1 multi-parton one-loop amplitudes with a vector boson for...
TRANSCRIPT
October 08
H. Ita HP2.2 U
niversidad de Buenos Aires
1
Mul
ti-P
arto
n O
ne-L
oop
Am
plitu
des
with
a V
ecto
r B
oson
for
the
LHC
.
Har
ald
Ita(U
CLA
)H
P2.
2 w
orks
hop
Uni
vers
idad
de
Bue
nos
Aire
s
Rec
ent w
ork:
arX
iv:0
803.
4180
, arX
iv:0
808.
0941
.In
col
labo
ratio
n w
ith:
C. B
erge
r, Z
. Ber
n, L
. Dix
on, F
. Feb
res
Cor
dero
, D
. For
de, D
. Kos
ower
, D. M
aitr
e.
October 08
H. Ita HP2.2 U
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2
Con
tent
:
�A
SU
SY
sig
nal.
�R
esul
ts fo
r (W
,Z,γ
)+3
jets
mat
rix e
lem
ents
.
�N
umer
ical
pre
cisi
on.
�T
imin
g.�
Con
clus
ions
.
October 08
H. Ita HP2.2 U
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3
A S
US
Y S
igna
l & B
ackg
roun
ds.
See
rev
iew
: Man
gano
, arX
iv:0
809.
1567
,D
ixon
, arX
iv:0
7123
064.
�S
cena
rio: p
rodu
ctio
n &
dec
ay o
f str
ongl
y in
tera
ctin
g gl
uino
san
d sq
uark
s.
�C
onsi
der
(a):
mul
ti-je
t+m
issi
ngtr
ansv
erse
ene
rgy.
�B
ackg
roun
d:Z
( v,v
)+4
jets
.
W(τ
,ν)+
3 je
ts, W
(l,ν)+
4 je
ts,
-eve
nts,
mul
ti-je
t eve
nts.
(a)
(b)
lept
ons
October 08
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4
Sig
nal:
�st
atis
tical
sig
nific
ance
su
ffici
ent t
o sh
ow S
M
anom
aly.
�un
settl
ing:
sim
ilar
shap
es!
Vas
en[A
tlas
Col
labo
ratio
n] 2
006.
mS
UG
RA
, ful
l det
ecto
r&ba
ckgr
ound
sim
ulat
ion:
accu
rate
theo
retic
al e
stim
ates
of b
ackg
roun
ds
& th
eir
valid
atio
n cr
ucia
l.
Gen
eric
Sig
nal P
rope
rtie
s.
October 08
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5
Impo
rtan
ce o
f NLO
for
W+
jets
.T
. Aal
tone
net
al.
[CD
F C
olla
bora
tion]
, arX
iv:0
711.
4044
SM
PR
-mod
el: M
rena
, Ric
hard
son,
200
4.M
LM-m
odel
: Alw
alle
t al.
arX
iv:0
706.
2569
.LO
,
Mos
tly s
cale
un
cert
aint
ies.
MC
FM
incl
udin
g B
ern,
D
ixon
, Kos
ower
, Wei
nzie
rlm
atrix
ele
men
ts.
NLO
.
October 08
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6
Pro
gres
s R
epor
t:
�W
ith B
lack
Hat
: lea
ding
col
orN
LO m
atrix
ele
men
ts
for:
�R
ely
on c
olor
supp
ress
ion.
(F
or 6
-poi
nt n
aïve
10%
ef
fect
of s
uble
adin
gco
lor
seem
s re
aliz
ed.)
�D
emon
stra
te n
umer
ical
sta
bilit
y.�
Abo
ut B
lack
Hat
: see
D. F
orde
’s.
Ber
ger,
Ber
n, D
ixon
, Feb
res
Cor
dero
, For
de, H
I, K
osow
er, M
aitr
e, a
rXiv
:080
8.09
41.
off-
shel
l
October 08
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7
Col
or S
truc
ture
.
�C
olor
dre
ssed
ggg
qqV
am
plitu
de.
�S
uppr
ess
ferm
ion
loop
co
ntrib
utio
ns w
ith a
xial
/vec
t. co
uplin
g.
�V
-bos
on c
oupl
ing:
+…
see
also
: Ber
n, D
ixon
, Kos
ower
: hep
-ph/
9708
239,
hep-
ph/9
4093
93.
October 08
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8
Prim
itive
Am
plitu
de:
�Le
adin
g co
lor
one-
loop
pr
imiti
ve a
mpl
itude
:
�F
rom
par
tial t
o pr
imiti
ve a
mpl
itude
s.
+/-
+/-
+/-
October 08
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9
Sta
bilit
y S
tudy
: Ber
ger,
Ber
n, D
ixon
, Feb
res
Cor
dero
, For
de,
HI,
Kos
ower
, Maî
tre,
080
8.09
41[h
ep-p
h]10
0 00
0 P
S p
oint
s,
ET
>0.
01 s
(1/2
), p
seud
orap
idity
<3,
sep
arat
ion
cut >
0.4
October 08
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10
Rem
inde
r: M
assl
ess
One
-Loo
p B
asis
.A
ll ex
tern
al m
omen
ta in
D=
4, lo
op m
omen
ta in
D=
4-2ε
(dim
ensi
onal
reg
ular
izat
ion)
.
See
Ber
n, D
ixon
, Dun
bar,
Kos
ower
, hep
-ph/
9212
308.
Rat
iona
l par
tC
ut p
art Pro
cess
dep
ende
nt D
=4 r
atio
nal i
nteg
ral c
oeffi
cien
ts
1/ε^2
, 1/ε
1/ε
October 08
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11
Uni
tarit
y M
etho
d.
�U
nita
rity
App
roac
h:
�B
ern,
Dix
on, D
unba
r, K
osow
er, h
ep-p
h/94
0322
6, h
ep-
th/9
4092
65.
�G
ener
aliz
ed U
nita
rity:
�
Ber
n, D
ixon
, Kos
ower
, hep
-ph/
9708
239,
hep
-ph/
0001
001.
�B
ritto
, Cac
hazo
, Fen
g, h
ep-t
h/04
1210
3.
�Im
pres
sive
Rec
ent A
dvan
ces:
�de
l Agu
ilaan
d P
ittau
, hep
-ph/
0404
120.
�O
ssol
a, P
apad
opou
los
and
Pitt
au, h
ep-p
h/06
0900
7.�
For
de, 0
704.
1835
[hep
-ph]
.�
Elli
s, G
iele
, Kun
szt,
0708
.239
8 [h
ep-p
h]; G
iele
, Kun
szta
nd
Mel
niko
v, 0
801.
2237
[hep
-ph]
; Elli
s, G
iele
, Kun
szt,
Mel
niko
v,
0806
.346
7 [h
ep-p
h].
October 08
H. Ita HP2.2 U
niversidad de Buenos Aires
12
Box
-Cut
: Orig
in o
f Spu
rious
Pol
es.
Un-
phys
ical
(=
spur
ious
) si
ngul
ariti
es fr
om p
aram
eter
izat
ion.
Hav
e to
can
cel e
vent
ually
: rol
e of
rat
iona
l ter
m R
.
Ber
ger,
Ber
n, D
ixon
, Feb
res
Cor
dero
, For
de,
H.I.
, Kos
ower
, Mai
tre
0803
.418
0;R
isag
er08
04.3
310.
October 08
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13
Hie
rarc
hy o
f Com
plex
ity.
�“B
oxes
= q
uadr
uple
cut
”.�
“Tria
ngle
s =
trip
le c
ut –
boxe
s”.
�“B
ubbl
es =
dou
ble
cut –
tria
ngle
s –
boxe
s”.
�R
atio
nal t
erm
s ex
trac
ted
from
all
of th
e ab
ove.
1)P
ropa
gatio
n of
err
ors.
2)A
ccum
ulat
ion
of in
vers
e G
ram
det
erm
inan
ts.
October 08
H. Ita HP2.2 U
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14
Num
eric
al In
stab
ilitie
s.
�C
heck
s:�
Use
con
sist
ency
con
ditio
ns fr
om k
now
nIR
/UV
pol
e st
ruct
ure
of a
mpl
itude
s.
�A
naly
tic tr
icks
:�
Use
“go
od”
varia
bles
. (se
e F
orde
’s ta
lk)
�P
rote
ctio
n:�
Num
eric
al im
plem
enta
tion
with
dyn
amic
pre
cisi
on in
B
lack
Hat
. �
Pre
cisi
on c
heck
fails
lo
cally
use
mul
ti-pr
ecis
ion.
October 08
H. Ita HP2.2 U
niversidad de Buenos Aires
15
The
Tai
l. (S
ix g
luon
MH
V.)
Dou
ble-
prec
isio
n nu
mer
ical
com
puta
tion.
Dyn
amic
mul
ti-pr
ecis
ion
com
puta
tion.
Ref
eren
ce: a
naly
tic ta
rget
s fr
om B
ern,
Dix
on, D
unba
r, K
osow
er, h
ep-
ph/9
4032
26, h
ep-p
h/94
0926
5, h
ep-p
h/05
0700
5.
Nat
ural
tail
Mul
ti-pr
ecis
ion
Nat
ural
tail
(III)
(I)
(I+
II)
Mul
ti-pr
ecis
ion
October 08
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16
Use
Uni
vers
al P
ole
Str
uctu
re:
�B
oxes
and
tria
ngle
s w
ith a
t lea
st o
ne m
assl
ess
corn
er
cont
ribut
e to
a
nd
p
oles
.
Rel
atio
n be
twee
n bo
x, tr
iang
le c
oeffi
cien
ts a
nd tr
ees.
Goo
d ch
eck
for
prec
isio
n!
�B
ubbl
es c
ontr
ibut
e to
pur
e
p
ole.
Exc
elle
nt c
heck
:“C
heck
I”
October 08
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17
Pow
er o
f
C
heck
:
�B
oxes
and
tria
ngle
s su
btra
cted
in c
ompu
tatio
n of
the
bubb
le:
�B
ubbl
e co
effic
ient
s ar
e lin
ear
func
tions
of b
ox a
nd
tria
ngle
coe
ffici
ents
. �
Err
ors
prop
agat
e to
bub
bles
.
Eno
ugh
to c
heck
bub
ble
coef
ficie
nts.
=-
--
October 08
H. Ita HP2.2 U
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18
Che
ck I:
Ons
et o
f che
ck.
October 08
H. Ita HP2.2 U
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19
Rat
iona
l Ter
ms.
�Lo
op-le
vel o
n-sh
ell r
ecur
sion
.�
Ber
n, D
ixon
, Kos
ower
, hep
-th/
0501
240,
hep-
ph/0
5050
55,
�B
erge
r, D
el D
uca,
Dix
on, h
ep-p
h/06
0818
0,�
For
de, K
osow
er, h
ep-p
h/05
0935
8, B
erge
r, B
ern,
Dix
on, F
orde
, K
osow
er, h
ep-p
h/06
0701
4�
Ber
n, B
jerr
um-B
ohr,
Dun
bar,
Ita,
hep
-ph/
0507
019.
�
D-d
im u
nita
rity.
�B
ern,
Mor
gan,
hep
-ph/
9511
336;
�
Ber
n, D
ixon
, Kos
ower
,hep
-ph/
9708
239;
�A
nast
asio
u et
al.,
hep
-th/
0609
191,
hep
-th/
0612
277,
Brit
to, F
eng,
he
p-ph
/061
2089
, 071
1.42
84; B
ritto
, Fen
g, M
astr
olia
, 080
3.19
89;
Brit
to, F
eng,
Yan
g, 0
803.
3147
;�
Oss
ola,
Pap
adop
olou
s, P
ittau
, 080
2.18
76; M
astr
olia
, Oss
ola,
P
apad
opol
ous,
Pitt
au, 0
803.
3964
;�
Gie
le, K
unsz
t, M
elni
kov,
080
1.22
37; E
llis,
Gie
le, K
unsz
t, M
elni
kov,
080
6.34
67;
Use
d he
re!
October 08
H. Ita HP2.2 U
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20
On-
shel
l Rec
ursi
ons:
R
atio
nal T
erm
s.
�In
ject
z-d
epen
dent
mom
entu
m: k
(z)=
k+z
q, k
(z)^
2=0.
�N
umer
ical
rec
onst
ruct
ion
of r
atio
nal f
unct
ion
in z
:Lo
catio
n of
pol
es:
Res
idue
s:pr
opag
ator
s:
F
rom
fact
oriz
atio
n.sp
urio
us p
oles
:
F
rom
Cut
-par
ts.
+z
q
-z q
See
For
de’s
talk
October 08
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21
Spu
rious
Pol
es.
�E
qual
-opp
osite
to
spur
ious
pol
es o
f cut
-par
ts.
Can
be
extr
acte
d fr
om c
ut-p
arts
.
�E
xam
ple:
ext
ract
spu
rious
res
idue
s fr
om
bubb
les:
for
give
n po
le
.
from
October 08
H. Ita HP2.2 U
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22
Pre
cisi
on C
heck
II.
�P
ole
stru
ctur
e im
plie
s: s
um o
f bub
bles
giv
es th
e tr
ee.
�T
ree
has
no s
purio
us p
oles
.
�C
heck
:spu
rious
res
idue
s on
a g
iven
pol
e ha
ve
to a
dd u
p to
zer
o.
All
bubb
les
All
bubb
les
All
bubb
les
October 08
H. Ita HP2.2 U
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23
Che
ck I+
II+III
.
Nat
ural
tail.
“Che
ck II
I”
“Che
cks
I&II”
Dis
cret
ized
cont
our
inte
gral
:•
Dyn
amic
al r
adiu
s•
Dyn
amic
s ev
alua
tion
step
s.
October 08
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24
Rem
ark:
�C
lose
to s
purio
us p
oles
: Lar
ge c
ance
llatio
ns
betw
een
ratio
nal &
cut
-par
t exp
ecte
d.
Use
hig
her
prec
isio
n.
October 08
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25
Tim
ing:
pp
(W
,Z,γ
)+3
jets
.
++
+: 4
.01m
s/4.
06m
s10
.6m
s/10
.7m
s
Hel
icity
:-+
+: 6
.41m
s/6.
64m
s41
.7m
s/42
.9m
s
++
-: 6
.47m
s/6.
67m
s28
.0m
s/28
.4m
s
-+-:
7.7
0ms/
7.92
ms
39.2
ms/
40.5
ms
Dou
ble
prec
isio
nD
ynam
ic m
ulti
prec
isio
n
Ful
l am
plitu
de4-
D c
ut-p
art
2.33
GH
z X
eon
Pro
cess
or
October 08
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26
Con
clus
ion:
�S
US
Y b
ackg
roun
d.�
Lead
ing
colo
rm
atrix
ele
men
ts fo
r:�
Num
eric
al s
tabi
lity
unde
r go
od c
ontr
ol.
Man
y ta
sks:
�T
owar
ds c
ross
sec
tions
.�
Sub
lead
ing
colo
r.�
Par
ticle
spe
ctru
m, m
asse
s....
Tha
nks!
October 08
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27
EX
TR
A S
LID
ES
:
.
October 08
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28
Ref
eren
ce V
alue
s:
October 08
H. Ita HP2.2 U
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29
NLO
nee
ded.
�T
ree-
leve
l (LO
) pr
edic
tions
qua
litat
ive,
due
to p
oor
conv
erge
nce
of e
xpan
sion
in s
tron
g co
uplin
g,
�la
rge
NLO
cor
rect
ions
can
be
30%
-80
% o
f LO
.
impl
ies
scal
e un
cert
aint
y:
•1 je
t abo
ut 1
2%•2
jets
abo
ut 2
4%•3
jets
abo
ut 3
6%