1 multi-parton one-loop amplitudes with a vector boson for...

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


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


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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


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

H. Ita HP2.2 U


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


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


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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


18

Che

ck I:

Ons

et o

f che

ck.

October 08

H. Ita HP2.2 U


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


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

H. Ita HP2.2 U


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


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


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


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

H. Ita HP2.2 U


27

EX

TR

A S

LID

ES

:

.

October 08

H. Ita HP2.2 U


28

Ref

eren

ce V

alue

s:

October 08

H. Ita HP2.2 U


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%

1 multi-parton one-loop amplitudes with a vector boson for...

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