Accurate predictions ! for Higgs Characterisation

Transcripción

Accurate predictions !
for Higgs Characterisation
!
!
Marco Zaro, LPTHE - UPMC Paris VI !
based on!
Artoisenet, de Aquino, Demartin, Frederix, Frixione, Maltoni, Mandal, Mathews, !
Mawatari, Ravindran, Seth, Torrielli, MZ, arXiv:1306.6464!
Maltoni, Mawatari, MZ, arXiv:1311.1829!
Demartin, Maltoni, Mawatari, Page, MZ, arXiv:1407.5089!
!
HEFT 2014 @IFT Madrid!
September 30, 2014
1
LHCPhenoNet
Any major discovery is the !
beginning of a new journey…
Marco Zaro, 30-09-2014
2
LHCPhenoNet
Any major discovery is the !
beginning of a new journey…
What is that peak??
2
LHCPhenoNet
Is it THE Higgs boson!
as expected in the SM?
NAME !
Higgs boson!
DATE OF BIRTH!
Jul 4th 2012 (presumed)!
SPIN 0!
CP even!
FERMIONIC COUPLING!
mf/v!
BOSONIC COUPLING!
2mv2/v!
SELF COUPLING!
λ=MH2/2v2
3
LHCPhenoNet
How to answer the question(s)?
• (at least) Two approaches can be used:
Anomalous couplings (AC)
e.g JHU (arXiv: 1001.3396, 1208.4018)!
✔ Only requirement is Lorentz
symmetry!
✔ Agnostic on new physics!
✘ Non renormalizable!
✘ Large number of extra couplings!
✘ Possibly violate unitarity, yet can
include model dependent form factors
Effective field theory (EFT)
!
✔ Based on SM symmetries!
✘ Valid only up to a scale Λ!
✔/✘ New physics heavier than the
resonance itself!
✔ Renormalizable (order by order in
1/Λ) ➝ can include QCD corrections!
✔ Reduce number of extra couplings
by using symmetries and dimensional
analyses
4
LHCPhenoNet
The HC-EFT approach
• Use the Higgs dim-6 effective Lagrangian and implement it in
FeynRules → UFO model!
• Add missing pieces needed for NLO QCD corrections UV/R2!
• SM + Hgg!
• Include QCD corrections in the MadGraph5_aMC@NLO
framework → events (rates & distributions) at NLO in QCD!
• Study different production and decay channels, keeping spincorrelations!
• Disclaimer: we assume the EFT approach to be valid in all the
phase-space
5
LHCPhenoNet
!
The MadGraph5_aMC@NLO
framework
Alwall, Frederix, Frixione, Maltoni, Mattelaer, Shao, Stelzer, Torrielli, Hirschi, MZ, arXiv:1405.0301
FKS
MadGraph
MadGraph5_aMC@NLO
MC@NLO
CutTools
6
LHCPhenoNet
Above the EW scale:
Introduction
HEFT in FEYNRULES
Phenomenological examples
Summary
D6 Higgs Effective Lagrangian
slide from K. Mawatari@MC4BSM 2014
Marco Zaro,
The30-09-2014
model file
✦
Wyler,
Nucl.Phys.B177
[ from Contino,Buchmuller,
Ghezzi, Grojean,
Muhlleitner,
Spira (JHEP(1986)!
’13) ]
Grzadkowski, Iskrzynski, Misiak,
Rosiek,
arXiv:1008.4884!
[ Alloul,
Fuks, Sanz
(1310.5150) ]
Contino, Ghezzi, Grojean, Muhlleitner, Spira, arXiv:1303.3876!
Alloul, Fuks, Sanz, arXiv:1310.5150
7
LHCPhenoNet
is publicly available. (https://feynrules.irmp.ucl.ac.be/wiki/HEL)
Below the EW scale:
Mapping between the D6 and D5 operators
slide from K. Mawatari@MC4BSM 2014
HC [arXiv: 1306.6464]
HEL [arXiv: 1310.5150]
The
two
approaches
are equivalent!
Two
approaches
equivalent
as they
can be mapped intoextendible
one another.to HEL
NLO implementation
8
LHCPhenoNet
atari, M. Zaro: Higgs characterisation via VBF and VH production
refs. [13, 32] (see e.g. eq. (3.46) of ref. [32]) not including the terms in LF1 and LF
hich
modify four-point
gXyy interactions,
⇥v
ZZ/W W and equivalent toZeq. (3) of ref. [26]. For a CP -odd
physics interactions
2m2Z/W of ref.
47↵ [32].
/18⇡
C(94c2W 13)/9⇡
an
automatically
atebethis
is equivalentXto= H
eq. (A.98)
X=A
0
4↵ /3⇡
2C(8c2W 5)/3⇡
raph5 aMC@NLO
Let us start
the interaction lagrangian relevant to fermions which, while bein
acterisation
can alsowith
Table 2. Values in units of vqtaken by the couplings gXyy for
tion
channel
[46], all illustrates our philosophy
↵
G m
tremely
simple,
well.
p
. Such a lagrangian is:
the EW gauge bosons. C =
8
2⇡
are covered.
X
dies in VBF and VH f
¯f c↵ Hf f gHf f + is↵ Af f gAf f 5 f X0 ,
(2.2
in H ! ZZ/W W L0 =
0
The Lagrangian:!
Spin-0!
EM
EM
EM
F
2
Z
0
in ref. [37]):
ges in the VBF and is (eq. (2.4)
f =t,b,⌧
rvables, e.g., the az⇢
⇥1
⇤
tagging jets
V
µ
+
µ
jj in
L0 = c↵ SM gHZZ Zµ Z + gHW W Wµ W
here
we Higgs
use the
on
of the
res- notation:
2
ween the Z and W
⇤
1⇥
µ⌫
µ⌫
e
c↵ H gH Aµ⌫ A + s↵ A gA Aµ⌫ A
s study, we focus on
c↵ ⌘ cos ↵ , s↵ ⌘ sin ↵ ,
(2.3
4
Higgs VBF and VH
⇤
1⇥
µ⌫
µ⌫
e
c↵ HZ gHZ Zµ⌫ A + s↵ AZ gAZ Zµ⌫ A
ecay.
nd
denote
by secgHf f = m21f ⇥/v (gAf f = mf /v) the strength of⇤ the scalar (pseudoscalar
In the
following
a
a,µ⌫
a e a,µ⌫
grangian of ref. [37],
c

+
s

↵
Hgg gHgg Gµ⌫ G
↵
Agg gAgg Gµ⌫ G
upling in the SM (in a 2HDM
with tan = 1). We point out that the constants i can b
4
to illustrate the phe⇤
1⇥
µ⌫
µ⌫
e
we present
the VBF any loss1of
ken
real without
generality,
except

in
eq. (2.4). For simplicity, we hav
c↵ HZZ Zµ⌫ Z + s↵ AZZH@W
Zµ⌫ Z
4⇤
f key observables in
sumed that
only the third-generation
of fermions
couple
to ⇤the scalar state; extension
1 1⇥
+
µ⌫
+ f µ⌫
dedicated
VBF cuts,
c↵ HW W Wµ⌫ W
+ s↵ AW W Wµ⌫ W
2⇤
H
andother
ZH producthe
families and flavour-changing
structures are trivial to implement, which can
⇥
1
gs in the concluding
µ⌫
µ⌫
c

Z
@
A

Z
@
Z
↵
H@
⌫
µ
H@Z
⌫
µ
directly done by users of⇤ FeynRules. As mentioned above, the interaction of eq. (2.2
dim=6 = ( † )Q
⇤
˜tR operator. Note also that al
n also parametrise the e↵ects
of
a
L
+
µ⌫
L
+ H@W W⌫Y @µ W
+ h.c.
X0 ,
(1)
quirements listed above are satisfied at the price of a small redundancy in the number o
9 tensors are defined as
where the (reduced) field strength
LHCPhenoNet
hich
modify four-point
gXyy interactions,
⇥v
2m2Z/W of ref.
47↵ [32].
/18⇡
C(94c2W 13)/9⇡
an
automatically
atebethis
is equivalentXto= H
eq. (A.98)
X=A
0
4↵ /3⇡
2C(8c2W 5)/3⇡
raph5 aMC@NLO
Let us start
acterisation
can alsowith
tion
channel
↵
G m
tremely
simple,
well.
p
8
2⇡
are covered.
X
(2.2
in H ! ZZ/W W L0 =
0
The Lagrangian:!
Spin-0!
EM
EM
EM
F
2
Z
0
in ref. [37]):
f =t,b,⌧
⇥1
⇤
tagging jets
V
µ
+
µ
jj in
here
we Higgs
use the
on
of the
res- notation:
2
ween the Z and W
⇤
1⇥
µ⌫
µ⌫
e
c↵ ⌘ cos ↵ , s↵ ⌘ sin ↵ ,
(2.3
4
Higgs VBF and VH
⇤
1⇥
µ⌫
µ⌫
e
ecay.
nd
denote
In the
following
a
a,µ⌫
a e a,µ⌫
c

+
s

↵
Hgg gHgg Gµ⌫ G
↵
Agg gAgg Gµ⌫ G
4
1⇥
µ⌫
µ⌫
e
we present
the VBF any loss1of
ken
real without
generality,
except

in
Zµ⌫ Z
4⇤
sumed that
of fermions
couple
1 1⇥
+
µ⌫
+ f µ⌫
dedicated
VBF cuts,
2⇤
H
andother
ZH producthe
⇥
1
µ⌫
µ⌫
c

Z
@
A

Z
@
Z
↵
H@
⌫
µ
H@Z
⌫
µ
dim=6 = ( † )Q
⇤
of
a
L
+
µ⌫
L
+ h.c.
X0 ,
(1)
SM
LHCPhenoNet
hich
modify four-point
gXyy interactions,
⇥v
2m2Z/W of ref.
47↵ [32].
/18⇡
C(94c2W 13)/9⇡
an
automatically
atebethis
is equivalentXto= H
eq. (A.98)
X=A
0
4↵ /3⇡
2C(8c2W 5)/3⇡
raph5 aMC@NLO
Let us start
acterisation
can alsowith
tion
channel
↵
G m
tremely
simple,
well.
p
8
2⇡
are covered.
X
(2.2
in H ! ZZ/W W L0 =
0
The Lagrangian:!
Spin-0!
EM
EM
EM
F
2
Z
0
in ref. [37]):
f =t,b,⌧
⇥1
⇤
tagging jets
V
µ
+
µ
jj in
here
we Higgs
use the
on
of the
res- notation:
2
ween the Z and W
⇤
1⇥
µ⌫
µ⌫
e
c↵ ⌘ cos ↵ , s↵ ⌘ sin ↵ ,
(2.3
4
Higgs VBF and VH
⇤
1⇥
µ⌫
µ⌫
e
ecay.
nd
denote
In the
following
a
a,µ⌫
a e a,µ⌫
c

+
s

↵
Hgg gHgg Gµ⌫ G
↵
Agg gAgg Gµ⌫ G
4
1⇥
µ⌫
µ⌫
e
we present
the VBF any loss1of
ken
real without
generality,
except

in
Zµ⌫ Z
4⇤
sumed that
of fermions
couple
1 1⇥
+
µ⌫
+ f µ⌫
dedicated
VBF cuts,
2⇤
H
andother
ZH producthe
⇥
1
µ⌫
µ⌫
c

Z
@
A

Z
@
Z
↵
H@
⌫
µ
H@Z
⌫
µ
dim=6 = ( † )Q
⇤
of
a
L
+
µ⌫
L
+ h.c.
X0 ,
(1)
SM
HD
LHCPhenoNet
hich
modify four-point
gXyy interactions,
⇥v
2m2Z/W of ref.
47↵ [32].
/18⇡
C(94c2W 13)/9⇡
an
automatically
atebethis
is equivalentXto= H
eq. (A.98)
X=A
0
4↵ /3⇡
2C(8c2W 5)/3⇡
raph5 aMC@NLO
Let us start
acterisation
can alsowith
tion
channel
↵
G m
tremely
simple,
well.
p
8
2⇡
are covered.
X
(2.2
in H ! ZZ/W W L0 =
0
The Lagrangian:!
Spin-0!
EM
EM
EM
F
2
Z
0
in ref. [37]):
f =t,b,⌧
⇥1
⇤
tagging jets
V
µ
+
µ
jj in
here
we Higgs
use the
on
of the
res- notation:
2
ween the Z and W
⇤
1⇥
µ⌫
µ⌫
e
c↵ ⌘ cos ↵ , s↵ ⌘ sin ↵ ,
(2.3
4
Higgs VBF and VH
⇤
1⇥
µ⌫
µ⌫
e
ecay.
nd
denote
In the
following
a
a,µ⌫
a e a,µ⌫
+
c

+
s

↵
Hgg gHgg Gµ⌫ G
↵
Agg gAgg Gµ⌫ G
4
1⇥
µ⌫
µ⌫
e
we present
the VBF any loss1of
ken
real without
generality,
except

in
Zµ⌫ Z
4⇤
sumed that
of fermions
couple
1 1⇥
+
µ⌫
+ f µ⌫
dedicated
VBF cuts,
2⇤
H
andother
ZH producthe
⇥
1
µ⌫
µ⌫
c

Z
@
A

Z
@
Z
↵
H@
⌫
µ
H@Z
⌫
µ
dim=6 = ( † )Q
⇤
of
a
L
+
µ⌫
L
+ h.c.
X0 ,
(1)
SM
HD
0
LHCPhenoNet
hich
modify four-point
gXyy interactions,
⇥v
2m2Z/W of ref.
47↵ [32].
/18⇡
C(94c2W 13)/9⇡
an
automatically
atebethis
is equivalentXto= H
eq. (A.98)
X=A
0
4↵ /3⇡
2C(8c2W 5)/3⇡
raph5 aMC@NLO
Let us start
acterisation
can alsowith
tion
channel
↵
G m
tremely
simple,
well.
p
8
2⇡
are covered.
X
(2.2
in H ! ZZ/W W L0 =
0
The Lagrangian:!
Spin-0!
EM
EM
EM
F
2
Z
0
in ref. [37]):
f =t,b,⌧
⇥1
⇤
tagging jets
V
µ
+
µ
jj in
here
we Higgs
use the
on
of the
res- notation:
2
ween the Z and W
⇤
1⇥
µ⌫
µ⌫
e
c↵ ⌘ cos ↵ , s↵ ⌘ sin ↵ ,
(2.3
4
Higgs VBF and VH
⇤
1⇥
µ⌫
µ⌫
e
ecay.
nd
denote
In the
following
a
a,µ⌫
a e a,µ⌫
+
c

+
s

↵
Hgg gHgg Gµ⌫ G
↵
Agg gAgg Gµ⌫ G
4
1⇥
µ⌫
µ⌫
e
we present
the VBF any loss1of
ken
real without
generality,
except

in
Zµ⌫ Z
4⇤
sumed that
of fermions
couple
1 1⇥
+
µ⌫
+ f µ⌫
dedicated
VBF cuts,
2⇤
H
andother
ZH producthe
⇥
1
µ⌫
µ⌫
c

Z
@
A

Z
@
Z
↵
H@
⌫
µ
H@Z
⌫
µ
dim=6 = ( † )Q
⇤
of
a
L
+
µ⌫
L
+ h.c.
X0 ,
(1)
SM
HD
0
0
LHCPhenoNet
hich
modify four-point
gXyy interactions,
⇥v
2m2Z/W of ref.
47↵ [32].
/18⇡
C(94c2W 13)/9⇡
an
automatically
atebethis
is equivalentXto= H
eq. (A.98)
X=A
0
4↵ /3⇡
2C(8c2W 5)/3⇡
raph5 aMC@NLO
Let us start
acterisation
can alsowith
tion
channel
↵
G m
tremely
simple,
well.
p
8
2⇡
are covered.
X
(2.2
in H ! ZZ/W W L0 =
0
The Lagrangian:!
Spin-0!
EM
EM
EM
F
2
Z
0
in ref. [37]):
f =t,b,⌧
⇥1
⇤
tagging jets
V
µ
+
µ
jj in
here
we Higgs
use the
on
of the
res- notation:
2
ween the Z and W
⇤
1⇥
µ⌫
µ⌫
e
c↵ ⌘ cos ↵ , s↵ ⌘ sin ↵ ,
(2.3
4
Higgs VBF and VH
⇤
1⇥
µ⌫
µ⌫
e
ecay.
nd
denote
In the
following
a
a,µ⌫
a e a,µ⌫
+
c

+
s

↵
Hgg gHgg Gµ⌫ G
↵
Agg gAgg Gµ⌫ G
4
1⇥
µ⌫
µ⌫
e
we present
the VBF any loss1of
ken
real without
generality,
except

in
Zµ⌫ Z
4⇤
sumed that
of fermions
couple
1 1⇥
+
µ⌫
+ f µ⌫
dedicated
VBF cuts,
2⇤
H
andother
ZH producthe
⇥
1
µ⌫
µ⌫
c

Z
@
A

Z
@
Z
↵
H@
⌫
µ
H@Z
⌫
µ
dim=6 = ( † )Q
⇤
of
a
L
+
µ⌫
L
+ h.c.
X0 ,
(1)
SM
HD
0
0
+Der 9
0
where the (reduced) field strength tensors are defined as
LHCPhenoNet
The Lagrangian:!
Spin-1!
[K. Hagiwara, R.D. Peccei, D. Zeppenfeld, Nuclear Physics B282 (1987)]
10
LHCPhenoNet
The Lagrangian:!
Spin-1!
‣ 1- in parity-conserving
scenarios
10
LHCPhenoNet
The Lagrangian:!
Spin-1!
‣ 1- in parity-conserving
scenarios
‣ 1+ in parity-conserving
scenarios
10
LHCPhenoNet
The Lagrangian:!
Spin-2!
1
L2 =
⇤
X
i=V, ,g,
i
ki Tµ⌫
X µ⌫
The minimal spin-2 particle is graviton like (2+)!
Higher dimension operators and 2- available
11
LHCPhenoNet
HC in the various !
production channels
gluo
n
vecto
r
VH
ttH
fusi
boso
n fusi
pro
du
c
pro
du
cti
on
on
tio
n
on
125
12
LHCPhenoNet
Chapter 1: !
spin/CP analysis in gg→X→…
Artoisenet, de Aquino, Demartin, Frederix, Frixione, Maltoni, Mandal,
Mathews, Mawatari, Ravindran, Seth, Torrielli, MZ, arXiv:1306.6464
are due to the different dominant initial
• Differences in shape
1
0
2
•
state (qq̄ for X , gg for X , X ) !
MLM distributions are harder (as expected), otherwise
agreement is quite good
13
LHCPhenoNet
Results:!
decay into V V→4l at LO!
!
0.2
1
pp → X(0±) → 4l at the LHC8
0.8
+
0.15
0 : κ SM=1
0+: κ HZZ=1
0+: κ H∂Z=1
0 : κ AZZ=1
0.1
0.6
0.4
0.05
0
0
0.2
20
40
60
80
100
m1,2 (GeV)
0
-1
-0.5
0
0.5
1
cosθ*
0.3
1
0.8
0.2
0.6
0.4
0.1
0.2
0
-1
-0.5
0
0.5
1
cosθ1
0
0
2
4
6
∆φ
Figure 1. Normalised distributions in pp ! X0 ! µ+ µ e+ e for di↵erent choices of X0 ZZ
couplings: the invariant masses of the two lepton pairs m1 , m2 (with m1 > m2 ), cos ✓⇤ , cos ✓1 , and
, as defined in ref. [10]. Event simulation performed at the leading order, parton level only (no
14
shower/hadronisation).
Angles defined in Bolognesi et al. arXiv:1208.4018
LHCPhenoNet
Results:!
decay into V V→4l /2l2ν at NLO+PS!
!
Figure
of the
in transverse
X(! W W ⇤ ) ! µ ⌫¯µ e+ ⌫e : (a) the transverse momentum
n X(!
ZZ ⇤ ) 8.
! Distributions
µ+ µ e+ e : (a)
andleptons
(b) the
Z2
+
1
the muon,
pµT , (b) the
invariant
mass
of
the
two
leptons
m(µ
e
).
st andoflowest
reconstructed
mass,
pZ
and
p
,
(c)
and
T
T
m`` corresponding to Z1 and Z2 .
largest invariant mass) for the di↵erent spin and parity hypotheses. As already noted in
thewhile
literature
[10, 92] the
lowest
pair invariant
proach,
aMC@NLO
may
be limited
by the mass is particularly sensitive to both spin
parity
assignments.
Finally,
the transverse
leptons
ments.
However,
spin
0 is obviously
a trivial
case (a
Marcoand
Zaro,
30-09-2014
15 momentum of one of the charged
LHCPhenoNet
⇤
raph5 aMC@NLO
acterisation can also
tion channel [46], all
are covered.
dies in VBF and VH
in H ! ZZ/W W
ges in the VBF and
rvables, e.g., the aztagging jets
jj in
on of the Higgs resween the Z and W
Higgs VBF and VH
decay.
In the following secgrangian of ref. [37],
to illustrate the phewe present the VBF
dedicated VBF cuts,
±
H and ZH producgs in the concluding
X=A
0
4↵EM /3⇡
2C(8c2W
5)/3⇡
Table 2. Values in units of vqtaken by the couplings gXyy0 for
↵EM GF m2
Z
p
.
8 2⇡
Chapter 2:!
HD iseffects
in
the
VVH
interactions
(eq. (2.4) in ref. [37]):
l setup, from the lak Marco
scenarios,
to event
Zaro, 30-09-2014
LV0
0+
=
⇢
Maltoni, Mawatari, MZ, arXiv:1311.1829
⇥1
c↵ SM gHZZ Zµ Z µ + gHW W Wµ+ W
2
µ
⇤
SM
⇤
1⇥
µ⌫
µ⌫
e
4
⇤
1⇥
µ⌫
µ⌫
e
2
⇤
1⇥
a
a,µ⌫
a e a,µ⌫
c↵ Hgg gHgg Gµ⌫ G
+ s↵ Agg gAgg Gµ⌫ G
4
⇤
1 1⇥
µ⌫
µ⌫
e
c↵ HZZ Zµ⌫ Z + s↵ AZZ Zµ⌫ Z
4⇤
⇤
1 1⇥
+
µ⌫
+ f µ⌫
2⇤
1 ⇥
c↵ H@ Z⌫ @µ Aµ⌫ H@Z Z⌫ @µ Z µ⌫
⇤
⇤
+
µ⌫
+ H@W W⌫ @µ W
+ h.c.
X0 ,
(1)
HD
0-
0 Der
+ strength tensors are defined as
where the (reduced) field
Vµ⌫ = @µ V⌫
@⌫ Vµ
(V = A, Z, W ± ) ,
Gaµ⌫ = @µ Ga⌫
@⌫ Gaµ + gs f16abc Gbµ Gc⌫ ,
(2)
(3)
LHCPhenoNet
!
VBF !
pp→X0jj (VBF) at the LHC8, NLO+PS
+
0 (SM)
+
0 (HD)
-1
0+ (HDder)
10
0+ (SM+HD)
+
0 (SM)
+
0 (HD)
-1
0+ (HDder)
10
0 (HD)
0- (HD)
0± (HD)
0± (HD)
10-3
aMC@NLO+HERWIG6
NLO+PS / NLO
NLO+PS / LO
pT
•
•
400
500
(GeV)
X
600
700
10-2
10-3
aMC@NLO+HERWIG6
300
0+ (SM+HD)
0 (HD)
10-3
200
+
0+ (HDder)
0± (HD)
10-2
100
+
0 (SM)
0 (HD)
10
-
10-2
0
0+ (SM+HD)
-
10-4
1.2
1
0.8
0.6
1.2
1
0.8
0.6
-1
10-4
1.2 NLO+PS / NLO
1
0.8
0.6
1.2 NLO+PS / LO
1
0.8
0.6
800
0
100
200
aMC@NLO+HERWIG6
300
pT
400
500
(GeV)
j1
600
700
10-4
1.2 NLO+PS / NLO
1
0.8
0.6
1.2 NLO+PS / LO
1
0.8
0.6
800
0
500
1000
1500
2000
m(j1,j2) (GeV)
2500
300
SM case shows a softer behaviour (not for Mjj)!
NLO and PS effects are important (in particular for jetrelated observables)
17
LHCPhenoNet
PS
0+ (SM)
!
+
0 (HD)
VBF !
0+ (HDder)
+
0 (SM+HD)
0- (HD)
±
0 (HD)
+
0 (SM)
+
0 (HD)
-1
0+ (HDder)
10
0+ (SM+HD)
+
0 (SM)
+
0 (HD)
-1
0+ (HDder)
10
0 (HD)
0- (HD)
0± (HD)
0± (HD)
10-3
aMC@NLO+HERWIG6
NLO+PS / NLO
NLO+PS / LO
pT
•
•
400
500
(GeV)
X
600
700
10-2
10-3
aMC@NLO+HERWIG6
300
0+ (SM+HD)
0 (HD)
10-3
200
+
0+ (HDder)
0± (HD)
10-2
100
+
0 (SM)
0 (HD)
10
-
10-2
0
0+ (SM+HD)
-
10-4
1.2
1
0.8
0.6
1.2
1
0.8
0.6
-1
10-4
1.2 NLO+PS / NLO
1
0.8
0.6
1.2 NLO+PS / LO
1
0.8
0.6
800
0
100
200
aMC@NLO+HERWIG6
300
pT
400
500
(GeV)
j1
600
700
10-4
1.2 NLO+PS / NLO
1
0.8
0.6
1.2 NLO+PS / LO
1
0.8
0.6
800
0
500
1000
1500
2000
m(j1,j2) (GeV)
2500
300
SM case shows a softer behaviour (not for Mjj)!
NLO and PS effects are important (in particular for jetrelated observables)
17
LHCPhenoNet
VBF
0.08
0.1
0+ (SM)
+
0+ (HD)
0 (HD)
0+ (HDder)
0+ (HDder)
0.08
+
0.06
+
0 (SM+HD)
0 (SM+HD)
0.06
0+ (SM)
0- (HD)
0- (HD)
0± (HD)
0± (HD)
0.06
0+ (SM)
0+ (HD)
0.04
+
0 (HDder)
0.04
0+ (SM+HD)
0- (HD)
0.04
0.02
0.02
aMC@NLO+HERWIG6
aMC@NLO+HERWIG6
0
1.2
1
0.8
0.6
1.2
1
0.8
0.6
0± (HD)
0.02
0
1.2
1
0.8
0.6
1.2
1
0.8
0.6
NLO+PS / NLO
NLO+PS / LO
-4
-3
-2
-1
0
η
•
•
j1
1
2
3
4
aMC@NLO+HERWIG6
0
1.2
1
0.8
0.6
1.2
1
0.8
0.6
NLO+PS / NLO
NLO+PS / LO
0
1
2
3
4
|∆η(j1, j2)|
5
6
7
8
NLO+PS / NLO
NLO+PS / LO
0
0.5
1
1.5
|∆φ(j1, j2)|
2
2.5
3
In SM case jets are more forward: HD scenarios feature a
different signature!
Jet correlations Δɸ, Δη are sensitive to the HVV structure
18
LHCPhenoNet
VBF !
(with extra Mjj cut):
0.08
0.1
0 (SM)
m(j1,j2)>500 GeV
0 (HD)
+
+
0+ (HDder)
0.08
0+ (SM+HD)
0.06
0 (SM)
m(j1,j2)>500 GeV
0 (HD)
+
+
0+ (HDder)
m(j1,j2)>500 GeV
0.06
0+ (SM+HD)
-
0 (HD)
0- (HD)
0± (HD)
0± (HD)
0.06
0+ (SM)
0+ (HD)
0.04
+
0 (HDder)
0.04
0+ (SM+HD)
0- (HD)
0.04
0.02
0.02
aMC@NLO+HERWIG6
0
1.2
1
0.8
0.6
1.2
1
0.8
0.6
0± (HD)
0.02
aMC@NLO+HERWIG6
0
1.2
1
0.8
0.6
1.2
1
0.8
0.6
NLO+PS / NLO
NLO+PS / LO
-4
-3
-2
-1
0
η
•
•
j1
1
2
3
4
aMC@NLO+HERWIG6
0
1.2
1
0.8
0.6
1.2
1
0.8
0.6
NLO+PS / NLO
NLO+PS / LO
0
1
2
3
4
|∆η(j1, j2)|
5
6
7
8
NLO+PS / NLO
NLO+PS / LO
0
0.5
1
1.5
|∆φ(j1, j2)|
2
2.5
3
The extra Mjj cut pushes jets to be more separated!
No dramatic effects on angular correlations
19
LHCPhenoNet
ZX0:
pp→X0Z (Z→e+e-) at the LHC8, NLO+PS
+
0 (HD)
0+ (HDder)
10-1
+
0 (SM)
0+ (SM+HD)
0.03
+
+
0 (HD)
0+ (HDder)
10-1
0+ (SM+HD)
0 (HD)
0- (HD)
0± (HD)
0± (HD)
-
10-2
10-2
0 (SM)
0.02
0+ (SM)
0.01
0+ (HD)
0+ (HDder)
0+ (SM+HD)
0- (HD)
aMC@NLO+HERWIG6
10-3
1.4
1.2
1
10-3
1.4
1.2
1
NLO+PS / NLO
NLO+PS / LO
1.4
1.2
1
0
100
•
•
•
1.4
1.2
1
200
300
pT
400
500
(GeV)
X
600
700
800
aMC@NLO+HERWIG6
0
1.4
1.2
1
NLO+PS / NLO
NLO+PS / LO
50
NLO+PS / NLO
NLO+PS / LO
1.4
1.2
1
100
0± (HD)
aMC@NLO+HERWIG6
150
200
250
lep,hard
pT
(GeV)
300
350
400
-1
-0.5
0
cosθlep
0.5
1
SM is softer, HD harder, HDder much harder (contact
interaction)!
QCD effects are less important than for VBF!
Similar features for WH
20
LHCPhenoNet
approximation as long
is not sensibly larger
EFT approach for the
1 limit, the resulting
production have been
been used by Powheg
O results matched with
NLO+PS predictions
] for the one-loop ma@NLO [35], that em37], are also available.
are for the SM Higgs
roduction for the CPO, yet with the exact
r we present NLO reroduction of a generic
sociation with one or
arton shower.
twodimensions.
independentThe
realcomplete
quantities
are at
needed
to parametrise
the
ing
basis
dimension
six has been
most general
CP violating
this parametrisation
known
for a long
time [47, interaction),
48] and recently
reconsidered in
has several
practical
advantages,
among
which
possibility
more
detail in
the context
of the Higgs
boson,
seethe
e.g.,
[49–51].
of easily
interpolating
CP-even
(c↵ = [52]
1, s↵imple= 0)
This
approach
has beenbetween
followed the
in the
FeynRules
and CP-odd
0, swhere
assignments.
↵ =
↵ = 1)the
mentation
of (c
ref.
[53],
e↵ective lagrangian is written
The Higgs
interaction
with
the top-quarks
inducesbreaking
a (nonin terms
of fields
above the
electroweak
symmetry
decoupling)
e↵ective
couplings
to photons,
gluons,
and photon(EWSB)
scale
and then
expressed
in terms
of gauge
eigenDemartin,
Maltoni,
Mawatari,
Page, MZ, arXiv:1407.5089
Z gauge
bosons
through
a top-quark
loop. In the HC framestates.
work,
e↵ective
lagrangian
such
loop-induced
interacAs the
already
mentioned
above,for
in ref.
[14]
we have followed
an
tions with vector
bosons
(eq.equivalent
(2.4) in ref.
alternative
approach
(andreads
yet fully
in [14]):
the context of
⇢
the phenomenological
applications of this paper, as explicitly
⇥
1
loop
a
a,µ⌫
+ the EFT
seenLin
tables
1
and
3
of
ref.
[53])
and
implemented
=
c

g
G
G
↵ Hgg Hgg
µ⌫
0
4 from the mass eigenstates, so below the
lagrangian starting
a e a,µ⌫ ⇤
P
EWSB scale, and for
spin-parity
assignments
(X(J
)
+ svarious

g
G
G
↵ Agg Agg
µ⌫
with J P = 0± , 1±1, ⇥2+ ). We have also used
FeynRules, whose
µ⌫
c↵ H gH Aµ⌫ A
output in the UFO
4 format [54, 55] can be directly passed to
MadGraph5 aMC@NLO [35]. We stress
µ⌫ ⇤ that this procedure
e
+ scomputations
Aµ⌫atALO, while at NLO the
↵  A gA
is fully automatic for
µ⌫
UFO model has 1to⇥c be supplemented
with suitable countert↵ HZ gHZ Zµ⌫ A
erms, as it will be2recalled in Sect. 2.2, a procedure that in this
work has been performed by hand.
µ⌫ ⇤
e
+s 
g
Zµ⌫ A
X0 ,
(2)
The term of interest↵ inAZthe AZ
e↵ective
lagrangian
can be written as (see eq. (2.2) in ref. [14]):
wheret the (reduced) field strength tensors are defined as
L0 = ¯t c↵ Htt gHtt + is↵ Att gAtt 5 t X0 ,
(1)
a
a
a
abc b c
G
=
@
G
@
G
+
g
f
(3)
s
µ ⌫the scalar
⌫ µ boson, cGµ
⌫ , ↵ and s ⌘ sin ↵ can
whereµ⌫
X labels
⌘Gcos
Chapter 3:!
CP properties of the top Yukawa
or arbitrary CP coule NLO corrections in
or quite some time [38,
done only recently, for
MC@NLO [40] and in
case only. The spinay products have been
th the help of Madections have been also
respectively. The pheMarco Zaro, 30-09-2014
0
0
this can be ach
e.g. the dimens
HC model. Fin
grangian the lo
parametrized b
tribution to th
In order to
we also write t
massive gauge
LZ,W
=
0
⇢
c
1 1⇥
c
4⇤
1 1⇥
c
2⇤
1 ⇥
c↵
⇤
where gHZZ =
plings, and ⇤ is
summarised in
0
↵
↵
In table 3 w
±
be thought
parameters,

are
the
dimenHtt,Att
Vµ⌫ = @asµ V“CP-mixing”
@
V
(V
=
A,
Z,
W
)
,
(4)
⌫
⌫ µ
sionless real coupling parameters, and gHtt = gAtt = mt /v (= use for illustrat
corresponds to
21
and the dual tensor is
LHCPhenoNet
0 (VBF, HD)
0.20
0 (VBF, HD)
±
0 (VBF, HD)
0.25
0.15
0.20
0.10
0.10
0.00
0.05
GF vs VBF
pp→X0jj at the LHC13
MG5_aMC@NLO + HERWIG6
0.00
0.35
GF uncertainties, NLO+PS
0+
0.30
0.20
0.10
0.00
-0.10
-0.20
0.30
0.20
0.10
0.00
-0.10
-0.20
0.30
0.20
0.10
0.00
-0.10
-0.20
PDF+αS
µR,F
µR,F
PDF+αS
0±
µR,F
PDF+αS
GF
m(j1uncertainties,
,j2) > 500 GeV NLO+PS
0+
0.30
0.30
0.20
0.10
0.00
0.25
-0.10
-0.20
0.20
0.30
0.20
0.10
0.15
0.00
-0.10
-0.20
0.10
0.30
0.20
0.10
0.05
0.00
-0.10
-0.20
0.00
-
NLO+PS (µ+PDF+αS)
LO+PS (µ+PDF)
0.30
0.20
2.00
0.10
0.00
1.50
-0.10
1.00
-0.20
2.00
1.50
1.00
µR,F
0-
µR,F
PDF+αs
0±
µR,F
PDF+αs
0.50
0.30
0.20
2.00
0.10
0.00
1.50
-0.10
-0.20
1.00
00-
NLO+PS (µ+PDF+αs)
0±
0±
NLO+PS (µ+PDF+αs)
1.00
0.50
0.30
0.20
2.00
0.10
0.00
1.50
-0.10
-0.20
1.00
0.50
0.50
0.50
0
2.00
LO+PS (µ+PDF)
1.50
1.00
0.50
±
NLO+PS (µ+PDF+αS)
0
2.00
LO+PS (µ+PDF)
1.50
0
1
2
3
4
| ∆η(j1,j2) |
5
6
0
7
2.00
1.50
1.00
0- (GF, SM)
0 (GF)
0± (GF)
0+ (VBF,
SM)s
PDF+α
+
0- (VBF, HD)
0± (VBF, HD)
0 (VBF, HD)
GF uncertainties,
NLO+PS
GF
NLO+PS/LO+PS
(with total uncertainties)
µR,F
PDF+α
++
0
NLO+PS (µ+PDF+αs)
LO+PS (µ+PDF)s
0
GF NLO+PS/LO+PS (with total uncertainties)
NLO+PS (µ+PDF+αS)
+
NLO+HERWIG6
0-
0+
(shape comparison)
µR,F
PDF+αs
LO+PS (µ+PDF)
µR,F
PDF+αs
LO+PS (µ+PDF)
• VBF-like cuts enhance the
MadGraph5_aMC@NLO
0.05
MadGraph5_aMC@NLO
Jet correlations in X0jj
0.15
t-channel gluon exchange,
which is more sensitive
to CP Hagiwara, Li, Mawatari, arXiv:0915.4314
• NLO corrections are
large, (~30%) and not flat
π/2
π
NLO+PS (µ+PDF+αs)
LO+PS (µ+PDF)
0+
| ∆φ(j1,j2) |
22
LHCPhenoNet
0 (VBF, HD)
0.20
0 (VBF, HD)
±
0 (VBF, HD)
0.25
0.15
0.20
0.10
0.10
0.00
0.05
GF vs VBF
pp→X0jj at the LHC13
MG5_aMC@NLO + HERWIG6
0.00
0.35
GF uncertainties, NLO+PS
0+
0.30
0.20
0.10
0.00
-0.10
-0.20
0.30
0.20
0.10
0.00
-0.10
-0.20
0.30
0.20
0.10
0.00
-0.10
-0.20
PDF+αS
µR,F
µR,F
PDF+αS
0±
µR,F
PDF+αS
GF
m(j1uncertainties,
,j2) > 500 GeV NLO+PS
0+
0.30
0.30
0.20
0.10
0.00
0.25
-0.10
-0.20
0.20
0.30
0.20
0.10
0.15
0.00
-0.10
-0.20
0.10
0.30
0.20
0.10
0.05
0.00
-0.10
-0.20
0.00
-
NLO+PS (µ+PDF+αS)
LO+PS (µ+PDF)
0.30
0.20
2.00
0.10
0.00
1.50
-0.10
1.00
-0.20
2.00
1.50
1.00
µR,F
0-
µR,F
PDF+αs
0±
µR,F
PDF+αs
0.50
0.30
0.20
2.00
0.10
0.00
1.50
-0.10
-0.20
1.00
00-
NLO+PS (µ+PDF+αs)
0±
0±
NLO+PS (µ+PDF+αs)
1.00
0.50
0.30
0.20
2.00
0.10
0.00
1.50
-0.10
-0.20
1.00
0.50
0.50
0.50
0
2.00
LO+PS (µ+PDF)
1.50
1.00
0.50
±
NLO+PS (µ+PDF+αS)
0
2.00
LO+PS (µ+PDF)
1.50
0
1
2
3
4
| ∆η(j1,j2) |
5
6
0
7
2.00
1.50
1.00
0- (GF, SM)
0 (GF)
0± (GF)
0+ (VBF,
SM)s
PDF+α
+
0- (VBF, HD)
0± (VBF, HD)
0 (VBF, HD)
GF uncertainties,
NLO+PS
GF
NLO+PS/LO+PS
µR,F
PDF+α
++
0
NLO+PS (µ+PDF+αs)
LO+PS (µ+PDF)s
0
NLO+PS (µ+PDF+αS)
+
NLO+HERWIG6
0-
0+
(shape comparison)
µR,F
PDF+αs
LO+PS (µ+PDF)
µR,F
PDF+αs
LO+PS (µ+PDF)
• VBF-like cuts enhance the
MadGraph5_aMC@NLO
0.05
MadGraph5_aMC@NLO
Jet correlations in X0jj
0.15
t-channel gluon exchange,
which is more sensitive
to CP Hagiwara, Li, Mawatari, arXiv:0915.4314
• NLO corrections are
large, (~30%) and not flat
π/2
π
NLO+PS (µ+PDF+αs)
LO+PS (µ+PDF)
0+
| ∆φ(j1,j2) |
22
LHCPhenoNet
pT(X0) > 200 GeV
pT(X0) > 200 GeV
0±
0
0±
0
0.09
0.16
0.08
0.14
Spin correlation effects !
in t tX
̄ 0
0.07
0.12
0.06
0.10
0.04
0.02
0.20
pp→ttX0 at the LHC13
0.00
0.18
NLO+HERWIG6
µR,F
0+ (SM)
0-±
0
PDF+αs
0-
µR,F
-0.10
1.00
-0.20
0.50
0.20
2.00
0.10
1.50
0.00
-0.10
1.00
-0.20
0.50
0.20
2.00
0.10
1.50
0.00
-0.10
1.00
-0.20
0.50
2.00
0.00
0.10
NLO+HERWIG6
0±
µR,F
PDF+αs
NLO+PS/LO+PS
ttX0 uncertainties,
NLO+PS
+
PDF+αs
NLO+PS (µ+PDF+αs) µR,F LO+PS (µ+PDF)
0
0-
0
NLO+PS (µ+PDF+αs)
±
0±
0
NLO+PS (µ+PDF+αs)
µR,F
µR,F
PDF+αs
LO+PS (µ+PDF)
PDF+αs
LO+PS (µ+PDF)
0 ttX0 NLO+PS/LO+PS
1
2 (with total uncertainties)
3
4
5
+
NLO+PS |(µ+PDF+α
LO+PS (µ+PDF)
0
∆η(jb,jb-s)) |
1.50
Marco
Zaro, 30-09-2014
-0.20
0.06
PDF+αs
0.20
0.04
0.10
0.00
0.02
-0.10
0.00
-0.20
0.20
2.00
0.10
1.50
0.00
pT(X0) > 200 GeV
ttX0 uncertainties, NLO+PS
0+
(shape comparison)
decay products kept with
MadSpin!
0+ (SM)
0-±
0
PDF+αs
µR,F
• Spin correlations of the top
0.00
0.07
-0.10
MadGraph5_aMC@NLO
0.10
0.20
0.10
0.08
0.00
-0.10
0.06
-0.20
0.01
0.11
0.09
0.20
0.08
0.10
0.10
0.14
0.00
-0.10
0.12
-0.20
0.02
0.20
0.05
0.10
0.00
0.04
-0.10
-0.20
0.03
0-
µR,F
PDF+αs
0±
µR,F
PDF+αs
0.20
0.02
0.10
0.00
0.01
-0.10
0.00
-0.20
0.20
2.00
0.10
1.50
0.00
-0.10
1.00
-0.20
0.50
0.20
2.00
0.10
1.50
0.00
-0.10
1.00
-0.20
0.50
0.20
2.00
0.10
1.50
0.00
-0.10
1.00
-0.20
0.50
-1.0
2.00
1.50
1.00
Artoisenet, Frederix, Mattelaer, Rietkerk, arXiv:1212.3460
MadGraph5_aMC@NLO
0.16
0.20
pT(X0) > 200 GeV
ttX0 uncertainties, NLO+PS
0+
(shape comparison)
0.03
NLO+PS/LO+PS
ttX0 uncertainties,
NLO+PS
+
PDF+αs
NLO+PS (µ+PDF+αs) µR,F LO+PS (µ+PDF)
0
• Requiring a boosted Higgs
•
reduces CP sensitivity for
angular correlations!
NLO effects of ~20%, not flat
0.11
0.10
NLO+HERWIG6
(shape comparison)
0+ (SM)
0-±
0
acceptance cuts only
0.09
0-
0
NLO+PS (µ+PDF+αs)
µR,F
PDF+αs
LO+PS (µ+PDF)
0.08
0.07
0.06
MadGraph5_aMC@NLO
0.06
0.04
MadGraph5_aMC@NLO
0.08
MadGraph5_aMC@NLO
0.05
0.05
±
0±
0
NLO+PS (µ+PDF+αs)
µR,F
PDF+αs
LO+PS (µ+PDF)
0.04
0.03
0.02
0.01
ttX0 NLO+PS/LO+PS
(with0.0
total uncertainties)
-0.5
0.5
1.0
+
+ s_)
NLO+PS (µ+PDF+α
LO+PS (µ+PDF)
0
cos θ(l ,l )
23
0.00
-1.0
-0.5
0.0
_
cos θ(l+,l )
0.5
1.0
LHCPhenoNet
!
Do it yourself!
• The code for the shown processes can be automatically
generated with MadGraph5_aMC@NLO (available at http://amcatnlo.cern.ch )!
• The HC-NLO model (with UV/R2 counterterms) is
publicly available on the FeynRules database https://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation!
• E.g.
t tX
̄ 0:
24
LHCPhenoNet
Do it yourself!
• The code for the shown processes can be automatically
generated with MadGraph5_aMC@NLO (available at http://amcatnlo.cern.ch )!
• The HC-NLO model (with UV/R2 counterterms) is
publicly available on the FeynRules database https://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation!
• E.g.
t tX
̄ 0:
> import model HC-NLO!
> generate p p > X0 t t~ [QCD]
24
LHCPhenoNet
Conclusions
• After the discovery of the Higgs boson, huge efforts have
been set up in order to tell wether it is the SM Higgs!
• EFT is a powerful tool for understanding the spin/CP/
coupling nature of the Higgs!
• No hypotheses on the NP!
• Can be improved beyond the LO!
• HC-EFT approach applied to all the main Higgs
production channels, including NLO+PS QCD corrections!
• Model publicly available and easy to use with
MadGraph5_aMC@NLO !
• The best is yet to come! (aka let’s wait for LHC13 data)
25
LHCPhenoNet
Thank you for your attention!
26
LHCPhenoNet
Backup slides
27
LHCPhenoNet
NLO: how to?
28
LHCPhenoNet
NLO: how to?
d
n
N LO
=
d
n
LO
+
d
28
n
V
+
Z
d
1
d
n+1
R
LHCPhenoNet
NLO: how to?
d
n
N LO
=
d
n
LO
+
d
n
V
+
Z
d
1
d
n+1
R
• Warning! Real emission ME is divergent!!
• Divergences cancel with those from virtuals (in D=4-2eps)!
• Need to cancel them before numerical integration (in D=4)
28
LHCPhenoNet
NLO: how to?
d
n
N LO
=
d
n
LO
+
d
n
V
+
Z
d
1
d
n+1
R
• Warning! Real emission ME is divergent!!
• Divergences cancel with those from virtuals (in D=4-2eps)!
• Need to cancel them before numerical integration (in D=4)
• Structure of divergences is universal:
(p + k) = 2Ep Ek (1
cos ✓pk )
p
+
k
p
2
k
lim |Mn+1 |2 ' |Mn |2 P AP (z)
p//k
2
lim |Mn+1 | '
k!0
28
X
ij
|Mnij |2
p i pj
pi k p j k
LHCPhenoNet
NLO: how to?
d
n
N LO
=
d
n
LO
+
d
29
n
V
+
Z
d
1
d
n+1
R
LHCPhenoNet
NLO: how to?
d
d
n
N LO
n
N LO
=d
=
n
LO
d
n
LO
+d
n
V
+
Z
d
d
1
Z
n+1
+ d 1d R
Z
C + d 1 C +d
n
V
n+1
R
• Add local counterterms in the singular regions and subtract its
integrated finite part (poles will cancels against the virtuals)!
• The n and n+1 body integral now are finite in 4 dimension!
• Can be integrated numerically
29
LHCPhenoNet
NLO: how to?
d
d
n
N LO
n
N LO
=d
=
n
LO
d
n
LO
+d
n
V
+
Z
d
d
1
Z
n+1
+ d 1d R
Z
C + d 1 C +d
n
V
n+1
R
• Add local counterterms in the singular regions and subtract its
integrated finite part (poles will cancels against the virtuals)!
• The n and n+1 body integral now are finite in 4 dimension!
• Can be integrated numerically
How to do this in an efficient way?
29
LHCPhenoNet
The FKS subtraction
Frixione, Kunszt, Signer, arXiv:hep-ph/9512328
• Soft/collinear singularities arise in many PS regions!
• Find parton pairs i, j that can give collinear singularities!
• Split the phase space into regions with one collinear sing!
are split into the collinear ones!
• Soft singularities
X
X
X
!
!
!
2
|M | =
2
ij
Sij |M | =
Sij ! 1 if ki · kj ! 0
ij
2
|M |ij
Sij = 1
Sij ! 0 if km6=i · kn6=j ! 0
• Integrate them independently!
• Parallelize integration!
• Choose ad-hoc phase space parameterization!
• Advantages:!
• # of contributions ~ n^2!
• Exploit symmetries: 3 contributions for X
30
Y > ng
LHCPhenoNet
Loops: the OPP Method
Ossola, Papadopoulos, Pittau, arXiv:hep-ph/0609007 & arXiv:0711.3596
• Passarino & Veltman reduction:!
• Write the amplitude at the integral level as linear
combination of 1-...-4-point scalar integrals!
A(q)
m
X1
=
d(i0 i1 i2 i3 )D0 (i0 i1 i2 i3 )
m
X1
+
c(i0 i1 i2 )C0 (i0 i1 i2 )
kn
i0 <i1 <i2
+
m
X1
i0 <i1
+
m
X1
q + k1
q
D0
Dm
b(i0 i1 )B0 (i0 i1 )
k2
k1
i0 <i1 <i2 <i3
1
D1
..
D2
.
D3
k3 k4
q + . . . + k5
!
!
!
!
!
!
!
!
k5
a(i0 )A0 (i0 )
i0
+
R
• Do this at the integrand level
31
LHCPhenoNet
Loops: the OPP Method
Ossola, Papadopoulos, Pittau, arXiv:hep-ph/0609007 & arXiv:0711.3596
• Sample the numerator at complex values of the loop momenta in
•
•
order to reconstruct the a,b,c,d coefficients and part of the rational
terms (R1)!
Use CutTools: fed with the loop numerator outputs the coefficients
of the scalar integrals and CC rational terms (R1)!
Add R2-rational terms/UV counterterms !
•
Model dependent but process-independent
32
LHCPhenoNet
Loop ME evaluation: MadLoop
Hirschi et al. arXiv:1103.0621
• Load the NLO UFO model!
• Generate Feynman diagrams to evaluate the loop ME!
• Add R2/UV renormalisation counter terms!
• Interface to CutTools or to tensor reduction programs
(in progress)!
if needed)!
• Check PS point stability (and switch to QP Cascioli,
Maierhofer, Pozzorini
Improved
with
the
OpenLoops
method!
•
arXiv:1111.5206
• And much more (can be used as standalone or external
OLP via the BLHA, handle loop-induced processes, …)
33
LHCPhenoNet
Matching in !
MC@NLO
• Use suitable counterterms to avoid double counting the emission
from shower and ME, keeping the correct rate at order αs:!
!d
!
M C@N LO
dO
!
=
✓
B+V +
Z
d
1M C
◆
d
n
n
IM
C (O) + (R
S-events
!
⌅ tM C , z M C , ⇤
MC =
⌅ 1
1
tM C
n
d
1
n+1
IM
C (O)
H-events
• MC depends on the PSMC’s Sudakov:!
!
M C) d
1
P zM C B
2⇥ 2⇥
s
• Available for Herwig6, Pythia6 (virtuality-ordered), Herwig++,
Pythia8 (in the new release)!
• MC acts as local counterterm!
• Some weights can be negative (unweighting up to sign)!
• Only affects statistics
34
LHCPhenoNet

Accurate predictions ! for Higgs Characterisation

Transcripción

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