MSSM Radiative Corrections. to Neutrino-nucleon Deep-inelastic Scattering. Oliver Brein

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1 MSSM Radiative Corrections to Neutrino-nucleon Deep-inelastic Scattering Oliver Brein Institute of Particle Physics Phenomenology, University of Durham in collaboration with olfgang Hollik and Benjamin Koch

2 outline : Introduction deep inelastic νn scattering at NuTeV possible explanations MSSM radiative corrections to N DIS definition of δr ν, ν = R ν, ν MSSM Rν, ν SM superpartner loop corrections MSSM-SM Higgs loop difference Results for δr ν, δr ν how to scan over MSSM parameters? MSSM parameter scan

3 Introduction deep inelastic νn scattering at NuTeV In the SM neutral (NC) and charged current (CC) neutrino nucleon scattering are described in LO by t-channel and exchange. µ d, ū s, c q u, d c, s u, d, s, c q u, d, s, c At NuTeV and beams of a mean energy of 25 GeV were scattered off a target detector and the ratios were measured. R ν = σν NC σ ν CC, R ν = σ ν NC σ ν CC

4 [ Introduction, νn NuTeV ] NuTeV measured also the weak mixing angle [NuTeV 02]. sin 2 θ on-shell w = ± ± This is about 3σ below the SM prediction! But the measurement is indirect, using the measurements of R ν, R ν making use of the Paschos-olfenstein relation and R = Rν rr ν r = 2 sin2 θ w +, r = σ ν CC σ ν CC 2.

5 [ Introduction, νn NuTeV ] More precisely, ratios of counting rates R ν exp = # of NC-like ν events # of CC-like ν events Rν, R ν exp are measured. = # of NC-like ν events # of CC-like ν events R ν R ν exp, R ν exp can be related to Rν, R ν by a detailed MC physics simulation. The deviation from the SM in terms of Rexp, ν R ν exp are [NuTeV 02]: R ν = Rexp ν Rexp(SM) ν = ± 0.003, R ν = R ν exp R ν exp(sm) = ± R ν, ν : simple starting point for studying MSSM radiative corrections

6 [ Introduction ] possible explanations statistical fluctuation, errors underestimated? re-analyses of E rad. corr. [Diener, Dittmaier, Hollik 03 & 05; Arbuzov, Bardin, Kalinovskaya 03] relevant SM effects neglected? asymmetry of strange sea-quarks in the nucleon (s s) isospin violation (u p d n ) nuclear effects etc.... new physics? modified gauge boson interactions (e.g. in extra dimensions) non-renormalizable operators (suppressed by powers of Λ new physics ) leptoquarks (e.g. R parity violating SUSY) SUSY loop effects (e.g. in MSSM) etc....

7 [ 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 q 2 -dependence use PDFs use NuTeV cuts on hadronic Energy in final state use mean neutrino beam energy (25 GeV)

8 MSSM radiative corrections to N DIS definition of δr ν, ν = R ν, ν MSSM Rν, ν SM The difference between MSSM and SM prediction, δr n = RMSSM n Rn SM with R n = σnc n /σn CC (n = ν, ν), using (σ n NC ) NLO = (σ n NC ) LO + δσ n NC (σ n CC ) NLO = (σ n CC ) LO + δσ n CC (n = ν, ν) (n = ν, ν) can be expanded in δσnc n and δσn CC ( ) ( δr n σ n = NC (δσ n NC ) MSSM (δσ σcc n NC n ) SM (σ LO NC n ) LO (δσn CC ) MSSM (δσcc n ) ) SM (σcc n ). LO Only differences between MSSM and SM radiative corrections and LO cross sections appear in δr n.

9 [ MSSM radiative corrections to N DIS, definition of δr ν, 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 -loop graphs without virtual Higgs Thus: δσ MSSM δσ SM = const. ( [superpartner loops] + [Higgs graphs MSSM Higgs graphs SM] ).

10 [ MSSM radiative corrections to N DIS ] superpartner loop corrections CC self energy insertions d µ u f χ i ν i ẽ s i ũ s i d t i CC vertex corrections d χ i µ ũ s u µ s χ 0 i χ i d s ũ t d s ũ t χ 0 χ i i χ i d s g µ s CC box corrections µs µ χ i d ũ t χ0 i u χ i d s ũ s d t χ i χ0 i µ s χ i

11 NC self energy insertions [ MSSM radiative corrections to N DIS, SP loop corrections ] q γ q f c f c f c χ i χ i γ γ f f f χ 0 j χ i χ j NC vertex corrections χ 0 j χ i χ j ũ s ũ t d s d t ũ s ũ t u ũ s u d s χ i g µ s χ i µ s χ i χ i χ i µ s µ s χ γ γ 0 i χ 0 j χ i χ j µ s µ t NC box corrections χ0 ν j χ 0 µ j χ j µ s χ i u ũ s u ũ s d t

12 [ MSSM radiative corrections to N DIS ] MSSM-SM Higgs loop difference + CC MSSM Higgs loops + NC MSSM Higgs loops d u h 0, H 0, A 0 h 0, H 0, A 0, H µ H d γ d H γ H H h 0, H 0, A 0, H h 0, H 0 G h 0, H 0 h 0, H 0 A 0 H H h 0, H 0 G 0 h 0, H 0 CC SM Higgs loops d u µ H SM H SM G H SM NC SM Higgs loops d d H SM H SM G 0 H SM

13 [ MSSM radiative corrections to N DIS, Higgs loop difference ] The partonic processes were calculated using FeynArts/FormCalc. [Küblbeck, Böhm, Denner 90], [Eck 95], [Hahn, Perez-Victoria 99], [Hahn 0], [Hahn, Schappacher 02] see :

14 Results for δr ν, δr ν 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 = M max M min dm d tan β max d tan β min d tan β F ( δr ν( ν) (M,..., tan β), M,..., tan β ) with VEGAS and store the sampled parameter points. automatically, the sample points will be enriched in the regions where F ( δr ν( ν) (M,..., tan β), M,..., tan β ) is large.

15 [ Results for δr ν, δr ν, how to scan? ] some sample choices of F: F = if parameters (M,..., tan β) not excluded 0 elsewhere enrich points in allowed region F = δr ν( ν) (M,..., tan β) if parameters (M,..., tan β) not excluded 0 elsewhere enrich points where δr ν( ν) is large in allowed region F = (δr ν (...)) 2 + (δr ν (...)) 2 if δr ν and δr ν < 0 0 elsewhere enrich points where δr ν, δr ν < 0 and... is large

16 [ Results for δr ν, δr ν ] MSSM parameter scan restrictions taken into account: mass exclusion limits for Higgs bosons and superpartners ρ-constraint on sfermion mixing quantities varied: M, M 2, M gluino : GeV µ : GeV M Sf. : GeV A b, A t, A τ : GeV m A 0 : GeV tan β :... 50

17 [ Results for δr ν, δr ν, MSSM parameter scan ] Scan for large values of δr ν and δr ν with parameter restrictions δr ν 2 X t [TeV] δr ν M Sf. [GeV] δr ν( ν) > M Sf. [GeV]

18 [ Results for δr ν, δr ν, MSSM parameter scan ] δr ν Scan for negative values of δr ν without parameter restrictions δr ν > m χ 0 [GeV] m χ ± [GeV]

19 [ Results for δr ν, δr ν, MSSM parameter scan ] δr ν 00 Scan for negative values of δr ν without parameter restrictions excluded excluded m χ ± [GeV] m χ 0 [GeV] δr ν > 0 3 m χ ± > 94GeV m χ 0 > 46GeV all interesting regions excluded

20 [ Results for δr ν, δr ν, MSSM parameter scan ] δr ν 00 Scan for negative values of δr ν without parameter restrictions excluded excluded m χ ± [GeV] m χ 0 [GeV] δr ν > 0 3 m χ ± > 94GeV m χ 0 > 46GeV all interesting regions excluded

21 [ Results for δr ν, δr ν, MSSM parameter scan ] R ν ents no restrictions restrictions NUTEV (+/- 2 sigma) R ν

22 Summary The NuTeV measurement of sin 2 θ w 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.