CP violation in top physics*

CP violation in top physics* CP violation from new physics in top-quark pair production and decay with T-odd correlations

one of my first papers with John

didn t get all the details right...

T-odd observables simple kinematic correlations of the form T-odd: change sign under `naive -T p p but no interchange of initial/final states These correlations can be: CP-odd if p i, p j involve particle anti-particle pairs CP-even but not at tree-level as they require a phase -- small and distinguishable `background The (jet) p p 1 ( p 2 p 3 ) can be that of a composite object sums over processes

T-odd correlations-2 triple product correlations appear in invariant matrix elements in the form ɛ(p t, p t, p l +, p l ) ɛ µναβ p µ t p ν t pα l + p β l 4 independent four-vectors needed, so unless one has an effective theory with vertices involving 5 particles at least, they originate from spin correlations top pair production is ideal `lab to look for them

Examples for LHC, Tevatron Heavy (bsm) Higgs with CP violation large intrinsic asymmetry hard to extract (if such a Higgs exists!) Anomalous top-quark couplings exhibits the correlations in the general case (including those between initial and final state momenta) contains examples that are truly CP odd and others that are not small asymmetries (by assumption...)

kinematics on-shell b or q q g(p1) g(p2) t Γ P t Γ D Γ D W + W - b l + l - or jets new physics with CP violation sum over final states such that CP conjugate pairs appear with equal probability

T-odd Spin correlations the underlying T-odd correlations are spin correlations, different observables correspond to different spin analyzers "( p t, p t,s t,s t ) Γ D "( p t, p b, p l +,s t ) CP violation in the production vertex Γ P Γ D CP violation in the decay vertex "( p t, p b, p l #,s t ) want the lab frame, not the top-rest frame G. Valencia (Iowa State), TOP 2010, Bruges

CP Violation via Neutral Higgs A neutral Higgs has the general coupling: which violates CP if both A and B are nonzero at the same time (multi-higgs models) Weinberg showed that under some assumptions with Yili Wang m t v H t (A + ibγ 5 ) t lightest neutral mass eigenstate is dominant different vevs have comparable sizes use upper bound for numerics AB 1 2

Case of H decay For a sufficiently heavy H, it decays to top pairs. The decay chain, for example, H t t b bw + W picks a CP odd correlation O 1 = ɛ(p t,p t,p b,p b) CP H C.M. pt ( ) ( ) which can be measured with a counting asymmetry such as A CP N events( p b ( p b p t ) > 0) N events ( p b ( p b p t ) < 0) N events ( p b ( p b p t ) > 0) + N events ( p b ( p b p t ) < 0) ( p b p b) p t ( p b p b ) = p t ( p b p b)

A CP 0.07 4 0 @ Can be easily computed s 1 4m2 t M 2 H AB 1 jaj 2 jbj 2 1 A 2M 2 W m 2 t 1 2M2 W m 2 t 2 2 0 @ 1 2m2 t MH 2 s 1 j j j j 1 2 jaj2 jbj 2 jaj 2 jbj 2 m 2 t M 2 H A 0.065 0.06 0.055 There is a large intrinsic asymmetry: near 7% for A=B and maximum CP violation A B =1/!2 " 0.05 400 600 800 M H (GeV)

But need to isolate the sample with the asymmetry.... VALENCIA AND YILI WANG pb dσ/dm tt (fb/gev) 1 10-2 10-4 A B = 1/ 2 10-6 400 600 800 top pair production at LHC (14 TeV) gluon fusion q q annihilation Higgs: top pairs from Higgs are swamped by others M tt (GeV)

How did we get a CP test? pp H t t (bw + )( bw ) (bµ + ν µ )( bµ ν µ ) p p initial state is not a CP eigenstate get good CP properties from final state: view LHC as a Higgs (or more generally a t!) factory this works for g g or q " initial states after we sum over spin and color won t work for q q initial state, need to reject it. pick final states such that this is a small contamination

top-quark anomalous couplings electric dipole moments indicate T violation (and thus CP violation) experimental limits on electron edm and neutron edm; for example d n < 2.9 x 10-26 e- cm one contribution to neutron edm is the light quark edm and also its cedm: H 1 2 e d q qσ µν γ 5 q F µν + 1 2 g s d q qσ µν γ 5 t a q G µν a

quark edm (cedm) beyond the SM these can be induced at oneloop for example models with scalars generate contributions such as d q, d q m 3 q perhaps heavy quarks can have large (c)edms? measure at a top-quark factory, LHC?

CP violating top-quark couplings For CP violation in the production process: a (chromo)-edm of the top-quark: It modifies the a L cedm = ig s d 2 t σ µν γ 5 tg µν t t g coupling and introduces ``seagull term with Oleg Antipin

gg or q q t t (bµ + ν µ )( bµ ν µ ) The differential cross section now contains the following CP-odd correlations: O 1 = ɛ(p t,p t,p µ +,p µ ) O 2 = (t u) ɛ(p µ +,p µ, P, q) O 3 = (t u) ( P p µ + ɛ(p µ,p t,p t,q)+p p µ ɛ(p µ +,p t,p t,q) ) where the sum and difference of parton momenta are denoted by P and q. for W as one jet: lepton b-jet momenta for more jets: lepton d-jet momenta Notice that they are quadratic in q (t u) =q (p t p t )

CP violation in the decay vertex For anomalous tbw couplings, there is only one that interferes with the SM amplitude in the limit of massless b quark: Γ µ W tb Γ µ W tb = g 2 V tb ū(p b ) [ γ µ (f L 1 P L + f R 1 P R ) iσ µν (p t p b ) ν (f L 2 P L + f R 2 P R ) ) u(p t ), = g 2 V tb v(p t) [ γ µ ( f L 1 P L + f R 1 P R ) iσ µν (p t p b) ν ( f L 2 P L + f R 2 P R ) ) v(p b), include absorptive phases also and take: no seagulls (with a gluon) are present f1 L = f 1 L = 1, f2 R = fe i(φ f +δ f ) L, f 2 = fe i( φ f +δ f ). SM

T-odd correlations this time they appear in the differential cross section as: absorptive phase CP odd phase M 2 T = f sin(φ f + δ f ) ɛ(p t, p b, p l +, Q t ) + f sin(φ f δ f ) ɛ(p t, p b, p l, Q t). Q is a four momentum (spin analizer), it is a linear combination of other momenta in the process the correlations are NOT CP odd, they can be also signal absorptive phases true CP odd observables can be constructed by comparing the top and anti-top decays

Observables We have the `theoretical correlations. Need some that only involve observable momenta. for LHC we use the di-lepton (muon) channel, for Tevatron the lepton (muon) + jets, and multijet channels: p µ +,p µ p b,p b, some observables require distinguishing them q P 1 P 2, = difference of proton momenta p j1,p j2 non b jets ordered by p T any CP-blind ordering of the jets should work

Some Correlations Di-muon channel basic one Õ 1 = ɛ(p b,p b,p µ +,p µ ) no need to distinguish b jets: b b CM p b ( p µ + p µ ) Lepton plus jets hardest non-b jet Multijet channels Õ 2 = q (p µ + p µ ) ɛ(p µ +,p µ,p b + p b, q) O = ɛ(p, p b + p b,p l,p j1 ) lab ( p b + p b) ( p l p j1 ) O 6 = ɛ(p b,p b,p j1 + p j2,p j1 + p j2 ) t t CM ( p j1 + p j2 ) ( p b p b) Many others including CP even tests...

example of a distribution 0.8 0.7 SM + CPV SM d = 0 (SM) 0.6 d =5 10 4 GeV 1 ) 4 t /M d!/d(o 1 0.5 0.4 0.3 ~ 0.2 0.1 0-1 -0.5 0 0.5 1 O 1 /M 4 t

Numbers in Perspective coupling ~ " 1 % d $ ' # & m t f " 1 % $ ' # & m t Theory Estimate with 10fb - 1 at 5 <10-13 SM * ~10-6 H + * ~10-3 SUSY * 0.03 QCD & (CP conserving and no phase) 0.05 ~ 0.10 (both CP and/or str.) units 3.0 10 4 GeV 1 = 0.05 m t * Atwood, Soni Phys.Rept.347:1-222,2001. & Li, Oakes, Yuan PRD43:3759-3762,1991. 5 10 18 g s cm

Conclusions We have studied several T-odd correlations that illustrate the different possibilities in searching for CP violation in top physics We have estimated the asymmetries for the simple cases of anomalous top-quark couplings in both top production and decay, and a multi-higgs model With these examples we have estimated the statistical sensitivity of the LHC and the Tevatron to the CP violating top-quark couplings The time is ripe for experimental studies of CP violation in top physics: any observation would signal new physics. We have D0 and Atlas students looking into this...