CP Violation in Supersymmetry and the LHC. Rohini M

CP violation in Supersymmetry and the LHC. Rohini M. Godbole

CP violation in Supersymmetry and the LHC.

Introduction. ♦ Eﬀects on CP violation on χ˜ , χ˜0 sector and the LHC. ♦ 2 CP mixing induced in the Higgs sector due to CP violation ♦ in soft SUSY breaking parameters.

Plugging the ’hole’ in tan β–MH + plane at low neutral Higgs ♦ masses, ( 10 – 50)GeV through the charged Higgs decay at the LHC.∼

Conclusions and & Summary. ♦

Physics at LHC 2004, July 13-18, 2004. page 1 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Introduction

Why CP violation in SUSY?

Why study CP 6

The phenomenon still lacks a fundamental understanding

CKM description vindicated by measurements of CP mixing in the B0 sector. • CKM CP not suﬃcient to explain quantitatively why • 6

Nb 10 N¯b 6.1 10− 0 (1) Nγ ∼ × Nγ ∼

Sources of CP violation beyond the CKM? •

Physics at LHC 2004, July 13-18, 2004. page 2 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

CP and SUSY 6 CP violation in SUSY: Ugly Duckling to Swan !

Large # (44 to be precise) of phases of the SUSY parameters e.g.µ, Af , Mi, i = 1, 3 can not be rotated away by a simple redeﬁnition of the ﬁelds.

Older days:

These generate unacceptably large electric dipole moments for fermions. Fine tune all the CP phases in SUSY to zero. 6 Now:

Ibrahim et al 97,Brhlik et al 98,Bartl et al 99,Falk et al 98,99

It is possible for some combination of phases to be O (1) and yet satisfy all the constraints on EDM’s provided the ﬁrst two generation of squarks are heavy.

Why does that make CP in MSSM a Swan? 6

Physics at LHC 2004, July 13-18, 2004. page 3 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

A few more things about CP : 6 1. CP in the Higgs sector is a theoretically attractive source of the additional CP 6required to explain the Barayon Asymmetry in the Universe. 6

2. CP posible only in Multi-Higgs models, of which SUSY is one example. 6

3. CP in the MSSM, large number of available phases, possible to satisfy all the 6constraints and still have enough CP to help Baryogenesis. 6

4. The MSSM CP phases induce CP mixing in the Higgs sector (which has no CP mixing at the6 tree level) of the MSSM through loop eﬀects Pilaftsis 98,Choi et al 00, Carena et al 00

5. CP mixing in the Higgs sector, one way for CP in SUSY to manifest itself: can aﬀect production rates at LHC as well. Dedes6 et al 99,Choi et al 01

Physics at LHC 2004, July 13-18, 2004. page 4 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Phenomenology of CP violating MSSM at colliders. 6 Which phases can be large?

µ , A and Mi , i = 1, 2. • | | | f | | | Can give rise to nonzero phases in the χ˜ and χ˜0 sector. ♦ Phases in the sfermion sector can also be non-zero. • What can the phases do? ♦ They can aﬀect the couplings, masses of the sparticles, aﬀect CP-even variables • the rates of production, decay widths, branching ratios.

CP odd observables constructed out of ﬁnal state decay products will have • non-zero value

+ Exhaustive discussion for the e e− case for the χ˜, χ˜0 and the sfermions, charged Higgses.

Choi et al 98,00,01,03,04,Kneur99, Barger 01, Bartl et al 02,03, Christova + Kraml 02, RG + Kraml + Gadosijk

+ Very often the CP-even variables, precision measurables, at e e− colliders oﬀer a better probe of phases due to the larger size of the eﬀects. Physics at LHC 2004, July 13-18, 2004. page 5 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Hadronic Colliders? χ˜ systems

CP violating phases can change the dilepton invariant mass distribution. ♦ — Eﬀect on phenomenology of cascade decay. — Can aﬀord information on phase if all the SUSY parameters are known.

For a pp¯ possible to construct CP-odd quantities, for χ˜ , χ˜0 system. ♦ Guchait, Choi et al, 0007276,9904276, Kane et al, 99. Studied trilepton signal from 0 pp¯ χ˜ χ. → 2 1 Eﬀects on ♦ 0 – σ(pp¯ χ˜−χ˜ ) → 1 2 0 0 0 + – (χ˜− χ˜ ` ν), (χ˜ χ˜ ` ` ) B 1 → 1 − B 2 → 1 −

Physics at LHC 2004, July 13-18, 2004. page 6 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

T-odd/CP-odd triple products

For the p¯p case possible to construct T-odd variables using initial (anti)proton ♦direction:

T = p~` (p~` p~` ), O 1 · 3 × 4 0 + `1 = ` of the chargino decay χ˜− χ˜ ` ν¯ , and `3 = ` , `4 = ` of the neutralino − 1 → 1 − ` 0− 0 decay χ˜0 χ˜0 ` ` +. 2 → 1 0− 0

``0 = p~p (p~ p~ ) OT · ` × `0 `, ` :any combination of two momenta among the three ﬁnal lepton momenta. { 0}

Physics at LHC 2004, July 13-18, 2004. page 7 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

2 20 fb−1 The shaded areas ruled out by EDM con- 30 fb−1 straints.

Contours show regions that can be π / probed at 5σ level, for a given luminosity. 1 1 Φ Thus Tevatron can probe CP violation in the MSSM through such studies.

EDM constraints have been imposed on 0 the SUSY phases. 0 1 2

Φµ/π

What about LHC?

At the LHC the initial state is not a CP eigenstate.

So far no studies exist how one can use the χ˜ sector to probe the CP phases at the LHC. 6

Investigations to estimate the eﬀect of these phases, on the studies using ,say, cascade decays at the LHC needed.

Physics at LHC 2004, July 13-18, 2004. page 8 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Eﬀect of SUSYCP on Higgs phenomenology 6 MSSM CP phases CP in the Higgs sector: 6 ⇒ 6 h,H A CP conserving MSSM Three Neutral Higgses CP -even CP -odd φ , φ , φ CP violation : 1 2 3 no ﬁxed CP property

mφ1 < mφ2 < mφ3

Sum rules exist for φiff¯ , φiV V (A. Mendez and A. Pomarol, PLB 272 (1991) 313. J.Gunion, H. Haber and J. Wudka, PRD 43 (1991) B.Grzadkowski, J.Gunion and J. Kalinowski, PRD 60 (1999) 075011)

g2 + g2 + g2 = g2m2 , i = j = k φiW W φjW W φkW W W 6 6 First proposed in a model independent way. The h, H, A now all mix and share the couplings with vector boson pair VV. Will aﬀect production rates.

Predictions in terms of SUSY CP phases in the MSSM for this mixing. 6 Physics at LHC 2004, July 13-18, 2004. page 9 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Three types of eﬀects on Higgs production rates

I] CP phases in MSSM CP in q˜q˜φ couplings aﬀect the gghi coupling: A. Dedes and6 S. Moretti, PRL 84 (2000)⇒ 6 22,... ⇒

II] CP phases in MSSM explicit CP mixing for Higgses 6 ⇒ A. Pilaftsis, PLB 435 (1998) 88, A. Pilaftsis, C. E. Wagner, NPB 553, 3 (1999), S. Y. Choi, M. Drees and J. S. Lee, PLB 481, 57 (2000)....

III] Eﬀects on the couplings with b

Enhanced production cross-sections through b-fusion: hep-ph 0401024, F. Borzmuati, J.S. Lee and W. Y. Song

Physics at LHC 2004, July 13-18, 2004. page 10 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

A few details of the mixing.

General two-Higgs-doublet Model:

Two complex Y = 1, SU(2)L doublet scalar ﬁelds, Φ1 and Φ2 Most general Higgs potential is:

2 2 2 V = m11 Φ† Φ1 + m22 Φ† Φ2 [m12 Φ† Φ2 + h.c.] 1 2 − 1 1 2 1 2 + λ1(Φ† Φ1) + λ2(Φ† Φ2) + λ3(Φ† Φ1)(Φ† Φ2) + λ4(Φ† Φ2)(Φ† Φ1) 2 1 2 2 1 2 1 2 1 2 + λ5(Φ1† Φ2) + λ6(Φ1† Φ1) + λ7(Φ2† Φ2) Φ1† Φ2 + h.c. 2 h i

m11, m22, λ1 4 Unitarity V { − } ∈ < ⇒ ∈ < ⇒ m12, λ5 7 {{ − } ∈ C

Notice that with one Higgs doublet, we can have no CP violation.

Physics at LHC 2004, July 13-18, 2004. page 11 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

MSSM:

Higgs potential as 2HDM above with

2 2 2 2 0 2 m = m µ λ1 = λ2 = (g + g )/8 11 − 1 − | | − 2 2 2 2 0 2 m = m µ λ3 = (g g )/4 22 − 2 − | | − − 2 2 m12 = µB λ4 = g /2

λ5 = λ6 = λ7 = 0

Vacuum expectation values:

1 0 1 iξ 0 Φ1 = Φ2 = e h i √2 v1 h i √2 v2

Physics at LHC 2004, July 13-18, 2004. page 12 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

At tree-level:

Minimisation conditions arg(m2 eiξ) = 0 ⇒ 12

Rotate phase away with an appropriate choice of Φ2

iξ Φ2 e Φ2 arg(m12) = 0 → − ⇒

No CP-violation in tree-level Higgs sector

Higgs bosons are CP-eigenstates

Physics at LHC 2004, July 13-18, 2004. page 13 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

At one-loop:

Now have arg(m2 eiξ) = 0 12 6 Potentially have CP-violation from soft-susy breaking terms At,b,τ , M3

~ f

2 mf A H 2 2 m(Af µ) ∝ m ˜ m ˜ = f1 − f2

iΦA iΦ3 iΦ write A = A e f , M3 = M3 e and µ = µ e µ f | f | | | | | CP-violation parameterised by Φ , Φ3, Φµ { Af } Higgs bosons are NOT CP-eigenstates

Physics at LHC 2004, July 13-18, 2004. page 14 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Electric Dipole Moments [Dedes, Moretti, Nucl. Phys. B 576 (2000) 29]

Φµ and ΦAf are constrained by experimental limits of the EDMs of electron and neutron:

27 26 de exp 4.3 10− e cm dn exp 6.3 10− e cm | | ≤ × | | ≤ × e.g. at leading order:

tan β = 2.7 µ = 600GeV | | Mq˜1,2 = 1000GeV

Mq˜3 = 300GeV M˜g = 300GeV MA = 200GeV

shaded areas excluded Require A > contour | |

Physics at LHC 2004, July 13-18, 2004. page 15 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Higher tan β more diﬃcult

tan β = 10 µ = 600GeV | | Mq˜1,2 = 300GeV

Mq˜3 = 300GeV M˜g = 300GeV MA = 200GeV

shaded areas excluded Require A > contour | |

Much of the allowed region depends on accidental SuSy cancellations (ﬁne tuning?)

Physics at LHC 2004, July 13-18, 2004. page 16 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

The CPX Scenario [Carena, Ellis, Pilaftsis & Wagner, Phys. Lett. B495 (2000) 155]

“designed to showcase the eﬀects of CP violation in the MSSM”

= = = = = MQ˜3 MU˜3 MD˜3 ML˜3 ME˜3 MSuSy

µ = 4MSuSy, A = 2MSuSy, M3 = 1T eV | t,b,τ | | |

Allow the following parameters to vary:

tan β, MH , MSuSy,

Φ , Φ , Φ , Φ3, Φµ { At Ab Aτ }

Physics at LHC 2004, July 13-18, 2004. page 17 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Masses and couplings [Carena, Ellis, Pilaftsis & Wagner, Nucl. Phys. B 625 (2002) 345]

CPX scenario with tan β = 5, MH = 150GeV, MSuSy = 500GeV, Φµ = 0, Φ˜g = 0 and π/2. masses:

M 150 GeV H3 ∼

Φ˜g does not have a big eﬀect (two-loop)

Physics at LHC 2004, July 13-18, 2004. page 18 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

couplings to VV:

Sum rule for couplings

3 g2 = g2 i=1 φiV V φiV V (SM) P

Often gφiZZ vanishes! light Higgs may have ⇒ escaped LEP limits

Physics at LHC 2004, July 13-18, 2004. page 19 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

LEP Limits Preliminary OPAL results : hep-ex/0406057

π Φ = Φ = Φ = Φ˜ = At Ab Aτ g 2

Φµ = 0

MSuSy = 500 GeV

Even have gaps at 0–50 GeV!

Physics at LHC 2004, July 13-18, 2004. page 20 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

gg φ cross-sections [Dedes, Moretti, Nucl. Phys. B 576 (2000) 29 → Lee, Pilaftsis, Carena, Choi, Drees, Ellis & Wagner, Comput. Phys. Commun. 156 (2004) 283]

g t φ

g igmt g ˜ ˜ = (µ∗ sin α At cos α) htLtR∗ 2MW sin β − g ~t φ gg φ cross-sections may be altered g → ~ g t

Physics at LHC 2004, July 13-18, 2004. page 21 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Fortunately, gg h only increases in allowed regions →

Physics at LHC 2004, July 13-18, 2004. page 22 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

gg H decreases (as expected from coupling sum rules) →

Physics at LHC 2004, July 13-18, 2004. page 23 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

gg A doesn’t change much →

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[Carena, Ellis, Mrenna, Pilaftsis & Wagner, Nucl. Phys. B 659 (2003) 145]

σ σ LEP(95)/TeV(3 )/LHC(5 ) for CPX0.5 20 40 60 80 100 120 20 40 60 80 100 120 40 40 30 30 Theory excluded 20 20

10 10 Allowed! 5 5

900 600 β 2 2 LEP excluded

tan 40 40 30 30 20 20 LHC search reach 10 10

5 5 Tevatron search reach 300 00 2 2 20 40 60 80 100 120 20 40 60 80 100 120

MH1 (GeV)

Gaps in coverage! Need to look at the light higgs searches again.

Physics at LHC 2004, July 13-18, 2004. page 25 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

A few observations

Small regions in tan β, M + plane where LHC,TEVATRON will have no reach • H

Caused by reduced φ1 coupling to W/Z AND top. •

There are regions where the three states will be degenerate, just as earlier discus- sions of ’intense coupling’ regime.

The higgs searches in CP scenario need to be looked at carefully. 6

Physics at LHC 2004, July 13-18, 2004. page 26 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

What happens to plots of yesterday?

preliminary results presented by M. Schumacher at the meeting on ’CP violation and nonstandard Higgs’ //http://kraml.home.cern.ch/kraml/CPstudies/

Warning by M.S.: NOT the oﬃcial ATLAS results.

A hole in the tan β M + plane: for m < 50, 100 < m < 110 and 130 < m < 180. − H φ1 φ2 φ3 The results of theory analysis veriﬁed.

Physics at LHC 2004, July 13-18, 2004. page 27 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Suggestion to ﬁll the hole via h+ decays

K. Assamgaan, D. Ghosh, R.G. and D.P. Roy, in preparation

+ Small tan β, light M + large B.R.(H φ1W ) . H ⇒ → Use t¯t production with :

+ t ¯bH ¯bφ1W ¯bb¯bW and ¯t ¯bW , with one W decaying leptonically the other → → → → hadronically. Hence both W 0s can be reconstructed.

Look at the W W bbbb events, 3 tagged b0s.

¯ ¯ The mass of the bb pair with the smallest value will cluster around mφ1 and bbW around MH +.

Physics at LHC 2004, July 13-18, 2004. page 28 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

70 tanb = 4.0 200 tanb = 4.6 tanb = 5.0 180 ϕ = 60 degree 60 tan β = 2 160 50 140

40 120 tan β = 2.2

(fb) 100 (fb) σ 30 σ 80 tan β = 2.4 20 60 40 10 β 20 tan = 3 0 0 10 15 20 25 30 35 40 45 50 55 60 10 15 20 25 30 35 40 45 50 55 60 MH1 (GeV) MH1 (GeV)

Physics at LHC 2004, July 13-18, 2004. page 29 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

reconstructed masses for h0,hp,t 9 'fort.81' using 1:3 'fort.82' using 1:3 8 'fort.83' using 1:3

0 0 20 40 60 80 100 120 140 160 180 200

LHC Signal : very clear clustering in the b¯b, b¯bW invariant masses corresponding to

+ ¯ mφ1 , MH also in bbbW invariant mass at mt. So detectability controlled by just the signal size.

Physics at LHC 2004, July 13-18, 2004. page 30 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Tools

CPSuperH FeynHiggs

Lee, Pilaftsis, Carena, Choi, Drees, Ellis & Wagner Hahn, Heinemeyer, Hollik & Weiglein http://theory.ph.man.ac.uk/ jslee/CPsuperH.html http://www.feynhiggs.de ∼ low energy parameters masses, BR’s, couplings... −→ RG improved eﬀective potential Feynman–diagrammatic approach for masses & couplings for masses & couplings leading log approx for one-loop full one-loop 2 2 leading log approx for O(αsαt, αt ), full O(αsαt, αt ) but but full phase dependence approx phase dependence

n O(αsαt) has (αs tan β) resummation and full complex phase dependence

Physics at LHC 2004, July 13-18, 2004. page 31 of 32 CP violation in Supersymmetry and the LHC. Rohini M. Godbole

Conclusions

CP violation in the MSSM will alter the sparticle phenomenology in a big way. ♦ Possibilities of probing/measuring this at hadronic colliders have not yet been explo♦ red.

Can aﬀect the Higgs search drastically, a hole in the tan β –MH + plane, for a scena♦ rio in which the phase eﬀects are maximised: LEP will have missed the signal and LHC/Tevatron will not see it.

+ Production of φ1 through the H decay produced in the t decay, can perhaps ♦help ﬁll the hole.

All studies very preliminary, even the tools to calculate CP scenarios still ♦need to be standardised. 6

Lot of work to do. ♦

Physics at LHC 2004, July 13-18, 2004. page 32 of 32