MSSM Radiative Corrections to Neutrino-nucleon Deep...
Transcript of MSSM Radiative Corrections to Neutrino-nucleon Deep...
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]
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
• 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.
[ 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.
[ 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
[ 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. . . .
[ 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)
• 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.
[ 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])
.
[ 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
[ 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
[ 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
[ 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
• 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.
[ 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
[ 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
[ 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
[ 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]
[ 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
[ 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
[ 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
Rν
Rν
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.