A T-odd observable sensitive to CP violating phases

Transcription

1 A T-odd observable sensitive to CP violating phases Motivations T-odd triple product Stop cascades at the LHC Experimental challenges PL, Gil Paz, Lian-Tao Wang, and Itay Yavin, hep-ph/

2 Motivations CP violating phases expected in field theory/string theory Probe of supersymmetry breaking sector Affect spectrum, interactions (e.g., Higgs, neutralinos, charginos) (Brhlik, Kane) Electric dipole moments (EDMs) Baryogenesis (e.g., electroweak) Many phases; want complementary probes

3 Previous studies of CP Violation at Colliders J. F. Donoghue and G. Valencia, Phys. Rev. Lett. 58, 451 (1987) [Erratum-ibid. 60, 243 (1988)]. C. J. C. Im, G. L. Kane and P. J. Malde, Phys. Lett. B 317, 454 (1993) [hep-ph/ ]. S. Dawson and G. Valencia, Phys. Rev. D 52, 2717 (1995) [hep-ph/ ]. A. Bartl, E. Christova, K. Hohenwarter-Sodek and T. Kernreiter, Phys. Rev. D 70, (2004) [hep-ph/ ]. V. D. Barger, T. Falk, T. Han, J. Jiang, T. Li and T. Plehn, Phys. Rev. D 64, (2001) [hep-ph/ ]. N. Arkani-Hamed, J. L. Feng, L. J. Hall and H. C. Cheng, Nucl. Phys. B 505, 3 (1997) [hep-ph/ ]. O. Nachtmann and C. Schwanenberger, Eur. Phys. J. C 32, 253 (2004) [hepph/ ]. A. Bartl, H. Fraas, S. Hesselbach, K. Hohenwarter-Sodek and G. A. Moortgat- Pick, JHEP 0408, 038 (2004) [hep-ph/ ]. G. Valencia and Y. Wang, Phys. Rev. D 73, (2006) [hep-ph/ ].

4 K. Kiers, A. Szynkman and D. London, Phys. Rev. D 74, (2006) [hep-ph/ ]. A. Bartl, H. Fraas, S. Hesselbach, K. Hohenwarter-Sodek, T. Kernreiter and G. Moortgat-Pick, hep-ph/ A. Szynkman, K. Kiers and D. London, hep-ph/

5 Electric dipole moments (EDMs) and phases can be found in [14, 2]. The dominant contribution is typically from xchange diagram and is proportional to sin θ µ. Thus the primary constraint coming ron EDM limits is an upper limit on the phase of µ. The subdominant neutralino e! e L " $ e R + e L " ±! $ e # R Stringent limits from electron, 199 Hg atom neutron, rams contributing to the electric dipole moment of the electron. The SUSY phases ossed vertices. e has a more complicated dependence on the SUSY phases, including both pieces o sin θ µ and sin γ e, where γ e = arg(a e + µ tan β). Cancellations can occur between chargino exchange contributions, and this serves to weaken the absolute limits on ses, although θ µ of O(1) requires either severe fine-tuning of parameters or a very m, as we will see below. on EDM is considerably more complicated, and until recently, the computation eutron EDM induced by SUSY phases has been plagued by very large theoretical The SUSY phases contribute both to the EDMs and color EDMs (cedms) of the the last year, the contribution to the neutron EDM both from the induced θ due Ms of the quarks [20] and from the quark EDMs and cedms themselves [21] have alculated using QCD sum rules, allowing a reduction in the theoretical uncertainty. ect is to reduce slightly the predicted neutron EDM, and with smaller error bars. Ms receive contributions from the chargino and neutralino exchange diagrams of! d $ Mainly sensitive to φ µ }{{} phase in µ (often choose φ 2 = 0) Limits weaker for larger masses φ 2 }{{} phase in M 2 (Pokorski, Rosiek, Savoy; Brhlik, Good, Kane; Ibrahim, Nath; Barger, Falk, Han, Jiang, Li, Plehn (figures); Pospelov, Ritz)

6 Electroweak baryogenesis Need strong first order phase transition and CP violation (+ sphalerons) q q broken phase φ = 0 becomes our world v Wall unbroken phase q q Neither strong enough in SM Only narrow window with light Higgs and stop in MSSM (Carena, Seco, Quiros, Wagner) Mainly sensitive to φ µ φ 2, constrained by EDMs _ q _ q CP Sph Γ B + L _~ 0 CP Sph Γ B + L (Figure: W. Bernreuther, hep-ph/ ) >> H _ q _ q

7 Singlet extensions of MSSM Extend MSSM by standard model singlet field S (may be charged under U(1) or other symmetries) Dynamical µ term: W = λ S H u H d + W ( S) µ eff = λ S Many models (NMSSM, nmssm, UMSSM, ; review: hep-ph/ ) Electroweak baryogenesis much easier (Pietoni; Davies, Froggatt, Moorhouse; Huber, Schmidt; Kang, PL, Li, Liu; Menon, Morrissey, Wagner; Huber, Konstandin, Prokopec, Schmidt) Tree-level cubic term, V = λa λ SH u H d + h.c. strong first order phase transition May be new CP phases in W ( S) and soft terms Aspects may be verifiable at LHC

8 T-odd triple product If p j, j = 0,..., 3 are independent, the triple product T = ɛ µναβ p µ 0 pν 1 pα 2 pβ 3 }{{} M 0 p 1 ( p 2 p 3 ) p 0 =(M 0, 0) is odd under T and P ( p j p j )

9 T invariance and Hermiticity (CPT): out f i in }{{} T out ī f in }{{} CPT in f ī out, where ī is T-reversed state T = 0 implies CP violating phases in interfering amplitudes, f i f ī and/or interfering strong final state phases, e.g., f out f in (may be strong, electromagnetic, unstable propagator, etc) Can separate by comparing decay process p 0 p 1 p 2 p N and its CP-conjugate decay p 0 c p 1 c p 2c p N c (i.e., replace particle of momentum p by antiparticle with p c = p)

10 P and T odd T = 0 requires interference of two amplitudes with different phases and parity p f H p 0 = A( p f )e i(ρ A+φ A ) + B( p f )e i(π 2 +ρ B+φ B ) p f c H p 0 c = A( p f c )e i(ρ A φ A ) + B( p f c )e i(π 2 +ρ B φ B ) where A( p) = A( p), B( p) = B( p) φ A,B are weak phases (change sign for CP conjugate process) ρ A,B are strong phases (do not change sign) e iπ/2 always present in interference for T when summed over spins, e.g., i in Tr γ 5 γ µ γ ν γ α γ β (could absorb in ρ B )

11 Then where T = 2K [sin(ρ A ρ B ) cos(φ A φ B ) + cos(ρ A ρ B ) sin(φ A φ B )] T = 2K [sin(ρ A ρ B ) cos(φ A φ B ) cos(ρ A ρ B ) sin(φ A φ B )] T = M 0 p 1 ( p 2 p 3 ) T = M 0 p 1c ( p 2 c p 3 c ) and K dp }{{ S} (T AB) phase space T + T = 4K cos(ρ A ρ B ) sin(φ A φ B ) isolates CP-odd term

12 Stop cascades at the LHC ( PL, Gil Paz, Lian-Tao Wang, and Itay Yavin, hep-ph/ ) Consider the cascade decay t t + Ñ a t + l + + l + Ñ 1 with T = M t p t ( p l + p l ) Assume Ñ a on-shell and Ñ 1 = LSP (stable). In examples, Ñ a = Ñ 2 = wino, Ñ 1 = bino. (Related: Bartl, Christova, Hohenwarter-Sodek, Kernreiter, PR D70, (2004))

13 Dimensionless asymmetry: θ angle between p t and p l + p l η = N + N N + + N = N + N N total N + = 1 0 dγ d cos θ d cos θ, N = 0 1 dγ d cos θ d cos θ η is not invariant Calculate η th in Ñ a rest frame

14 Measure η exp = Dη th in lab (detector) frame: D 0.3 is dilution factor Need N = 1 = 1 ηexp 2 D 2 ηth 2 observed cascade decays for 1σ measurement CP- conjugate decay t c t c + Ñ a t c + l + l + + Ñ 1 with T = M t p t c ( p l p l +) (θ = angle between p t c and p l p l +)

15 Asymmetry in t t + Ñ a t + l + + l + Ñ 1 t l l + f N1 t l + l f N1 fn a e l + fn a e l et et (a) (b) Assume dominated by slepton l η or T 0: interference of two diagrams (Majorana neutralinos) Typeset Princeton by FoilTEX (March, 2007) Paul 1Langacker (IAS)

16 Interference with Ñ a ZÑ 1 l + l Ñ 1 could also contribute. (assume suppressed by couplings (e.g., gauginos) or kinematics for illustration) t l l + f N1 t l + l f N1 fn a e l + fn a e l et t l l + f N1 et + fn a Z et Typeset by FoilTEX 1

17 Amplitudes Define vertices G f L,R isl, containing fermion, sfermion, neutralino mixings and phases (i.e., take neutralino masses real) f s Ñ l i ( G f L isl P L + G f R isl P R ) f i

18 Amplitudes im a = iū(p t ) G t R P t ta L + G t L q + MÑa P t ta R G l R jka P L + G l L jka P R 0 1 k1 2 M A 2 l ū(pñ1 ) k v(p l ) j q 2 M 2 Ña G l L ik1 P L + G l R! ik1 P R v(p l + ) 0 im b = iū(p t ) G t R P t tb L + G t L P t tb q + M Ñ b q 2 M 2 Ñ b G l L ilb P L + G l R ilb P R v(p l + ) i 0 1 k2 2 M A 2 l ū(pñ1 ) l G l R jl1 P L + G l L jl1 P R 1 A i v(p l ), j where q = p t p t, k 1 = p l + i + pñ1, k 2 = p l j + pñ1

19 The on-shell case t l l + f N1 t l + l f N1 fn a e l + fn a e l et et (a) (b) Largest rate for on-shell sleptons Both diagrams cannot be on-shell in narrow width approximation (except for set of measure zero) η suppressed by 1 Γ l α e π π M l Typeset by FoilTEX 1 (too small, even for maximal CP phases)

20 The off-shell case Off-shell sleptons suppress decay rate, but allow large asymmetries η Re spin M am b Im (a R a L ) ( ) a R = q 2 G t L t ta Gt L G l R t tb jka G l L ilb G l L ik1 G l R jl1 ( ) + MÑa MÑ1 G t R t ta Gt R G l R t tb jka G l R ilb G l R ik1 G l R jl1 ( ) + MÑb MÑ1 G t R t ta Gt R G l L t tb jka G l L ilb G l L ik1 G l L jl1 ( ) + MÑa MÑb G t R t ta Gt R G l R t tb jka G l L ilb G l L ik1 G l R jl1 with L R for a L

21 Neglect off-diagonal mixing elements and take Ñ a = Ñ b : Im (a R a L ) = 2M 2 Ñ a ( g qa R 2 g qa where L 2) Im ( g la ( + MÑa MÑ1 g qa R 2 g qa L [ 2) (g ) la 2 ( Im R g l1 R ) 2 + ( g la L R gla L ) 2 ( ) g l1 2 ] L ) gl1 R gl1 L = 2M 2 Ñ a ( g qa R 2 g qa L 2) g la R gla L gl1 R gl1 L sin ( ϕ l1 R + ϕl1 L ϕla R ϕla L )) + MÑa MÑ1 ( g qa R 2 g qa L 2) [ g la R 2 g l1 R 2 sin ( 2(ϕ l1 R ϕla R )) + (R L) ] G t R,L t ta gqa R,L G l R,L ika gla R,L G l R,L ik1 g l1 R,L g g e iϕ

22 Example: Ñ a = pure wino, Ñ 1 = pure bino η = µ1 ( ) F (µ 1 ) 2 G 1 (µ 1 ) + G 2 (µ 1 ) cos(2 ϕ) sin(2 ϕ) where ϕ = ϕ l1 L ϕla L is difference between bino and wino phases (nonuniversal gauginos), µ 1 = M 2 /M 2, and F, G Ñ 1 Ñ i are kinematic a functions

23 ive number of events is doubled if one combines the tl l and t l l asymm Δ ϕ = π/2 2Δ ϕ = π/4 2 Δ ϕ = π /8 η µ 1

24 For MÑ1 /MÑa 0.7, need N 1 η 2 th 100 sin 2 (2 ϕ) (need factor 10 more including experimental limitations) events Expected LHC cross sections for t L t c L and rates for tl+ l, with M l = 300 GeV, M Ñ 2 = 140 GeV, MÑ1 = 100 GeV and heavy g, q (B( t tñ 2 ) 1/3; B(Ñ 2 l + l Ñ 1 ) 1/6 for l = e or µ) M t L σ (fb) N[tl + l ] L = 300fb 1 (1 ab 1 ) 500 GeV (24000) 800 GeV (1800) 1 TeV (400) 1.2 TeV 1 30 (100) Promising for M t L 800 GeV, especially after upgrade

25 Experimental challenges Many experimental complications. full simulation) Approximate discussion (need Dilution from missing LSP Cannot construct t rest frame Probability w 0.33 of flip of sign of cos θ between lab and Ñ a frames 1 Need factor = 1 10 more events D 2 (1 2w) 2

26 3 2.5 Stop s velocity distribution in the lab frame M~ = 600 GeV t M~ = 1 TeV t (normalized to unit area) M~ = 2 TeV t β~ t

27 Flip probability vs the stop s mass w M~ - M~ = 200 GeV t l M~ - M Na = 160 GeV l M Na - M N1 = 40 GeV M~ (GeV) t

28 Tagging of t or t c in pair production via gluon fusion In wino example, relative branching ratios for t into b C + and t Ñ 2 are 2 : 1. Determine whether t or t c cascades by opposite side tag. Identification of leptons from cascade Determining t momentum and charge Other channels, e.g., b b c ; single quark q + g g + q

29 Final state interactions (theory estimates (small) or combining t and t c asymmetries) t l l + f N1 t l + l f N1 fn a e l + fn a e l et t l l + f N1 γ et + fn a el et Typeset by FoilTEX 1

30 Conclusions CP phases expected, e.g., in string constructions Phases needed for electroweak baryogenesis (EWBG) T-odd asymmetries may be observable at LHC for ( ) / sin 2 (2 ϕ) identified t t + l + + l + Ñ 1 cascades Need lucky spectrum (e.g., on-shell Ñ a, off-shell slepton) Rates favorable for M t 800 GeV, especially after upgrade Different phase combinations than probed in EDMs Need full simulations of experimental issues Need study of singlet extensions of MSSM (more promising for EWBG)