Cross Section and Forward-Backward Asymmetry of t t ¯ Production in the Model with Four Color Symmetry
aa r X i v : . [ h e p - ph ] O c t Cross Section and Forward-Backward Asymmetry of t ¯ t Production in the Model with Four ColorSymmetry
M. V. Martynov a ∗ , A. D. Smirnov a † a Division of Theoretical Physics, Department of Physics,Yaroslavl State University, Sovietskaya 14,150000 Yaroslavl, Russia.
Abstract
The contributions to the cross section σ t ¯ t and to the forward-backward asymmetry A t ¯ t FB of t ¯ t production at the Tevatron from Z ′ -boson and scalar leptoquarks S ( ± ) a and scalar gluons F a predicted by the minimal model with four color quark-lepton symmetry are calculated.These contributions are shown to be small in tree approximation and can be significant withaccount of the 1-loop gt ¯ t effective vertex induced by the scalar doublets. The lower masslimit for scalar gluons m F & GeV from the Tevatron data is obtained and it is shownthat for m F . GeV the scalar gluon F can be evident at LHC at the significance notless that 3 σ (for √ s = 14 TeV, L = 10 f b − ). The search for a new physics beyond the Standard Model (SM) is now one of the aims of thehigh energy physics. One of the new physics can be induced by the possible four color symmetrytreating leptons as quarks of the fourth color [1]. This symmetry can be unified with the SMby the gauge group G new = G c × SU L (2) × U R (1) (1)where G c is the group of the four color symmetry. The color group G c can be the vectorlikegroup G c = SU V (4) or the general chiral group G c = SU L (4) × SU R (4) or one of the specialgroups of the left or right four color symmetry G c = SU L (4) × SU R (3), G c = SU L (3) × SU R (4).The Minimal four color Quark-Lepton Symmetry model (MQLS-model) is based on thegauge group G new = SU V (4) × SU L (2) × U R (1) (2)as on the minimal group containing the four color symmetry of quarks and leptons [2, 3].According to this group in addition to gluons G jµ , j = 1 , , . . . , W ± -, Z -bosons thegauge sector predicts the new gauge particles: vector leptoquarks V ± αµ , α = 1 , , Q emV = ± / SU V (4)-quartets ψ paA , A = 1, 2, 3, 4, a = 1,2, p = 1, 2, 3, . . . ψ ′ p A : (cid:18) u ′ α ν ′ e (cid:19) , (cid:18) c ′ α ν ′ µ (cid:19) , (cid:18) t ′ α ν ′ τ (cid:19) , · · · ∗ e-mail : [email protected] † e-mail : [email protected] ′ p A : (cid:18) d ′ α e −′ (cid:19) , (cid:18) s ′ α µ −′ (cid:19) , (cid:18) b ′ α τ −′ (cid:19) , · · · where Q ′ L,Rpaα , ℓ ′ L,Rpa are the basic left and right quark and lepton fields.Each lepton have SU V (4) ”color” A = 4.Fermion mixing in MQLS.The basic left and right quark and lepton fields Q ′ L,Rpaα , ℓ ′ L,Rpa can be written, in general, assuperpositions Q ′ L,Rpaα = X q (cid:16) A L,RQ a (cid:17) pq Q L,Rqaα , l ′ L,Rpa = X q (cid:16) A L,Rl a (cid:17) pq l L,Rqa , (3)of mass eigenstates Q L,Rqaα , ℓ L,Rqa . Here A L,RQ a and A L,Rℓ a are unitary matrices diagonalizing themass matrices of quarks and leptons respectively.( A LQ ) + A LQ ≡ C Q = V CKM is Cabibbo-Kobayashi-Maskawa matrix ( A Lℓ ) + A Lℓ ≡ C ℓ is theanalogous lepton mixing matrix (( C l ) + = U P MNS ) ( A L,RQ a ) + A L,Rℓ a ≡ K L,Ra are the new mixing matrices which are specific for the models withthe four color symmetry.The interaction of the gauge fields with the fermions has the form L gaugeψ = L Vψ + L Wψ + L QCDψ + L QEDψ + L NCψ , (4)where L Vψ = g √ (cid:8)(cid:0) ¯ Q paα (cid:2)(cid:0) K La (cid:1) pq γ µ P L + (cid:0) K Ra (cid:1) pq γ µ P R (cid:3) ℓ qa (cid:1) V αµ + h.c. (cid:9) , (5) L Wψ = g √ (cid:8)(cid:2) ¯ Q p α (cid:0) C Q (cid:1) pq γ µ P L Q q α + ¯ ℓ p (cid:0) C ℓ (cid:1) pq γ µ P L ℓ q (cid:3) W + µ + h.c. (cid:9) , (6) L QCDψ = g st G jµ (cid:0) ¯ Qγ µ t j Q (cid:1) , (7) L QEDψ = −| e | A µ (cid:0) ¯ ψγ µ Q em ψ (cid:1) , (8) L NCψ = − Z µ J Zµ − Z ′ µ J Z ′ µ . (9)Features of Z ′ -boson originating from the four color symmetry.In general case the mass eigenstates Z and Z ′ are superposition of two basic fields Z and Z . In MQLS model the Z − Z ′ mixing angle is small ( θ m < . Z − Z ′ mixing believing Z ≈ Z and Z ′ ≈ Z . The interaction of the neutral gauge fields withthe fermions has the form L gaugeNC = − eZ µ J Z µ − ec W Z µ J Z µ , (10) J Z µ = ¯ f γ µ ( v Z f + a Z f γ ) f, (11) J Z µ = ¯ f γ µ ( v Z f + a Z f γ ) f, with couplings v Z f a = 1 s S q − s W − s S " c W r
23 ( t ) f − (cid:18) Q f a − ( τ ) aa (cid:19) s S , (12) a Z f a = s S q − s W − s S ( τ ) aa . (13)2he fermionic decays of Z ′ boson are defined by the coupling constants (13) and the corre-sponding partial widths of Z ′ boson decays to f a ¯ f a pairs for m f a ≪ M Z ′ have the form [4]Γ( Z ′ → f a ¯ f a ) = N f M Z ′ α (cid:0) ( v Z ′ f a ) + ( a Z ′ f a ) (cid:1) , (14)where the color factor N f = 1(3) for leptons(quarks) f = l ( q ).Writing the interaction of Z ′ boson with scalar field Φ as L Z ′ ΦΦ = ig Z ′ ΦΦ Z ′ µ ( ∂ µ Φ ∗ Φ − Φ ∗ ∂ µ Φ) , (15)where g Z ′ ΦΦ is the corresponding coupling constant for the width of Z ′ boson decay into Φ ˜Φpair we have the expressionΓ( Z ′ → Φ ˜Φ) = N Φ M Z ′ g Z ′ ΦΦ π (cid:18) − m M Z ′ (cid:19) / (16)where N Φ is the color factor ( N F a = 8 for scalar gluons, N S ( ± ) a = 3 for scalar leptoquarks, N Φ ′ a = 1 for the additional colorless scalar doublet) and m Φ is a mass of the scalar particle.The scalar gluons F a and the scalar leptoquarks S ( ± ) a gives the main contribution into Z ′ boson width of type (16). The coupling constants of these particles with Z ′ boson are predictedby the MQLS model as g Z ′ F a F a = − e σs W c W , g Z ′ S ( ± ) a S ( ± ) a = − e (cid:18) σ s W c W ± t W σ (cid:19) , (17)where t W = tan θ W and σ = s W s S / q − s W − s S .The parameter s S is defined by the mass scale M c ∼ M V of the four-color symmetry breakingand by the intermediate mass scale M ′ ∼ M Z ′ . For example for M ′ ∼ T eV and for M c =10 T eV, T eV, T eV we have s s = 0 . , . , .
154 respectively [2]. For numericalestimations we use below the value s s = 0 .
114 which corresponds to M Z ′ ∼ − T eV and M c ∼ T eV . With these values of s s and of the masses of scalar particles the relative totalwidth of Z ′ − boson Γ Z ′ /M Z ′ occurs to be equal toΓ Z ′ /M Z ′ = 4 . . , . , . . , . , . . , . M Z ′ of about respectively 1 TeV, 3 TeV, 5 TeV and above, the corresponding values of therelative widths of the Z ′ decays respectively into scalar particles and into fermions are shownin parenthesis.The scalar sector contains in general four multiplets [2, 3, 5](4 , ,
1) : Φ (1) = S (1) αη + χ (1) + iω (1) √ ! , (1 , ,
1) : Φ (2) a = δ a η √ φ (2) a , ( , , ) :Φ (3) a = ( F a ) αβ S (+) a α S ( − ) a α ! + Φ (3)15 ,a t , (19)(15 , ,
0) : Φ (4) = F (4) αβ √ S (4) α ∗ S (4) α ! + ( η + χ (4) ) t , transforming according to the (4,1,1)-,(1,2,1)-,(15,2,1)-,(15,1,0)- representations of the SU V (4) × SU L (2) × U R (1)-group respectively. Here Φ (3)15 ,a = δ a η + φ (3)15 ,a , η , η , η , η are the vacuumexpectation values. 3hird multiplet (15 . .
1) interacts with quarks.(15 . .
1) : Φ (3) : S (+)1 α S (+)2 α ! ; S ( − )1 α S ( − )2 α ! ; (cid:18) F k F k (cid:19) ; Φ (3)1 , Φ (3)1 , ! , (20)where S ( ± ) a α and F ak (k=1,2...8) are the scalar leptoquark and scalar gluons doublets. Φ (3)15 − Φ (2) -mixing gives the SM Higgs doublet Φ ( SM ) and an additional Φ ′ doublet. These scalar doubletshave the electric charges Q em : (cid:18) / / (cid:19) ; (cid:18) / − / (cid:19) ; (cid:18) (cid:19) ; (cid:18) (cid:19) . In general S (+)2 α = X m =0 c (+) m S m , ∗ S ( − )2 = X m =0 c ( − ) m S m , where S m are three physical leptoquarks with electric charge 2/3 and S is the Goldstone mode, c ( ± ) m are the elements of the unitary scalar leptoquark mixing matrix, | c ( ± )0 | = g η /m V ≪ m LQ &
250 GeV . (21)The indirect data set the limits on the relations of scalar leptoquark coupling constants totheir masses.In MQLS-model the leptoquark Yukawa coupling constants are (due their Higgs origin)proportional to the ratios m f /η of the fermion masses m f to the SM VEV η . As a result thesecoupling constants are known (up to mixing parameters) and are small for light quarks. So, theindirect mass limits for MQLS scalar leptoquarks are weaker then those from direct searchers.Mass limits for scalar gluons F ak .
100 200 300 400 m F , TeV -3 -2 -1 s (cid:2) p p fiFF + X (cid:3)(cid:4) pb (cid:214) s = 1.96 TeV S a F a = -1 Figure 1: Cross sections of SS ∗ -, F F ∗ -pair production at the Tevatron as functions of the massesof scalar particles.The partonic cross sections of scalar gluon pair production are known [7–9], which gives nowpossibility to calculate cross section of scalar gluon pair production at the Tevatron in depen-dence on scalar gluon mass. In these calculations we use PDF’s set AL’03 [10] (NLO, variable-favor-number) with the K-factor chosen as K = 1 .
45 for consistency with theoretically predicteddependence of σ NLO ( t ¯ t ) on m t [11, 12]. 4ur estimate for mass limits for scalar gluons F a from direct searches at Tevatron is m F a &
320 GeV. (22)Possibility of the direct searches scalar gluon at the LHCThe production cross section of scalar gluons F at the LHC with masses m F . GeV is shown to be sufficient for the effective ( N events & L = 10 f b − ) [8].At m F . GeV from analysis statistical significance the number of the signal t ¯ tb ¯ b eventswill exceed the SM background by 3 σ (LHC L = 10 f b − ) [9].The interaction of the fermions with the scalars.The Yukawa interaction of the fermions with the scalar SU L (2)- doublets φ (2) and φ (3) i has,in general, the form L Y ukawaψ = − ¯ ψ ′ LpaA (cid:2)(cid:0) h b (cid:1) pq φ (2) ba δ AB + (cid:0) h ′ b (cid:1) pq φ (3) bia (cid:0) t i (cid:1) AB (cid:3) ψ ′ RqbB + h.c., (23)where φ (2)2 a = φ (2) a , φ (2)1 a = ε ac ( φ (2) c ) ∗ , φ (3)2 ia = φ (3) ia , φ (3)1 ia = ε ac ( φ (3) ic ) ∗ , i = 1, 2, . . . , 15, ε ac isantisymmetrical symbol, h b and h ′ b are four arbitrary matrices.After symmetry breaking this Lagrangian gives the arbitrary masses to the quarks andleptons and gives the interactions of fermions with the scalar fields L int Ψ = L χ ( SM ) ff + L Φ ′ ff + L F QQ + L SQl . (24) h ∼ m f /η,m u /η ∼ m d /η ∼ − , m s /η ∼ − , m c /η ∼ m b /η ∼ − ,m t /η ∼ . . !!!The interactions of the scalar leptoquarks S ( ± ) aα with quarks and leptons: L S (+)1 u i l j = ¯ u iα h ( h L + ) ij P L + ( h R + ) ij P R i l j S (+)1 α + h . c .,L S ( − )1 ν i d j = ¯ ν i h ( h L − ) ij P L + ( h R − ) ij P R i d jα S ( − )1 α + h . c ., (25) L S m u i ν j = ¯ u iα h ( h L m ) ij P L + ( h R m ) ij P R i ν j S mα + h . c .L S m d i l j = ¯ d iα h ( h L m ) ij P L + ( h R m ) ij P R i l j S mα + h . c . The interactions of the scalar gluons with quarks: L F u i d j = ¯ u iα h ( h LF ) ij P L + ( h RF ) ij P R i ( t k ) αβ d jβ F k + h . c .,L F u i u j = ¯ u iα h ( h L F ) ij P L i ( t k ) αβ u jβ F k + h . c ., (26) L F d i d j = ¯ d iα h ( h R F ) ij P R i ( t k ) αβ d jβ F k + h . c . Scalar leptoquarks S ( ± )1 , S m couplings to fermions:5 h L + ) ij = p / η sin β h m u i ( K L C l ) ij − ( K R ) ik m ν i ( C l ) kj i , ( h R + ) ij = − p / η sin β h ( C Q ) ik m d k ( K R ) kj − m l j ( C Q K L ) ij i , ( h L − ) ij = p / η sin β h (+ K R ) ik m u k ( C Q ) kj − m ν j (+ K L C Q ) ij i , (27)( h R − ) ij = − p / η sin β h ( C l + K L ) ij m d j − ( C l ) ik m l k (+ K R ) kj i , ( h L,R m ) ij = − p / η sin β h m u i ( K L,R ) ij − ( K R,L ) ij m ν j i c ( ± ) m , ( h L,R m ) ij = − p / η sin β h m d i ( K L,R ) ij − ( K R,L ) ij m l j i c ( ∓ ) m , where β is Φ (2) a − Φ (3)15 mixing angle in MQLS model, tgβ = η /η , C Q = V CKM , C l = U P MNS and K L,Ra = ( A L,RQ a ) + A L,Rl a are the mixing matrices specific for the MQLS model.Scalar gluons F a couplings to fermions:( h LF ) ij = √ η sin β h m u i ( C Q ) ij − ( K R ) ik m ν k (+ K L C l ) kj i , ( h RF ) ij = −√ η sin β h ( C Q ) ij m d i − ( C l K L ) ik m l k (+ K R ) kj i , ( h L F ) ij = −√ η sin β h m u i δ ij − ( K R ) ik m ν k (+ K L ) kj i , (28)( h R F ) ij = −√ η sin β h m d i δ ij − ( K L ) ik m l k (+ K R ) kj i , ( h R F ) ij = 0 , ( h L F ) ij = 0 . The largest couplings h ∼ m t /η : S (+)1 ¯ tτ : ( h L + ) = p / m t η sin β ( K L C l ) ,S ( − )1 ¯ ν τ b : ( h L − ) = p / m t η sin β (+ K R ) ( C Q ) , (29) S m ¯ tν τ : ( h L,R m ) = − p / m t η sin β ( K L,R ) c ( ± ) m ,F ¯ tb : ( h LF ) = √ m t η sin β ( C Q ) ,F ¯ tt : ( h L F ) = −√ m t η sin β .m t /η ∼ . t ¯ t Production at the Tevatron
With account these large couplings of scalars with t-quarks, scalar leptoquarks and scalar gluonsmay give significant contribution in t ¯ t -quark production at Tevatron.6he latest CDF data on cross section and forward-backward asymmetry of the t ¯ t productionat the Tevatron CDF [14, 15] σ t ¯ t = 7 . ± . stat ) ± . syst ) ± . lumi )pb , (30) A t ¯ t FB = 0 . ± .
065 (stat) ± .
024 (sys) . (31) σ t ¯ t SM prediction [11] : σ SMt ¯ t = 7 . +0 . − . (scale) +0 . − . (PDFs)[CTEQ6 .
5] pb ÷ (32)7 . +0 . − . (scale) +0 . − . (PDFs)[MRST2006nnlo] pb .A t ¯ t FB SM prediction [16] : A t ¯ t FB = 0 . , (33) A t ¯ t FB = N t (cos θ > − N t (cos θ < N t (cos θ >
0) + N t (cos θ < . (34)The measured at CDF forward-backward asymmetry has significant ( ≈ σ ) deviation frompredictions [16]. This may be indication of new physics.The LO parton subprocesses of p ¯ p → t ¯ t in SM are described by diagrams at Fig. 2 of order α s . q ¯ q t ¯ tg Figure 2: Partonic subprocesses q ¯ q → t ¯ t , gg → t ¯ t The well-known p ¯ p → t ¯ t LO cross sections have form dσ ( q ¯ q → t ¯ t ) d cos ˆ θ = α s πβ s (cid:0) β c + 4 m t / ˆ s (cid:1) , (35) σ ( q ¯ q → t ¯ t ) = 4 πα s β s (cid:0) − β (cid:1) ,dσ ( gg → t ¯ t ) d cos ˆ θ = α s πβ s (cid:18) − β c − (cid:19) (cid:18) β c + 2(1 − β ) − − β ) − β c (cid:19) , (36) σ ( gg → t ¯ t ) = πα s s (cid:20)(cid:0) β − β + 33 (cid:1) log (cid:18) β − β (cid:19) + β (cid:0) β − (cid:1)(cid:21) , where c = cos ˆ θ , ˆ θ is the scattering angle of t -quark in the parton center of mass frame, ˆ s isthe invariant mass of t ¯ t system, β = p − m t / ˆ s .No sources of order α s for the forward-backward asymmetry.MQLS model contributions in t ¯ t productionIn MQLS there are three kind of contributions in t ¯ t -production.7. Z’ tree s-channel process,2. Scalar gluons tree processes,3. 1-loop gt ¯ t effective vertex.Z’ tree s-channel process q ¯ q t ¯ tγ, Z, Z ′ Figure 3: Subprocess q ¯ q γ, Z, Z ′ → t ¯ t Partonic subprocess q ¯ q γ, Z, Z ′ → t ¯ t is pictured at Fig. 3. Because initial quarks have singletcolor state these diagrams do not interfere with octet state QCD tree processes.We obtain differential cross section of q ¯ q γ, Z, Z ′ → t ¯ t with account masses of final t -quarks inthe form dσ ( q ¯ q γ, Z, Z ′ → t ¯ t ) d cos ˆ θ = πα em ˆ sβ X i,j = γ,Z,Z ′ K ij Re( P i (ˆ s ) P ∗ j (ˆ s )) , (37)cos ˆ θ ≡ c .Here, K ij = A ij (cid:0) β ( c − (cid:1) + B ij β ( c + 1) + 2 C ij βc,A ij = ( a qi a qj + v qi v qj ) v ti v tj ,B ij = ( a qi a qj + v qi v qj ) a ti a tj , (38) C ij = ( a qi v qj + v qi a qj )( a ti v tj + v ti a tj ) ,P i (ˆ s ) = 1ˆ s − M i + iM i Γ i ,v qi , a qi – vector and axial-vector couplings of q -quark with i -th neutral boson.For M Z ′ > . Z ′ to cross sectionand FB asymmetry of the t ¯ t production is small due smallness of couplings∆ σ ( p ¯ p → t ¯ t ) ∼ +0 . ÷ . , (39)∆ A t ¯ tF B ∼ +0 . . (40)Scalar gluons tree processesContributions of diagrams at Fig. 4 are suppressed by factors m q / ˆ s or | ( V CKM ) i | ∆ σ ( p ¯ p → t ¯ t ) ∼ . , (41)∆ A t ¯ tF B ∼ − . (42)1-loop gt ¯ t effective vertex 8 a F a σ ∼ m q / ˆ s σ ∼ | ( C Q ) i | Figure 4: s - and t -channel diagrams of q ¯ q → F a → t ¯ t . F tttF F τS (+)1 S (+)1 bF F ν τ S ( ± )2 S ( ± )2 F bb Figure 5: 1-loop main contributions into effective gt ¯ t -vertex in MQLS-model.The significant contributions to t ¯ t production may arise from loop corrections to the gt ¯ t -vertex.Following the parametrization in Ref. [17, 18], the effective matrix element of gt ¯ t , includingthe one-loop corrections, can be written as − ig s T a ¯ u t Γ µ v ¯ t , (43)with Γ µ = (1 + α ) γ µ + iβσ µν q ν + ξ (cid:18) γ µ − m t ˆ s q µ (cid:19) γ . (44)where the loop-induced form factors α , β and ξ are usually refereed as the chromo-charge,chromo-magnetic-dipole and chromo-anapole, respectively. Here, g s is the strong couplingstrength, T a are the color generators, q = p t + p ¯ t , and ˆ s = q . After summing over the fi-nal state and averaging over the initial state colors and spins, the partonic total cross sectionof q ¯ q → g → t ¯ t is [17]ˆ σ = 8 πα s s r − m t ˆ s (cid:26) ˆ s + 2 m t + 2Re (cid:2) (ˆ s + 2 m t ) α + 3 m t ˆ s β (cid:3)(cid:27) , (45)where α s ≡ g s / (4 π ), and Re denotes taking its real part. In MQLS-model main 1-loop contri-butions into effective gt ¯ t -vertex are described by diagrams at Fig.5. The parameters α , β canbe calculated using the diagrams shown in Fig. 5 and the coupling constants (27-28). • The contributions to the cross section σ t ¯ t and to the forward-backward asymmetry A t ¯ t FB of t ¯ t production at the Tevatron from new Z ′ , S ( ± ) a , F a particles predicted by the MQLS-9odel are calculated. • These contributions in tree approximation are shown to be small (∆ σ ∼ . A t ¯ t FB ∼ . • The scalar doublets S ( ± ) a , F a may give the significant contributions to the 1-loop gt ¯ t effective vertex. • The lower mass limits for scalar gluons m F & GeV are obtained from the data on direct searches at Tevatron. • At m F . GeV the scalar gluon F can be evident at LHC at the significance not lessthat 3 σ (for L = 10 f b − ).AcknowledgementThe work is supported by the Ministry of Education and Science of Russia under state con-tract No.P2496 of the Federal Programme ”Scientific and Pedagogical Personnel of InnovationRussia” for 2009-2013 years. References [1] J. C. Pati, A. Salam, Lepton number as the fourth ’color’, Phys. Rev. D (1), 275–289(1974).[2] A. D. Smirnov, Minimal four-color model with quark-lepton symmetry and constraints onthe Z’-boson mass, Phys. At. Nucl. (12), 2137–2143 (1995).[3] A. D. Smirnov, The Minimal Quark-Lepton Symmetry Model and the Limit on Z’-mass,Physics Letters B , 297 (1995). arXiv:hep-ph/9503239 .[4] A. D. Smirnov, Y. S. Zaitsev, On a possible manifestation of the four color symme-try Z ′ boson in µ + µ − events at the LHC, Mod. Phys. Lett. A24 , 1199–1207 (2009). arXiv:0902.2931 .[5] A. V. Povarov, A. D. Smirnov, Phys. At. Nucl. , P. 74 (2001).[6] C. Amsler, et al. (PDG), Review of Particle Physics, Phys. Lett. B , 1 (2008).[7] A. V. Manohar, M. B. Wise, Flavor Changing Neutral Currents, an Extended ScalarSector, and the Higgs Production Rate at the LHC, Phys. Rev. D74 , 035009 (2006). arXiv:hep-ph/0606172 .[8] M. V. Martynov, A. D. Smirnov, Colored scalar particles production in pp -collisions andpossible mass limits for scalar gluons from future LHC data, Mod. Phys. Lett. A23 ,2907–2913 (2008). arXiv:0807.4486 .[9] M. V. Martynov, A. D. Smirnov, Production of Colored Scalar Particles in pp Collisionsand Masses of Scalar Gluons from Future LHC Data, Phys. At. Nucl. (7), pp. 1207–1213(2010).[10] S. Alekhin, Parton distributions from deep-inelastic-scattering data, Phys.Rev.D ,014002 (2003). 1011] M. Cacciari, S. Frixione, M. L. Mangano, P. Nason, G. Ridolfi, Updated predictions forthe total production cross sections of top and of heavier quark pairs at the Tevatron andat the LHC, JHEP , 127 (2008). arXiv:0804.2800 .[12] N. Kidonakis, R. Vogt, The Theoretical top quark cross section at the Tevatron and theLHC, Phys. Rev. D78 , 074005 (2008). arXiv:0805.3844 .[13] M. V. Martynov, A. D. Smirnov, Chiral color symmetry and possible G ′ -boson effects atthe Tevatron and LHC, Mod. Phys. Lett. A24 , 1897–1905 (2009). arXiv:0906.4525 .[14] CDF Collaboration, Combination of CDF top quark pair production cross section measurements with up to 4.6 f b − ,Public Note 9913 (2009).[15] CDF Collaboration, Measurement of the Forward-Backward Asymmetry in Top Pair Production in 3.2/fb of ppbar collisions at sqrt(s)=1.96 TeV,CDF/ANAL/TOP/PUBLIC/9724 (2009).[16] O. Antunano, J. H. Kuhn, G. Rodrigo, Top Quarks, Axigluons and Charge Asymmetriesat Hadron Colliders, Phys. Rev. D77 , 014003 (2008), arXiv.org:0709.1652.[17] A. Stange, S. Willenbrock, Yukawa correction to top quark production at the Tevatron,Phys. Rev.
D48 , 2054–2061 (1993). arXiv:hep-ph/9302291 .[18] Q.-H. Cao, C.-R. Chen, F. Larios, C. P. Yuan, Anomalous gtt couplings in the LittlestHiggs Model with T-parity, Phys. Rev.
D79 , 015004 (2009). arXiv:0801.2998arXiv:0801.2998