' & $ % Measuring Sfermion Mixing Angles and CP Violating Phases At

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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

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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)  Q u uL Z β u u  2 2 2  mu (Au + µ cot β) MU + mu + guR MZ c2β 

• Down-type squark mass matrix

2 2 2 M + m + g M c2 m (A + µ tan β)  Q d dL Z β d d  2 2 2  md (Ad + µ tan β) MD + md + gdR MZ c2β 

• 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 eiϕ  LL | LR|  2 −iϕ 2  |MLR|e MRR  for each sfermion flavor (neglecting flavor violating mixings). • ϕ 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 ϕ 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.

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˜ + • 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

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• 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.

Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 17 & % ' $

Slepton LR mixing at the NLC

• Classic τ˜ analysis by Nojiri,Fujii,Tsukamoto, hep-ph/9606370, assuming no CP violation. • What is the impact of a CP-violating stau phase? Vienna Group, hep-ph/0204071,hep-ph/0207186 • With suﬃcient amount of information (i.e. all staus, charginos and neutralinos kinematically accessible at NLC) the underlying parameters can be extracted very precisely (TESLA TDR). • However, it is worth reanalyzing the situation with a more realistic spectrum, where only a limited part of the spectrum is 0 available (e.g. τ˜1, lightest χ and χ ). (See Project III later.)

Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 18 & % ' $

Charginos and neutralinos at NLC

• χ˜0 and χ˜ reconstruction with CP-violating phases:

• S. Y. Choi et al., EPJ C 8, 669 (1999), hep-ph/9812236.

• J. L. Kneur and G. Moultaka, PRD 61, 095003 (2000), hep-ph/9907360.

• V. Barger et al., PLB 475, 342 (2000), hep-ph/9907425.

• S. Y. Choi et al., PLB 479, 235 (2000), hep-ph/0001175.

• S. Y. Choi et al., EPJ C 14, 535 (2000), hep-ph/0002033.

• V. Barger et al., PRD 64, 056007 (2001), hep-ph/0101106.

• S. Y. Choi et al., EPJ C 22, 563 (2001), hep-ph/0108117.

• S. Y. Choi et al., hep-ph/0202039.

• J. Kalinowski and G. Moortgat-Pick, hep-ph/0202083.

Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 19 & % ' $

Project I: ˜bL − ˜bR mixing at the LHC

• We have seen studies of t˜ and τ˜ LR mixing determinations at the LHC. What about ˜b? There are three possibilities:

• it’s been studied and I missed it.

• it has not been studied and it cannot be done

• it has not been studied but it could be done

• Why is the sbottom signal interesting? There are generic regions of parameter space (even in MSUGRA) where one encounters the following mass hierarchy:

mLSP < m˜b1 ∼ mt˜1 < mg˜ < mq˜, m˜b2 , mt˜2

The gluino is forced to decay as

0 0 g˜ → tt˜1 → tt¯χ˜ or g˜ → b˜b1 → b¯bχ˜

However, because of the large mt, g˜ → tt˜1 might be closed and

then BR(g˜ → b˜b1) = 100%.

Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 20 & % ' $

Project II: CP violation at the LHC

• There have been no feasibility studies on the possible determination of CP-violating parameters in the strong sector

(squarks, gluino) at the LHC. M3 can have a phase, as well as 2 MLR for any squark flavor (notice: flavor conserving!). • Impossible according to J. Wells’s “coffee theorems” (see last meeting), but that was a guess. Needs to be confirmed by detailed studies. • What is the relevant CP-violating observable?

Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 21 & % ' $

Project III: CP violation in sfermion production at NLC

• The setup: only the lightest sleptons can be produced,

m 0 < m˜ < ECM , χ˜1 `1 simple parametrization of the slepton mass matrix:

M 2 M 2 eiϕ  LL | LR|  2 −iϕ 2  |MLR|e MRR 

• For ` = e, µ, τ: can we measure ϕ from the slepton decay distributions? • Repeat for squarks?

Sfermion mixing angles and phases Konstantin Matchev, University of Florida - 22 & %