precision calculations for lhc physicsweb.physik.rwth-aachen.de/~mkraemer/mkraemer_dpg.pdf ·...

DPG Fruhjahrstagung, February 2008

Precision calculations for LHC physics

Michael Kramer (RWTH Aachen)

Sponsored by:

SFB/TR 9 “Computational Particle Physics”, Helmholtz Alliance “Physics at the Terascale”, BMBF-

Theorie-Verbund, Marie Curie Research Training Network “Heptools”, Graduiertenkolleg “Elemen-

tarteilchenphysik an der TeV-Skala”

Michael Kramer page 1 DPG Fruhjahrstagung 2008

Why precision calculations for discoveries?

We do not need theory input for LHC discoveries

8000

6000

4000

2000

080 100 120 140

mγγ (GeV)

Higgs signal

Eve

nts

/ 500

MeV

for

105

pb-

1

HSM γγ

Simulated 2γ mass plotfor 105 pb-1 mH =130 GeV

in the lead tungstate calorimeter

D_D

_105

5c

CMS, 105 pb-1

but only if we see a resonance. . .


Contents


– lessons from the past

– prospects: Higgs physics & BSM searches at the LHC

Theoretical tools for LHC phenomenology

– (N)NLO multi-leg calculations

– matching with parton showers & hadronization



Tevatron jet cross section at large ET

Et (GeV)-0.5

0

0.5

1(D

ata

- The

ory)

/ The

ory

200 300 40010050

CTEQ3MCDF (Preliminary) * 1.03D0 (Preliminary) * 1.01




Et (GeV)-0.5

0

0.5

1(D

ata

- The

ory)

/ The

ory

200 300 40010050


⇒ new physics? + ?




Et (GeV)-0.5

0

0.5

1(D

ata

- The

ory)

/ The

ory

200 300 40010050


LBSM ⊇g2

M2ψγµψ ψγµψ ⇒

data − theory

theory∝ g2 E

2T

M2




(GeV)TInclusive Jet E0 100 200 300 400 500 600

(nb/

GeV

)η

d T /

dEσ2

d

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-11

10

102

CDF Run II PreliminaryIntegrated L = 85 pb-1

0.1 < |ηDet| < 0.7JetClu Cone R = 0.7

Run II DataCTEQ 6.1 Uncertainty+/- 5% Energy Scale Uncertainty

⇒ just QCD. . . (uncertainty in gluon pdf at large x)



Tevatron bottom quark cross section

[D0, PLB 487 (2000)]

⇒ new physics?




[Berger et al., PRL 86 (2001)]

10-1

1

10

10 2

10 3

10 4

10 5

10 102

SumQCDg → b~

D0 Data

CDF Data

√S = 1.8 TeV

mg = 14 GeV

mb = 3.5 GeV

mb = 4.75 GeV

~

~

pT (GeV)min

σ b(p T

≥ p

T )

(nb

)m

in

⇒ light gluino/sbottom production?




[Mangano, AIP Conf.Proc, 2005]

⇒ just QCD. . . (αs, low-x gluon pdf, b→ B fragmentation & exp. analyses)



Signals of discovery include

– mass peaks

– anomalous shapes of kinematic distributions

e.g. jet production at large ET

– excess of events after kinematic selection

e.g. bottom cross section




– mass peaks

– anomalous shapes of kinematic distributionse.g. jet production at large ET

– excess of events after kinematic selectione.g. bottom cross section




– mass peakse.g. Higgs searches in H → γγ/ZZ∗ final states

– anomalous shapes of kinematic distributionse.g. SUSY searches in multijet + ET,miss final states

– excess of events after kinematic selectione.g. Higgs searches in H → WW ∗ final states

Experiments measure multi-parton final states in restricted phase space region

→ Need flexible and realistic precision calculations

– precise → including loops & many legs

– flexible → allowing for exclusive cross sections & phase space cuts

– realistic → matched with parton showers and hadronization


Searches at the LHC: outline

Examples from Higgs physics

– discovery from excess of events: pp→ H → WW ∗ → l+νl−ν

– backgrounds: beware of cuts

– beyond discovery: measuring Higgs couplings

Examples from beyond the standard model physics

– anomalous shapes: SUSY searches with multi-jets + ET,miss signatures

– backgrounds: multi-leg calculations needed

Theoretical tools for LHC physics

– LO and NLO multi-leg calculations

– matching with parton showers and hadronization



Examples from Higgs physics




• Examples from beyond the standard model physics



• Theoretical tools for LHC physics




Searches at the LHC: pp → H → WW ∗→ l+νl−ν

g

g

H

W−

W+

ν

l−

l+

ν

– neutrinos in final state

→ no invariant Higgs mass peak

– large background from QCD

process qq → WW

– exploit lepton rapidity distributions

and angular correlations to sup-

press background(Dittmar, Dreiner) 0

100

200

300

0 50 100 150 200 250

mT (GeV)

Eve

nts

/ 5 G

eV

⇒ a precise theoretical description of the background is crucial



LO background from qq scattering

��

��

��

� � ��

� �

��

��

��

� � ��

experimental selection cuts may enhance the importance of higher-order

corrections for background processes: gg → WW → lνl′ν′

[Binoth, Ciccolini, Kauer, MK; Duhrssen, Jakobs, van der Bij, Marquard]

W−

W+

γ, Z

ν

`

W+γ, Z, H

g

gq

q

q

g

gq

q

q

g

gd

d u

W−d

W+

ν ′

¯′

`

ν

`

ν

ν ′

¯′

ν ′

¯′

→ formally NNLO

→ but enhanced by Higgs search cuts

gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%




��

��

��

� � ��

��

��

��

��

� � ��




W−

W+

γ, Z

ν

`

W+γ, Z, H

g

gq

q

q

g

gq

q

q

g

gd

d u

W−d

W+

ν ′

¯′

`

ν

`

ν

ν ′

¯′

ν ′

¯′

→ formally NNLO


gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%




��

!

"�# $

! # %&�

'()

��

!

"�# $

! # %&�




W−

W+

γ, Z

ν

`

W+γ, Z, H

g

gq

q

q

g

gq

q

q

g

gd

d u

W−d

W+

ν ′

¯′

`

ν

`

ν

ν ′

¯′

ν ′

¯′

→ formally NNLO


gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%




*�+*�,

-.-

/+0 1

. 0 23,

456

*+*�,

-.-

/+0 1

. 0 23,




W−

W+

γ, Z

ν

`

W+γ, Z, H

g

gq

q

q

g

gq

q

q

g

gd

d u

W−d

W+

ν ′

¯′

`

ν

`

ν

ν ′

¯′

ν ′

¯′

→ formally NNLO


gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%



• Examples from Higgs physics




Examples from beyond the standard model physics



• Theoretical tools for LHC physics




Searches at the LHC: BSM physics

Many model for new physics are addressing two problems:

– the hierarchy/naturalness problem

– the origin of dark matter

→ spectrum of new particles at the TeV-scale with weakly interacting & stable particle

→ generic BSM signature at the LHC involves cascade decays with missing energy,

eg. supersymmetry

D_D

_204

7.c.

1

q

q

q

q

q~

~

~

~

—

—

—b

b

l+

l+

g

~g

W— W+t

t

t1

ν

χ1

~χ10

~χ20

Gluino/squark production event topology al lowing sparticle mass reconstruction

3 isolated leptons+ 2 b-jets+ 4 jets

+ Etmiss

~l

+

l-

Such cascade decays allow to reconstructsleptons, neutralinos, squarks, gluinos...in favorable cases with %level mass resolutions



• simple discriminant for SUSY

searches: effective mass

Meff = ET,miss +∑4

i=1 pjetT

• excess of events with large Meff

→ initial discovery of SUSY

LHC Point 5

10-13

10-12

10-11

10-10

10-9

10-8

10-7

0 1000 2000 3000 4000Meff (GeV)

dσ/d

Mef

f (m

b/40

0 G

eV)



• simple discriminant for SUSY

searches: effective mass

Meff = ET,miss +∑4

i=1 pjetT

• excess of events with large Meff

→ initial discovery of SUSY

Modern LO Monte Carlo tools predict much larger multi-jet background

What will disagreement between Monte Carlo and data mean?

→ Need precision NLO calculations to tell!



• Examples from Higgs physics




• Examples from beyond the standard model physics








Need flexible and realistic precision calculations

– precise → including loops & many legs

– flexible → allowing for exclusive cross sections & phase space cuts

– realistic → matched with parton showers and hadronization

Mini review of current status for LHC QCD multi-leg

– LO calculations

– LO calculations & parton showers

– NLO calculations

– NLO calculations & parton showers

Note: focus on QCD tools for LHC cross section predictions. Do not cover important QCD and elec-

troweak precision calculations for masses, couplings, decays and renormalization group evolutions in

the SM and beyond. . .


LO calculations

Automation of LO calculations: several program packages exist for the automatic calcu-

lation of generic 2 → N cross sections (N ≤ 8) including integration over phase space:

HELAC/PHEGAS, MADGRAPH/MADEVENT, COMPHEP, GRACE, SHERPA/AMEGIC,

O’MEGA/WHIZARD, ALPGEN, ...

→ Non-trivial achievement:

consider number of Feynman graphs e.g. for gg → N gluons:

N jets 2 3 4 5 6 7 8

# diag’s 4 25 220 2485 34300 5 × 105 107


LO calculations

Automation of LO calculations: several program packages exist for the automatic calcu-

lation of generic 2 → N cross sections (N ≤ 8) including integration over phase space:

HELAC/PHEGAS, MADGRAPH/MADEVENT, COMPHEP, GRACE, SHERPA/AMEGIC,

O’MEGA/WHIZARD, ALPGEN, ...

→ matrix element calculations crucial for the description of multi-leg processes:

(Mangano)

11

Exact, LO matrix

element estimate

Shower MC result

N.B . R eliability/system atics of M C tools: Shower M C vs M atrix elem ent results


LO calculations with parton showers & hadronization

Include parton showers and hadronization to sum soft/collinear parton emission

and predict realistic final states

→ Beware of double counting: N -jet cross section from 2 → N parton process or from 2 →

N − (1, 2, . . .) parton process plus parton shower

→ Construct matching schemes: CKKW-L (Catani, Kuhn, Krauss, Webber; Lonnblad), MLM (Mangano), SCET (Bauer,

Schwarz), implemented in HELAC, MADGRAPH, SHERPA, ARIADNE, ALPGEN

(Alwell et al.)

dσ/d

E⊥

1 (p

b/G

eV)

(a)Alpgen

AriadneHelac

MadEventSherpa

10-2

10-1

100

101

102

E⊥1 (GeV)

-1-0.5

0 0.5

1

0 50 100 150 200 250 300 350 400 450 500

dσ/d

E⊥

2 (p

b/G

eV)

(b)

10-2

10-1

100

101

102

E⊥2 (GeV)

-1-0.5

0 0.5

1

0 50 100 150 200 250 300 350 400

dσ/d

E⊥

3 (p

b/G

eV)

(c)

10-3

10-2

10-1

100

101

E⊥3 (GeV)

-1-0.5

0 0.5

1

0 50 100 150 200 250 300

dσ/d

E⊥

4 (p

b/G

eV)

(d)

10-3

10-2

10-1

100

101

E⊥4 (GeV)

-1-0.5

0 0.5

1

0 50 100 150 200

Validation, systematic comparison & tuning of MC tools crucial


NLO calculations

Want to test & explore models, eg. measure Higgs couplings

[Duhrssen et al.]

→ ratios of Higgs couplings can be measured with an accuracy of 10-30%

→ must be matched by theoretical accuracy in cross section and BR predictions


NLO calculations

An accuracy δσ/σ ∼< 20% is only possible at NLO or beyond!

for example σ(pp→ ttH) ∝ g2ttH

[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]

σ(pp → tt_ H + X) [fb]

√s = 14 TeV

MH = 120 GeV

µ0 = mt + MH/2

NLO

LO

µ/µ0

0.2 0.5 1 2 5200

400

600

800

1000

1200

1400

1

⇒ δσ/σ ≈

{

100% LO

15% NLO


NLO calculations

cross sections are obtained from counting events after selection cuts

→ need acceptance and efficiency

→ need flexible (N)NLO calculations

modern (N)NLO calculations are set up as parton-level Monte Carlo programs

– e.g. at NLO using (dipole) subtraction [Catani, Seymour, Dittmaier, Trocsanyi, . . . ]

σNLO

=

Z

dPSm+1

»

dσreal

−dσsub

–

| {z }

finite

+

Z

dPSm

»

dσvirtual

+dσsub1

–

| {z }

finite

⇒ parton-level events (4-momenta) with positive or negative weights

– recent progress at NNLO, e.g. for Higgs production [Anastasiou, Melnikov, Petriello; Grazzini]

Note: (N)NLO parton-level Monte Carlo programs are not parton shower event generators

– they do not include parton showers and hadronization

– they do not generate unweighted events


(QCD-) NLO calculations at the LHC: status

2 → 2: anything you want. . . (cf. MCFM (Campbell, Ellis, . . . ))

2 → 3: pp → jjj (Bern, Dixon, Kosower; Kunszt, Signer, Troscanyi; Giele, Kilgore, Nagy)

pp → V jj (Campbell, Glover, Miller)

pp → Hjj[GF] (Campbell, Ellis, Zanderighi)

pp → Htt (Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas; Dason, Reina, Wackeroth, Orr, Jackson;)

pp → γγj (de Florian, Kunszt; Del Duca, Maltoni, Nagy, Troscani, Binoth, Guillet, Mahmoudi)

pp → Hjj(j)[WBF] (Figy, Hankele, Oleari, Zeppenfeld)

pp → HHH (Plehn, Rauch; Binoth, Karg, Kauer, Ruckl)

pp → V V jj[WBF] (Jager, Oleary, Zeppenfeld)

pp → ZZZ (Lazopoulos, Melnikov, Petriello)

pp → WWZ (Hankele, Zeppenfeld)

pp → ttj (Dittmaier, Uwer, Weinzierl)

pp → V V j (Dittmaier, Kallweit, Uwer; Campbell, Ellis, Zanderighi; Binoth, Guillet, Karg, Kauer, Sanguinetti)

2 → 4: no LHC process yet. . .


An experimenters wishlist. . .

Theorists reply: In your dreams. . .



Main bottleneck for multi-leg NLO calculations:

tensor-reduction of Pentagon/Hexagon/Heptagon loop integrals, e.g.

77

89

:8

;:;

89

:8

<=> ?

With current techniques

pp→ 3 partons @ NLO is “straightforward but tedious”

pp→ 4 partons @ NLO is possible

Need breakthrough in technology for pp→ 4 partons @ NLO

spinors & twistors, on-shell methods. . . ?

⇒ NLO (parton-level) Monte Carlo programs will not be available for all potentially

relevant (background) processes in the near future





@@

AB

CA

DCD

AB

CA

EFG H












II

JK

LJ

MLM

JK

LJ

NOP Q









Need for NNLO at the LHC?

NNLO calculations are needed

– for high-precision measurements (αs, MW , pdf’s,. . . )

– if there are large corrections & scale dependence at NLO, eg. for gg → H

– if NLO accuracy is reduced after cuts:

Ht

g

g

g

is

{

NLO for σinclusive

LO for dσ/dpT


Need for NNLO at the LHC?

NNLO calculations are needed

– for high-precision measurements (αs, MW , pdf’s,. . . )

– if there are large NLO corrections & scale dependence, eg. for gg → H

– if NLO accuracy is reduced after cuts:

(Anastasiou, Dissertori, Stockli)


NLO calculations with parton showers & hadronization



Fixed-oder calculations have limitations

– they do not predict realistic final states

experimentally theoretically at LO




– they do not predict realistic final states

experimentally theoretically at NLO




– they break down for certain kinematic configurations

[MK, Mrenna, Soper]

-0.1

0

0.1

0 5 10 15 20

e+e– → 3 jets: jet-mass distribution df3/dM [GeV-1]

NLO

(√s = MZ; µ = √s/6, kT algorithm, ycut = 0.05)

M [GeV]

⇒ wrong jet structure for M → 0




⇒ add parton showers → summation of multi-parton emission

[MK, Mrenna, Soper]

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20

e+e– → 3 jets: jet-mass distribution f -13 df3/dM [GeV-1]

NLO+Pythia

NLO

(√s = MZ; µ = √s/6, kT algorithm, ycut = 0.05)

M [GeV]

⇒ realistic jet structure and accurate (NLO) prediction for rate



NLO⊕PS matching formalism

– avoid double counting: parton showers include part of the short-distance physics already

included in the NLO calculation

– various schemes have been proposed (Frixione, Webber, Nason, Oleari, Collins, Zu, Soper,MK, Nagy, Weinzierl, Giele, Kosower, Skands, Bauer, Schwarz,. . . )

MC@NLO (Frixione, Webber, . . . ) is still top of the class

– well tested and supported

– includes many processes: pp → V, H, ll, lν, QQ, HV, single top, V V

(Near?) future: variety of general NLO⊕PS matching formalisms

– independent of specific shower algorithm → combine NLO with any MC

– in terms of commonly used dipole subtraction formalism→ easy to use for NLO practitioner

Note: There are also new development in parton showers designed for NLO matching and showersincluding quantum interference (Gieseke, Stephens, Webber, Seymour, Siodmok,. . . ; Sjostrand, Skands,. . . ; Nagy, Soper; Dinsdale,

Ternick, Weinzierl, Schumann, Krauss; Giele, Kosower)


Conclusions & outlook . . .

Signal cross sections in the SM and MSSM are (or will rather soon be) known at

NLO accuracy

– theoretical uncertainty ≈ 15% for inclusive cross sections

– larger uncertainty for exclusive observables

– can predict distributions and observables with cuts

– in general no parton showers/hadronization

Progress in matching (N)LO calculations with parton showers and hadronization

Many backgrounds (multi-leg processes) are only know at LO

(Need breakthrough in techniques to do pp→> 4 partons at NLO)

First LHC data will allow us to focus on the relevant processes. . .


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