LO NLO dist HTjets HAZ12 - lpthe.jussieu.frsalam/talks/repo/2011-giantK-Valencia.pdf · Gavin Salam CERN, Princeton & LPTHE/CNRS (Paris) Work performed with Mathieu Rubin and Sebastian

Giant K factors

Gavin Salam

CERN, Princeton & LPTHE/CNRS (Paris)

Work performed with Mathieu Rubin and Sebastian Sapeta, arXiv:1006.2144

Kick-off meeting of LHCPhenoNet Initial Training NetworkValencia, Spain, 1–4 February 2011

Many searches for New Physics (eg. SUSY) rely onLeading Order predictions for backgrounds.

eg. Z+4jet background to gluino pair production

with NLO technology rapidly becoming mature for such cases

LO often considered good to within a factor of 2NLO to within 10-20%

This talk is about cases where such “rules of thumb” fail(spectacularly)

G. Salam (CERN/Princeton/LPTHE) Giant K -factors 2011-02-02 2 / 16

The Z+jet process[Introduction]

Use MCFM to examinevarious properties of suchevents at LO and NLO.




10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400dσ

/dp t

,Z [f

b / 1

00 G

eV]

pt,Z [GeV]

pp, 14 TeV

LO

NLO

pt spectrum of Z boson gets K -factor of 1.5

Fairly standard kind of occurrence




10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400dσ

/dp t

,j1 [f

b / 1

00 G

eV]

pt,j1 [GeV]

pp, 14 TeV

LO

NLO

pt spectrum of leading jet gets K -factor of 5–10

related issues in Butterworth, Davison, Rubin & GPS ’08

Bauer & Lange ’09; Denner, Dittmaier, Kasprzik & Much ’09




10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400dσ

/dH

T,je

ts [f

b / 1

00 G

eV]

HT,jets [GeV]

pp, 14 TeV

LO

NLO

HT ,jets ≡∑

i∈jets pt,iHT ,jets ≡∑

i∈jets pt,iHT ,jets ≡∑

i∈jets pt,i gets K -factor of up to 100

Such things are not supposed to happen with αs = 0.1!


Why the large K -factors?[Introduction]

Leading Order

αsαEW

Next-to-Leading Order

α2sαEW

LHC probes scales well above EW scale,√s ≫ MZ .

EW bosons are light. New log-enhanced topologies appear.

HT ,jets is extreme, because at LO HT ,jets ≃ pt,jet 1; NLO: HT ,jets ≃ 2pt,jet 1G. Salam (CERN/Princeton/LPTHE) Giant K -factors 2011-02-02 4 / 16


Leading Order

αsαEW


α2sαEW





Leading Order

αsαEW


α2sαEW ln2

pt

MZ





Leading Order

αsαEW


α2sαEW ln2

pt

MZ





Leading Order

αsαEW


α2sαEW ln2

pt

MZ




We calculated Z+jet@NLO.

But giant K-factors are dominated by “LO” Z+2-partonpiece of Z+jet@NLO.

We know LO calculations aren’t reliable.

We’d ideally want to combine Z+jet@NLO withZ+2-jet@NLO

without double counting

without having to do full Z+jet@NNLO calculation


First try something simpler:

Take the “leading” process[Z + jet @ LO]

and add in process with one extra jet.

[i.e. include Z + 2 jets @ LO]

approximate the 1-loop Z+jet term, by requiringcancellation of all divergences

[those from singly unresolved limit of Z + 2 jets]


The LoopSim idea: n̄LO[LoopSim]

[The idea]

p3

p1

p2

Z + 2 partons

|M2(p1, p2, p3)|

◮ Identify softest or most collinear parton [with help of a jet algorithm]

◮ “Loop” it ≡ remove it from event, reshuffle other momenta;weight of looped event is (−1)× weight of tree-level event



[The idea]

p3

p1

p2

softest

Z + 2 partons

|M2(p1, p2, p3)|





[The idea]

p3

p1

p2

softest

Z + 2 partons

|M2(p1, p2, p3)|

+

~

~p1

p2

looped

Z + 1 parton + 1 sim. loop

−−−|M2(p1, p2, p3)|





[The idea]

p3

p1

p2

softest

Z + 2 partons

|M2(p1, p2, p3)|

+

~

~p1

p2

looped

Z + 1 parton + 1 sim. loop

−−−|M2(p1, p2, p3)|



This cancels all the “single-unresolved” divergences in the Z+2 events


n̄LO results (K -factors, normalised to LO)[LoopSim]

[The idea]

ptptpt of Z-boson ptptpt of jet 1 HT, jets =∑

jets pt,jHT, jets =∑


jets pt,j

0.5

1

1.5

2

2.5

3

250 500 750 1000 1250

K-f

acto

r w

rt L

O

pt,Z (GeV)

MCFM 5.7, CTEQ6Mpp, 14 TeV

anti-kt, R=0.7pt,j1 > 200 GeV

LONLO–nLO (µ dep)–nLO (RLS dep)

0

2

4

6

8

10

250 500 750 1000 1250

K-f

acto

r w

rt L

O

pt,j1 (GeV)



LONLO–nLO (µ dep)–nLO (RLS dep)

1

10

100

1000

500 1000 1500 2000 2500

K-f

acto

r w

rt L

O

HT,jets (GeV)

MCFM 5.7, CTEQ6Mpp, 14 TeVanti-kt, R=0.7pt,j1 > 200 GeV

LONLO

–nLO (µ dep)–nLO (RLS dep)

When the K -factors are large, n̄LO agrees well with NLO

MLM matching also does a similar job

cf. de Aquino, Hagiwara, Li & Maltoni ’11


Differences between and LoopSim andMLM/CKKW matching:

1. Does not rely on shower (✓: simplicity; ✗: not easilyintegrated with shower MCs)

2. Does not need arbitrary separation of Z+1/Z+2/etc.

samples with (hard-to-choose) momentum cutoff

3. Can easily be extended beyond LO matching


n̄n̄LO and n̄NLO[LoopSim]

[n̄NLO]

add tree-level Z+3,cancel divergences in single + doubly unresolved limits: n̄n̄LO

p4p3

p1

p2

|M2(p1, p2, p3, p4)|



[n̄NLO]


p4p3

p1

p2

|M2(p1, p2, p3, p4)|

+

p4~

~

~p1

p2

−|M2(p1, p2, p3, p4)|

+

~

~

~

p3

p1

p2

−|M2(p1, p2, p3, p4)|

+

provides approximation of 1-loop



[n̄NLO]


p4p3

p1

p2

|M2(p1, p2, p3, p4)|

+

p4~

~

~p1

p2

−|M2(p1, p2, p3, p4)|

+

~

~

~

p3

p1

p2

−|M2(p1, p2, p3, p4)|

+

~

~p1

p2

+|M2(p1, p2, p3, p4)|

provides approximation of 1-loop and 2-loop contributions; total sums to zero



[n̄NLO]


p4p3

p1

p2

|M2(p1, p2, p3, p4)|

+

p4~

~

~p1

p2

−|M2(p1, p2, p3, p4)|

+

~

~

~

p3

p1

p2

−|M2(p1, p2, p3, p4)|

+

~

~p1

p2

+|M2(p1, p2, p3, p4)|

provides approximation of 1-loop and 2-loop contributions; total sums to zero

add in (exact Z+2 @ 1-loop) − (approximate Z+2 @ 1-loop)+ extra simulated 2-loop piece to cancel new Z+2@1-loop divergences

This is n̄NLO

allows combination of Z+1@NLO with Z+2@NLOG. Salam (CERN/Princeton/LPTHE) Giant K -factors 2011-02-02 10 / 16

Testing NLO Merging, in 3 processes

1. Z@NLO with Z+j@NLO

2. Z+j@NLO with Z+2j@NLO

3. 2j@NLO with 3j@NLO


Validation: Drell-Yan lepton pt , n̄NLO v. NNLO[n̄NLO results]

[Drell-Yan]

n̄LO v. NLO

102

103

104

105

0 10 20 30 40 50 60 70 80 90 100

dσ/d

p t,m

ax [f

b/G

eV]

pt,max [GeV]

pp, 14 TeV66 < me+e- < 116 GeV

LO

NLO–nLO

Z (i.e. DY) with Z+j from MCFM & LoopSim

For pt ell &12MZ + ΓZ (giant K -factor!) it had to work

For pt,ℓ .12MZ + ΓZ it’s remarkable that it still works


[Drell-Yan]

n̄LO v. NLO n̄NLO v. NNLO

102

103

104

105

0 10 20 30 40 50 60 70 80 90 100

dσ/d

p t,m

ax [f

b/G

eV]

pt,max [GeV]

pp, 14 TeV66 < me+e- < 116 GeV

LO

NLO–nLO

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

10 20 30 40 50 60 70 80 90 100K

fact

or w

rt N

LOpt,max [GeV]

pp, 14 TeV66 < me+e- < 116 GeV

NLO–nNLO (µ dep)–nNLO (RLS dep)

NNLO

NNLO from DYNNLO, Z (i.e. DY) with Z+j from MCFM & LoopSim




[Drell-Yan]

n̄LO v. NLO n̄NLO v. NNLO

102

103

104

105

0 10 20 30 40 50 60 70 80 90 100

dσ/d

p t,m

ax [f

b/G

eV]

pt,max [GeV]

pp, 14 TeV66 < me+e- < 116 GeV

LO

NLO–nLO

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

10 20 30 40 50 60 70 80 90 100K

fact

or w

rt N

LOpt,max [GeV]

pp, 14 TeV66 < me+e- < 116 GeV

NLO–nNLO (µ dep)–nNLO (RLS dep)

NNLO

NNLO from DYNNLO, Z (i.e. DY) with Z+j from MCFM & LoopSim



n̄NLO for Z+j observables[n̄NLO results]

[Z+jet]

ptptpt of Z-boson

0.5

1

1.5

2

2.5

3

250 500 750 1000 1250

K-f

acto

r w

rt L

O

pt,Z (GeV)



LONLO–nNLO (µ dep)–nNLO (RLS dep) ◮ ptZ distribution didn’t have

giant K -factors.

◮ n̄NLO brings no benefitTo get improvement you would

need exact 2-loop terms



[Z+jet]

ptptpt of jet 1

0

2

4

6

8

10

250 500 750 1000 1250

K-f

acto

r w

rt L

O

pt,j1 (GeV)



LONLO–nNLO (µ dep)–nNLO (RLS dep) ◮ ptj distribution seems to

converge at n̄NLO

◮ scale uncertainties reduced by∼ factor 2



[Z+jet]

HT, jets =∑



jets pt,j

1

10

100

1000

500 1000 1500 2000 2500

K-f

acto

r w

rt L

O

HT,jets (GeV)

MCFM 5.7, CTEQ6Mpp, 14 TeVanti-kt, R=0.7pt,j1 > 200 GeV

LONLO

–nNLO (µ dep)–nNLO (RLS dep)

◮ Signficiant furtherenhancement for HT ,jets

◮ n̄NLO brings clear message:

HT ,jetsHT ,jetsHT ,jets is not a goodobservable!


What’s the problem with HT?[n̄NLO results]

[Z+jet]

HTHTHT (effective mass) type observables are widely used in searches

◮ HT has a steeply falling distribution (like ptj , ptZ )

◮ At each order (NLO, NNLO), an extra (soft) jet contributes to theHT sum e.g. from ISR

◮ That shifts HT up, which translates to a substantial increase in thecross section

We can test this hypothesis for plain jet events, using a truncated sum,

HT ,n =n∑

i=1

pt,jet i


HT ,n in (di)jet events[n̄NLO results]

[dijets]

HT ,2HT ,2HT ,2 HT ,3HT ,3HT ,3 HT ,∞HT ,∞HT ,∞

0

0.5

1

1.5

2

2.5

3

100 200 300 400 500 600 700 800 900

ratio

to L

O (

x µ=

1)

12− HT,2 [GeV]

pp, 7 TeV, anti-kt R=0.7

NLOJet++, CTEQ6M

LONLO

–nNLO (µ)–nNLO (RLS) 0

0.5

1

1.5

2

2.5

3

100 200 300 400 500 600 700 800 900

ratio

to L

O (

x µ=

1)

12− HT,3 [GeV]


NLOJet++, CTEQ6M

LONLO

–nNLO (µ)–nNLO (RLS) 0

0.5

1

1.5

2

2.5

3

100 200 300 400 500 600 700 800 900

ratio

to L

O (

x µ=

1)

12− HT [GeV]


NLOJet++, CTEQ6M

LONLO

–nNLO (µ)–nNLO (RLS)

A clear message:for a process with n objects at lowest order, use HT ,n

Do you know what gets used in your experiment’s searches?

Many writers of LHC SUSY proceedings didn’t...


Some take-home messages[Closing]

Be aware that giant K -factors existAlways look one order beyond the leading order, for example with

MLM/CKKW matching

New tool to get good predictions in such cases: LoopSimBasically an “operator” to generate approximations to unknown loops

Combine Z+j@NLO, Z+2j@NLO to get “n̄NLO” Z+jet

It sometimes works even beyond “giant-K -factor” regions

Watch out for HT

Even for simple processes, it converges very poorly

unless you define it carefully (limit number of objects in sum)


EXTRAS


Add Z+1jet, Z+2jet + shower[Extras]

[How MLM works]

Z+parton



[How MLM works]

shower Z+parton



[How MLM works]

Z+2partons

+

shower Z+parton



[How MLM works]

shower Z+2partons

+

shower Z+parton



[How MLM works]

showergenerates hard gluon

of Z+parton

v.

shower Z+2partons

+

shower Z+parton



[How MLM works]


of Z+parton

v.

shower Z+2partons

+

shower Z+parton



[How MLM works]

DOUBLECOUNTING


of Z+parton

v.

shower Z+2partons

+

shower Z+parton

Z + parton implicitly includes part of Z + 2 partons

It’s just that the 2nd parton isn’t always explicitly “visible”


cartoon of MLM merging of Z+j and Z+2j[Extras]

[How MLM works]


of Z+parton

v.

shower Z+2partons

+

shower Z+parton

◮ MLM merging relies on parton shower to help figure out what fraction ofZ + parton is really Z + 2 partons.

◮ Our aim is to do that without the parton shower



[How MLM works]

pt cut

Qmerge

ACCEPT ACCEPT REJECT


of Z+parton

v.

shower Z+2partons

+

shower Z+parton





[How MLM works]

pt cut

Qmerge

ACCEPT ACCEPT REJECT


of Z+parton

v.

shower Z+2partons

+

shower Z+parton




Testing Alpgen + Herwig + MLM Matching[Extras]

[MLM results]

ptptpt of Z-boson

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

p t,Z

[fb

/ 100

GeV

]

pt,Z [GeV]

pp, 14 TeV

LO

NLO



[MLM results]

ptptpt of Z-boson

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

p t,Z

[fb

/ 100

GeV

]

pt,Z [GeV]

pp, 14 TeV

LO

NLO

Alpgen+HW6 Z+jet



[MLM results]

ptptpt of Z-boson

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

p t,Z

[fb

/ 100

GeV

]

pt,Z [GeV]

pp, 14 TeV

LO

NLO

Alpgen+HW6 Z+jet

Alpgen+HW6 Z+jet/Z+2jets

All predictions similarand stable



[MLM results]

ptptpt of jet 1

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

p t,j1

[fb

/ 100

GeV

]

pt,j1 [GeV]

pp, 14 TeV

LO

NLO



[MLM results]

ptptpt of jet 1

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

p t,j1

[fb

/ 100

GeV

]

pt,j1 [GeV]

pp, 14 TeV

LO

NLO

Alpgen+HW6 Z+jet

Showered Z+j ≃ LO



[MLM results]

ptptpt of jet 1

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

p t,j1

[fb

/ 100

GeV

]

pt,j1 [GeV]

pp, 14 TeV

LO

NLO

Alpgen+HW6 Z+jet


Showered Z+j ≃ LO

Showered Z+j/Z+2j≃ NLO



[MLM results]

HT, jets =∑



jets pt,j

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

HT

,jets

[fb

/ 100

GeV

]

HT,jets [GeV]

pp, 14 TeV

LO

NLO



[MLM results]

HT, jets =∑



jets pt,j

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

HT

,jets

[fb

/ 100

GeV

]

HT,jets [GeV]

pp, 14 TeV

LO

NLO

Alpgen+HW6 Z+jet

Showered Z+j 6= LO



[MLM results]

HT, jets =∑



jets pt,j

10-2

10-1

1

10

102

103

104

200 300 400 500 600 700 800 900 1000

dσ/d

HT

,jets

[fb

/ 100

GeV

]

HT,jets [GeV]

pp, 14 TeV

LO

NLO

Alpgen+HW6 Z+jet


Showered Z+j 6= LO

Showered Z+j/Z+2j≃ NLO


Documents

LO NLO dist HTjets HAZ12 - lpthe.jussieu.frsalam/talks/repo/2011-giantK-Valencia.pdf · Gavin Salam CERN, Princeton & LPTHE/CNRS (Paris) Work performed with Mathieu Rubin and Sebastian