precision calculations for bsm physics at the lhcbsm searches at the lhc many model for new physics...

MPIK Heidelberg, April 2009

Precision calculations for BSM physics at the LHC

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 “Elementarteilchenphysik

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: SUSY searches at the LHC

page 3

Contents




page 4


Tevatron jet cross section at large ET

Et (GeV)-0.5

0

0.5

1

(Dat

a - T

heor

y)/ T

heor

y

200 300 40010050

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

page 5



Et (GeV)-0.5

0

0.5

1

(Dat

a - T

heor

y)/ T

heor

y

200 300 40010050


⇒ new physics? + ?

page 6



Et (GeV)-0.5

0

0.5

1

(Dat

a - T

heor

y)/ T

heor

y

200 300 40010050


LBSM ⊇g2

M2ψγµψ ψγµψ ⇒

data − theory

theory∝ g2 E

2T

M2

page 7



(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)

page 8


Tevatron bottom quark cross section

[D0, PLB 487 (2000)]

⇒ new physics?

page 9



[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?

page 10



[Mangano, AIP Conf.Proc, 2005]

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

page 11


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 12



– mass peaks

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

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

page 12



– 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 13

Contents




page 14

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 15


• 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 16


• 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 17


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 18




)2 (GeV/cg~

M0 100 200 300 400 500 600

)2 (G

eV/c

q~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~

= Mq~M

)2 (GeV/cg~

M0 100 200 300 400 500 600

)2 (G

eV/c

q~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

→ needs accurate theoretical predictions

page 19

SUSY particle production at hadron colliders

SUSY particles would be producedcopiously at hadron colliders viaQCD processes, eg.

g

g

SUSY signal LHC −→

σ(qq + gg + gq) ≈ 2 nb (Mq,g ≈ 300 GeV)

0.1 1 1010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

σjet(ETjet > √s/4)

LHCTevatron

σttbar

σHiggs(MH = 500 GeV)

σZ

σjet(ETjet > 100 GeV)


σW


σbbar

σtot

σ (n

b)

√s (TeV)

even

ts/s

ec f

or L

= 1

033 c

m-2

s-1

page 20


SUSY particles would be producedcopiously at hadron colliders viaQCD processes, eg.

g

g

SUSY signal Tevatron −→

σ(qq + gg + gq) ≈ 2 nb (Mq,g ≈ 300 GeV)

0.1 1 1010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109


LHCTevatron

σttbar


σZ

σjet(ETjet > 100 GeV)


σW


σbbar

σtot

σ (n

b)

√s (TeV)

even

ts/s

ec f

or L

= 1

033 c

m-2

s-1

page 21


MSSM sparticle pair production at NLO (Beenakker, Hopker, MK, Plehn, Spira, Zerwas)

− squarks & gluinos pp/pp→ q¯q, gg, qg

− stops pp/pp→ tt

− gauginos pp/pp→ χ0χ0, χ±χ0, χ+χ−

− sleptons pp/pp→ ll

− associated production pp/pp→ qχ, gχ

References of LO calculations:

Kane, Leveille, ’82; Harrison, Llewellyn Smith, ’83; Reya, Roy, ’85; Dawson, Eichten, Quigg, ’85; Baer, Tata, ’85,. . .

page 22


MSSM sparticle pair production at NLO (Beenakker, Hopker, MK, Plehn, Spira, Zerwas)

− squarks & gluinos pp/pp→ q¯q, gg, qg

− stops pp/pp→ tt

− gauginos pp/pp→ χ0χ0, χ±χ0, χ+χ−

− sleptons pp/pp→ ll

− associated production pp/pp→ qχ, gχ

References of LO calculations:

Kane, Leveille, ’82; Harrison, Llewellyn Smith, ’83; Reya, Roy, ’85; Dawson, Eichten, Quigg, ’85; Baer, Tata, ’85,. . .

page 23

Example: Top-squark production

LO graphs

q

q

g

t1

¯t1

g

g

σLO[gg] =α2

sπ

s

[β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

](β2=1−4m2/s)

⇒ no MSSM parameter dependence

pp cross section: σ = Fnon−pert.(µ) ⊗(C0α

Bs (µ) + C1(µ)αB+1

s (µ) + . . .)pert.

Scale dependence through factorization of IR contributions and renormalization of UV contributions

LO scale dependence

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

LO

NLO

LO

σ(pp– → t1t

−1+X) [pb]

LO

σ(pp → t1t−1+X) [pb]

µ/m(t1)

µ/m(t1)

√s=2 TeV; m(t1) = 200 GeV

→ theoretical uncertainty ≈ ±100% at LO

⇒ must include NLO corrections

page 24

Example: Top-squark production

LO graphs

q

q

g

t1

¯t1

g

g

σLO[gg] =α2

sπ

s

[β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

](β2=1−4m2/s)

⇒ no MSSM parameter dependence

pp cross section: σ = Fnon−pert.(µ) ⊗(C0α

Bs (µ) + C1(µ)αB+1

s (µ) + . . .)pert.

Scale dependence through factorization of IR contributions and renormalization of UV contributions

NLO scale dependence (Beenakker, MK, Plehn, Spira, Zerwas)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

LO

NLO

LO

σ(pp– → t1t

−1+X) [pb]

LO

NLO

σ(pp → t1t−1+X) [pb]

µ/m(t1)

µ/m(t1)

√s=2 TeV; m(t1) = 200 GeV

→ theoretical uncertainty ≈ ±15% at NLO

page 25

Top-squark searches

Top-squark search in pp→ t1¯t1 → cχ0

1cχ01 channel (CDF PRD 2007)

)2) (GeV/c1t~M(

70 80 90 100 110 120 130 140 150

(pb)

2)) 10 χ∼

c→ 1t~

(BR

(×) 1t~ 1t~

→ p(pσ

1

10

102

CDF Upper Limit, 95% CLObservedExpected

Theory Cross Section (Prospino)NLO

Uncertainty (scale+PDF)

)-1CDF Run II Preliminary (295 pb

2)=50 GeV/c10χ∼M(

⇒ 105 GeV ≤Mt1≤ 130 GeV

page 26

Top-squark searches

Top-squark search in pp→ t1¯t1 → cχ0

1cχ01 channel (CDF PRD 2007)

→ no exclusion based on LO cross sections

page 27

MSSM particle production at the LHC

NLO SUSY-QCD corrections for MSSM particle production at hadron colliders

→ public code PROSPINO (Beenakker, Hopker, MK, Plehn, Spira, Zerwas)

10-2

10-1

1

10

10 2

10 3

100 150 200 250 300 350 400 450 500

⇑

⇑ ⇑ ⇑

⇑

⇑⇑

χ2oχ1

+

t1t−1

qq−

gg

νν−

χ2og

χ2oq

NLOLO

√S = 14 TeV

m [GeV]

σtot[pb]: pp → gg, qq−, t1t

−1, χ2

oχ1+, νν

−, χ2

og, χ2oq

References: Beenakker, Hopker, Spira, Zerwas, 1995, 1997; Beenakker, MK, Plehn, Spira, Zerwas, 1998; Baer, Hall, Reno, 1998; Beenakker, Klasen,

MK, Plehn, Spira, Zerwas, 1999; Beenakker, MK, Plehn, Spira, Zerwas, 2000; Berger, Klasen, Tait, 1999-2002; Beenakker, MK, Plehn, Spira, Zerwas,

2007

page 28

Current limits on sparticle masses

)2Gluino Mass (GeV/c0 100 200 300 400 500 600

)2S

quar

k M

ass

(GeV

/c

0

100

200

300

400

500

600-1DØ Run II Preliminary L=310 pb

UA

1

UA

2

LEP 1+2

CD

F IB

DØ

IA

DØ IB

DØ II

)10χ∼)<m(q~m(

no mSUGRA

solution+/

-χ∼

LEP

2

l~LEP2

mass limits (roughly)

Mg ∼> 250 GeV

Mq ≈Mgluino ∼> 400 GeV

Mt1 ∼> 100 GeV

Mχ01 ∼> 50 GeV

Mχ±

1 ∼> 100 GeV

Msleptons ∼> 100 GeV

page 29








page 30




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

]

2m

ass [

GeV

/c

0

100

200

300

400

500

600

700

800

900

1000 LH2 NM6 NM4 CS7

HA

HWHZ

HidH

iu

0

1χ∼

±1

χ∼02

χ∼

Rd~Lu~Ru~Ld~

g~

1τ∼ Rl~

01

χ∼

±1

χ∼02

χ∼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 31




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

]

2m

ass [

GeV

/c

0

100

200

300

400

500

600

700

800

900

1000 LH2 NM6 NM4 CS7

HA

HWHZ

HidH

iu

0

1χ∼

±1

χ∼0

2χ∼

Rd~Lu~Ru~Ld~

g~

1τ∼ Rl~

0

1χ∼

±1

χ∼02

χ∼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 31




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

q + q → q + ¯qq

q

g

t1

¯t1

g

t

t t1

¯t1

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 32




“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 33




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 34




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 (mmaxll )2 = (m2

χ02

−m2

lR)(m2

lR−m2

χ01

)/(m2

lR)

sensitive to mass differences

page 35




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 36




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 2000mg~

0

10

20

30

40

σ (f

b)

TH100 fb-1 errorTH ±15%TH ±15% ±100%BGBG

LE

P2 e

xclu

ded

→ ∆mgluino = ±8%

page 37




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 38




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 39




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 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]

page 41




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 42




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 43




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 44




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 45



→ 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 46






10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

101

' ( ' ' ) ' ' ' ) ( ' ' * ' ' '

pmissT +�, - . /

dσ

dpmiss

T

[pb/GeV]

Z + jet, 0 12 3 45 6 7 3 8 6 19 7


→ spoiled by QCD uncertainties. . .page 47






10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

101

: ; : : < : : : < ; : : = : : :

pmissT >�? @ A B

dσ

dpmiss

T

[pb/GeV]

Z + jet? C DE F GH I J F K I DL J


→ include NLO-QCD corrections (Karg, MK, Li, Zeppenfeld, in progress)

page 48

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 49

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

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 bsm physics at the lhcbsm searches at the lhc many model for new physics...

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