Precision calculations for LHC physicsmkraemer/mkraemer_psi.pdf · 2009-06-18 · Why precision...

Colloquium PSI, Mai 2009

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”page 1

Why precision calculations for LHC physics?

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. . .

page 2

Contents


– lessons from the past

– prospects: Higgs & BSM searches

Theoretical tools for LHC phenomenology

– (N)NLO multi-leg calculations

– matching with parton showers & hadronization

page 3

Contents




Theoretical tools for LHC phenomenology

talking about theoretical tools at PSI:

carrying coals to Newcastle. . .

page 4

Contents




page 5


Tevatron jet cross section at large ET

Et (GeV)

-0.5

0

0.5

1

(Dat

a -

The

ory)

/ The

ory

200 300 40010050

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

page 6



Et (GeV)

-0.5

0

0.5

1

(Dat

a -

The

ory)

/ The

ory

200 300 40010050


⇒ new physics? + ?

page 7



Et (GeV)

-0.5

0

0.5

1

(Dat

a -

The

ory)

/ The

ory

200 300 40010050


LBSM ⊇g2

M2ψγµψ ψγµψ ⇒

data − theory

theory∝ g2 E

2T

M2

page 8



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

(n

b/G

eV)

η d

T /

dE

σ2d

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

102

CDF Run II Preliminary

Integrated L = 85 pb-1

0.1 < |ηDet| < 0.7

JetClu Cone R = 0.7

Run II Data

CTEQ 6.1 Uncertainty

+/- 5% Energy Scale Uncertainty

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

page 9


Tevatron bottom quark cross section

[D0, PLB 487 (2000)]

⇒ new physics?

page 10



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

10-1

1

10

10 2

10 3

10 4

10 5

10 102

Sum

QCD

g → 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?

page 11



[Mangano, AIP Conf.Proc, 2005]

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

page 12


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

page 13



– mass peaks

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

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

page 13



– 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

page 14

Searches at the LHC: outline

Examples from Higgs physics

– discovery from excess of events: pp→ H → WW

pp→ ttH→ be aware of backgrounds. . .

Examples from beyond the standard model physics:

BSM searches with multi-jet + ET,miss signatures

– no excess over SM expectations

→ exclude models / set limits on model parameters

– excess in inclusive jets + ET,miss signal (early LHC phase)

→ discriminate BSM models

– exploring BSM models (later LHC phase)

→ determine masses & spins

page 15

Higgs searches at the LHC: be aware of backgrounds

pp→ H → WW

• pp→ ttH

page 16

Higgs 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

page 17


LO background from qq scattering

��

��

��

� � ��

� �

��

��

��

� � ��

experimental selection cuts may enhance the importance of higher-order

corrections for background processes: gg → WW → lν l′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

qq (NLO) gg corr.

σtot 1373 fb 54 fb 4%

σbkg 4.8 fb 1.39 fb 30%

page 18



��

��

��

� � ��

� �

��

��

��

� � ��


corrections for background processes:

gg → WW → lν l′ν ′


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


qq (NLO) gg corr.

σtot 1373 fb 54 fb 4%

σbkg 4.8 fb 1.39 fb 30%

page 18



��

��

��

� � ��

� �

��

��

��

� � ��


corrections for background processes: gg → WW → lν l′ν ′


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


qq (NLO) gg corr.

σtot 1373 fb 54 fb 4%

σbkg 4.8 fb 1.39 fb 30%

page 18

Higgs searches at the LHC: be aware of backgrounds

• pp→ H → WW

pp→ ttH

page 19

Higgs searches at the LHC: pp → ttH(→ bb)

g

g

H0t–,t

t

t–

b

b–

b

b–

W+

W-

q

q–'

l

ν–

+ ...

– small cross section: σ(ttH)/σ(H + X) ≈ 1/100

→ only relevant for MH ∼< 140 GeV

– distinctive final state: pp → t(→ W+b) t(→ W−b) H(→ bb)

– cross section ∝ g2ttH

→ unique way to measure top-Higgs Yukawa coupling

page 20


theoretical uncertainty of signal ≈ 20% at NLO

[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

page 21


invariant mass spectrum

[CMS (Benedetti et al.)]

Note N233

b-likelihood cut

0 0.1 0.2 0.3 0.4 0.5

b-likelihood cut

0 0.1 0.2 0.3 0.4 0.5

BS

/

0

0.5

1

1.5

2

2.5

3

= 115 GeVHm

= 120 GeVHm

= 130 GeVHm

b-likelihood cut

0 0.1 0.2 0.3 0.4 0.5

b-likelihood cut

0 0.1 0.2 0.3 0.4 0.5

S/B

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Figure 8. Significance (left) and purity (right), prior to inclusion of systematic uncertainties, for

three different Higgs boson masses (115, 120 and 130 GeV/c2) as a function of the cut on the

b-tagging likelihood LbTag, for an integrated luminosity of 60 fb−1 for the semi-leptonic (muon

and electron) ttH decay channel. No mass window requirement has been applied. The error bars

indicate the statistical error due to the finite sizes of datasets. Bin-to-bin correlations also occur

here because of the sliding cut on the b-tagging likelihood.

]2Higgs mass [GeV/c

0 50 100 150 200 250 300 350

2#

eve

nts

pe

r 2

0 G

eV

/c

0

5

10

15

20

25

]2Higgs mass [GeV/c

0 50 100 150 200 250 300 350

2#

eve

nts

pe

r 2

0 G

eV

/c

0

50

100

150

200

250

300

350ttH 115ttNj

ttbb

ttZ

Figure 9. Invariant Higgs boson mass spectrum for an LbTag cut of 0.225 and mH = 115 GeV/c2,

after an integrated luminosity of 60 fb−1. Only signal events are shown at left. The combinatorial

background is shaded grey. The plot at the right adds all relevant physical backgrounds (ttZ, ttbb

and ttN j) to the ttH signal (including the combinatorial background). The contributions from all

sources are stacked on top of each other.

physical backgrounds (ttZ, ttbb and ttN j) and the ttH signal stacked on top of each other.

Due to the limited amount of available Monte Carlo statistics for the ttN j background and the

large scale factors that have to be applied to the remaining events, the statistical fluctuations

in figure 9 are large.

The preselection and selection efficiencies, together with the corresponding numbers of

expected events and signal significances, prior to consideration of systematic uncertainties,

are reported in table 4 for the channel with a muon or an electron in the final state. The table

presents results for two working points: a ‘loose’ working point, which optimizes S/√

B, and

a ‘tight’ working point, which optimizes the purity S/B.

Thus far, no mass window requirement has been used. If one applies the requirement

mH < 150 GeV/c2, the purity can be increased by about 10%, while the significance does

not change appreciably. This improvement is very minor because the shape of the Higgs

⇒ similar shapes for signal and background (tt + n jets, ttbb, ttZ)

→ counting experiment

→ precise knowledge of event rates required

page 22


need to know backgrounds much better than 10%!

[CMS (Benedetti et al.)]

→ try to determine reducible backgrounds from data

→ need accurate theory to extrapolate into signal region

page 23


pp→ ttbb+X at NLO [Bredenstein, Denner, Dittmaier, Pozzorini ’09]

NLOLO

σ [fb]

µ0/2 < µ < 2µ0

mt = 172.6 GeV

pp→ ttbb + X

mbb, cut

[GeV]

20018016014012010080604020

10000

1000

100

10

page 24

Searches at the LHC: outline

• Examples from Higgs physics

– discovery from excess of events: pp→ H → WW

pp→ ttH→ be aware of backgrounds. . .

Examples from beyond the standard model physics:

BSM searches with multi-jets + ET,miss signatures

– no excess over SM expectations


– excess in inclusive jets + ET,miss signal (early LHC phase)


– exploring BSM models (later LHC phase)


page 25

BSM searches at the LHC

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

page 26


• 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)

page 27


• 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!

page 28

Precision calculations for BSM physics at the LHC

no excess over SM expectations


excess in inclusive jets + ET,miss signal (early LHC phase)


exploring BSM models (later LHC phase)


page 29




)2

(GeV/cg~

M0 100 200 300 400 500 600

)2 (

GeV

/cq~

M

0

100

200

300

400

500

600CDF Run II Preliminary -1L=2.0 fb

no mSUGRAsolution

LEP 1 + 2

UA

1

UA

2

FNAL Run I

g~

= M

q~M

)2

(GeV/cg~

M0 100 200 300 400 500 600

)2 (

GeV

/cq~

M

0

100

200

300

400

500

600observed limit 95% C.L.

expected limit

<0µ=5, β=0, tan0A

Theoretical uncertainties includedin the calculation of the limit

page 30




] 2 [GeV/cg~

M250 300 350 400 450

NL

O C

ross

Sec

tio

n [

pb

]

-210

-110

1

10 NLO: PROSPINO CTEQ6.1M

Ren.)⊕syst. uncert. (PDF observed limit 95% C.L.

expected limit 95% C.L.

q~ = M

g~M

CDF Run II PreliminaryTheoretical uncertainties not included

in the calculation of the limit

-1L=2.0 fb

page 31




Prospino: PROduction of Suspersymmetric Particles In NlO[Beenakker, Hopker, MK, Plehn, Spira, Zerwas (’95-’08)]

page 32




“look-alike models” (Hubisz, Lykken, Pierini, Spiropulu)

]

2m

ass

[GeV

/c

0

100

200

300

400

500

600

700

800

900

1000LH2 NM6 NM4 CS7

HA

HWHZ

HidH

iu

0

1χ∼

±1

χ∼0

2χ∼

Rd~Lu~Ru~Ld~

g~

1τ∼ Rl~

0

1χ∼

±1

χ∼0

2χ∼

Ru~Rd~Lu~

1τ∼Ld~Rl

~

g~

0

1χ∼

1τ∼Rl~

±1

χ∼0

2χ∼

g~

Rd~ Ru~Lu~

Ld~

– Little Higgs model LH2 and

SUSY models NM4 and CS7

give same number of events

after cuts

– “twin models” LH2 and NM6

(SUSY) have different cross

sections and event counts

→ distinguish models with

same spectrum but different

spins through event count

page 33




“ancient wisdom”: cross sections depend on spin, e.g.

q + q → q + ¯q

σLO[qq → q¯q] =α2

sπ

s

4

27β3 (β2 = 1 − 4m2/s)

c.f. top production:

σLO[qq → QQ] =α2

sπ

s

8

27

(s+ 2m2)

s2β

→ σtop/σstop ∼ 10 at the Tevatron

page 34




“ancient wisdom”: cross sections depend on spin

(Kane, Petrov, Shao, Wang)

160 170 180 190 200mass HGeVL

0.5

1

5

10

50

100

CrossSection

HpbL

tst�s

tt�

CDFD0

→ no production of scalar quarks (assuming same mass and couplings as top. . . )

page 35




how to discriminate “look-alike models”? (Hubisz, Lykken, Pierini, Spiropulu)

(GeV/c)T

p0 100 200 300 400 500 600 700 800 900 1000

num

ber

of e

vent

s

0

200

400

600

800

1000

1200

1400– consider ratios of event counts, e.g.

σ(pT > 250, 500, . . . GeV)/σ

→ systematic uncertainties cancel

→ normalization important

– NLO affects shape of distributions:

K ≡σNLO(pp → tt)

σLO(pp → tt)

=

1.4 (pT > 100 GeV)

0.5 (pT > 1000 GeV)

→ no proper tools to perform realistic NLO analysis of BSM decay chains

page 36




Mass measurements from cascade decays, e.g.�

�

��

��

��

�

��

��

Allanach et al.

0

500

1000

1500

0 20 40 60 80 100 m(ll) (GeV)

Eve

nts/

1 G

eV/1

00 fb

-1→ kinematic endpoint (mmax

ll )2 = (m2χ0

2

−m2

lR)(m2

lR−m2

χ01

)/(m2

lR)

sensitive to mass differences

page 37




Mass measurements from total rate, e.g. gluino mass in SUSY models with heavy

scalars (FP dark matter scenarios)

LO

NLO

σ(pp→ gg + X) [pb]

mg[GeV]

140012001000800600

10

1

0.1

0.01

0.001

mgluino =

{785 ± 35 (LO)

870 ± 15 (NLO)

page 38




Mass measurements from total rate, e.g. gluino mass in SUSY models with heavy

scalars (FP dark matter scenarios)

(Baer, Barger, Shaunghnessy, Summy, Wang)

1000 1500 2000m

g~

0

10

20

30

40

σ (f

b)

TH

100 fb-1

errorTH ±15%TH ±15% ±100%BGBG

LE

P2

exc

lud

ed → ∆mgluino = ±8%

page 39




qL

qL

lR-

χ20

lR+ (near)

lR- (far)

χ10

no spin correlations:

0

0.5

1

1.5

2

0 50 100 150 200 250 300

tree unpol. dσ/dmql+near

mql+near[GeV]

page 40




qL

qL

lR-

χ20

lR+ (near)

lR- (far)

χ10

with spin correlations:

0

0.5

1

1.5

2

0 50 100 150 200 250 300

tree pol.tree unpol

dσ/dmql+near

mql+near[GeV]

cannot determine mql+neardistribution experimentally

→ consider charge asymmetry A = (dσ/dmql+−dσ/dmql−)/(dσ/dmql++dσ/dmql−)

page 41




qL

qL

lR-

χ20

lR+ (near)

lR- (far)

χ10

(Barr)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 100 200 300 400 500mlq / GeV

A+-

cannot determine mql+neardistribution experimentally

→ consider charge asymmetry A = (dσ/dmql+−dσ/dmql−)/(dσ/dmql++dσ/dmql−)

page 42




qL

qL

lR-

χ20

lR+ (near)

lR- (far)

χ10

with spin correlations:

0

0.5

1

1.5

2

0 50 100 150 200 250 300

tree pol.tree unpol

dσ/dmql+near

mql+near[GeV]

page 43




qL

qL

lR-

χ20

lR+ (near)

lR- (far)

χ10

with spin correlations @ NLO:

0

0.5

1

1.5

2

0 50 100 150 200 250 300

tree pol.tree unpolNLO pol

dσ/dmql+near

mql+near[GeV]

→ radiative corrections affect shape of distributions (Horsky, MK, Muck, Zerwas)

page 44




qL

qL

lR-

χ20

lR+ (near)

lR- (far)

χ10

(Horsky, MK, Muck, Zerwas)

A (NLO)A (Born)

Mql

350300250200150100500

1

0.5

0

−0.5

−1

consider charge asymmetry A = (dσ/dmql+ − dσ/dmql−)/(dσ/dmql+ + dσ/dmql−)

→ radiative corrections cancel in charge asymmetry

page 45




consider invariant jet-mass distributions in decay chains like

pp→ g + g → qqR + qqL → qqχ01 + qqχ0

2

g

g

q

q

q

q

→ information on gluino spin in jet event shapes (MK, Popenda, Spira, Zerwas)

page 46




consider invariant jet-mass distributions in decay chains like

pp→ g + g → qqR + qqL → qqχ01 + qqχ0

2

uRuL :< Mjet >= 102 GeVuRuR :< Mjet >= 116 GeV

without spin correlations: < Mjet >= 116 GeV

with the lowest pT

Mjet calulated from the two jets

mχ1/2= 98/184 GeV

muR/L= 547/565 GeV

mg = 607 GeVSPS1a’:

1/σtot dσ/dMjet (g(→ uu(→ uχ))g(→ uu(→ uχ)) [1/GeV]

Mjet[GeV]

5004003002001000

0.01

0.009

0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

→ information on gluino spin in jet event shapes (MK, Popenda, Spira, Zerwas)

page 47



→ determine masses & spins . . . or the number of extra dimensions?

consider graviton production in ADD scenarios (Arkani-Hamed, Dimopoulos, Dvali)

pp→ G+ jet → monojet signature

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

101

� � � � � � � � � � � � � � � �

pmissT ��

dσ

dpmiss

T

[pb/GeV]

Z + jet

� ��

δ = 3, Ms = 5TeVδ = 4, Ms = 5TeVδ = 5, Ms = 5TeV

→ determine number of extra dimensions δ?page 48






10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

101

� � � � � � � � � � � � � � � �

pmissT ��

dσ

dpmiss

T

[pb/GeV]

Z + jet

� ��

δ = 3, Ms = 5TeVδ = 4, Ms = 5TeVδ = 5, Ms = 5TeV

→ spoiled by QCD uncertainties. . .page 49






0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 200 400 600 800 100012001400160018002000

pT,miss

1

2

3

500 1000 1500

LO

NLO

→ include NLO-QCD corrections (Karg, MK, Li, Zeppenfeld, prelim.)

page 50






0

0.5

1

1.5

2

2.5

3

0.1 1 10µ/µ0

σ(µ)/σ(µ0 = pT,miss)

PP → G + jet

(δ = 4, Ms = 4TeV)

LONLO

→ include NLO-QCD corrections (Karg, MK, Li, Zeppenfeld, prelim.)

page 51

Progress in SUSY precision calculations at the LHC

Sparticle production cross sections

– NLO QCD → Prospino: Beenakker, Hopker, MK, Plehn, Spira, Zerwas

(cf. Baer, Hall, Reno; Berger, Klasen, Tait)

– threshold summation for Mq , Mg∼

> 1 TeV

(Bozzi, Fuks, Klasen; Kulesza, Motyka; Langenfeld, Moch;

Beenakker, Brensing, MK, Kulesza, Laenen, Niessen)

– electroweak corrections(Hollik, Kollar, Mirabella, Trenkel; Bornhauser, Drees, Dreiner, Kim;

Beccaria, Macorini, Panizzi, Renard, Verzegnassi)

– beyond MSSM: NLO QCD for RPV SUSY(Debajyoti Choudhury, Swapan Majhi, V. Ravindran; Yang, Li, Liu, Li; Dreiner, Grab, MK, Trenkel)

Sparticle decays

– total rates → Sdecay: (Muhlleitner, Djouadi, Mambrini) plus work by many authors. . . ...

– only few results for shapes (Drees, Hollik, Xu; Horsky, MK, Muck, Zerwas)

Sparticle production ⊕ decay: generic BSM cascades (SUSY, UEDs, LH,. . . )

– so far only tree level → challenge for LHC theory community. . .

page 52

Precision calculations at the LHC: 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 NLO calculations with parton showers and hadronization

EWK corrections: important for high accuracy or scales �MW,Z

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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Precision calculations for LHC physicsmkraemer/mkraemer_psi.pdf · 2009-06-18 · Why precision...

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