Model independent analysis of top FB asymmetry at the Tevatron

Transcription

1 Model independent analysis of top FB asymmetry at the Tevatron Pyungwon Ko Korea Institute for Advanced Study (KIAS) in collaboration with Dr. J.-S. Lee, Dr. D.W. Jung (and Dr. S.H. Nam) based on arxiv: , PLB and arxiv: and work in preparation < Seminar at NTCS, NTHU, Dec. 07 (2010) > Pyungwon Ko (KIAS) A FB of top quark production 1 / 38

2 Outline 1 Introduction 2 Effective Lagrangian Approach Forward-Backward Asymmetry Helicity Amplitude Spin-Spin Correlation 3 Models including new resonances explicitly Spin-1 Resonances Spin-0 Resonances Wilson Coefficients from Resonances Examples of Resonances 4 Longitudinal Pol of (anti)top quark P violation and Longitudinal Pol s 5 Summary Pyungwon Ko (KIAS) A FB of top quark production 2 / 38

3 Introduction Top pair production via strong interaction Tevatron: LHC: 90% 10% Pyungwon Ko (KIAS) A FB of top quark production 3 / 38

4 Introduction Motivation Top physics has began to enter a new era after its first discovery, due to the high luminosity achieved at the Tevatron, and precision study will be possible at the LHC in the coming years. Forward-backward asymmetry A FB in t t production has been off the SM prediction ( 0.078(9)) by 2σ in the t t rest frame (CDF2008): A t FB N t(cos θ 0) N t (cos θ 0) = 0.24 ± 0.13 ± 0.04 N t (cos θ 0) + N t (cos θ 0) This 2σ deviation stimulated some speculations on new physics scenarios We adopt a model independent approach using effective Lagrangian in order to accommodate the current measurement of A t FB, since there is no clear evidence for any new particles coupling to top at the Tevatron Pyungwon Ko (KIAS) A FB of top quark production 4 / 38

5 Introduction New CDF data with 5.6 fb 1 presented this summer ± ± Less deviation than before Any new physics scale is probably too high to be explored directly at the Tevatron Still interesting to speculate what type of new physics can modify top physics at what level In fact, our approach based on the effective lagrangian could be more useful in this case, than other approaches Also could be used to set substructure scale of top quark, as in the light quark system Pyungwon Ko (KIAS) A FB of top quark production 5 / 38

6 Introduction SM contribution to A FB Series of papers by Kühn and Rodrigo LO: top quark production angle is symmetric with respect to beam direction. NLO: asymmetry due to interference effects. Born Box ISR FSR Pyungwon Ko (KIAS) A FB of top quark production 6 / 38

7 Introduction Related works SM predictions: Kühn and Rodrigo Interference between tree (one gluon exchange) and one-loop (two gluon exchange) (anti)quark-gluon scattering into t tg initial (final) gluon emission q q t tg Axigluon: Godbole et al.; Rodrigo et al.; Frampton, Shu, Wang; Chivukular, Simmons, CP Yuan Extra Z : Jung, Murayama, Pierce, Wells Extra W : Cheung, Keung, TC Yuan RS KK gluon: Djouadi et al. Color sextet or antitriplet: Tait et al.; CH Chen et al.; Berger et al.; RPV and LR model: Cao, Heng, Wu, Yang Comprehensive study: Cao, McKeen, Rosner, Shaughnessy, Wagner Effective Lagrangian Approach : this talk Apologies to those who are not listed Pyungwon Ko (KIAS) A FB of top quark production 7 / 38

8 Introduction Wisdom from EW sector The first evidence of asymmetry was found in angular distribution of muons from e + e collisions at PETRA in the 80 s ( s 30 GeV, well below the Z 0 pole) Source of A FB is a term linear in cos θ from interference between γ or Z vector coupling and the axial vector Z coupling. Pyungwon Ko (KIAS) A FB of top quark production 8 / 38

9 Effective Lagrangian Approach Dim-6 Contact Interaction t t production at the Tevatron dominated by q q channel Enough to consider dimension-6 four-quark operators assuming new physics scale is high enough: L 6 = g2 [ ] s Λ 2 C1q AB ( q Aγ µ q A )( t B γ µ t B ) + C8q AB ( q AT a γ µ q A )( t B T a γ µ t B ) where A,B T a = λ a /2, {A, B} = {L, R}, L, R (1 γ 5 )/2 (q = u, d, s, c, b) Other d=6 operators are all reducible to the above operators after Fierzing (Hill and Parke 1994) We ignore flavor changing dim-6 operators such as d R γ µ s R t R γ µ t R, since those contributions to the t t production cross section will be of a order 1/Λ 4 Pyungwon Ko (KIAS) A FB of top quark production 9 / 38

10 Effective Lagrangian Approach Digress on Top Substructure Our appraoch is useful even if the A FB approaches the SM prediction This contact term used to explore light quark substructures Similar analysis has been done for light quark and lepton systems using qq qq, qq ll, and ll ll, with various Dirac and color structures One can do exactly the same analysis for top compositeness scale The scale Λ in our effective lagrangian could be interpreted as Compositemess scale of a top quark seen by a light quark Bound on Λ can be derived from M or t t pt T distributions at the Tevatron Pyungwon Ko (KIAS) A FB of top quark production 10 / 38

11 Effective Lagrangian Approach Helicity Amplitude Squared The squared helicity amplitude is given by M(t L t L + t R t R ) 2 = 4 g4 s 9 ŝ m2 t Mt L t R + t R t L ) 2 = 2 g4 s 9 [ 2 + ŝ ] Λ 2 (C 1 + C 2 ) ) 2Λ 2 (C 1 + C 2 ) [ ( 1 + ŝ + ˆβ t ( ŝ Λ 2 (C 1 C 2 ) ) ] cˆθ s 2ˆθ (1 + c 2ˆθ ) where C 1 C LL 8q + C RR 8q, C 2 C8q LR + C8q RL ˆβ 2 t = 1 4m 2 t /ŝ, sˆθ sin ˆθ, cˆθ cos ˆθ The term linear in cos ˆθ could generate the foreward-backward asymmetry which is propotional to C C 1 C 2. Pyungwon Ko (KIAS) A FB of top quark production 11 / 38

12 Effective Lagrangian Approach Allowed region in the (C 1, C 2 ) plane 6 C 2 (1 TeV/!) " = 7.98 pb " = 7.02 pb I A FB = 0.10 A FB = 0.38 III C 1 (1 TeV/!) 2 II IV Pyungwon Ko (KIAS) A FB of top quark production 12 / 38

13 Effective Lagrangian Approach Validity of our approach Our Validity Criteria: σint < rσ SM (straight line) σnp < rσ int (ellipses passing through the origin) σnp < r 2 σ SM (ellipses centered at the origin) Take r = 0.3, r = 0.5, and r = 1.0 Our predictions pass these validity criteria even for r = 0.3, and could be considered reliable Another Issue: Violation of Unitarity by dim-6 op s Any nonrenormalizable interactions violate unitarity, which is very subtle issue at hadron colliders, since ŝ is not fixed Our criteria is hopefully stronger than unitarity constraint Pyungwon Ko (KIAS) A FB of top quark production 13 / 38

14 Effective Lagrangian Approach Validity of our approach σ NP is obtained using M NP 2 = 4g4 s ŝ 2 9ŝ 2 4Λ 4 { [9 ( (C LL 1q) 2 + (C1q RR ) 2) + 2 ( (C8q) LL 2 + (C8q RR ) 2)] ( û mt 2 + [ 9 ( (C1q RL ) 2 + (C1q LR ) 2) + 2 ( (C8q RL ) 2 + (C8q LR ) 2)] (ˆt ) 2 mt 2 + [ 9 ( C1qC LL 1q LR + C1q RR C1q RL ) ( + 2 C LL 8qC8q LR + C8q RR C8q RL )] ( )} 2ŝm 2 t, ) 2 where û m 2 t = ŝ (1 + ˆβ t cˆθ )/2, ˆt m 2 t = ŝ (1 ˆβ t cˆθ )/2 Pyungwon Ko (KIAS) A FB of top quark production 14 / 38

15 Effective Lagrangian Approach Validity region 10 C 2 (1 TeV/!) " = 7.98 pb " = 7.02 pb I II A FB = 0.10 IV A FB = III C 1 (1 TeV/!) 2 Pyungwon Ko (KIAS) A FB of top quark production 15 / 38

16 Effective Lagrangian Approach Validity region with the updated data 6 C 2 (1 TeV/Λ) σ = 7.02 pb σ = 7.98 pb I II III IV A FB = 0.09 A FB = C 1 (1 TeV/Λ) 2 Pyungwon Ko (KIAS) A FB of top quark production 16 / 38

17 Effective Lagrangian Approach M t t distribution 10-1 d! / dm tt [pb " GeV -1 ] SM Pt.I Pt.II 10-5 Pt.III Pt.IV CDF II Data, # L $ 2.7 fb M tt [GeV] Pyungwon Ko (KIAS) A FB of top quark production 17 / 38

18 Effective Lagrangian Approach Spin-Spin Correlation chiral structure of new physics affecting q q t t is also sensitive to the top quark spin-spin correlation (in the helicity basis): K = C = σ(t L t L + t R t R ) σ(t L t R + t R t L ) σ(t L t L + t R t R ) + σ(t L t R + t R t L ) SM prediction for helicity basis: K = 0.47 (LO) and (NLO) [Bernreuther et al., NPB (2004)] New CDF data: K = 0.48 ± 0.48 ± 0.22 New physics should have chiral couplings both to light quarks and top quark P must be broken Any new observable? Longitudinal top quark polarization Pyungwon Ko (KIAS) A FB of top quark production 18 / 38

19 Effective Lagrangian Approach New Spin-Spin Correlation C FB 6 C 2 (1 TeV/!) C= C= C= SM I II C FB = 0.00 C FB = C FB = III IV C 1 (1 TeV/!) 2 Pyungwon Ko (KIAS) A FB of top quark production 19 / 38

20 Effective Lagrangian Approach Proposing a NEW Spin-Spin Correlation The usual C is correlated with σ t t, and not to A FB We propose a new spin-spin correlation C FB : Separate the events in forward and backward directions, and form C FB C FB C(cos θ 0) C(cos θ 0) C(cos θ 0( 0)) implies the cross sections in the numerator of C are obtained for the forward (backward) region: cos θ 0( 0) Advantages of the new C FB : Larger spin-spin correlation Stronger correlation with AFB This new C FB could be also useful for testing the QCD in the top sector Pyungwon Ko (KIAS) A FB of top quark production 20 / 38

21 Effective Lagrangian Approach Spin-Spin Correlation 6 C 2 (1 TeV/!) C= C= C= SM I II C FB = 0.00 C FB = C FB = III IV C 1 (1 TeV/!) 2 Pyungwon Ko (KIAS) A FB of top quark production 21 / 38

22 Spin-1 Resonances One can consider the following interactions of quarks with spin-1 flavor-conserving (changing) color-singlet V 1 (Ṽ1) and color-octet V a 8 (Ṽ a 8 ) vectors (A = L, R) relevant to At FB : [ ] L V = g s V µ 1 g1q A ( q Aγ µ q A ) + g1t A ( t A γ µ t A ) A [ ] +g s V aµ 8 g8q A ( q Aγ µ T a q A ) + g8t A ( t A γ µ T a t A ) A [Ṽ µ +g s 1 g 1q A ( t A γ µ q A ) + Ṽ aµ 8 g 8q A ( t A γ µ T a q A ) + h.c. ] A A Pyungwon Ko (KIAS) A FB of top quark production 22 / 38

23 Spin-0 Resonances Following interactions of quarks with spin-0 flavor-changing color-singlet S1 and color-octet S 8 a scalars could also contribute to A t FB : L S = g s [ S1 η 1q A ( taq) + S 8 a η 8q A ( tat a q) + h.c. ] A One can also consider color-triplet S γ k and color-sextet scalars S αβ ij with minimal flavor violating interactions with the SM quarks (Arnold, Pospelov, Trott, Wise): [ η3 ] L S = g s 2 ɛ αβγɛ ijk uir α uβ jr Sγ k + η 6uiR α uβ jr Sαβ ij + h.c. A Pyungwon Ko (KIAS) A FB of top quark production 23 / 38

24 Wilson Coefficients from Resonances After integrating out the heavy vectors and scalars, we obtain the Wilson coefficients as follows: C8q LL Λ 2 = 1 mv 2 g8q L gl 8t 1 m 2 Ṽ C8q RR Λ 2 = 1 mv 2 g8q R gr 8t 1 m 2 Ṽ C8q LR Λ 2 = 1 mv 2 g8q L gr 8t 1 m 2 S C8q RL Λ 2 = 1 mv 2 g8q R gl 8t 1 m 2 S [2 g L1q 2 1Nc g L8q 2 ] [2 g R1q 2 1Nc g R8q 2 ] η 3 2 [ η L 1q 2 1 η 8q L 2N 2 c [ η 1q R 2 1 η 8q R 2N 2 c ] ] m 2 S η 6 2 m 2 S 6 Pyungwon Ko (KIAS) A FB of top quark production 24 / 38

25 Examples of Resonances Axigluon model corresponding to flavor universal chiral couplings (Pati and Salam 1975): g L 8q = gl 8t = gr 8q = gr 8t = 1 New gauge boson Z with dominant coupling to u t (Jung, Murayama, Pierce, and Wells 2009): V 1 = Ṽ1 = Z, g s g R 1q = g X, g s g R 1q = g X ɛ U ( ɛ U 1) New charged gauge boson W ± contributions (Cheung, Keung, and Yuan 2009): Ṽ = W, g s g 1q A = g g A Some RS scenarios with large flavor mixing in the right-handed quark sector (Aquino et al 2007; Agashe et al 2008): g8q L = gr 8q = gr 8b 0.2, gl 8t = gl 8b (1 2.8) g8t R (1.5 5), gl 8q V tq, g 8q R 1 Pyungwon Ko (KIAS) A FB of top quark production 25 / 38

26 Scores for each model New particle couplings C 1 C 2 1 σ favor V 8 (spin-1 FC octet) Ṽ 1 (spin-1 FV singlet) Ṽ 8 (spin-1 FV octet) g L,R 8q,8t indefinite indefinite g L,R 1q 0 g L,R 8q + 0 S 1 (spin-0 FV singlet) η L,R 1q 0 S 8 (spin-0 FV octet) η L,R 8q 0 + S3 α (spin-0 FV triplet) η 3 0 S αβ 6 (spin-0 FV sextet) η Pyungwon Ko (KIAS) A FB of top quark production 26 / 38

27 1-σ favored region for V 8 g R 8t / gl 8q ( 1 TeV / M V ) r q = 2 r q = 0.5 r q = -0.5 r q = -1 r q = g L 8t / gl 8q ( 1 TeV / M V ) r q = g R 8q/g L 8q and g L 8q = 1 Pyungwon Ko (KIAS) A FB of top quark production 27 / 38

28 Constraints on masses and couplings 1-σ favored values of the couplings Updated data: Ṽ 8 : S 1 : 1 N c S αβ 13 : 2 ( 1 TeV ( 1 TeV m S mṽ ) 2 ( g L 8q 2 + g R 8q 2) 0.76(0.64), ) 2 ( η L 1q 2 + η R 1q 2) 0.62(0.49), ( ) 1 TeV 2 η (0.64) m S6 These could be discovered and tested at the LHC, by measuring the mass and the couplings Pyungwon Ko (KIAS) A FB of top quark production 28 / 38

29 A FB implies P violation If P were conserved in the light quark sector, C8q LL = CRL 8q, and C8q LR = CRR 8q If P were conserved in the top sector, C8q LL = CLR 8q and CRR 8q = CRL 8q In either case, we would have C 1 C 2 = 0, and no effects on A FB Most important message of nonzero A FB from new physics is Parity should be vilolated in the quark sector What would be the observable consequences of this new PV interaction? In the top sector, the top longitudinal polarization can be nonzero in general, unlike QCD S t ˆn 0 If ˆn p, it becomes helicity Pyungwon Ko (KIAS) A FB of top quark production 29 / 38

30 P violation and Longitudinal Pol s Keeping only the longitudinal pol s of (anti)top, we have } {D 0 + D 1 (P L + P L ) + D 2 (P L P L ) + D 3 P L PL M 2 = g4 s ŝ 2 D 1 and D 2 are P-violating. D 1 term needs strong phase (CP T violating), from the propagator of the exchanged new particle, which is not seen in our approach (Future work) with D 2 ŝ [(C 9 Λ C 2 ) ˆβ t (1 + c 2ˆθ ) + (C 1 C 2 )(5 3 ˆβ ] t 2 )cˆθ. C 1 CRR 8q CLL 8q, C 2 CLR 8q CRL 8q. Different informations on the chiral structures of NP from A FB Pyungwon Ko (KIAS) A FB of top quark production 30 / 38

31 When we integrate over the polar angle ˆθ, only the first term involving (C 1 + C 2 ) = CRR 8q CLL 8q + CLR 8q CRL 8q survives. On the other hand, if we separate the forward and the backward top samples and take the difference, the orthogonal combination in the second term survives: (C 1 C 2 ) = CRR 8q Consider the two new observables: D CLL 8q CLR 8q + CRL 8q. σ(t R t L ) σ(t L t R ) σ(t R t R ) + σ(t L t L ) + σ(t L t R ) + σ(t R t L ), D FB D(cos ˆθ 0) D(cos ˆθ 0) which involve the sum and difference of the coefficients C 1 and C 2, respectively. Pyungwon Ko (KIAS) A FB of top quark production 31 / 38

32 C 2 (1 TeV/Λ) D=0.1 D=-0.1 D=-0.3 (, ) D FB =-0.3 D=0.3 (+, ) SM (,+) D FB =-0.1 (+,+) D FB =0.1 D FB = C 1 (1 TeV/Λ) 2 Figure: The P-violating spin correlations D and D FB in the (C 1, C 2 ) plane. The signs of (D, D FB ) are denoted. Pyungwon Ko (KIAS) A FB of top quark production 32 / 38

33 The polarization coefficients could be measured by studying the angular distributions of the top-quark decay products. For dilepton decay channels of t t (in the helicity basis), one has { M 2 = g4 s ŝ 2 D 0 + D 1 (cos θ + + cos θ ) +D 2 (cos θ + cos θ ) + D 3 cos θ + cos θ }. where θ + (θ ) is the angle between the charged lepton l + (l ) in the top (anti-top) rest frame and the direction of the top (anti-top) in the t t rest frame. M T 2 could be helpful for this study (Work in progress) Pyungwon Ko (KIAS) A FB of top quark production 33 / 38

34 [t] New particle exchanges and the signs of induced couplings C AB (A, B = R, L), C 1 C 2, C 1 + C 2, and C 1 C 2. Res. C RR C LL C LR C RL C 1 C 2 C 1 + C 2 C 1 C 2 Ṽ 1R Ṽ 1L Ṽ 8R Ṽ 8L S 1R S 1L S 8R S 8L S α S αβ V 8R ± ± ± ± ( Pyungwon Ko (KIAS) A FB of top quark production 34 / 38

35 ~ S 1R ~ V 8R, V 8R, S αβ 13 D FB ~ V 8L, V 8L ~ S1L Figure: The predictions for D and D FB of the models under consideration, being consistent with the σ t t and A FB measurements at the 1-σ level. We assume only one resonance exists or dominates. D Pyungwon Ko (KIAS) A FB of top quark production 35 / 38

36 Summary We performed a model independent study of t t productions at the Tevatron using dimension-6 q qt t contact interactions with all the possible Dirac and color structures. Our results encode the necessary conditions for the underlying new physics in a compact and an effective way when those new particles are too heavy to be produced at the Tevatron. Proposed a new FB spin-spin correlation C FB A FB Suggested to measure P L and P L to probe the chiral structure of new physics in q q t t We considered the s, t and u channel exchanges of spin-0 and spin-1 particles whose color quantum number is either singlet, octet, triplet or sextet. Pyungwon Ko (KIAS) A FB of top quark production 36 / 38

37 Future Study A FB vs M t t or η Detailed study of resonance productions at the LHC ( Resonances in the t t or t q channel ) Top polarization in general (transverse, longitudinal) at the Tevatron and at the LHC In the presence of resonance, there could be nonzero P L + P L Need more study the D 1 term Those new particles might leave imprints on the low energy flavor physics such as K or B physics (mixing and CP violation), if u(d) t transitions are employed Pyungwon Ko (KIAS) A FB of top quark production 37 / 38

38 Thank you very much Pyungwon Ko (KIAS) A FB of top quark production 38 / 38