Higher order effects in top quark production at hadron colliders.

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Higher order effects in top quark production at hadron colliders.

Higher
Order
Effects
in
Top
Quark


Produc8on
at
Hadron
Colliders


M.
Czakon


RWTH
Aachen


Ustroń,
September
14 th 
2011



Some
QuesBons


• Why
are
topquarks
important
for
the
LHC
physics
program
?


• What
do
we
need
the
total
producBon
cross
secBon
for
?


• Why
are
there
large
perturbaBve
correcBons
?


• How
much
is
the
theoreBcal
error
?


too
much
!


• How
much
can
one
improve
it
with
liOle
effort
? 
not
enough
!


• Do
we
really
need
to
invest
any
more
Bme
in
the
problem
?
yes
!



Cool
Stuff
for
the
Theorist


• SoR
singulariBes
in
QCD
with
massive
partons


• ResummaBon
with
colored
final
states


• RelaBon
between
resummaBon
for
differenBal
distribuBons
and


total
cross
secBons


• Next‐to‐next‐to
leading
order
virtual
correcBons
with
massive
final


state
partons


• SubtracBon
schemes
for
next‐to‐next‐to
leading
order
calculaBons


Higher
logarithmic
accuracy
in
parton
showers



Intro



Why
Top
Quarks?


• 8
million
topquark
pairs
per
year


in
the
low
luminosity
phase


• Major
goals


o Top
quark
mass
measurement
with
a


precision
below
1
GeV


o ProducBon
cross
secBon


measurement
to
beOer
than
10%


(hopefully
about
5%)


o ProducBon
and
decay
mechanisms
to


1‐2%


o Spin
correlaBons
to
3‐5%



Searching
for
New
Resonances


Expected
distribuBon
for
vector


resonances
with
M
=
2
TeV


Expected
distribuBon
for
gravitons


in
an
N=3
extra‐dimensions
model


Backgrounds
to
SUSY
searches


Frederix,
Maltoni
‘07



Measuring
the
Mass


• Top
topquark
mass
has
a
high



impact
on
electroweak
physics


• It
is
measured
in
the
pair



producBon
channel
exclusively


• The
method
is
based
on



kinemaBc
reconstrucBon
and
fiing


• An
alternaBve
is
the
measurement
from



the
cross
secBon
normalizaBon


• At
the
TeVatron,
the
precision
from
the



cross
secBon
normalizaBon
is
about
5
GeV


• At
the
LHC,
one
expects
2‐3
GeV
or
beOer



∆σ tt

σ tt

=5 ∆m t

m t


CalibraBon


• One
of
the
main
problems
is



idenBfying
jets
with
b‐quarks



(b‐tagging)


• This
can
be
improved
with
samples



that
have
been
idenBfied
as
top
pair



events
(also
used
for
jet
energy
scale)


• Another
applicaBon
is
luminosity
(PDF)
determinaBon
for


processes
induced
by
the
gluon
flux


• This
is
aOracBve
if
both
theory
and
experiment
have
uncertainBes


at
the
level
of
5%




The
TheoreBcal
Framework


• It
all
begins
with
the
factorizaBon
theorem…



valid
up
to
power
correcBons
1/Q 2 


p

q, g

x 1 p 1

t

X

q, g

p, p

x 2 p 2

t

RenormalizaBon
scale


∫ 1

∫ 1

FactorizaBon
scale


σ h1 h 2 →tt (s, m2 t )= ∑ ij

0

0

dx 1 dx 2

φ i/h1 (x 1 ,µ 2 F )φ j/h2 (x 2 ,µ 2 F )ˆσ ij (ŝ, m 2 t , α s (µ 2 R),µ 2 R,µ 2 F )

Parton
DistribuBon
FuncBons



Meaningless
Without
Input


• …and
the
Parton
DistribuBon
FuncBons


x ! i/p (x,m t )

100

10

1

0.1

CTEQ6m

gluon

u

d

dbar

ubar

s,sbar

c,cbar

0.01

1e-04 0.001 0.01 0.1 1

x


Importance
of
the
Threshold


• Strong
rise
of
the
PDF
translates
into
an
enhacement
of
the


contribuBon
from
the
threshold
region


• The
effect
on
the
total
cross
secBon
is
best
seen
through
the
flux


σ = ∑ ∫ (

ηmax

∫ 1

( ) ) dx ŝ

dη ρ

ij 0

ŝ/s x φ i(x)φ j ˆσ ij (η)

sx

ρ = 4m2 t

β = √ 1 − ρ η = ŝ − 1

s

Φ

80

70

LHC

4m 2 t

0.2

LO

NLO-LO

! gg (",m t )

60

50

40

30

20

m 2 /! s

2 "gg -> tT

0.15

0.1

0.05

10

0

-4 -3 -2 -1 0 1 2 3

log 10 " = log 10 ( s/4m t

2 - 1 )

0

0 0.2 0.4 0.6 0.8 1

#


So
What
?


90%
 90%


next‐to‐leading
order
diagrams



The
Physics


soR
gluon
emission


large
effects

m 2 /! s

2 "gg -> tT

0.2

0.15

0.1

0.05

LO

NLO-LO

0

0 0.2 0.4 0.6 0.8 1

#

Coulomb



aOracBon/repulsion


small
effects

t‐channel
gluon
exchange


negligible
effects

All
effects
can
be
resummed
!!!



Threshold
Behavior



ResummaBon
Theory



Drell‐Yan
and
SoR
Gluons



Drell‐Yan
and
SoR
Gluons



Drell‐Yan
and
SoR
Gluons



The
Mellin
Transform



The
Mellin
Transform



ExponenBaBon



Drell‐Yan
and
ResummaBon



Tops
Again


ResummaBon
for
Tops


Originally
developed
at
NLL
by
Bonciani,
Catani,
Mangano
&
Nason
‘98


Moch
&
Uwer
‘08
proposed
an
extension
to
NNLL



Threshold
Expansion


• 
Progress


Hagiwara,
Sumino,
Yokoya`08;
MC,
Mitov
`08





















 
(matching
coefficients)


Beneke,
Falgari,
Schwinn
`09;
MC,
Mitov,
Sterman
`09





 
(NNLL
soR
gluon
resummaBon)


Beneke,
MC,
Falgari,
Mitov,
Schwinn,
`09 
 









 
(potenBal
effects)


• 
Threshold
expansion
of
the
gg
‐>
O
cross
secBon
at
NNLO


σ (0)

gg

( αs


) 2
 (68.5471 1

β 2 + (496.3 log2 β + 321.137 log β − 8.62261) 1 β

+4608 log 4 β − 1894.91 log 3 β − 912.349 log 2 β + 2456.74 log β + C (2)

gg

)

• 
Since
then


Ahrens,
Ferroglia,
Neubert,
Pecjak,
Yang
`10





















 
(SCET
improved
distribuBons)


Beneke,
Falgari,
Klein,
Schwinn
`11
 
 
 
 
 
(NNLL
soR
gluon/Coulomb)



NNLL
ResummaBon


• 

The
resummaBon
looks
now
rather
like


• 

Can
be
cast
into
the
tradiBonal
formula
with
a
modified
D QQ



 


MC,
Mitov,
Sterman
`09


• 

The
same
result
obtained
with
SCET






Beneke,
Falgari,
Schwinn
`09
(separaBon
of
Coulomb
effects
made
transparent)


• 

The
hard
funcBon
contains
Coulomb
effects,
the
mixing
generates






terms
of
the
form
log
β
x
1/β



PotenBal
ContribuBons


• 
Apart
from
soR
gluon
effects,
there
are
enhanced
contribuBons




coming
gluon
exchanges
between
the
propagaBng
heavy
quarks


• 
These
are
described
by
potenBals,
but
not
only
Coulomb!


• 
Can
be
computed
in
NRQCD,
but
also
obtainable
from
results
of




Czarnecki,
Melnikov
’97
’01





on
topquark
pair
producBon
in
e + e ‐ 
and
γγ
collisions



• 
TransiBon
from
singlet
to
octet


Tricky
Points





CF
‐>
CF
‐
CA/2
works
in
this
case
too
!


• 
Subleading
mixing
between
soR
and
potenBal
interacBons




CorrecBons
jump
by
two
powers
of
the
velocity
–
harmless
!




(analysis
of
the
ultrasoR
and
potenBal
regions
to
arbitrary
order)



Future



Do
We
Need
ResummaBon
?


• 

Partonic
gg
cross
secBon


1000

NNNLO


500

450

100

NNLO


400

350

300

250

10

Resummed


200

150

100

50

1

0.0001 0.001 0.01 0.1 1 10 100

• 

ARer
mulBplicaBon






with
the
flux


0

0.0001 0.001 0.01 0.1 1 10 100

• 

The
third
order
of
the
expansion
contributes
less
than
1%





























NO,
WE
DON’T
!!!



Fixed
Order
Cross
SecBon


Difficult
2‐loop
amplitudes


1‐loop
amplitude
squared
not‐easy


trivial
phase‐space


1

ɛ 2n

Similar
to
tT+jet,
but


difficulBes
at
the
phase
space


boundaries


A
window
to
new
methods


for
1‐loop
integrals


dˆσ NNLO

tt

= dˆσ VV

2 + dˆσ VR

2+1 + dˆσ RR

2+2

Trivial
amplitude


difficult
phase
space


dˆσ n = dΦ n |M n | 2 DREG
singulariBes


Amplitude
 M l = 1

Phase
space


ɛ 2l + . . .


Cross
SecBons
for
Top
ProducBon


MC
`11



Conclusions


• InteresBng
applicaBons
of
the
total
cross
secBon,
currently
mass


measurement
and
gluon
PDF
improvement,
require
an
error
≈
5%


• We
count
on
the
experimentalists
to
make
it
to
this
level
!


• Scale
variaBon
at
NLO
esBmates
the
theory
error
at
≈
12%


• SoR
gluon
resummaBons
can
only
do
slightly
beOer
and
do
not
fit


Monte
Carlos
generators


• The
only
soluBon
is
NNLO:
Recently
solved
the
last
famous


problem
of
real
radiaBon


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