SUSY-particle production at Hadron Collidersmkraemer/NRW-SUSY.pdf · SUSY-particle production at Hadron Colliders Michael Kramer¤ (RWTH Aachen) Basics of SUSY particle production

NRW Phanomenologie-Treffen, Januar 2006

SUSY-particle production at Hadron Colliders

Michael Kramer

(RWTH Aachen)

Basics of SUSY particle production at hadron colliders

The calculation of SUSY-QCD corrections

Work done in collaboration with W. Beenakker, R. Hopker, M. Klasen, T. Plehn, M. Spira, P.M. Zerwas

Michael Kramer Page 1 NRW Panomenologie-Treffen, Januar 2006

Introduction: Why Supersymmetrie?

There are many good reasons to study supersymmetric field theoriesand TeV-scale SUSY at colliders:

– SUSY is the unique extension of the Lorentz-symmetry

– SUSY provides a solution to the hierarchy problem

– SUSY allows for gauge coupling unification

– SUSY provides a dark matter candidate

– SUSY can generate EWSB dynamically

– . . .


The Minimal Supersymmetric Standard Model

The MSSM particle spectrum

Gauge Bosons S = 1 Gauginos S = 1/2

gluon, W±, Z, γ gluino, W , Z, γ

Fermions S = 1/2 Sfermions S = 0(

uL

dL

)(νe

L

eL

) (uL

dL

)(νe

L

eL

)

uR, dR, eR uR, dR, eR

Higgs Higgsinos(

H02

H−

2

)(H+

1

H01

) (H0

2

H−

2

)(H+

1

H01

)


SUSY particle production at hadron colliders

In the MSSM one imposes a symmetryR = (−1)3B+L+2S

{= +1 SM

= −1 SUSYto avoid proton decay

→ SUSY particles produced pairwise

→ lightest SUSY particle stable (dark matter candidate)

The interactions of MSSM particles are determined by gauge symmetry and SUSY

example: gluonµ, a

p, i

q, j

squark

squark

= −i gs (Ta)ij(p + q)µ

→ no new coupling!

SUSY particles should be produced copiously at hadron colliders through QCD processes, e.g.

g

g




{= +1 SM





example: gluonµ, a

p, i

q, j

squark

squark




g

g




{= +1 SM





example: gluonµ, a

p, i

q, j

squark

squark




g

g




{= +1 SM





example: gluonµ, a

p, i

q, j

squark

squark




g

g


Squark and gluino cross section at the LHC

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

−→ SUSY signal:

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

↪→≈ 108squarks & gluinos/year (∫L = 30 fb−1)


Squark and gluino cross section at the LHC

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

−→ SUSY signal:

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

↪→≈ 108squarks & gluinos/year (∫L = 30 fb−1)


SUSY searches at hadron colliders

Distinctive signature due to cascade decays:

multiple jets (and/or leptons) with large amount of missing energy

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

→ LHC discovery reach for squarks and gluinos: Mq,g ∼< 2.5 TeV


SUSY searches at hadron colliders

Distinctive signature due to cascade decays:

multiple jets (and/or leptons) with large amount of missing energy

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

→ LHC discovery reach for squarks and gluinos: Mq,g ∼< 2.5 TeV


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∼LE

P2

l~LEP2

mass limits (roughly)

Mg ∼> 200 GeV

Mq ≈ Mgluino ∼> 300 GeV

Mt1 ∼> 100 GeV

Mχ01 ∼> 50 GeV

Mχ±

1 ∼> 100 GeV

Msleptons ∼> 100 GeV


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∼LE

P2

l~LEP2

mass limits (roughly)

Mg ∼> 200 GeV

Mq ≈ Mgluino ∼> 300 GeV

Mt1 ∼> 100 GeV

Mχ01 ∼> 50 GeV

Mχ±

1 ∼> 100 GeV

Msleptons ∼> 100 GeV


MSSM particle production at hadron colliders

production dynamics

P

P

i

j

¯Q

˜Q

fP

i

f P

i

σ

σ(pp/pp → q¯q) =∫

dx1fPi (x1, µ)

∫dx2f

Pj (x2, µ) σ(ij → q¯q)

+O(Λ/Mq)

→ effective energy for (s)particle production√

s =√

x1x2s <√

s



Scale dependence

σ =

∫dx1f

Pi (x1, µF )

∫dx2f

Pj (x2, µF )

×∑

n

αns (µR) Cn(µR, µF )

finite order in perturbation theory

→ artificial µ-dependence:

dσ

d ln µ2

R

=

N∑

n=0


= O(αs(µR)N+1)

⇒ scale dependence ∼ theoretical

uncertainty due to HO corrections

Example: Stop-pair production at leading order

20

30

40

50

60

70

80

90

100

1

LO

σ(pp → t1t−1+X) [pb]

µ/m(t1)

√s=14 TeV; m(t1) = 200 GeV

→ theoretical uncertainty

∼> ± 100% at LO

⇒ must include NLO corrections



Scale dependence

σ =

∫dx1f

Pi (x1, µF )

∫dx2f

Pj (x2, µF )

×∑

n


finite order in perturbation theory

→ artificial µ-dependence:

dσ

d ln µ2

R

=

N∑

n=0


= O(αs(µR)N+1)

⇒ scale dependence ∼ theoretical

uncertainty due to HO corrections

Example: Stop-pair production at leading order

20

30

40

50

60

70

80

90

100

1

LO

σ(pp → t1t−1+X) [pb]

µ/m(t1)

√s=14 TeV; m(t1) = 200 GeV

→ theoretical uncertainty

∼> ± 100% at LO

⇒ must include NLO corrections



MSSM sparticle pair production

− 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


Top-squark production

tL, tR mix to form mass states t1, t2 → potentially small t1 mass

LO parton reations

q + q → ti + ¯ti (i = 1, 2)

q

q

g

t1

¯t1

g

t

t t1

¯t1

σLO[qq] =α2

sπ

s

2

27β3 (β2 = 1 − 4m2/s)

c.f. top production: σLO[qq] ≈ α2

sπ

s1227 β

→ σtop/σstop ∼ 10 at the Tevatron

g + g → ti + ¯ti (i = 1, 2)

g

g

σLO[gg] =α2

sπ

s

[β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

]

⇒ no MSSM parameter dependence




LO parton reations

q + q → ti + ¯ti (i = 1, 2)

q

q

g

t1

¯t1

g

t

t t1

¯t1

σLO[qq] =α2

sπ

s

2

27β3 (β2 = 1 − 4m2/s)


sπ

s1227 β


g + g → ti + ¯ti (i = 1, 2)

g

g

σLO[gg] =α2

sπ

s

[β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

]





LO parton reations

q + q → ti + ¯ti (i = 1, 2)

q

q

g

t1

¯t1

g

t

t t1

¯t1

σLO[qq] =α2

sπ

s

2

27β3 (β2 = 1 − 4m2/s)


sπ

s1227 β


g + g → ti + ¯ti (i = 1, 2)

g

g

σLO[gg] =α2

sπ

s

[β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

]





LO parton reations

q + q → ti + ¯ti (i = 1, 2)

q

q

g

t1

¯t1

g

t

t t1

¯t1

σLO[qq] =α2

sπ

s

2

27β3 (β2 = 1 − 4m2/s)


sπ

s1227 β


g + g → ti + ¯ti (i = 1, 2)

g

g

σLO[gg] =α2

sπ

s

[β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

]



SUSY-QCD corrections

self energies: + · · ·

vertex corrections: + · · ·

box diagrams: + · · ·

+ · · ·

gluon emission: + · · ·

gluon-quark scattering: + · · ·

NLO cross section depends on

squark & gluino masses

stop mixing angle

→ dependence numerically small

NLO cross section near threshold β � 1:

σqq ≈α2

s(µ2)

m2

π

54β

3

×

(1 + 4παs(µ

2)

{−

1

48β+

2

3π2ln

2(8β

2)

−107

36π2ln(8β

2) −

2

3π2ln(8β

2) ln

(µ2

m2

)})

σgg ≈α2

s(µ2)

m2

7π

384β

×

(1 + 4παs(µ

2)

{11

336β+

3

2π2ln

2(8β

2)

−183

28π2ln(8β

2) −

2

3π2ln(8β

2) ln

(µ2

m2

)})

→ large NLO corrections in gg channel






+ · · ·





stop mixing angle



σqq ≈α2

s(µ2)

m2

π

54β

3

×

(1 + 4παs(µ

2)

{−

1

48β+

2

3π2ln

2(8β

2)

−107

36π2ln(8β

2) −

2

3π2ln(8β

2) ln

(µ2

m2

)})

σgg ≈α2

s(µ2)

m2

7π

384β

×

(1 + 4παs(µ

2)

{11

336β+

3

2π2ln

2(8β

2)

−183

28π2ln(8β

2) −

2

3π2ln(8β

2) ln

(µ2

m2

)})







+ · · ·





stop mixing angle



σqq ≈α2

s(µ2)

m2

π

54β

3

×

(1 + 4παs(µ

2)

{−

1

48β+

2

3π2ln

2(8β

2)

−107

36π2ln(8β

2) −

2

3π2ln(8β

2) ln

(µ2

m2

)})

σgg ≈α2

s(µ2)

m2

7π

384β

×

(1 + 4παs(µ

2)

{11

336β+

3

2π2ln

2(8β

2)

−183

28π2ln(8β

2) −

2

3π2ln(8β

2) ln

(µ2

m2

)})



SUSY-QCD corrections: results

reduced scale dependence ∼<15%

(Beenakker, MK, Plehn, Spira, Zerwas)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

σ(pp– → t1t

−1+X) [pb]

µ/m(t1)

LO

NLO

√s=2 TeV; m(t1) = 200 GeV

K-faktor K = σ(NLO)/σ(LO) ∼ 1 − 1.5


1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

100 200 300

pp/pp– → t1t

−1+X

K = σ(NLO)/σ(LO)

m(t1)

Tevatron (√s=2 TeV)

LHC





0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

σ(pp– → t1t

−1+X) [pb]

µ/m(t1)

LO

NLO

√s=2 TeV; m(t1) = 200 GeV



1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

100 200 300

pp/pp– → t1t

−1+X

K = σ(NLO)/σ(LO)

m(t1)


LHC





0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

σ(pp– → t1t

−1+X) [pb]

µ/m(t1)

LO

NLO

√s=2 TeV; m(t1) = 200 GeV



1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

100 200 300

pp/pp– → t1t

−1+X

K = σ(NLO)/σ(LO)

m(t1)


LHC


Top-squark production: NLO cross sections

Tevatron

10-4

10-3

10-2

10-1

1

10

10 2

280 300 320 340 360 380 400 420

10-4

10-3

10-2

10-1

1

10

10 280 100 120 140 160 180 200

NLO

LO

:

: µ = m(t)µ = [ m(t)/2 , m(t) , 2m(t) ]µ = m(t)

m(t2) [GeV]

m(t1) [GeV]

pp– → t t

− + X

σtot[pb]

√S = 1.8 TeV

t1t−1

t2t−2

LHC

10-1

1

10

400 420 440 460 480 500 520 540 560 580 60010

-1

1

10

200 220 240 260 280 300 320 340 360 380 400

NLO

LO

:

: µ = m(t)µ = [ m(t)/2 , m(t) , 2m(t) ]µ = m(t)

m(t2) [GeV]

m(t1) [GeV]

pp → t t− + X

σtot[pb]

√S = 14 TeVt1t

−1

t2t−2

→ small dependence on SUSY-Parameters


Top-squark searches

• Top-squark search in e±e±+ ≥ 2j final startes (CDF, Phys. Rev. Lett. 83 (1999))

10-1

1

100 110 120 130 140 150

∆MLO

∆MNLO

σNLOσLO

: µ=[m(t)/2 , 2m(t)]: µ=[m(t)/2 , 2m(t)]

m(t1) [GeV]

σ(pp– → t1t

−1 + X) · BR(t1t

−1 → ee + ≥ 2j) [pb]

CDF 95% C.L. upper limit (prel.)

m(χ1o)=m(t1)/2

⇒ Mt1

>

110 ± 15 GeV LO

120 ± 5 GeV NLO


Current project: associated pp/pp → qχ, gχ production

semi-weak process, but χs are light in most models

pp/pp → gχ q

q

q χ

g

Beenakker, MK, Plehn, Spira, Zerwas; Berger, Klasen, Tait

pp/pp → qχ q

g

q χ

q

LO scale uncertainty O(100%) ⇒ need NLO calculation




pp/pp → gχ q

q

q χ

g


pp/pp → qχ q

g

q χ

q





pp/pp → gχ q

q

q χ

g


pp/pp → qχ q

g

q χ

q





pp/pp → gχ q

q

q χ

g


pp/pp → qχ q

g

q χ

q




+ · · ·

+ · · ·

q

g

q χ

q

g

+ · · ·

q

g

g

χ

q

q

+ · · ·

SUSY breaking in dimensional regularization

g, χ: 2 d.o.f.

g, γ, Z : (n − 2) d.o.f.

→ restauration through finite counter terms

double counting: gg → q¯q → qχq (if mq > mχ)

dσres

dM2= σ(gg → q¯q)

mqΓq/π

(M2 − m2q)2 + m2

qΓ2

q

BR(¯q → χq)

−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2

q)

→ resonance contributions to be subtracted



+ · · ·

+ · · ·

q

g

q χ

q

g

+ · · ·

q

g

g

χ

q

q

+ · · ·


g, χ: 2 d.o.f.

g, γ, Z : (n − 2) d.o.f.



dσres


mqΓq/π

(M2 − m2q)2 + m2

qΓ2

q

BR(¯q → χq)

−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2

q)




+ · · ·

+ · · ·

q

g

q χ

q

g

+ · · ·

q

g

g

χ

q

q

+ · · ·


g, χ: 2 d.o.f.

g, γ, Z : (n − 2) d.o.f.



dσres


mqΓq/π

(M2 − m2q)2 + m2

qΓ2

q

BR(¯q → χq)

−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2

q)



SUSY-QCD corrections: preliminary results

reduced scale dependence

Tevatron

Beenakker, MK, Plehn, Spira, Zerwas

preliminaryσ(pp

_ → q

~ χ2+X)[pb]

√s = 1.96 TeV

LO

NLO

CTEQ5M

Q/m0.1 0.2 0.5 1 2 5 10

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

10-1

1 10

LHC

Beenakker, MK, Plehn, Spira, Zerwas

preliminaryσ(pp→ q

~ χ2+X)[pb]

√s = 14 TeV

LO

NLO

CTEQ5M

Q/m0.1 0.2 0.5 1 2 5 10

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10-1

1 10


Summary

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

→ public code PROSPINO (Beenakker, 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


Summary

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

→ public code PROSPINO (Beenakker, 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


Documents

SUSY-particle production at Hadron Collidersmkraemer/NRW-SUSY.pdf · SUSY-particle production at Hadron Colliders Michael Kramer¤ (RWTH Aachen) Basics of SUSY particle production