' $ Measuring sfermion mixing angles and CP violating phases at the LHC and NLC Konstantin Matchev University of Florida 1036 Super B Factory Workshop, SLAC, October 22, 2003 & % ' $ Outline • Sfermion mixing: • L-R mixing • flavor mixing • CP-violation (parametrization, EDM constraints) • Hadron colliders • Squark parameters: masses and LR mixing angles • Stau LR mixing • Slepton flavor mixing in combination with CP violation • Gluino phase (at FNAL) • Lepton colliders • Sfermion LR mixing angles and CP-violation. • Charginos and neutralinos (references) • Sample projects! Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 2 & % ' $ Sfermions (squarks and sleptons) • Up-type squark mass matrix 2 2 2 M + m + g M c2 m (A + µ cot β) 0 Q u uL Z β u u 1 2 2 2 @ mu (Au + µ cot β) MU + mu + guR MZ c2β A • Down-type squark mass matrix 2 2 2 M + m + g M c2 m (A + µ tan β) 0 Q d dL Z β d d 1 2 2 2 @ md (Ad + µ tan β) MD + md + gdR MZ c2β A • Diagonalization leads to LR mixing angles, in general complex. LR mixing is only significant for third generation sfermions (stops, sbottoms, staus). • In addition, there could be mixing among generations (6x6 mass matrix). Squark 1-2 mixing severely constrained by K − K¯ mixing, difficult to observe directly anyway. Slepton 1-2 mixing yields interesting signals at both LHC and NLC. • What about CP violation? Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 3 & % ' $ CP violation in the MSSM • The general MSSM contains many parameters: • 33 masses • 41 phases • 31 SCKM angles • Typical simplification: unification of the gaugino masses and A-terms; ignore sfermion flavor violating mass terms and the associated phases. This leaves us with only 2 CP-violating parameters: the phases of µ and A0 (MSUGRA). • Relaxing gaugino unification allows for independent phases in M1 and M3. • EDM's constrain some combination of the phases that are present, e.g. electron EDM: γ γ ∼ χ± e χ + e ∼ e eL eR L ν R Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 4 & % ' $ EDM constraints • MSUGRA-type model (only 2 independent phases), combined constraints from de, dn and dHg . Barger et al., PRD 64, 056007 (2001) 2 SUGRA 2 θµ/π θµ/π 1.5 1.5 1 1 0.5 0.5 0 0 0 0.5 1 1.5 2 0 250 500 750 θ π [ ] A/ m1/2 GeV 2 2 θµ/π θµ/π 1.5 1.5 1 1 0.5 0.5 0 0 0 250 500 750 1000 2 4 6 8 10 [ ] β m0 GeV tan Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 5 & % ' $ EDM constraints • A more general model (23-parameter MSSM), combined constraints from de, dn and dHg . ◦ are fine tuned, ◦ are ruled out. Barger et al., PRD 64, 056007 (2001) 23 parameter MSSM 2 2 θµ/π θµ/π 1.5 1.5 1 1 0.5 0.5 0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 φ π φ π 1/ 3/ 2 2 θµ/π θµ/π 1.5 1.5 1 1 0.5 0.5 0 0 -2 -1 2 4 6 8 10 10 10 1 tan β tuning ∆X/X Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 6 & % ' $ Sfermion parametrization • Since we are interested in studying sfermion mixings, a model-independent parametrization capturing all relevant features of L-R mixing and CP-violation is simply M 2 M 2 ei' 0 LL j LRj 1 2 −i' 2 @ jMLRje MRR A for each sfermion flavor (neglecting flavor violating mixings). • ' is unconstrained! • The experimental measurements of production cross-sections, masses, couplings, widths, etc. for a given flavor will provide constraints which are nothing but hypersurfaces in this 4 parameter space. • Relevant questions: • Can we perform a sufficient number of measurements so that to determine all 4 parameters above? • If not, then can we at least prove the presence of CP-violation (i.e. that ' 6= 0)? Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 7 & % ' $ Squark measurements at hadron colliders • Mass measurements? No \threshold scan", so the only possibility is the cross-section measurement. Little SM background, but many problems: • How do we tell squark species apart? We can't, except for stops and sbottoms. • We can't measure an absolute squark cross-section unless we know the squark branching fractions. • How do we isolate events of a certain class? Squark pair production can be confused with associated squark-gluino production and gluino pair production. t~ and ~b are often the lightest squarks and gluinos prefer to decay into them. • If the LSP is neutral, the (energy, momentum, mass...) distributions contain information about mass differences. • LR mixing is only important for t~ and ~b. Good news! However, t~ and ~b are strongly produced and LR mixing does not enter the cross-section. We are forced to look at their decays. Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 8 & % ' $ Stop mixing at the LHC Hisano, Kawagoe, Nojiri, hep-ph/0304214 • Consider gluino production and subsequent decays to stops: g~ ! tt~1 ! tbχ~ • The top quark above is polarized: • left-handed, for t~1 = t~L • right-handed, for t~1 = t~R • Bottom quark angular distribution in polarized top decay: 1 dΓ m 2 θ θ θ θ t / t sin2 + 2 cos2 ≈ 4:78 sin2 + 2 cos2 ; Γt d cos θ mW 2 2 2 2 θ = (p~b; ~st) in the top rest frame. θ = π is preferred =) the b from the t decay goes opposite to the t spin, while the b from the t~ decay goes opposite to the t momentum =) Mbb is a measure of the top polarization. Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 9 & % ' $ Stop mixing at the LHC - results • Mbb distribution for t~1 = t~L (solid) and t~1 = t~R (dashed). • Too optimistic? Neglects contributions from other gluino decay chains. • Spin correlations only exist in HERWIG... Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 10 & % ' $ Stau mixing at the LHC Guchait, D.P. Roy, hep-ph/0205015 • Staus can be produced indirectly at the LHC in large numbers in squark and gluino cascade decays, e.g. + − q~¯q~ ! qq¯W~ 1 W~ 1 ! qq¯νν¯τ~τ~ ! qq¯νν¯Z~1Z~1ττ; 0 0 q~¯q~ ! qq¯W~ 1 Z~2 ! qq¯ντ τ~τ~ ! qq¯νZ~1Z~1τ ττ; • The tau polarization in τ~ decay is given by 2 2 aR − aL Pτ = 2 2 aR + aL 0 aR ∼ g N11 cos θτ + λτ N13 sin θτ ; 0 aL ∼ (g N11 + gN12) sin θτ − λτ N13 cos θτ : • Two limits: • small tan β: θτ << 1, λτ << 1 ) aR >> aL ) Pτ = +1. • large tan β: both θτ and λτ non-negligible, but because of cancellations in aL, again aR >> aL ) Pτ = +1. • In contrast, Pτ 0 = −1 for the tau coming from Z~2 decay. On average, we expect to see an effect. Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 11 & % ' $ Stau mixing at the LHC Guchait, D.P. Roy, hep-ph/0205015 • MSUGRA plot for A0 = 0; tan β = 30; µ > 0. <¥1¥ ¢¡¤£ ;A 1¥ ;A¥1¥ ¥§¦©¨ ¥§¦© ¨< 1¥ $ (*) ¨<¥1¥ 9 : ! #" ¥§¦© %©&' =< 1¥ =<¥1¥ >? 1¥ +-,/.1032 >?¥1¥ >@¥<¥ >? 1¥ =1¥<¥ =< 1¥ ¨<¥1¥ ¨1 1¥ ;¤¥1¥ ;¤ 1¥ 1¥1¥ 1 1¥ 465¢7¢8 ~ + • Diagonal dots: W1 ! τ~1ντ threshold. ~ + • Dashed: BR(W1 ! τ~1ντ ). ~ + + ~0 • Vertical dots: W1 ! W Z1 threshold. • Dotdash: Pτ = 0:9. Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 12 & % ' $ Tau polarization measurement at the LHC • Tag tau jets and form the ratio momentum of charged tracks R = total jet energy in calorimeter ( Guchait, D.P. Roy, hep-ph/0205015 )- #( ) +! #( + ,! #( , ¢¡¤£¨§ © ¡ £ © ©. #( ¢¡¤£¦¥ © ¥! #( ¥ ¥! #, ¥! #+ ¥! *) ¥! #( ¥! #' ¥! &% ¥! #$ ¥! #" © • An effect is seen, needs to be confirmed by a detailed study, including backgrounds and realistic detector simulation. Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 13 & % ' $ Slepton flavor mixing and CP violation at the LHC Arkani-Hamed, Cheng, Feng, Hall hep-ph/9704205 • Assume the following is true: • large CP-violating phases in the slepton sector • large flavor-violating slepton mixing angles • all three sleptons have some degree of degeneracy • the two sleptons of the highest degeneracy have ∆m ∼ Γ (typically e~ and µ~). • Strong production of squarks and gluinos yields secondary sleptons which then oscillate to give CP-violating observables like − − N(e+µ ) − N(e µ+) 6= 0: • Advantage: small SM backgrounds! Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 14 & % ' $ Slepton flavor mixing and CP violation at the LHC Arkani-Hamed, Cheng, Feng, Hall hep-ph/9704205 • LHC sensitivity to CP violation in slepton oscillations (3σ) ∼ J 10-3 10-2 10 300 500 700 900 1100 ___∆m Γ 1 10-1 10-1 1 sin2θ • J~ is the SUSY analogue to the Jarlskog invariant and is not constrained by EDMs. Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 15 & % ' $ Gluino phase measurement - I Mrenna, Kane, Wang hep-ph/9910477 • The gluino provides an unique opprotunity because of the lack of a mixing angle confusion. Gluino production at FNAL: 0 0 g~g~ ! qqq¯q¯χ~1χ~1 Correct Combination of Jets 0.12 φ=0 0.1 φ=π/2 φ=π 0.08 /dM σ 0.06 d σ 1/ 0.04 0.02 0 0 20 40 60 80 100 120 140 160 Invariant Mass of Jet Pairs (GeV) • Mjj contains information about the phase, but assumes • very heavy squarks • no background • correct jet pairing • known Mg~ Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 16 & % ' $ Gluino phase measurement - II Mrenna, Kane, Wang hep-ph/9910477 • A CP-violating observable insensitive to the assumptions: pµpν pρpσ = µνρσ 1 2 3 4 E1E2E3E4 0.25 1/2 Width at 1/2 Max φ=0 1.00 φ=π/2 1.30 0.2 φ=π 1.50 ε 0.15 /d σ d σ 1/ 0.1 0.05 0 -3 -2 -1 0 1 2 3 Epsilon Product of Jet 4-Vectors • Backgrounds? What about the LHC? What about polution from squark production? • Gluinos are problematic at the NLC.