All-order Corrections to Multi-jet Rates using t

Introduction
t-channel factorisation
Application
Conclusions
All-order Corrections to Multi-jet Rates
using t-channel Factorised Scattering Matrix
Elements
Jeppe R. Andersen (CERN)
in collaboration with Jenni Smillie (UCL)
RADCOR
October 27, 2009
Introduction
t-channel factorisation
Application
Conclusions
What, Why, How?
What?
Develop a framework for reliably calculating many-parton rates
inclusively (ensemble of 2, 3, 4, . . . parton rates) and in a
flexible way (jets, W+jets, Z+jets, Higgs+jets,. . . )
Why?
(n + 1)-jet rate not necessarily small compared to n-jet rate
Inclusive (hard) perturbative corrections important for e.g. hard
end of W p⊥ -spectrum.
How?
Establish universal behaviour of radiative corrections (in the
so-called High Energy Limit)
Introduction
t-channel factorisation
Application
Conclusions
What, Why, How?
What?
Develop a framework for reliably calculating many-parton rates
inclusively (ensemble of 2, 3, 4, . . . parton rates) and in a
flexible way (jets, W+jets, Z+jets, Higgs+jets,. . . )
Why?
(n + 1)-jet rate not necessarily small compared to n-jet rate
Inclusive (hard) perturbative corrections important for e.g. hard
end of W p⊥ -spectrum.
How?
Establish universal behaviour of radiative corrections (in the
so-called High Energy Limit)
Introduction
t-channel factorisation
Application
Conclusions
What, Why, How?
What?
Develop a framework for reliably calculating many-parton rates
inclusively (ensemble of 2, 3, 4, . . . parton rates) and in a
flexible way (jets, W+jets, Z+jets, Higgs+jets,. . . )
Why?
(n + 1)-jet rate not necessarily small compared to n-jet rate
Inclusive (hard) perturbative corrections important for e.g. hard
end of W p⊥ -spectrum.
How?
Establish universal behaviour of radiative corrections (in the
so-called High Energy Limit)
Introduction
t-channel factorisation
Application
Conclusions
What, Why, How?
Goal
Sufficiently simple model for radiative corrections that the
all-order sum can be evaluated explicitly (completely
exclusive)
Sufficiently accurate that the description is relevant
Introduction
t-channel factorisation
Application
Conclusions
Do we need a new approach?
Already know how to calculate. . .
Shower MC: at most 2→2 "hard" processes with additional
parton shower
Flexible Tree level calculators:
MadGraph, AlpGen, SHERPA,. . .
Allow most 2 → 4, some 2 → 6 processes to be calculated
at tree level.
Interfaced with Shower MC makes for a powerful mix!
MCFM: Many relevant 2 → 3 processes at up to NLO
(i.e. including 2 → 4-contribution).
. . . hyour favourite method herei
Could all be labelled “Standard Model contribution”, but give
vastly different results depending on the question asked!
Introduction
t-channel factorisation
Application
All Order Resummation Necessary?
Are tree-level (or generally fixed order) calculation always sufficient?
Sometimes the (n + 1)-jet rate is as large as the n-jet rate
Higgs Boson plus n jets at the LHC at leading order
σj [fb]
500
Full Tree-level QCD
450
400
350
300
|y -y |>4.2; |y |<4.5, m =120GeV
250
y y <0, p >40GeV, R=0.6
ja
ja jb
jb
i
H
ji
200
150
100
50
0
2
3
4
5
6
# jets
Conclusions
Introduction
t-channel factorisation
Application
Conclusions
All Order Resummation Necessary?
Are tree-level (or generally fixed order) calculation always sufficient?
Sometimes the (n + 1)-jet rate is as large as the n-jet rate
Higgs Boson plus n jets at the LHC at leading order
σj [fb]
500
Full Tree-level QCD
450
400
350
300
|y -y |>4.2; |y |<4.5, m =120GeV
250
y y <0, p >40GeV, R=0.6
ja
ja jb
jb
i
H
ji
200
150
100
50
0
2
3
4
5
6
# jets
Indication that we need to go further! However, fixed order tools exhausted (full 2 → 3 with a massive leg at two loops untenable!).
Introduction
t-channel factorisation
Application
Conclusions
All Order Resummation Necessary?
Are tree-level (or generally fixed order) calculation always sufficient?
Sometimes the (n + 1)-jet rate is as large as the n-jet rate
Higgs Boson plus n jets at the LHC at leading order
σj [fb]
500
Full Tree-level QCD
450
400
350
300
|y -y |>4.2; |y |<4.5
250
y y <0, p >40GeV, R=0.6
200
ja,j the two hardest jets
ja
ja jb
jb
i
ji
b
150
100
50
0
2
3
4
5
6
# jets
Require that the two jets passing the rapidity cut are also the two
hardest jets. Reduces the 3-jet phase space and the HO corrections
from real emission. Sensitivity to yet HO pert. corrections?
Introduction
t-channel factorisation
Application
All Order Resummation Necessary?
Are tree-level (or generally fixed order) calculation always sufficient?
Sometimes the (n + 1)-jet rate is as large as the n-jet rate
Higgs Boson plus n jets at the LHC at leading order
Conclusions
Introduction
t-channel factorisation
Application
All Order Resummation Necessary?
Are tree-level (or generally fixed order) calculation always sufficient?
Sometimes the (n + 1)-jet rate is as large as the n-jet rate
Higgs Boson plus n jets at the LHC at leading order
Conclusions
Introduction
t-channel factorisation
Application
Conclusions
All Order Resummation Necessary?
Are tree-level (or generally fixed order) calculation always sufficient?
Sometimes the (n + 1)-jet rate is as large as the n-jet rate
Higgs Boson plus n jets at the LHC at leading order
σj [fb]
500
Full Tree-level QCD
450
400
350
300
|y -y |>4.2; |y |<4.5, m =120GeV
250
y y <0, p >40GeV, R=0.6
ja
ja jb
jb
i
H
ji
200
150
100
50
0
2
3
4
5
6
# jets
The method we develop will be applicable to both set of cuts, but crucially will allow a stabilisation of the perturbative series by resummation
Introduction
t-channel factorisation
Application
Conclusions
Resummation and Matching
Consider the perturbative expansion of an observable
R = r0 + r1 αs + r2 α2 + r3 α3 + r4 α4 + · · ·
Fixed order pert. QCD will calculate a fixed number of terms in this
expansion. rn may contain logarithms so that αs ln(· · · )is large.
R = r0 + r1LL ln(· · · ) + r1NLL αs + r2LL ln2 (· · · ) + r2NLL ln(· · · ) + r2SL α2s +· · ·
X
X
= r0 +
rnNLL αs (αs ln(· · · ))n +sub-leading terms
rnLL (αs ln(· · · ))n +
n
n
Need simplifying assumptions to get to all orders - useful iff the terms
really do describe the dominant part of the full pert. series.
Matching combines best of both worlds:
R = r0 + r1 αs + r2 α2 + r3LL ln3 (· · · ) + r3NLL ln2 (· · · ) + r3SL α3 + · · ·
Introduction
t-channel factorisation
Application
Factorisation of QCD Matrix Elements
Conclusions
Introduction
t-channel factorisation
Application
Conclusions
Factorisation of QCD Matrix Elements
It is well known that QCD matrix elements factorise in certain
kinematical limits:
Soft limit → eikonal approximation → enters all parton
shower (and much else) resummation.
Like all good limits, the eikonal approximation is applied
outside its strict region of validity.
Will discuss the less well-studied factorisation of scattering
amplitudes in a different kinematic limit, better suited for
describing perturbative corrections from hard parton emission
Factorisation only becomes exact in a region outside the
reach of any collider. . .
Introduction
t-channel factorisation
Application
Conclusions
Factorisation of QCD Matrix Elements
It is well known that QCD matrix elements factorise in certain
kinematical limits:
Soft limit → eikonal approximation → enters all parton
shower (and much else) resummation.
Like all good limits, the eikonal approximation is applied
outside its strict region of validity.
Will discuss the less well-studied factorisation of scattering
amplitudes in a different kinematic limit, better suited for
describing perturbative corrections from hard parton emission
Factorisation only becomes exact in a region outside the
reach of any collider. . .
Introduction
t-channel factorisation
Application
Conclusions
Factorisation of QCD Matrix Elements
It is well known that QCD matrix elements factorise in certain
kinematical limits:
Soft limit → eikonal approximation → enters all parton
shower (and much else) resummation.
Like all good limits, the eikonal approximation is applied
outside its strict region of validity.
Will discuss the less well-studied factorisation of scattering
amplitudes in a different kinematic limit, better suited for
describing perturbative corrections from hard parton emission
Factorisation only becomes exact in a region outside the
reach of any collider. . .
Introduction
t-channel factorisation
Application
Conclusions
Factorisation of QCD Matrix Elements
It is well known that QCD matrix elements factorise in certain
kinematical limits:
Soft limit → eikonal approximation → enters all parton
shower (and much else) resummation.
Like all good limits, the eikonal approximation is applied
outside its strict region of validity.
Will discuss the less well-studied factorisation of scattering
amplitudes in a different kinematic limit, better suited for
describing perturbative corrections from hard parton emission
Factorisation only becomes exact in a region outside the
reach of any collider. . .
Introduction
t-channel factorisation
Application
Conclusions
The Possibility for Predictions of n-jet Rates
The Power of Reggeisation
kb , yb
k4 , y4
High Energy Limit
−→
|t̂| fixed, ŝ → ∞
k3 , y3
k2 , y2
k1 , y1
AR2→2+n
Γ ′
= A2A
q0
n
Y
e
ω(qi )(yi−1 −yi ) V
i=1
Pi−1
qi =ka +
k
l=1 l
(qi , qi+1 )
2
qi2 qi+1
!
ka , y0
e
ω(qn+1 )(yn −yn+1 )
ΓB ′ B
2
qn+1
LL: Fadin, Kuraev, Lipatov; NLL: Fadin, Fiore, Kozlov, Reznichenko
Maintain (at LL) terms of the form
„
«
ŝij
αs ln
|t̂i |
to all orders in αs .
Ji
At LL only gluon production; at
NLL also quark–anti-quark pairs
produced.
Approximation of any-jet rate possible.
Introduction
t-channel factorisation
Application
Conclusions
Comparison of 3-jet scattering amplitudes
Universal behaviour of scattering amplitudes in the HE limit:
∀i ∈ {2, . . . , n − 1} : yi−1 ≫ yi ≫ yi+1
∀i, j : |pi⊥ | ≈ |pj⊥ |
2
4 s2 g 2 CA
MRK
M
gg→g···g = 2
NC − 1 |p1⊥ |2
2
4 s2 g 2 CF
MRK
Mqg→qg···g = 2
NC − 1 |p1⊥ |2
2
4 s2 g 2 CF
MRK
MqQ→qg···Q = 2
NC − 1 |p1⊥ |2
n−1
Y
i=2
n−1
Y
i=2
n−1
Y
i=2
4 g 2 CA
|pi⊥ |2
!
g 2 CA
.
|pn⊥ |2
4 g 2 CA
|pi⊥ |2
!
g 2 CA
,
|pn⊥ |2
4 g 2 CA
|pi⊥ |2
!
g 2 CF
,
|pn⊥ |2
Allow for analytic resummation (BFKL equation).
However, how well does this actually approximate the
amplitude?
Introduction
t-channel factorisation
Application
Comparison of 3-jet scattering amplitudes
Study just a slice in phase space:
-6
|M|^2/(256 π5 s2) [GeV ]
0.12
× 10-12
MRK limit
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
∆y
Conclusions
Introduction
t-channel factorisation
Application
Comparison of 3-jet scattering amplitudes
Study just a slice in phase space:
-6
|M|^2/(256 π5 s2) [GeV ]
0.12
× 10-12
MRK limit
A(qQ->qQg)
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
∆y
Conclusions
Introduction
t-channel factorisation
Application
Comparison of 3-jet scattering amplitudes
Study just a slice in phase space:
-6
|M|^2/(256 π5 s2) [GeV ]
0.12
× 10-12
MRK limit
A(qQ->qQg)
Cf /CA*A(qg->qgg)
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
∆y
Conclusions
Introduction
t-channel factorisation
Application
Comparison of 3-jet scattering amplitudes
Study just a slice in phase space:
-6
|M|^2/(256 π5 s2) [GeV ]
0.12
× 10-12
MRK limit
A(qQ->qQg)
Cf /CA A(qg->qgg)
(C /CA)2 A(gg->ggg)
0.1
0.08
f
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
∆y
Conclusions
Introduction
t-channel factorisation
Application
Comparison of 3-jet scattering amplitudes
Study just a slice in phase space:
-6
|M|^2/(256 π5 s2) [GeV ]
0.12
× 10-12
MRK limit
A(qQ->qQg)
Cf /CA A(qg->qgg)
(C /CA)2 A(gg->ggg)
0.1
0.08
f
A(qQ->qQg)Effective
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
∆y
Conclusions
Introduction
t-channel factorisation
Application
Conclusions
Comparison of 4-jet scattering amplitudes
Study just a slice in phase space:
× 10
|M|^2/(4096π 8s2)/GeV
−8
−18
2.5
2
gg−>gggg * (4/9)2
qg−>qggg * 4/9
qQ−>qggQ
MRK limit
1.5
1
0.5
0
0
2
4
6
8
10
12
14
∆
Introduction
t-channel factorisation
Application
Conclusions
Comparison of W+3-jet scattering amplitudes
16
|M|^2/(2 π 11s2)/GeV
−10
Study just a slice in phase space:
35
× 10−27
30
25
20
15
qg−>(W )e ν qgg *4/9
+ +
us−>(W )e ν ugs
+ +
ud−>(W )e ν dgd
MRK limit
+
10
5
0
0
1
2
3
4
5
6
+
7
8
∆
Introduction
t-channel factorisation
Application
Conclusions
Comparison of W+4-jet scattering amplitudes
Study just a slice in phase space:
× 10
80
70
20
|M|^2/(2 π 14s2)/GeV−12
−33
90
60
50
40
30
qg−>(W )e ν qggg *4/9
+ +
us−>(W )e ν uggs
+ +
ud−>(W )e ν uggd
MRK limit
+
20
10
0
0
1
2
3
4
5
6
7
+
8
9
10
∆
Introduction
t-channel factorisation
Application
Conclusions
Comparison of H+2-jet scattering amplitudes
Study just a slice in phase space:
× 10
|M|^2/(256π 5s2)/GeV
−6
−9
2.5
2
1.5
1
gg−>gHg * (4/9)2
qg−>qHg * 4/9
qQ−>qHQ
0.5
MRK limit
0
0
1
2
3
4
5
6
7
8
∆
Introduction
t-channel factorisation
Application
Conclusions
Comparison of H+3-jet scattering amplitudes
0.12
|M|^2/(256π 5s2)/GeV
−8
Study just a slice in phase space:
× 10−12
0.1
0.08
0.06
gg−>gHgg * (4/9)2
0.04
qg−>qHgg * 4/9
qQ−>qHgQ
0.02
MRK limit
0
0
1
2
3
4
5
6
7
8
9
10
∆
Introduction
t-channel factorisation
Application
Conclusions
Conclusion from Study of Partonic Cross Sections
Correct limit is obtained - but outside LHC phase space.
Limit alone irrelevant.
Universality obtained before limit is reached.
Will build frame-work which has the right MRK limit but also
retains correct behaviour at smaller rapidities
Introduction
t-channel factorisation
Application
Conclusions
Scattering of qQ-Helicity States
Start by describing quark scattering. Simple matrix element for
q(a)Q(b) → q(1)Q(2):
Mq − Q − →q − Q − = h1|µ|ai
g µν
h2|ν|bi
t
t-channel factorised: Contraction of (local) currents across
t-channel pole
2
t
MqQ→qQ =
Extend to 2 → n . . .
1
4
(NC2
− 1)
SqQ→qQ 2
1
· g CF
t1
1
2
.
· g CF
t2
2
J.M.Smillie and JRA: arXiv:0908.2786
Introduction
t-channel factorisation
Application
Conclusions
Building Blocks for an Amplitude
Identification of the dominant contributions to the
perturbative series in the limit of well-separated particles
qν
1 exp (α̂(q)∆y)
q
q2
qi−1
pA
p1
q1
q2
pB
µ V µ (qi−1 , qi )
qi
j ν = ψγ ν ψ
p2 V ρ (q1 , q2 ) = − (q1 + q2 )ρ
p3
+
pAρ
2
−
pBρ
2
„
„
p2 · pB
p2 · pn
q12
+
+
p2 · pA
pA · pB
pA · pn
p2 · pA
p2 · p1
q22
+
+
p2 · pB
pB · pA
pA · p1
«
«
+ pA ↔ p1
− pB ↔ p3 .
Introduction
t-channel factorisation
Application
Conclusions
Building Blocks for an Amplitude
pg · V = 0 can easily be checked (gauge invariance)
The approximation for qQ → qgQ is given by
2
t
MqQ→qgQ =
1
4
(NC2
·
·
− 1)
SqQ→qQ 2
1
g CF
t1
2
·
1
g CF
t2
2
−g 2 CA µ
V (q1 , q2 )Vµ (q1 , q2 ) .
t1 t2
Introduction
t-channel factorisation
Application
Conclusions
3 Jets @ LHC
[nb]
4
dσud->ugd / d∆ y
ja j
b
Full ME
3.5
t-channel factorised ME
3
|y |<4.5, p >40GeV
2.5
i
i
MSTW2008NLO, µ =µ r =40GeV
f
2
kt-jet(R=0.7), pp @ s=10TeV
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
∆y
9
ja j
b
J.M.Smillie and JRA: arXiv:0908.2786
Introduction
t-channel factorisation
Application
Conclusions
3 Jets @ LHC
dσud->ugd / dφ
ja j
b
[nb/rad]
10
9
Full ME
8
t-channel factorised ME
7
6
5
|y |<4.5, p >40GeV
i
i
MSTW2008NLO, µ =µ r =40GeV
f
kt-jet(R=0.7), pp @ s=10TeV
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
φ
ja j
b
J.M.Smillie and JRA: arXiv:0908.2786
Introduction
t-channel factorisation
Application
Conclusions
Building Blocks for an Amplitude
The approximation for qQ → qg · · · gQ is given by
2
t
MqQ→qg...gQ =
1
SqQ→qQ 2
4 (NC2 − 1)
1
1
· g 2 CF
· g 2 CF
t1
tn−1
n−2
Y −g 2 CA
µ
·
V (qi , qi+1 )Vµ (qi , qi+1 ) ,
ti ti+1
i=1
Introduction
t-channel factorisation
Application
Conclusions
dσud−>uggd / d∆ y
j a jb
[pb]
4 Jets @ LHC
1.6
Full ME
1.4
1.2
1
t−channel factorised ME
|yi|<4.5, p >40GeV
i
MSTW2008NLO, µ =µr =40GeV
f
kt−jet(R=0.7), pp @ s=10TeV
0.8
0.6
0.4
0.2
0
0
1
2
J.M.Smillie and JRA: arXiv:0908.2786
3
4
5
6
7
8
∆ yj
9
j
a b
Introduction
t-channel factorisation
Application
Conclusions
4 Jets @ LHC
[pb/rad]
4
3.5
t−channel factorised ME
b
ja j
dσud−>uggd / dφ
Full ME
3
2.5
2
|yi|<4.5, p >40GeV
i
MSTW2008NLO, µ =µ =40GeV
r
f
kt−jet(R=0.7), pp @ s=10TeV
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
φ
j j
a b
J.M.Smillie and JRA: arXiv:0908.2786
Introduction
t-channel factorisation
Application
W+Jets
Two currents to calculate for W + jets:
ℓ
ℓ
i
µ
ℓ̄
o i
µ
ℓ̄
o
pℓ̄
pℓ
p1
pA
V ρi (qti , qti+1 )
pB
.
.
.
.
.
.
pi+1
pn
Conclusions
Introduction
t-channel factorisation
Application
Conclusions
W+ 3 Jets @ LHC
[fb]
500
dσud->e+ν dgd / d∆ y
ja j
b
450
Full ME
t-channel factorised ME
400
|y |<4.5, |y e|<2.5
i
p >40GeV, p e,ν>20GeV
350
i
MSTW2008NLO, µ =µ r=40GeV
f
300
kt-jet(R=0.7), pp @ s=10TeV
250
200
150
100
50
0
0
1
2
3
4
5
6
7
∆y
8
ja j
b
J.M.Smillie and JRA: arXiv:0908.2786
Introduction
t-channel factorisation
Application
dσud->e+ν dgd / dpe [fb/GeV]
W+ 3 Jets @ LHC
40
Full ME
35
t-channel factorised ME
30
25
20
|y |<4.5, |y e|<2.5
i
p >40GeV, p e,ν>20GeV
i
15
MSTW2008NLO, µ =µ r =40GeV
f
kt-jet(R=0.7), pp @ s=10TeV
10
5
0
0
20
40
J.M.Smillie and JRA: arXiv:0908.2786
60
80
100
120
140
160
180 200
pe [GeV]
Conclusions
Introduction
t-channel factorisation
Application
dσud->e+ν dgd / dpν [fb/GeV]
W+ 3 Jets @ LHC
30
Full ME
t-channel factorised ME
25
20
15
|y |<4.5, |y e|<2.5
i
p >40GeV, p e,ν>20GeV
i
10
MSTW2008NLO, µ =µ r =40GeV
f
kt-jet(R=0.7), pp @ s=10TeV
5
0
0
20
40
J.M.Smillie and JRA: arXiv:0908.2786
60
80
100
120
140 160 180 200
pν = ET miss [GeV]
Conclusions
Introduction
t-channel factorisation
Application
Conclusions
Quark-Gluon Scattering
“What happens in 2 → 2-processes with gluons? Surely the
t-channel factorisation is spoiled!”
pa
p1 pa
p1 pa
p1
pb
p2 pb
p2 pb
p2
−
−
−
−
Direct calculation (q g → q g ):
s
s !
−
∗
2
p
p2−
p
g
2 b
b 2
b
te1
−
t
t
hb|σ|2i × h1|σ|ai.
× 2⊥ tae
M=
ae e1
|p2⊥ |
p2−
pb−
t̂
Complete t-channel factorisation!
J.M.Smillie and JRA
Introduction
t-channel factorisation
Application
Conclusions
Quark-Gluon Scattering
The t-channel current generated by a helicity non-flipping gluon
is that of a quark with a colour factor
!
pb− p2−
1
1
1
CA −
+ − +
−
2
CA
CA
p2
pb
instead of CF . Tends to CA in MRK limit.
Introduction
t-channel factorisation
Application
Conclusions
60
Full ME
t−channel factorised ME
t−channel factorised ME (CAM)
t−channel factorised ME (CAM+flip)
dσug−>ugg / d∆ y
j a jb
[nb]
Quark-Gluon Scattering
50
40
30
|yi|<4.5, p >40GeV
i
MSTW2008NLO, µ =µr =40GeV
20
f
kt−jet(R=0.7), pp @ s=10TeV
10
0
0
J.M.Smillie and JRA
1
2
3
4
5
6
7
8
∆ yj
9
j
a b
Introduction
t-channel factorisation
Application
Conclusions
Full ME
t−channel factorised ME
t−channel factorised ME (CAM)
t−channel factorised ME (CAM+flip)
14
dσug−>uggg / d∆ y
j a jb
[pb]
Quark-Gluon Scattering
12
|yi|<4.5, p >40GeV
i
MSTW2008NLO, µ =µr =40GeV
10
f
kt−jet(R=0.7), pp @ s=10TeV
8
6
4
2
0
0
J.M.Smillie and JRA
1
2
3
4
5
6
7
8
∆ yj
9
j
a b
Introduction
t-channel factorisation
Application
Conclusions
All-Orders and Regularisation
Have prescription for 2 → n matrix element, including
virtual corrections
Organisation of cancellation of IR (soft) divergences easy
Can calculate the sum over the n-particle phase space
explicitly (n ∼ 25) to get the all-order corrections
V. Del Duca, C.D. White, JRA arXiv:0808.3696, J.M. Smillie, JRA arXiv:0908.2786
Introduction
t-channel factorisation
Application
Conclusions
Effect of Central rapidity jet veto in H+diJets
σ(yc) [fb]
450
400
|y -y |>4.2; |y |<4.5; m =120GeV
ja jb
i
H
y y <0, p >40GeV, R=0.6
350
ji
ja jb
300
p
250
p
200
p
150
=40GeV
veto
=30GeV
veto
=20GeV
veto
100
50
0
0
0.5
∀j ∈ {jets with pj⊥
1
1.5
2
2.5
3
3.5
4
yc
ya + yb > p⊥,veto } \ {a, b} : yj −
> yc
2 Introduction
t-channel factorisation
Application
Conclusions
Outlook and Conclusions
Conclusions
Emerging framework for the study of processes with
multiple hard jets
For each number of particles n, the approximation to the
matrix element (real and virtual) is sufficiently simple to
allow for the all-order summation to be constructed as an
explicit sum over n-particle final states (exclusive studies
possible)
Resummation based on approximation which really does
capture the behaviour of the scattering processes at the
LHC
Matching will correct the approximation where the full
matrix element can be evaluated

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