Michael Kramer¤ - RWTH Aachen Universitymkraemer/susy_qcd.pdf · The hierarchy problem: why is MHiggs ˝ MPlanck? Quantum corrections to the Higgs mass have quadratic UV divergencies!

Frontiers in QCD, DESY Hamburg, September 2006

SUSY-particle and MSSM Higgs production at the LHC

Michael Kramer

(RWTH Aachen)

We want to discover and explore models of new physics at the LHC

→ determine masses, quantum numbers, couplings by comparing theory and data

→ need accurate theoretical predictions including higher-order corrections

Michael Kramer Page 1 Frontiers in QCD, September 2006

The hierarchy problem: why is MHiggs � MPlanck?

Quantum corrections to the Higgs mass have quadratic UV divergencies

� ��

� � ��

→ δm2H ∼ α

π(Λ2 + m2

F )

The cutoff Λ represents the scale up to which the Standard Model remains valid.

→ need Λ of O(1 TeV) to avoid unnaturally large corrections

Most popular new physics models

– Supersymmetry

– Dynamical EWSB

– Extra dimensions

– Little Higgs models

Quantum corrections due to superparticles cancel the quadratic UV divergences

� ��

� � ��

→ δm2H ∼ −α

π(Λ2 + m2

F )

δm2H ∼ α

π(m2

F − m2F ) → no fine-tuning if m ∼< O(1 TeV)


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

)


Outline

SUSY-particle production at the LHC

MSSM Higgs boson production at the LHC


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 QCDprocesses, e.g.

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)

σHiggs(MH = 150 GeV)

σW

σjet(ETjet > √s/20)

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


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

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

References of LO calculations:

Kane, Leveille, 1982; Harrison, Llewellyn Smith, 1983; Reya, Roy, 1985; Dawson, Eichten, Quigg, 1985; Baer, Tata, 1985,. . .


MSSM particle production at hadron colliders

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

References of LO calculations:

Kane, Leveille, 1982; Harrison, Llewellyn Smith, 1983; Reya, Roy, 1985; Dawson, Eichten, Quigg, 1985; Baer, Tata, 1985,. . .


Top-squark production

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

LO cross section

q

q

g

t1

¯t1

g

g

σLO[qq+gg] =α2

sπ

s

[2

27β3 + β

(5

48+

31m2

24s

)+

(2m2

3s+

m4

6s2

)log

1 − β

1 + β

](β2=1−4m2/s)

⇒ no MSSM parameter dependence

LO scale dependence

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


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


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

(Beenakker, MK, Plehn, Spira, Zerwas)

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


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


SUSY-QCD corrections

+ · · ·

+ · · ·

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

qΓ2q

BR(¯q → χq)

−→ σ(gg → q¯q)BR(¯q → χq)δ(M2− m2

q)

→ resonance contributions to be subtracted


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


MSSM particle production at the LHC

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

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, 2006


SUSY with R-Parity violation

SUSY models without R-parity allow for resonant single sparticle production

Example: resonant slepton production:

L = λ′ijk

(dRk

dLjνLi

− dRkuLj

lLi

)

→ σLO =λ′2π

12sδ(1 − τ) with τ =

M2

sq

q

S

NLO (SUSY-)QCD corrections sizeable (Dreiner, Grab, MK, Trenkel 2006)

m0 m1/2 A0 tanβ sgn(µ) m( dR) m( dL) m(g) m(νe)

A0

[TeV]ν ~m0.5 1 1.5 2

K-F

acto

r

1.1

1.2

1.3

1.4

1.5

1.6

QCD

QCD + SUSY (A = 0TeV’)

QCD + SUSY (A = 1TeV

QCD + SUSY (A = -1TeV)

SPS 1a’

[TeV]ν ~m0.5 1 1.5 2

K-F

acto

r

1.1

1.2

1.3

1.4

1.5

1.6

QCD

QCD + SUSY (A = 0TeV)

QCD +SUSY (A = 1TeV)


SPS 2

(TeV)ν ~m0.5 1 1.5 2

K-F

acto

r

1.1

1.2

1.3

1.4

1.5

1.6

QCD




SPS 3

λ′

11i = 0.01√

S = 14A

K

∼ 500− 600 ∼ 150∼ 800 ∼ 800 − 900

KK


SUSY Searches

Hans-Peter Nilles, Physics Reports 110, 1984:

“Experiments within the next 5-10 years will enable us to decide whether su-

persymmetry, as a solution of the naturalness problem of the weak interaction

is a myth or reality”

Hans-Peter Nilles, private communication, quoted from hep-ex/9907042

“One should not give up yet. . . ”

“Perhaps a correct statement is:

it will always take 5-10 years to discover SUSY.”


A crucial test of the MSSM: the light Higgs

MSSM Higgs sector: two Higgs doublets to give mass to up- and down-quarks

→ 5 physical states: h, H , A, H±

The MSSM Higgs sector is determined by tan β = v2/v1 and MA.

The couplings in the Higgs potential and the gauge couplings are related by super-

symmetry. At tree level one finds Mh ≤ MZ . This relation is modified by radiative

corrections so that

MH ∼< 130 GeV (in the MSSM)

The existence of a light Higgs boson is a generic prediction of SUSY models.


A crucial test of the MSSM: the light Higgs

One of the SUSY Higgs bosons will be seen at the LHC

ATLAS

LEP 2000

ATLAS

mA (GeV)

tan

β

1

2

3

4

56789

10

20

30

40

50

50 100 150 200 250 300 350 400 450 500

0h 0H A

0 +-H

0h 0H A

0 +-H

0h 0H A

00h H

+-

0h H+-

0h only

0 0Hh

ATLAS - 300 fbmaximal mixing

-1

LEP excluded

but it may look like the SM Higgs. . .


Higgs production in the MSSM

Higgs production in the SM through

top-quark loops

Ht

g

g

ttH production

g

g

t

t

H

∝ m2top×dPS(ttH)



Higgs production in the MSSM through

t, b-quark loops + squark loops

Ht, b

g

g

+ Ht

g

g

ttH production and bbH production

g

g

t

t

H

g

g

b

b

H

∝ m2top×dPS(ttH) ∝ m2

b tan β ×dPS(bbH)



Cross section predictions: light and heavy scalar h and H

[Spira]

10-3

10-2

10-1

1

10

10 2

10 3

10 4

102

gg→H (SM)

gg→H

Hbb–

Htt–

Hqq

HZ HW

tan β = 30Maximal mixing

Ù H

Ù

h

mh/H (GeV)

Cro

ss-s

ectio

n (p

b)


Higgs production in the MSSM: “gluophobic Higgs”

Ht, b

g

g

+ Ht

g

g

→ interference effects

“Gluophobic Higgs scenario” [Djouadi; Carena et al.; Harlander, Steinhauser; Muhlleitner, Spira]

[Harlander, Steinhauser]

0

20

40

60

80

100

300 400 500 600 700 800 900

σ(pp→h+X) [pb]

m [GeV]t2~

SUSY, NNLO’SUSY, NLOSUSY, LOSM, NNLO’SM, NLOSM, LO

LHC

MSSM parameters

mt1= 200 GeV

mg = 1 TeV

tan β = 10

α = 0

θt = π/4


Higgs production in the MSSM: associated bbh production

Associated QQ-Higgs production

P

P

g

g

Q

Q′

φ is crucial as a

− Higgs discovery channel

− to measure the heavy-quark–Higgs Yukawa couplings

In the MSSM one has

pp → QQ + h, H, A pp → QQ′ + H±

Relative importance depends on MSSM parameters tan β and MA, eg.:

gMSSMbbh = − sin α

cos βgSM

bbH

tan β�1−→ tan β gSM

bbH (Mh'MA'MZ)


QQH production mechanism

At leading order

︸︷︷︸︸︷︷︸︸︷︷︸

MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2

s ln(MH/MQ) ∼ α2s

Summation of ln(MH/MQ) terms by using heavy quark PDFs

[Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,. . . ]

MQ � MH-


Inclusive bbH production: two calculational schemes

4-flavour scheme 5-flavour scheme

+ exact g → bb splitting & mass effects

− no summation of ln(MH/Mb) terms

+ summation of ln(MH/Mb) terms

− LL approximation to g → bb splitting

Comparison at LO

→ strong scale dependence

→ σ(bb → H) � σ(gg → bbH) at µ = MH

→ discrepancy reduced at µF = MH/4

[Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]

→ Choice of scale? Impact of HO corrections?

→ comparison at the NLO/NNLO level


NLO corrections to 4-flavour scheme: gg → bbH

NLO Feynman graphs:

g

g

Q

Q

H

g

g

Q

Q

H + · · ·

Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas; Dawson, Jackson, Orr, Reina, Wackeroth

4-flavour scheme: scale dependence at the LHC (SM Higgs):

[Dittmaier, MK, Spira]

σ(pp → bb_

H + X) [fb]√s = 14 TeVMH = 120 GeVµ0 = mb + MH/2

pTb and pTb_ > 20 GeV

tot

NLO

LO

NLO

LO

µ/µ0

0.1 0.2 0.5 1 2 5 10

10

20

50

100

200

500

1000

2000

5000

10

10 2

10 3

10-1

1 10


NNLO corrections to 5-flavour scheme: bb → h

Renormalization and factorization scale dependence [Harlander, Kilgore]

0

0.2

0.4

0.6

0.8

1

1.2

10-1

1 10

σ(pp → (bb )H+X) [pb]

µR/MH

LHCMH=120 GeV

µF = MH/4

LONLONNLO

0

0.2

0.4

0.6

0.8

1

1.2

10-1

1 10

σ(pp → (bb )H+X) [pb]

µF/MH

LHCMH=120 GeV

µR=MH

LONLONNLO


Inclusive Higgs plus bottom-quark production

Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC)

[Harlander, Kilgore; Dittmaier, MK, Spira]

σ(pp → bb_

h + X) [fb]

√s = 14 TeV

µ = (2mb + Mh)/4

Mh [GeV]

bb_

→ h (NNLO)

gg → bb_

h (NLO)10

10 2

10 3

100 150 200 250 300 350 400

– 4-flavour calculation includes Higgs radiation off top loops ≈ −10%

– calculations employ different PDF fits

→ consistent comparison should reveal even better agreement


Associated Heavy Quark Higgs Production: Status

– gg → h/H + QQ: QCD corrections, full SUSY-QCD in progress[Peng, Wen-Gan, Hong-Sheng, Ren-You, Liang, Yi; Dittmaier, Hafliger, MK, Spira, in preparation]

– gg → A + QQ: QCD corrections [Dittmaier, MK, Spira, preliminary]

– gg → H± + QQ′: (SUSY)-QCD corrections[Peng, Wen-Gan, Ren-You, Yi, Liang, Lei; Dittmaier, Spira, MK, Walcher, in preparation]

– bb → h/H/A: NNLO QCD corrections [Harlander, Kilgore]

MSSM EW corrections [Dittmaier, MK, Muck, in preparation]

– bg → h/H/A + b, bg → H± + t: NLO (SUSY-)QCD corrections[Plehn; Zhu; Campbell, Ellis, Maltoni, Willenbrock; Berger, Han, Jiang, Plehn; Alves, Plehn,. . . ]

⇒ Lots of activity and ongoing calculations. . .


Summary

Production cross sections (and decay rates) for MSSM SUSY particles and Higgs

bosons are (or will soon be) known at NLO (SUSY-)QCD

→ theoretical uncertainty reduced to ≈ 15%

But still lots of work to be done . . .

– only few results exist for other SUSY models (e.g. RPV SUSY)

– electroweak corrections are only partially known

– many backgrounds (multi-parton processes) are only know at LO


Documents

Michael Kramer¤ - RWTH Aachen Universitymkraemer/susy_qcd.pdf · The hierarchy problem: why is MHiggs ˝ MPlanck? Quantum corrections to the Higgs mass have quadratic UV divergencies!