for X+ jets
,→ can be used to extend validity of H+j POWHEG when jet becomes unresolved
23 / 35
“Improved” MiNLO & NLOPS merging
so far, no statements on the accuracy for fully-inclusive quantities
24 / 35
“Improved” MiNLO & NLOPS merging
so far, no statements on the accuracy for fully-inclusive quantities
Carefully addressed for HJ-MiNLO
[Hamilton et al., 1212.4504]
HJ-MiNLO describes inclusive observables at order αS (relative to inclusive H @ LO)
to reach genuine NLO when inclusive, “spurious” terms must be of relative order α2S ,
i.e.
OHJ−MiNLO = OH@NLO + O(αb+2
)
S
(b = 2 for gg → H)
b
if O is inclusive (H@LO ∼ αS ).
b+3/2
“Original MiNLO” contains ambiguous O(αS
) terms.
24 / 35
“Improved” MiNLO & NLOPS merging
so far, no statements on the accuracy for fully-inclusive quantities
Carefully addressed for HJ-MiNLO
[Hamilton et al., 1212.4504]
HJ-MiNLO describes inclusive observables at order αS (relative to inclusive H @ LO)
to reach genuine NLO when inclusive, “spurious” terms must be of relative order α2S ,
i.e.
OHJ−MiNLO = OH@NLO + O(αb+2
)
S
(b = 2 for gg → H)
b
if O is inclusive (H@LO ∼ αS ).
b+3/2
“Original MiNLO” contains ambiguous O(αS
) terms.
Possible to improve HJ-MiNLO such that H @ NLO is recovered (NLO(0) ) , without
spoiling NLO accuracy of H+j (NLO(1) ) .
- proof based on careful comparisons between MiNLO and analytic resummation
- need to include B2 coefficient in MiNLO-Sudakovs
- need to evaluate αS
(NLO)
in HJ-MiNLO at scale qT , and µF = qT
Effectively as merging NLO(0) and NLO(1) samples, without merging different
samples (no merging scale used: there is just one sample).
24 / 35
MiNLO merging: results
[Hamilton et al., 1212.4504]
dσ/dyH [pb]
101
100
10−1
10−2
1.5
1.0
0.5
-4
H+Pythia
HJ+Pythia
ratio
ratio
dσ/dyH [pb]
101
-3
-2
-1
0
yH
1
2
3
4
100
10−1
10−2
1.5
1.0
0.5
-4
HJ+Pythia
H+Pythia
-3
-2
-1
0
yH
1
2
3
4
“H+Pythia”: standalone POWHEG (gg → H) + PYTHIA (PS level) [7pts band, µ = mH ]
“HJ+Pythia”: HJ-MiNLO* + PYTHIA (PS level) [7pts band, µ from MiNLO]
! very good agreement (both value and band)
Notice: band is ∼ 20 − 30%
25 / 35
matching NNLO with PS
I
Higgs production at NNLOPS
26 / 35
NNLO+PS I
HJ-MiNLO* differential cross section (dσ/dy)HJ−MiNLO is NLO accurate
W (y) = dσ
dy
dσ
dy
NNLO
=
c2 α2S + c3 α3S + c4 α4S
c4 − d 4 2
'1+
αS + O(α3S )
c2 α2S + c3 α3S + d4 α4S
c2
HJ−MiNLO
thus, reweighting each event with this factor, we get NNLO+PS
- obvious for yH , by construction
- α4S accuracy of HJ-MiNLO* in 1-jet region not spoiled, because W (y) = 1 + O(α2S )
2+3/2
- if we had NLO(0) + O(αS
), 1-jet region spoiled because
(1)
[NLO(1) ]NNLOPS = NLO(1) + O(α4.5
+ O(α5S )
S ) 6= NLO
27 / 35
NNLO+PS I
HJ-MiNLO* differential cross section (dσ/dy)HJ−MiNLO is NLO accurate
W (y) = dσ
dy
dσ
dy
NNLO
=
c2 α2S + c3 α3S + c4 α4S
c4 − d 4 2
'1+
αS + O(α3S )
c2 α2S + c3 α3S + d4 α4S
c2
HJ−MiNLO
thus, reweighting each event with this factor, we get NNLO+PS
- obvious for yH , by construction
- α4S accuracy of HJ-MiNLO* in 1-jet region not spoiled, because W (y) = 1 + O(α2S )
2+3/2
- if we had NLO(0) + O(αS
), 1-jet region spoiled because
(1)
[NLO(1) ]NNLOPS = NLO(1) + O(α4.5
+ O(α5S )
S ) 6= NLO
* Variants for W are possible:
R
W (y, pT ) = h(pT ) R
dσA = dσ h(pT ),
NNLO δ(y − y(Φ))
dσA
MiNLO δ(y − y(Φ))
dσA
dσB = dσ (1 − h(pT )),
+ (1 − h(pT ))
h=
(βmH )2
(βmH )2 + p2T
* h(pT ) controls where the NNLO/NLO K-factor is spread
* β (similar to resummation scale) cannot be too small, otherwise resummation spoiled
27 / 35
NNLO+PS II
In 1309.0017, we used
R
W (y, pT ) = h(pT )
dσA = dσ h(pT ),
R
MiNLO δ(y − y(Φ))
dσ NNLO δ(y − y(Φ)) − dσB
R
+ (1 − h(pT ))
MiNLO δ(y − y(Φ))
dσA
dσB = dσ (1 − h(pT )),
h=
(βmH )2
(βmH )2 + p2T
one gets exactly (dσ/dy)NNLOPS = (dσ/dy)NNLO (no α5S terms)
we used h(pjT1 ) (hardest jet at parton level)
inputs for following plots:
- results are for 8 TeV LHC
- scale choices: NNLO input with µ = mH /2, HJ-MiNLO “core scale” mH
(other powers are at qT )
- PDF: everywhere MSTW8NNLO
- NNLO always from HNNLO
- events reweighted at the LH level
- plots after kT -ordered PYTHIA 6 at the PS level (hadronization and MPI switched off)
28 / 35
NNLO+PS (fully incl.)
NNLO with µ = mH /2, HJ-MiNLO “core scale” mH
[NNLO from HNNLO, Catani,Grazzini]
(7Mi × 3NN ) pts scale var. in NNLOPS, 7pts in NNLO
dσ/dy [pb]
101
100
10−1
10−2
1.1
1.0
0.9
-4
NNLOPS
HNNLO
Ratio
Ratio
dσ/dy [pb]
101
-3
-2
-1
0
y
1
2
3
4
100
10−1
10−2
1.1
1.0
0.9
-4
HNNLO
NNLOPS
-3
-2
-1
0
y
1
2
3
4
Notice: band is 10%
4
4
[Until and including O(αS ), PS effects don’t affect yH (first 2 emissions controlled properly at O(αS ) by MiNLO+POWHEG)]
29 / 35
NNLO+PS (pH
T)
β = 1/2
dσ/dpHT [pb/GeV]
100
HQT
10−1
NNLOPS
10−2
10−3
1.4
1.0
0.6
Ratio
Ratio
dσ/dpHT [pb/GeV]
β = ∞ (W indep. of pT )
0
50
100
150 200
pHT [GeV]
250
300
HqT: NNLL+NNLO, µR = µF = mH /2 [7pts],
100
HQT
NNLOPS
10−1
10−2
10−3
1.4
1.0
0.6
0
50
100
150 200
pHT [GeV]
Qres ≡ mH /2
250
300
[HqT, Bozzi et al.]
! β = 1/2 & ∞: uncertainty bands of HqT contain NNLOPS at low-/moderate p
T
β = 1/2: HqT tail harder than NNLOPS tail (µHqT < ”µMiNLO ”)
β = 1/2: very good agreement with HqT resummation [“∼ expected”, since
Qres ≡ mH /2]
30 / 35
NNLO+PS (pH
T)
β = 1/2
dσ/dpHT [pb/GeV]
100
NNLOPS
HQT
10−1
10−2
10−3
1.4
1.0
0.6
Ratio
Ratio
dσ/dpHT [pb/GeV]
β = ∞ (W indep. of pT )
0
50
100
150 200
pHT [GeV]
250
300
HqT: NNLL+NNLO, µR = µF = mH /2 [7pts],
100
NNLOPS
HQT
10−1
10−2
10−3
1.4
1.0
0.6
0
50
100
150 200
pHT [GeV]
250
300
Qres ≡ mH /2
β = 1/2: NNLOPS tail → NLOPS tail [ W (y, pT mH ) → 1 ]
larger band (affected just marginally by NNLO, so it’s ∼ genuine NLO band)
31 / 35
NNLO+PS (pjT1 )
0.8
1.0
NNLOPS
JETVHETO
ε(pT,veto )
ε(pT,veto )
1.0
0.6
0.4
0.8
JETVHETO
NNLOPS
0.6
0.4
Anti−kT
Anti−kT
1.1
1.0
0.9
10
R = 1.0
#/εcentral
#/εcentral
R = 1.0
20
30
50
pT,veto [GeV]
ε (pT,veto ) =
70
100
Σ(pT,veto )
1
= tot
σ tot
σ
1.1
1.0
0.9
10
Z
20
30
50
pT,veto [GeV]
70
100
j
dσ θ pT,veto − pT1
JetVHeto: NNLL resum, µR = µF = mH /2 [7pts], Qres ≡ mH /2, (a)-scheme only
[JetVHeto, Banfi et al.]
nice agreement, differences never more than 5-6 %
Separation of H → W W from tt̄ bkg: x-sec binned in N
jet
0-jet bin (W W -dominated) ⇔ jet-veto accurate predictions needed !
32 / 35
Conclusions and Outlook
I
Especially in absence of very clear singals of new-physics, accurate tools are needed for
LHC phenomenology
I
In the last decade, impressive amount of progress: new ideas, and automated tools
⇒ Shown results of merging NLOPS for different jet-multiplicities without merging scale
⇒ Shown first working example of NNLOPS
What next?
33 / 35
Conclusions and Outlook
I
Especially in absence of very clear singals of new-physics, accurate tools are needed for
LHC phenomenology
I
In the last decade, impressive amount of progress: new ideas, and automated tools
⇒ Shown results of merging NLOPS for different jet-multiplicities without merging scale
⇒ Shown first working example of NNLOPS
What next?
I
Drell-Yan: conceptually the same as gg → H, technically slightly more involved,
phenomenologically important (standard candle + W mass extraction, pdfs,...)
33 / 35
Drell-Yan NNLOPS
preliminary results!
Born kinematics more complicated: W (y) → W (mll , yZ , θl ); β = 1.
350
300
100
NNLO+NNLL
NNLOPS
200
d σ/d pT,Z [pb/GeV]
d σ/d yZ [pb]
250
150
100
DYNNLO
Zj-MiNLO
NNLOPS
50
0
1.05
1
0.95
10
1.2
1.1
1
0.9
0.8
1
0.9
0.8
-4
-3
-2
-1
0
1
2
3
4
yZ
0
10
20
30
40
50
pT,Z [GeV]
! reproduce NNLO
! very good agreement with analytic resummation
34 / 35
Conclusions and Outlook
I
Especially in absence of very clear singals of new-physics, accurate tools are needed for
LHC phenomenology
I
In the last decade, impressive amount of progress: new ideas, and automated tools
⇒ Shown results of merging NLOPS for different jet-multiplicities without merging scale
⇒ Shown first working example of NNLOPS
What next?
I
Drell-Yan: conceptually the same as gg → H, technically slightly more involved,
phenomenologically important (e.g. W mass extraction, pdfs,...)
35 / 35
Conclusions and Outlook
I
Especially in absence of very clear singals of new-physics, accurate tools are needed for
LHC phenomenology
I
In the last decade, impressive amount of progress: new ideas, and automated tools
⇒ Shown results of merging NLOPS for different jet-multiplicities without merging scale
⇒ Shown first working example of NNLOPS
What next?
I
Drell-Yan: conceptually the same as gg → H, technically slightly more involved,
phenomenologically important (e.g. W mass extraction, pdfs,...)
I
for more complicated processes, a more analytic-based approach might be needed
I
merging for higher multiplicity / NNLO matching for e.g. tt̄...
35 / 35
Conclusions and Outlook
I
Especially in absence of very clear singals of new-physics, accurate tools are needed for
LHC phenomenology
I
In the last decade, impressive amount of progress: new ideas, and automated tools
⇒ Shown results of merging NLOPS for different jet-multiplicities without merging scale
⇒ Shown first working example of NNLOPS
What next?
I
Drell-Yan: conceptually the same as gg → H, technically slightly more involved,
phenomenologically important (e.g. W mass extraction, pdfs,...)
I
for more complicated processes, a more analytic-based approach might be needed
I
merging for higher multiplicity / NNLO matching for e.g. tt̄...
Thank you for your attention!
35 / 35
Extra slides
36 / 35
“Improved” MiNLO & NLOPS merging II
Resummation formula
o
dσ
d n
= σ0 2 [Cga ⊗ fa ](xA , qT ) × [Cgb ⊗ fb ](xB , qT ) × exp S(qT , Q) + Rf
2
dqT dy
dqT
Z Q2
i
Q2
dq 2 αS (q 2 ) h
Af log 2 + Bf
S(qT , Q) = −2
2
2
q
2π
q
qT
(1)
If Cij included and Rf is LO(1) , then upon integration we get NLO(0)
Take derivative, then compare with MiNLO :
1
∼ σ0 2 [αS , α2S , α3S , α4S , αS L, α2S L, α3S L, α4S L] exp S(qT , Q) + Rf
qT
2
L = log(Q2 /qT
)
highlighted terms are needed to reach NLO(0) :
Z Q2
2
n−(m+1)/2
dqT
Lm αS n (qT ) exp S ∼ αS (Q2 )
2
qT
(scaling in low-pT region is α2S L ∼ 1!)
2
if I don’t include B2 in MiNLO ∆g , I miss a term (1/qT
) α2S B2 exp S
3/2
upon integration, violate NLO(0) by a term of relative O(αS )
(NLO)
“wrong” scale in αS
in MiNLO produces again same error
37 / 35
Parton Showers
Sudakov FF from infinitesimal emission probabilities
Pino emiss (t → t0 ) '
Z
N N Y
Y
αS (tk ) δt X
dφ 1 − dPiemiss (tk ) =
1−
Pi,jl (z) dz
2π
t
2π
k
k=1
k=1
(jl)
0
This reduces to the Sudakov form factor ∆i (t, t ) in the continuum limit N → +∞.
We can state that, in Parton Showers, virtual corrections are included in a probabilistic
way.
Choice of the ordering variable affects double-log structure
- angular ordering is the correct choice
- exact in HERWIG, approximate in other generators
The use of αS = αS (p2T ), in the radiation scheme, allows to include (part of) the 2-loop
splitting kernels
Nominal accuracy is LL, although it’s common believe that in practice it’s better.
For some observables (e.g. low-pT DY) NLL can be achieved.
Momentum conservation (via reshuffling/recoil) is respected (and this is a NLL effect).
38 / 35
Color coherence
Soft emissions from final-state-partons add coherently
After azimuthal average, color coherence force emissions to be angular ordered
In the above figure, the soft large-angle gluon sees the net colour charge of the initial quark,
and not the charges of each emitter.
In non angular-ordered Shower, this is not taken into account → need of corrections to the
algorithm without spoiling the collinear accuracy.
If the Shower is angular-ordered, the coherence is built-in: large-angle soft emissions are
generated first.
The hardest emission (highest pT ), in general, happens later.
39 / 35
CKKW in a nutshell I
start from ME weight
B(Φn )
40 / 35
CKKW in a nutshell I
find “most-likely”
shower history (via
kT -algo)
40 / 35
CKKW in a nutshell I
find “most-likely”
shower history (via
kT -algo)
clustering scale
q 1 = kT
40 / 35
CKKW in a nutshell I
find “most-likely”
shower history (via
kT -algo)
40 / 35
CKKW in a nutshell I
find “most-likely”
shower history (via
kT -algo)
clustering scale
q 2 = kT
40 / 35
CKKW in a nutshell I
find “most-likely”
shower history (via
kT -algo)
40 / 35
CKKW in a nutshell I
find “most-likely”
shower history (via
kT -algo)
clustering scale
q 3 = kT
40 / 35
CKKW in a nutshell I
Hard process
scale Q
40 / 35
CKKW in a nutshell I
q3
q2
Q
q1
most-likely shower
history
40 / 35
CKKW in a nutshell
ME weight B(Φn ) ⇒ “most-likely” shower history (via kT -algo): Q > q3 > q2 > q1 ≡ Q0
q3
q2
Q
q1
New weight:
α5S (Q)B(Φ3 )
→
α2S (Q)B(Φ3 )
∆g (Q0 , Q) ∆g (Q0 , Q) ∆g (Q0 , q3 )
∆g (Q0 , q2 ) ∆g (Q0 , q3 ) ∆g (Q0 , q1 )
∆g (Q0 , q2 )∆g (Q0 , q2 )∆g (Q0 , q3 )∆g (Q0 , q1 )∆g (Q0 , q1 )
αS (q1 )αS (q2 )αS (q3 )
where typically
Z
log ∆f (qT , Q) = −
Q2
2
qT
i
Q2
dq 2 αS (q 2 ) h
A1,f log 2 + B1,f
2
q
2π
q
Fill phase space below Q0 with vetoed shower
41 / 35
MiNLO merging, results
H+Pythia
HJ+Pythia
−1
10
10−2
10−3
1.5
1.0
0.5
dσ/dpHT [pb/GeV]
10
ratio
ratio
dσ/dpHT [pb/GeV]
[Hamilton et al., 1212.4504]
0
0
50 100 150 200 250 300 350 400
pHT [GeV]
0
10
HJ+Pythia
H+Pythia
10−1
10−2
10−3
1.5
1.0
0.5
0
50 100 150 200 250 300 350 400
pHT [GeV]
Good agreement
At high pT , bands as expected (LO vs NLO)
( POWHEG (gg → H) with hfact = mH /1.2, YR2 )
42 / 35
MiNLO: results
VJJ-MiNLO [Campbell,Ellis,Nason,Zanderighi, 1303.5447]
102
dσ/dpj1
[pb/GeV]
T
WJJ-MiNLO
ATLAS
100
10−1
10−2
Njet ≥ 2
pjT > 20 GeV
1.5
1
0.5
0
50
100
150 200
pj1
[GeV]
T
250
300
WJJ-MiNLO
ATLAS
101
100
10−1
Njet ≥ 1
pjT > 20 GeV
10−2
#/Data
#/Data
dσ/dpj1
[pb/GeV]
T
101
1.5
1
0.5
0
50
100
150 200
pj1
[GeV]
T
250
300
Start from W + 2 jets @ NLO, good agreement with data also
when requiring Njet ≥ 1 !
This is not possible in a standard NLO...
43 / 35
MiNLO details
MiNLO: All αS in Born term are chosen with CKKW (local) scales q1 , ..., qn
αn
S (µR )B ⇒ αS (q1 )αS (q2 )...αS (qn )B
Normal NLO structure (µ = µR ):
n+1
(µ) C + nb0 log(µ2 /Q2 )B + αn+1
σ(µ) = αn
(µ)R
S (µ)B + αS
S
| {z } |
{z
} | {z }
Born
Real
Virtual
Explicit µ dependence of virtual term as required by RG invariance:
h
i
n+1
0
)
αn
(µ) log(µ02 /µ2 ) B + O(αn+2
S (µ )B = αS (µ) −nb0 αS
S
Virtual(µ0 ) = Virtual(µ) +αn+1
(µ)nb0 log(µ02 /µ2 ) B + O(αn+2
)
S
S
⇒ σ(µ0 ) − σ(µ) = O(αn+2
)
S
In MiNLO “scale compensation” kept if
C + nb0 log(µ2R /Q2 )B ⇒ C + nb0 log(µ̄2R /Q2 )B
with µ̄2R = (q1 q2 ...qn )2/n
44 / 35
MiNLO details
Few technicalities for original MiNLO:
µF = Q0 (as in CKKW)
Cluster with CKKW also V and R kinematics
- Actual implementation uses FKS mapping for first cluster of Φn+1
- Ignore CKKW Sudakov for 1st clustering of Φn+1 (inclusive on extra radiation)
(NLO)
Some freedom in choice of αS
* suggested average of LO αS
* not free for “improved” MiNLO
(entering V , R and ∆(1) ):
Used full NLL-improved Sudakovs (A1 , B1 , A2 )
Improved MiNLO: where are terms coming from when differentiating resum. formula?
2
1/qT
, always from integration in Sudakov
αS from C (0) × B1 , ...
α2S from C (0) × B2 , ...
...
αS L from A1 term in exponent
αS L2 from A2 term in exponent
...
45 / 35
NNLOPS
pH
T spectrum:
“µHJ−MiNLO = mH , mH , pT ”
At high pT , µHJ−MiNLO = pT
If β = 1/2, NNLOPS → HJ-MiNLO at high pT
Ratio
dσ/dpHT [pb/GeV]
NNLO/NLO ∼ 1.5, because HNNLO with µ = mH /2, µHJ−MiNLO,core = mH
100
1.516 × HJ−MINLO PY
HJ−MINLO PY
β = ∞ NNLOPS
β = 12 NNLOPS
10−1
10−2
10−3
1.0
0.7
0
50
100
150 200
pHT [GeV]
250
300
46 / 35