Monte Carlo Simulations for Top Physics

hep.phy.cam.ac.uk

Monte Carlo Simulations for Top Physics

Monte Carlo Simulations

for Top Physics

Event generation issues

Extra jets in top production

Extra jets in top decay

Spin correlations

Mass measurement with M T2

`Global inclusive’ observables

Conclusions

Bryan Webber: Top Physics Simulations 1

CERN Top Quark Institute 09


General-purpose event generators

HERWIG

Angular-ordered shower, cluster hadronization

v6 Fortran, now Herwig++

PYTHIA

Virtuality/k T -ordered shower, string hadronization

v6 Fortran, v8 C++

SHERPA

Virtuality/dipole shower, cluster hadronization

C++ ab initio

Bryan Webber: Top Physics Simulations 2

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Issues for event generators

Matrix elements

Internal/external generation

Spin, widths, off-shell effects

Parton showers

Matching to NLO and/or LO n-jet MEs

Coherence, mass and spin effects, 1/N

NLO showering?

Non-perturbative

Hadronization, decays

PDFs, underlying event, intrinsic p T

Bryan Webber: Top Physics Simulations 3

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ME-PS matching

Two rather different objectives:

Matching to NLO MEs without double counting

MC@NLO

POWHEG

Matching to LO n-jet MEs, minimizing jet

resolution dependence

CKKW

Dipole

MLM matching

Bryan Webber: Top Physics Simulations 4

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MC@NLO & POWHEG for ttX

Frixione, Nason & Ridolfi, 0707.3088

Bryan Webber: Top Physics Simulations 5

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MADEVENT+PYTHIA matching

200 400 600 800 1000 1200 1400

10

-3

P T

-3

(GeV)

200 400 600 800 1000 1200 1400

(GeV)

P T

(pb/bin)

T

d!/dP

10

2

tt Pt of the 1rst jet, matched

wimpy q

power q

wimpy pt

power pt

2

tt Pt of the 1rst jet, unmatched

1st jet, PS only

scales uncertainty

10

10

1

1

(pb/bin)

-1

10

T

d!/dP

10

2

1st jet, matched

50 100 150 200 250 300 350 400

2nd jet, matched

tt Pt of the 2nd jet, matched

-1

50 100 150 200 250 300 350 400

2nd jet, PS only

ttPt of the 2nd jet, unmatched

2

10

10

1

1

-1

10

-1

50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400

(GeV)

(GeV)

P T

Matching removes sensitivity to shower options

gure 3: p ⊥ spectrum for the first and second hardest radiated jet in (a) ˜g˜g and (b) t¯t events. The

ht column in each group of plots shows the spread of Pythia predictions with different choices

the shower evolution variable (virtuality- and p ⊥

Alwall, -ordered) de and Visscher starting & scale Maltoni, for the 0810.5350 evolution

beled

Bryan Webber:

as “wimpy”

Top Physics

and

Simulations

“power” showers respectively).

6

The left column

CERN

presents

Top Quark

the

Institute

results

09

P T


Extra jets in top

production

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( ) [ ]

NLO tt + dσ fb

dp T,jet GeV

1000

pp → t¯t + jet + X

√ s = 14 TeV

( ) [ ]

dσ fb

dp T,t¯t GeV

1000

( ) [ ]

dσ fb

dp T,jet GeV

1000

100

10

0

2.0

1.5

1.0

0.5

0

Most events have jets

with p T > 30 GeV

Top p T degraded at NLO

100

100

( ) [ ]

dσ fb

dp T,t

200

200

NLO

300

LO

K = NLO/LO

300

400

p T,jet [GeV]

pp → t¯t + jet + X

√ s = 14 TeV

400

500

500

600

600

700

700

( ) [ ]

dσ fb

dp T,t¯t GeV

1000

100

10

0

2.0

1.5

1.0

0.5

0

100 200 300 400 500 600 700 0 100 200 300 400 500 600 700

2.0

At least inK =

the

NLO/LO

regions of the K = NLO/LO

1.5

distributions in which the rate is not too mu

100

Dittmaier, Uwer 100 & Weinzierl, 0810.0452 100

200

300

400

p T,t¯t[GeV]

pp → t¯t + jet + X

√ s = 14 TeV

GeV

Bryan Webber: Top Physics Simulations 8

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500

NLO

10

p T,jet,cut [GeV] LO LO NLO

600

700

0.5

0

0.5

0

100

( ) [ ]

dσ fb

dp T,t GeV

1000

100

200

200

σ t¯tjet[pb]

20 710.8(8) +358

−221

692(3)3 −40

0 100 200 300 400 500 600

−62

700

2.0

50 326.6(4) +168

K −103

376.2(6) +17

= NLO/LO −48

1.5

100 146.7(2) +77

1.0

−47

175.0(2) +10

−24

200 46.67(6) +26 52.81(8)

−15 +0.8

−6.7

300

400

p T,jet [GeV]

Table 3.2: Cross section σ t¯tjet at the LHC for different values of p T,jet,cut for µ = µ

The upper and lower indices are the shifts towards µ = m t /2 and µ = 2m t .

300

400

p T,t [GeV]

500

500

600

pp → t¯t + jet + X

√ s = 14 TeV

The reduction of the forward–backward asymmetry A t FB

discussed above i

NLO corrections is clearly visible in the η t and y t distributions. The correction

100

the forward direction. The asymmetry in the LO distributions is thus reduce

corrections. It is hardly conceivable that this higher-order effect can be abs

NLO

NLO

predictions by phase-space-dependent 10 scale choices. It should be realized tha

LO

LO

backward-symmetric rapidity distribution of the hard jet gets distorted by the

well. The corrections increase for large values of |y jet |.

the NLO corrections reduce the scale 1.0 uncertainty of the LO distributions in a

observed for the integrated cross section.

3.3 Results for the LHC

600

700

700

10

0

2.0

1.5

1.0

0.5

0

100

100

Figure 3.3: Transverse-momentum distributions of the har

(p T,t¯t), and of the top-quark (p T,t ) at the LHC. The lower pane


ALPGEN & MC@NLO

ALPGEN can generate samples of tt¯+ n jets; can be compared to NLO+PS;

• Disadvantage: worse normalization (no NLO)

expect: ALPGEN x K-factor OK for top distributions

• Advantage: better high jet multiplicities (exact ME)

MC@NLO deficit for (extra) N jets > 2

Comparison ALPGEN-MC@NLO carried out in detail

(Mangano, Moretti,Piccinini,Treccani, Nov.06)

ALPGEN:

K = 1.51

MC@NLO:

generated

by shower

Mangano, Moretti, Piccinini & Treccani, hep-ph/06611129

73

Bryan Webber: Top Physics Simulations 9

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Jet contamination

Fully leptonic tt: 2 jets (+2 leptons + MET)

Matched = top decay parton within

and ∆ E/E=0.3

∆R=0.5

MC@NLO (no underlying event)

Bryan Webber: Top Physics Simulations 10

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E T ordering of jets

P(1 or both leading jets unmatched) > 50%

Bryan Webber: Top Physics Simulations 11

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POW

MC@

Rapidity of hardest extra jet

Hardest non-top jet

MC@NLO strictly LO in HERWIG ‘dead region’

Dip in central region in MC@NLO also in tt¯ a

Bryan Webber: Top Physics Simulations 12

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ISR jets in fHERWIG

Angular ordering gives ISR jet cones

¯θ

‘Dead’ region filled by matrix element

cos θ ∗ g

cos ¯θ = −1 −0.5

0

0.5

M 2 Q

¯Q


Bryan Webber: Top Physics Simulations 13

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Discrepancies in y jet

ALPGEN and POWHEG agree

Is MC@NLO within HO uncertainty?

Results as expected but for 1 observable

POWHEG’s distribution as in ALPGEN (i.e., no dip);

Notice: size of discrepancy can be attributed to different treatment

of higher order terms. Is this “feature” really there?

Bryan Webber: Top Physics Simulations 14

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Third jet rapidity in dijets

0.08-

0.06-

(4 _ (b)

- HERWIG - ;SAJET

. DATA l DATA

$ 0.02

b)

6

6

“o”

q\ ; ./

.- k

c,

_ PYTHIA

_ PYTHIA+

CJ 0.06

l

P

DATA

l DATA

L

0.f f+++)+\+ 1 &f&w

qqqf

restriction cone for q’

0

I .I

LP

l

l

.

-4 -2

L I I

-1

q

restriction cone for q

Figure 11:

E T1 > 110 GeV, E T3 > 10 GeV

Figure 3:

Colour coherence => central dip!

CDF: Abe et al., PRD 50 (94) 5562

Bryan Webber: Top Physics Simulations 15

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1.0

1.0

0.5

−4

−3

−2

NLO jet rapidity

4

η t

−1

0

1

2

3 4

η t

0.5

−4

−3

−2

−1

0

1

2

3

4

y t

( )


dy jet

[fb]

100000

10000

NLO

LO

No dip at small y jet

K = 1.2 at y jet = 0

1000

−4

2.0

1.5

−3

−2

pp → t¯t + jet + X

√ s = 14 TeV

−1

0

1

2

K = NLO/LO

3

4

MC@NLO lacks K-

factor at small y

1.0

0.5

−4

−3

−2

−1

0

1

2

3

4

y jet

Dittmaier, Figure 3.4: Distributions Uwer & Weinzierl, in the pseudo-rapidity 0810.0452 (η t ) and rapidity (y t ) of the top-quark, and in

the rapidity (y jet ) of the hard jet at the LHC. The lower panels show the ratios K = NLO/LO as

well as the LO and NLO scale uncertainties corresponding to a rescaling of µ = µ fact = µ ren = m t

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Extra jets in top decay

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t

bWg matrix element

Cut on Durham y bg in top rest frame:

y D bg = 2 min{E 2 b , E 2 g}(1 − cos θ bg )/m 2 t

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ME+PS in top decay

Γ t ∼ 1.4 GeV

Narrow-width approximation ( ):

production & decay treated separately

x W

bWg phase space

Herwig++:

B = b shower

T1,2 = ‘t ISR’

D = ‘dead’ region

(filled by M.E.)

x g

Hamilton & Richardson, hep-ph/0612236

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Resolving an extra decay jet

Herwig++ e + e -

tt at 360 GeV

Stable w.r.t. shower rescaling

Hamilton & Richardson, hep-ph/0612236

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m t from B(→ J/ψ)l

(PS+ME)

(PS)

Effect of hard radiation in decay:

∆m t ∼ 1.5 GeV for all m Bl

∆m t ∼ 1 GeV for m Bl > 50 GeV

Corcella, Mangano & Seymour, hep-ph/0004179

Bryan Webber: Top Physics Simulations 21

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Spin correlations

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Dilepton azimuthal correlation

m t¯t < 400 GeV

√ŝ

< 400 GeV

MC@NLO

Strong correlation at low invariant mass!

S Parke talk here, 25/05/09

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Spin correlations in MC@NLO

Narrow width approximation

Exact NLO correlations in hard emission regions

In soft/collinear regions:

NLO factorizable correlations

LO non-factorizable correlations

Parton showers in production

PS + ME corrections in decays

High MC efficiency

Frixione, Laenen, Motylinski & BW, hep-ph/0702198

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Dilepton correlation: m tt dependence

1/σ dσ/d∆φ (/bin)

MC@NLO

∆φ

Correlation lost by m tt < 500 GeV (50% of data)

Bryan Webber: Top Physics Simulations 25

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Correlations in single top

u/ ¯d

d/ū

Motylinski, 0905.4754

g

W

t

¯b

/ bin


dcos θ

T

σ 1

0.006

0.005

0.004

Beamline basis

Spectator basis

MC@NLO at LHC

0.003

t-channel process

hadron-level cuts

lepton angle in tRF

0.002

0.001

0

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

cos θ

Bryan Webber: Top Physics Simulations 26

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Mass measurement

with M T2

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M T2 variable

pp YYX, Y aN, Y bN

a,b visible, N invisible

Lester & Summers, hep-ph/9906349

Here Y=t, a,b=(l+jet), N=

ν

Then

Transverse mass:

Figure 1:

m 2 T (p 1 T , p a T ; µ N ) = µ 2 N + m 2 a + 2 ( ET 1 ET a − p 1 T · p a )

T

An event with two invisible particles N, each from a decay of a heavy

methods using the variable m T 2 [9], which is sometimes called the strans

m T 2 is defined event by event as a function of the invisible particle mass. I

m 2 [

T 2(µ N ) ≡ min max{m

2

or maximal T (p 1 value over many events, denoted by m max

2 , gives an estimate of

p 1 particle’s mass in the beginning of the decay chain. When the invisible par

T +p2 T =/p T , p a T ; µ N ), m 2 T (p 2 T , p b T ; µ N )} ]

T

is unknown, one has to use a trial mass to calculate m T 2 and only obtains

of the mass difference. However, it has been shown in Ref. [10] that if the

≤ m 2 Y when µ N = m

particles decay N through three-body decays to the invisible particles, a “kink

the m max

T 2 curve as a function of the trial mass. The position of the kink is act

Bryan Webber: Top Physics Simulations true value28

of the invisible particle mass, which CERN allows Top Quark us to simultaneously

Institute 09


CDF top mass from M T2

CDF note 9679

3.2 fb -1 => m t = 168.0 +5.6/-5.0 GeV (prelim.)

Bryan Webber: Top Physics Simulations 29

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Top mass from M T2 at LHC

-1

Events / 3 GeV / 10 fb

300

250

200

150

Cho, Choi, Kim & Park, 0804.2185

! 2

/ ndf

21.33 / 14

p0 171.1

±

1.1

p1 4.998 ±

0.731

p2 558.5 ±

55.4

p3 142.9 ±

1.5

100

50

0

60 80 100 120 140 160 180 200 220 240

m T2

(m = 0 GeV) [GeV]

in

Input mass 170.9 GeV; PYTHIA+PGS; b-tagging 50%

10 fb -1 @ LHC (14 TeV) => m t = 171.1 +/- 1.1 GeV

~

Bryan Webber: Top Physics Simulations

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Reducing ISR contamination

Idea: demand more jets, select lowest M T2

As long as one is correct, this cannot raise edge

7 fb -1 MC@NLO, no b-tagging

> 50% events have extra jets

Hardest 2 jets (red) =>

ISR contaminates edge

Smallest M T2 from 3 hardest

(blue) => less contamination

Alwall, Hiramatsu, Nojiri & Shimizu, 0905.1201

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Global inclusive

observables

Bryan Webber: Top Physics Simulations

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Inclusive observables

How can jets from hard subprocess be

distinguished from ISR jets?

In principle, there is no way! So let’s look at

“global inclusive” observables

Consider e.g. the total invariant mass M visible in

the detector:

M =


E 2 − P 2 z − ̸E 2 T

or (Konar, Kong & Matchev, 0812.1042)


ŝ 1/2

min (M inv) =

√M 2 + ̸ET 2 + Minv 2 + ̸E2 T

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Inclusive observables for tt

H T = E T + ̸E T

ŝ 1/2

min (0) = √M 2 + ̸E 2 T + ̸E T

ˆ

ˆ

Bryan Webber: Top Physics Simulations

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Konar, Kong & Matchev, 0812.1042

CERN Top Quark Institute 09


ISR effects on inclusive observables

−η max

η max

x 1

x 2

¯x 1 θ ¯x 2

∫ ( ) ( )


dM 2 = d¯x1 d¯x 2

x1

x2

dx 1 dx 2 f(¯x 1 , Q c )f(¯x 2 , Q c )K ; Q c , Q K ; Q c , Q ˆσ(x 1 x 2 S)δ(M 2 − ¯x 1¯x 2 S)

¯x 1 ¯x 2 ¯x 1 ¯x 2

ISR at

θ > θ c ∼ exp(−η max )

enters detector

Hard scale

Q 2 ∼ ŝ = x 1 x 2 S

but

M 2 = ¯x 1¯x 2 S

PDFs sampled at Q c ∼ θ c Q

Papaefstathiou & BW, 0903.2013

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ISR evolution kernel

K(x/¯x; Q c , Q) =

ŝ 1/2

M

gg

q¯q

∫ +i∞

−i∞

dN (¯x/x) N K N (Q c , Q)

K N (Q c , Q) =

(Γ N ) ab =

pp

∫ 1

0

ttX @ LHC (14 TeV)

gg dominant

[

αS (Q c )

α S (Q)

qq shifted less

] ΓN /β 0

dz z N−1 P ab (z)

Bryan Webber: Top Physics Simulations 36

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ISR effects: MC results


ŝ 1/2

min (M inv) =

√M 2 + ̸ET 2 + Minv 2 + ̸E2 T


M = E 2 − Pz 2 − ̸ET

2 H T = E T + ̸E T

fHERWIG6.510

evolution

{

. .

Papaefstathiou & BW, 0903.2013

Bryan Webber: Top Physics Simulations 37

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Dependence on

η max

E, M, s min strongly dependent; E T , E T , H T not

Bryan Webber: Top Physics Simulations 38

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Conclusions

Many sophisticated simulation tools available

ME, PS, matching, merging

Important to take account of extra jets

ISR, decay, interference?

Spin correlations are significant

Sensitive to new physics

Testing ground for new physics searches

M T2 , global inclusive observables, ...

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