MSSM Radiative Corrections to Neutrino-nucleon Deep...

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MSSM Radiative Corrections to Neutrino-nucleon Deep-inelastic Scattering Oliver Brein Institute of Particle Physics Phenomenology, University of Durham in collaboration with Wolfgang Hollik and Benjamin Koch e-mail: [email protected]

Transcript of MSSM Radiative Corrections to Neutrino-nucleon Deep...

Page 1: MSSM Radiative Corrections to Neutrino-nucleon Deep ...susy06.physics.uci.edu/talks/1/brein.pdfNeutrino-nucleon Deep-inelastic Scattering Oliver Brein Institute of Particle Physics

MSSM Radiative Corrections

to

Neutrino-nucleon Deep-inelastic Scattering

Oliver Brein

Institute of Particle Physics Phenomenology,

University of Durham

in collaboration with Wolfgang Hollik and Benjamin Koch

e-mail: [email protected]

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outline :

• Introduction

– deep inelastic νN scattering at NuTeV

– possible explanations

• MSSM radiative corrections to νµN DIS

– definition of δRν,ν = Rν,νMSSM −R

ν,νSM

– superpartner loop corrections

– MSSM-SM Higgs loop difference

• Results for δRν, δRν

– how to scan over MSSM parameters?

– MSSM parameter scan

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• Introduction

– deep inelastic νN scattering at NuTeV

In the SM neutral (NC) and charged current (CC) neutrino nucleon scatte-

ring are described in LO by t-channel W and Z exchange.

νµ

d, us, c

µ

u, dc, s

↓qW

νµ

u, d, s, c

νµ

u, d, s, c

↓qZ

At NuTeV νµ and νµ beams of a mean energy of 125 GeV were scattered

off a target detector and the ratios

Rν =σνNC

σνCC

, Rν =σνNC

σνCC

were measured.

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[ Introduction, νN DIS @ NuTeV ]

NuTeV measured also the weak mixing angle [NuTeV ’02].

sin2 θon-shellw = 0.2277± 0.0013± 0.0009

→ This is about 3σ below the SM prediction !

But the measurement is indirect, using the measurements of Rν, Rν and

making use of the Paschos-Wolfenstein relation

R− =Rν − rRν

1− r=

1

2− sin2 θw + · · · , r =

σνCC

σνCC

≈ 1

2.

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[ Introduction, νN DIS @ NuTeV ]

More precisely, ratios of counting rates

Rνexp =

# of NC-like ν events

# of CC-like ν events≈ Rν, Rν

exp =# of NC-like ν events

# of CC-like ν events≈ Rν

are measured.

Rνexp, Rν

exp can be related to Rν, Rν by a detailed MC physics simulation.

The deviation from the SM in terms of Rνexp, Rν

exp are [NuTeV ’02]:

∆Rν = Rνexp −Rν

exp(SM) = −0.0032± 0.0013 ,

∆Rν = Rνexp −Rν

exp(SM) = −0.0016± 0.0028 .

→ ∆Rν,ν : simple starting point for studying MSSM radiative corrections

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[ Introduction ]

– possible explanations

• statistical fluctuation, errors underestimated ?

→ re-analyses of EW rad. corr.

[Diener, Dittmaier, Hollik ’03 & ’05; Arbuzov, Bardin, Kalinovskaya ’03]

• relevant SM effects neglected ?

→ asymmetry of strange sea-quarks in the nucleon (s 6= s)

→ isospin violation (up 6= dn)

→ nuclear effects

→ etc. . . .

• new physics ?

→ modified gauge boson interactions (e.g. in extra dimensions)

→ non-renormalizable operators (suppressed by powers of Λ−1new physics)

→ leptoquarks (e.g. R parity violating SUSY)

→ SUSY loop effects (e.g. in MSSM)

→ etc. . . .

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[ Introduction, possible explanations ]

Although the NuTeV ”anomaly” is far from being settled,

it is interesting, if the MSSM could account for such an effect.

Earlier Studies:

• Davidson et al. [’02]

− rough study in terms of oblique corrections

(i.e. momentum transfer q = 0)

− no Parton Distribution Functions (PDFs) used

• Kurylov, Ramsey-Musolf, Su [’04] :

− detailed parameter dependence studied

− momentum transfer q = 0 approximation

− no PDFs used

results so far: MSSM not responsible (size ok, but wrong sign)

• our calculation: try to include kinematic effects [OBr, Koch, Hollik]

− full q2-dependence

− use PDFs

− use NuTeV cuts on hadronic Energy in final state

− use mean neutrino beam energy (125 GeV)

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• MSSM radiative corrections to νµN DIS

– definition of δRν,ν = Rν,νMSSM −R

ν,νSM

The difference between MSSM and SM prediction, δRn = RnMSSM − Rn

SM

with Rn = σnNC/σn

CC(n = ν, ν), using

(σnNC)NLO = (σn

NC)LO + δσnNC (n = ν, ν)

(σnCC)NLO = (σn

CC)LO + δσnCC (n = ν, ν)

can be expanded in δσnNC and δσn

CC

δRn =

(

σnNC

σnCC

)

LO

(

(δσnNC)MSSM − (δσn

NC)SM

(σnNC)LO

− (δσnCC)MSSM − (δσn

CC)SM

(σnCC)LO

)

.

→ Only differences between MSSM and SM radiative corrections

and LO cross sections appear in δRn.

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[ MSSM radiative corrections to νµN DIS, definition of δRν,ν ]

Because of R parity conservation in the MSSM:

− Born cross section : SM = MSSM (very good approx.)

− real photon emission corrections : SM = MSSM (very good approx.)

− SM = MSSM for SM-like 1-loop graphs without virtual Higgs

Thus:

δσMSSM − δσSM = const.×(

[superpartner loops]

+ [Higgs graphs MSSM−Higgs graphs SM])

.

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[ MSSM radiative corrections to νµN DIS ]

– superpartner loop corrections

CC self energy insertions

νµ

d

µ

u

W

Wf

W

Wχ0

i χi

W

Wνi es

i

W

Wus

i dti

CC vertex corrections

νµ

d

µ

u

W

us

χi χ0i

W

ds

χ0i χi

W

χ0i

ds utW

g

ds ut

W

νµ

χ0i

χiW

µs

χi χ0i

W

χ0i

νµ µs

CC box corrections

νµ

d

µ

u

χi

µs

ut

χ0i χ0

i

νµ

ds

χi νµ χ0iχi

us

µsχiχ0

i

dt

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[ MSSM radiative corrections to νµN DIS, SP loop corrections ]

NC self energy insertions

νµ

q

νµ

q

Zγ fc

Z

γfc fc

Z

γχi χi

Z

Zf

Z

Zf f

Z

Zχ0

iχ0

j

Z

Zχi χj

NC vertex correctionsνµ

u

νµ

u

Z

us

χ0i

χ0j

Z

ds

χi χjZ

χ0i

us utZ

χi

ds dtZ

g

us ut

γ

µs

χi χiγ

χi

µs µs

Z

νµ

χ0i χ0

jZ

µs

χi χjZ

χ0i

νµ νµZ

χi

µs µt

NC box corrections

νµ

u

νµ

u

χ0i

νµ

us

χ0j

νµ χ0iχ0

j

us

µsχiχj

dt

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[ MSSM radiative corrections to νµN DIS ]

– MSSM-SM Higgs loop difference

+ CC MSSM Higgs loops + NC MSSM Higgs loops

d

νµ

u

µ

W

W h0, H0, A0, H−

W

W

h0, H0, A0

H−

W

Wh0, H0 G−

W

Wh0, H0 W

d

νµ

d

νµ

γ

ZH−

γ

ZH− H−

Z

Z

h0, H0,A0, H−

Z

Zh0, H0 A0

Z

ZH− H−

Z

Zh0, H0 G0

Z

Zh0, H0 Z

− CC SM Higgs loops − NC SM Higgs loopsd

νµ

u

µ

W

WHSM

W

WHSM G−

W

WHSM W

d

νµ

d

νµ

Z

ZHSM

Z

ZHSM G0

Z

ZHSM Z

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[ MSSM radiative corrections to νµN DIS, Higgs loop difference ]

The partonic processes were calculated using

FeynArts/FormCalc.

[Kublbeck, Bohm, Denner’90],

[Eck ’95], [Hahn, Perez-Victoria ’99], [Hahn ’01],

[Hahn, Schappacher ’02]

see : www.feynarts.de

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• Results for δRν, δRν

– how to scan over MSSM parameters?

goal : find regions of parameter space, where the MSSM might explain

the NuTeV anomaly.

→ difficult, large dimensionality of MSSM parameter space

scanning strategy : ”adaptive scan” [OBr’04]:

→ exploit adaptive integration by importance sampling

method: calculate an approximation to the integral

I =

∫ Mmax1

Mmin1

dM1 · · ·∫ d tan βmax

d tan βmind tanβ F

(

δRν(ν)(M1, . . . , tanβ), M1, . . . , tanβ)

with VEGAS and store the sampled parameter points.

→ automatically, the sample points will be enriched in the regions where

F(

δRν(ν)(M1, . . . , tanβ), M1, . . . , tanβ)

is large.

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[ Results for δRν, δRν, how to scan? ]

some sample choices of F:

• F =

1 if parameters (M1, . . . , tanβ) not excluded

0 elsewhere

→ enrich points in allowed region

• F =

δRν(ν)(M1, . . . , tanβ) if parameters (M1, . . . , tanβ) not excluded

0 elsewhere

→ enrich points where |δRν(ν)| is large in allowed region

• F =

(δRν(. . .))2 + (δRν(. . .))2 if δRν and δRν < 0

0 elsewhere

→ enrich points where δRν, δRν < 0 and√

. . . is large

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[ Results for δRν, δRν ]

– MSSM parameter scan

restrictions taken into account:

• mass exclusion limits for Higgs bosons and superpartners

• ∆ρ-constraint on sfermion mixing

quantities varied:

M1, M2, Mgluino : 10 . . .1000GeV µ : −2000 . . .2000GeV

MSf. : 10 . . .1000GeV Ab, At, Aτ : −2000 . . .2000GeV

mA0 : 10 . . .1000GeV tanβ : 1 . . .50

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[ Results for δRν, δRν, MSSM parameter scan ]

Scan for large values of |δRν| and |δRν| with parameter restrictions

δRν

100 200 300 400 500 600 700 800 900 1000

-2

-1

0

1

2←− Xt [TeV] −→

MSf. [GeV]

δRν

100 200 300 400 500 600 700 800 900 1000

-2

-1

0

1

2

MSf. [GeV]

δRν(ν)

0− 1 · 10−5

1 · 10−5 − 5 · 10−5

5 · 10−5 − 1 · 10−4

1 · 10−4 − 3 · 10−4

3 · 10−4 − 8 · 10−4

8 · 10−4 − 1 · 10−3

> 1 · 10−3

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[ Results for δRν, δRν, MSSM parameter scan ]

−δRν

Scan for negative values of δRν

without parameter restrictions

0 10 20 30 40 50 60 70 80 90 100 0

20

40

60

80

100

−δRν

0− 1 · 10−5

1 · 10−5 − 5 · 10−5

5 · 10−5 − 1 · 10−4

1 · 10−4 − 3 · 10−4

3 · 10−4 − 8 · 10−4

8 · 10−4 − 1 · 10−3

> 1 · 10−3

mχ01[GeV]

mχ±1

[GeV]

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[ Results for δRν, δRν, MSSM parameter scan ]

−δRν

Scan for negative values of δRν

without parameter restrictions

0 10 20 30 40 50 60 70 80 90 100 0

20

40

60

80

100

−δRν

0− 1 · 10−5

1 · 10−5 − 5 · 10−5

5 · 10−5 − 1 · 10−4

1 · 10−4 − 3 · 10−4

3 · 10−4 − 8 · 10−4

8 · 10−4 − 1 · 10−3

> 1 · 10−3

mχ01[GeV]

mχ±1

[GeV]

excludedmχ0

1> 46GeV

excluded

mχ±1

> 94GeV

↑ ↑

−→ all interesting regions excluded

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[ Results for δRν, δRν, MSSM parameter scan ]

−δRν

Scan for negative values of δRν

without parameter restrictions

0 10 20 30 40 50 60 70 80 90 100 0

20

40

60

80

100

−δRν

0− 1 · 10−5

1 · 10−5 − 5 · 10−5

5 · 10−5 − 1 · 10−4

1 · 10−4 − 3 · 10−4

3 · 10−4 − 8 · 10−4

8 · 10−4 − 1 · 10−3

> 1 · 10−3

mχ01[GeV]

mχ±1

[GeV]

excludedmχ0

1> 46GeV

excluded

mχ±1

> 94GeV

↑ ↑

−→ all interesting regions excluded

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[ Results for δRν, δRν, MSSM parameter scan ]

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

-0.008 -0.006 -0.004 -0.002 0 0.002 0.004

no restrictionsrestrictions

NUTEV (+/- 2 sigma)PSfrag replacements

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Summary

• The NuTeV measurement of sin2 θw is intriguing

but has to be further established

(especially confirmation by other experiment(s) is desirable).

• Loop effects in the MSSM are not capable

of explaining the NuTeV ”anomaly”.

(size can be right, but sign is wrong).

• If the ”anomaly” was established,

the MSSM would be in trouble.

Our result can be easily combined with the one-loop SM result.

→ The complete MSSM one-loop prediction for νN scattering

is available for future analyses.