Mass limits for the chiral color symmetry G ′ -boson from LHC dijet data
aa r X i v : . [ h e p - ph ] J un Mass limits for the chiral color symmetry G ′ -bosonfrom LHC dijet data I. V. Frolov ∗ , A. D. Smirnov † Division of Theoretical Physics, Department of Physics,Yaroslavl State University, Sovietskaya 14,150000 Yaroslavl, Russia.
Abstract
The contributions of G ′ -boson predicted by the chiral color symmetry of quarksto the differential dijet cross-sections in pp -collisions at the LHC are calculated andanalysed in dependence on two free parameters of the model, the G ′ mass m G ′ and mixing angle θ G . The exclusion and consistency m G ′ − θ G regions imposedby the ATLAS and CMS data on dijet cross-sections are found. Using the CT10(MSTW 2008) PDF set we show that the G ′ -boson for θ G = 45 ◦ , i.e. the axigluon,with the masses m G ′ < . .
6) TeV and m G ′ < .
35 (3 .
25) TeV is excluded at theprobability level of 95% by the ATLAS and CMS dijet data respectively. For theother values of θ G the exclusion limits are more stringent. The m G ′ − θ G regionsconsistent with these data at CL = 68% and CL = 90% are also found.Keywords: New physics; chiral color symmetry; axigluon; massive color octet; G ′ -boson; dijet cross section. The search for the possible effects of new physics beyond the Standard Model (SM) isnow one of the main goals of the experiments at the LHC. By now there are many modelspredicting new particles which can manifest themselves at the LHC energy through thepossible new physics effects. Among such particles there are new quarks and leptonsof the fourth generation of fermions, supersymmetric particles of the supersymmetrymodels, new scalar particles of two Higgs models, new gauge bosons of the weak left-rightsymmetry model, gauge and scalar leptoquarks of the four color quark-lepton symmetrymodels, etc. The unobservation of the new physics effects induced by these particles atthe LHC will set new limits on the parameter of corresponding models.One of such models which also predict new particles and can induce the new physicseffects at the LHC energy is based on the gauge group of the chiral color symmetry ofquarks G c = SU cL (3) × SU cR (3) M chc −→ SU c (3) (1)which is assumed to be valid at high energies and is spontaneously broken to usual QCD SU c (3) at some low energy scale M chc . The idea of the originally chiral character of SU c (3) ∗ e-mail : [email protected] † e-mail : [email protected] g L = g R in refs. [1–4] and then it was extended to the more general case of g L = g R [5–8].The chiral color symmetry of quarks in addition to the usual gluons predicts imme-diately a new massive gauge particle – the axigluon G A (in the case of g L = g R ) withpure axial vector couplings to quarks or G ′ -boson (in the case of g L = g R ) with vectorand axial vector couplings to quarks defined by the gauge group (1). In both cases thisnew particle interacts with quarks with coupling constants of order g st and can induceappreciable effects in the processes with quarks. In particular G ′ -boson could give riseat the LHC to the charge asymmetry of t ¯ t production as well as to the appearance ofa resonant peak in the invariant mass spectrum of dijet events. The possible effect of G ′ -boson on the charge asymmetry of t ¯ t production at the LHC (and at the Tevatron)and the corresponding G ′ -boson mass limits have been discussed in [6–9].In the present paper we calculate and analyse the possible G ′ -boson contributions tothe differential dijet cross-sections in pp -collisions at the LHC in comparison with theATLAS [10] and CMS [11, 12] data on dijet cross-sections and find the G ′ -boson masslimits imposed by these experimental data.The basic gauge fields of the group (1) G Lµ and G Rµ form the usual gluon field G µ andthe field G ′ µ of an additional G ′ -boson as superpositions G µ = g R G Lµ + g L G Rµ p ( g L ) + ( g R ) ≡ s G G Lµ + c G G Rµ , (2) G ′ µ = g L G Lµ − g R G Rµ p ( g L ) + ( g R ) ≡ c G G Lµ − s G G Rµ , (3)where G L,Rµ = G L,Riµ t i , G µ = G iµ t i , G ′ µ = G ′ iµ t i , i = 1 , , ..., t i are the generators of SU c (3)group, s G = sin θ G , c G = cos θ G , θ G is G L − G R mixing angle, tg θ G = g R /g L and g L , g R are the coupling constants of the group (1).The interaction of the G ′ -boson with quarks can be written as L G ′ qq = g st ( M chc ) ¯ qγ µ ( v + aγ ) G ′ µ q, (4)where g st ( M chc ) = g L g R p ( g L ) + ( g R ) is the strong interaction coupling constant at the mass scale M chc of the chiral colorsymmetry breaking and the vector and axial-vector coupling constants v and a are definedby the group (1) and with account of the relations (2), (3) take the form v = c G − s G s G c G = cot(2 θ G ) , a = 12 s G c G = 1 / sin(2 θ G ) . (5)After spontaneously breaking the symmetry (1) the G ′ -boson acquires some mass m G ′ and as a result we obtain two free parameters in the model, the G ′ -boson mass m G ′ andthe G L − G R mixing angle θ G . For g L = g R we have θ G = 45 ◦ , v = 0 , a = 1 and G ′ -bosonin this case coincides with the axigluon.The interaction (4) gives to the G ′ -boson the hadronic widthΓ G ′ = X Q Γ( G ′ → QQ ) , (6)2here Γ( G ′ → QQ ) = α s m G ′ " v (cid:18) m Q m G ′ (cid:19) + a (cid:18) − m Q m G ′ (cid:19) − m Q m G ′ (7)is the width of G ′ -boson decay into QQ -pair. From (5)–(7) follow the next estimationsfor the relative width of G ′ -boson Γ G ′ /m G ′ = 0 . , . , . , . , .
71 for θ G =45 ◦ , ◦ , ◦ , ◦ , ◦ respectively.The chiral color symmetry of quarks needs the extensions of the fermion sector of themodel for cancellations of the chiral γ -anomalies which are produced by quarks in the caseof the chiral color symmetry (1) as well as of the scalar one for giving necessary masses tothe fermions and gauge particles of the model. For discussing these extensions the chiralcolor symmetry (1) should be unified with the electroweak SU L (2) × U (1) symmetry ofthe SM for example in the simplest way by the group G = SU cL (3) × SU cR (3) × SU L (2) × U (1) , (8)where the first two factors are given by the group (1) and the second ones form the usualSM electroweak symmetry group.There are many approaches for cancellation of the chiral γ -anomalies produced bythe SM fermions through extensions of the SM fermion sector by introducing additionalexotic fermions. The most simple and natural looks the variant [13] in which in the caseof the group (8) for each SM doublet q of quarks q a , a = 1 , q L : (3 , , , Y q L ) , (9) q Ra : (1 , , , Y q Ra ) (10)with the SM quark hypercharges Y q L = 1 / , Y q R = 4 / , Y q R = − / q a transforming under the group (8) as˜ q La : (1 , , , Y ˜ q a ) , (11)˜ q Ra : (3 , , , Y ˜ q a ) , (12)where Y ˜ q = ˜ Y , Y ˜ q = − ˜ Y + 2 / Y is anarbitrary hypercharge. With patricular choice of ˜ Y = 4 / G ′ -boson in the form L G ′ ˜ q ˜ q = g st ( M chc ) ¯˜ qγ µ ( v − aγ ) G ′ µ ˜ q, (13)where the constants v and a are given by the expressions (5). Additionally the ex-otic quarks have the vector-like interactions with the photon and SM Z -boson. As seenfrom (13) the axial-vector coupling constant of the exotic quarks with the G ′ -boson hasthe opposite sign relatively to that of the SM quarks, which ensures the cancellation ofthe chiral γ -anomalies in diagrams with the G ′ -bosons.For giving necessary masses to the fermions and gauge particles the scalar sector ofthe model should be appropriately extended. The masses to the usual quarks and leptons3an be given by the scalar doublets (Φ (1 , a ) αβ and Φ (3) a transforming under the group (8)as (Φ (1) a ) αβ : (3 , ¯3 , , − , (14)(Φ (2) a ) αβ : (3 , ¯3 , , +1) , (15)Φ (3) a : (1 , , , +1) (16)with VEVs h (Φ ( b ) a ) αβ i = δ αβ δ ab η b / (2 √
3) for b = 1 , h Φ (3) a i = δ a η / √ a = 1 , SU L (2) index and α, β = 1 , , SU cL (3) and SU cR (3) indices.The mass to the G ′ -boson can be given by the scalar field Φ (0) αβ transforming under thegroup (8) as (Φ (0) ) αβ : (3 , ¯3 , ,
0) (17)with VEV h Φ (0) αβ i = δ αβ η / (2 √ G ′ -boson acquiresthe mass m G ′ = g st s G c G p η + η + η √ . (18)The field Φ (0) αβ can interact with the exotic quarks as L Φ (0) ˜ q ˜ q = ¯˜ q Riaα ( h a ) ij (Φ (0) ) αβ ˜ q Ljaβ + ¯˜ q Liaα ( h + a ) ij ((Φ (0) ) + ) αβ ˜ q Rjaβ , (19)where ( h a ) ij form the matrices of Yukawa coupling constants, i, j are the generationindeces. By biunitary transformations these matrices can be reduced to the diagonal form( h ia ) δ ij and after the symmetry breaking the mass eigenstates ˜ q ′ ia of the exotic quarks pickup the masses m ˜ q ′ ia = h ia η √ . (20)As a result of the decomposition (3 L , ¯3 R ) = 1 SU c (3) + 8 SU c (3) of the representation(3 L , ¯3 R ) of the group (1) the multiplets (Φ (1 , a ) αβ and Φ (0) αβ after the chiral color symmetrybreaking give the color singlets (Φ (1 , a ) αβ = Φ (1 , a δ αβ / √ (0;0) αβ = Φ (0)0 δ αβ / √ SU c (3) octets (Φ (1 , a ) αβ = Φ (1 , ia ( t i ) αβ , Φ (0;8) αβ = Φ (0) i ( t i ) αβ . The color singletsΦ (1 , a and Φ (3) a are the SU L (2) doublets. These doublets are mixed and form the SM Higgsdoublet Φ ( SM ) a with the SM VEV η SM = p η + η + η ≈ GeV and two additionaldoublets Φ ′ a , Φ ′′ a . As a result the chiral color symmetry reproduces in the scalar sectorthe SM Higgs doublet Φ ( SM ) a and predicts the new scalar fields: two colorless doublets Φ ′ a and Φ ′′ a , two doublets of color octets Φ (1 , ia , the color octet Φ (0) i and the colorless SU L (2)singlet Φ (0)0 with the VEV η . The interactions of the doublet Φ ( SM ) a with the SM quarksand leptons and with W ± and Z bosons have the standard form.The differential cross section of the process pp → cd + X of the inclusive productionof two partons c and d in pp collisions can be written in the usual way as dσ ( pp → cd + X ) = X ab Z Z f pa ( x ; µ F ) f pb ( x ; µ F ) dσ ( ab → cd ) dx dx , (21)where a = q i , ¯ q i , g ; b = q j , ¯ q j , g are the initial partons, i, j = 1 , , ..., f pa ( x ; µ F ) are the parton distribution function (PDF) of quark,4ntiquark or gluon, x , are the momentum fractions of proton carried by initial partons, µ F is the factorization scale and dσ ( ab → cd ) = (2 π ) δ (4) ( p + p − p − p ) | M ab → cd | s d p E (2 π ) d p E (2 π ) (22)are the parton differential cross sections, p , and p , = { E , , ~p , } are the four momentaof the initial and final partons, ˆ s = ( p + p ) .The amplitudes of parton processes ab → cd can be presented as M ab → cd = M SMab → cd + M G ′ ,LOab → cd , (23)where M SMab → cd = M SM,LOab → cd + M SM,NLOab → cd (24)are the SM amplitudes calculated up to next to leading order and the amplitudes M G ′ ,LOab → cd give the G ′ -boson contributions in the leading order.The amplitudes M G ′ ,LOab → cd are described by the diagrams shown in the Fig. 1. G ′ q i G ′ + δ ijq i q i q i q j q j q j q j G ′ G ′ + δ ik δ jl δ ij δ kl q i q k q i q k ¯ q j ¯ q l ¯ q j ¯ q l q i ( p ) q j ( p ) → q i ( p ) q j ( p ) : q i ( p )¯ q j ( p ) → q k ( p )¯ q l ( p ) : Figure 1: Diagrams describing the leading-order G ′ -boson contributions to the ampli-tudes M G ′ ,LOab → cd of the partonic processes q i q j → q i q j and q i ¯ q j → q k ¯ q l (diagrams for theprocesses ¯ q i ¯ q j → ¯ q i ¯ q j can be obtained from the diagrams of the processes q i q j → q i q j bychanging the directions of the fermion lines)For the squared amplitudes | M ab → cd | we use the expressions | M ab → cd | = | M SMab → cd | + | M G ′ ,LOab → cd | + 2 Re ( M SM,LOab → cd ∗ M G ′ ,LOab → cd ) + ..., (25)where the dots denote the terms 2 Re ( M SM,NLOab → cd ∗ M G ′ ,LOab → cd ) omitted because of their small-ness. 5or the calculation of the G ′ -boson contribution in dijet mass spectrum we use apackage for calculation of Feynman diagrams and integration over multi-particle phasespace CalcHEP [14] and for calculation of differential dijet NLO cross section in the SMwe use the program for computation of inclusive jet cross sections at hadron collidersMEKS [15].As a result of calculations for the terms | M G ′ ,LOab → cd | and 2 Re ( M SM,LOab → cd ∗ M G ′ ,LOab → cd ) in (25)we obtain the expressions | M G ′ ,LOq i q j → q i q j | = | M G ′ ,LO ¯ q i ¯ q j → ¯ q i ¯ q j | =4 g st ( M chc )27 δ ij (cid:0) ˆ t A + ˆ s B (cid:1) (ˆ u − m G ′ ) − δ ij ˆ s B (cid:0) ˆ t − m G ′ (cid:1) (ˆ u − m G ′ ) + 3 (ˆ u A + ˆ s B ) (cid:0) ˆ t − m G ′ (cid:1) ! , (26) | M G ′ ,LOq i ¯ q j → q k ¯ q l | = 4 g st ( M chc )27 δ ik δ jl (ˆ s A + ˆ u B ) (cid:0) ˆ t − m G ′ (cid:1) − δ ij δ jk ˆ u (ˆ s − m G ′ ) B (cid:16) (ˆ s − m G ′ ) + m G ′ Γ G ′ (cid:17)(cid:0) ˆ t − m G ′ (cid:1) + 3 δ ij δ kl (cid:0) ˆ t A + ˆ u B (cid:1) (ˆ s − m G ′ ) + m G ′ Γ G ′ ! (27)and2 Re ( M SM,LOq i q j → q i q j ∗ M G ′ ,LOq i q j → q i q j ) = 2 Re ( M SM,LO ¯ q i ¯ q j → ¯ q i ¯ q j ∗ M G ′ ,LO ¯ q i ¯ q j → ¯ q i ¯ q j ) =8 g st ( µ R ) g st ( M chc )27 u A + ˆ s (cid:0) u − δ ij ˆ t (cid:1) C ˆ t ˆ u (cid:0) ˆ t − m G ′ (cid:1) + δ ij (cid:0) t A + ˆ s (3ˆ t − ˆ u ) C (cid:1) ˆ t ˆ u (ˆ u − m G ′ ) ! , (28)2 Re ( M SM,LOq i ¯ q j → q k ¯ q l ∗ M G ′ ,LOq i ¯ q j → q k ¯ q l ) = 8 g st ( µ R ) g st ( M chc )27 δ jl (cid:0) δ ik ˆ s A +ˆ u (3 δ ik ˆ s − δ ij δ jk ˆ t ) C (cid:1) ˆ s ˆ t (cid:0) ˆ t − m G ′ (cid:1) + (ˆ s − m G ′ ) (cid:0) ˆ u (cid:0) δ ij δ kl ˆ t − δ ij δ jk ˆ s (cid:1) C +3 δ ij δ kl ˆ t A (cid:1) ˆ s ˆ t (cid:16) (ˆ s − m G ′ ) + m G ′ Γ G ′ (cid:17) , (29)where A = ( v − a ) , B = ( a + 6 a v + v ) , C = ( v + a ) and ˆ s = ( p + p ) ,ˆ t = ( p − p ) , ˆ u = ( p − p ) , µ R is the renormalization scale.In order to compare the cross-section defined by the equations (21)–(29) with theexperimental dijet double-differential cross-sections measured by the ATLAS collabora-tion [10] we have calculated the double-differential cross-sections averaged over the binsof ref. [10] as d σ ( pp → jet jet ) dm jj d | y ∗ | = 1∆ m jj | y ∗ | m + jj Z m − jj | y ∗ | + Z | y ∗ | − d σ ( pp → jet jet ) dm jj d | y ∗ | dm jj d | y ∗ | , (30)where m ± jj = m jj ± ∆ m jj / | y ∗ | ± = | y ∗ | ± ∆ | y ∗ | / m jj ( | y ∗ | ) and ∆ m jj (∆ | y ∗ | ) are thecentral value and the width of the invariant mass (half the rapidity separation) bin. Thedijet double-differential cross-section d σ ( pp → jet jet ) dm jj d | y ∗ | in (30) has been calculated from thecross-section (21), (22) with | M ab → cd | defined by the equations (25)–(29) by using thepackage CalcHEP [14] and the program MEKS [15] with account the kinematic relationsˆ s = x x s, ˆ t = − ˆ s − tanh( y ∗ )) , ˆ u = − ˆ s y ∗ )) , (31) y ∗ = y − y , y , = 12 ln E , + p , z E , − p , z , (32)6here √ s is the center of mass energy of colliding protons, y , are the rapidities of thefinal partons and m jj = ˆ s = x x s is the invariant mass of two jets.For comparing the cross-section (21)–(29) with the experimental dijet differential cross-sections measured by the CMS collaboration [11] we have calculated the differential cross-sections averaged over the bins of ref. [11] as dσ ( pp → jet jet ) dm jj = 1∆ m jj m + jj Z m − jj | η ∗ | max Z d σ ( pp → jet jet ) dm jj d | η ∗ | d | η ∗ | , (33)where the dijet double-differential cross-section d σ ( pp → jet jet ) dm jj d | η ∗ | in (33) is obtained from d σ ( pp → jet jet ) dm jj d | y ∗ | in (30) by the substitution y ∗ → η ∗ with η ∗ = η − η , η , = − ln[tan( θ , / , where η , and θ , are the pseudorapidities and the polar scattering angles of the finaljets. The upper limit | η ∗ | max in (33) is defined by the CMS experiment. The variable | η ∗ | relates to the pseudorapidity separation | ∆ η jj | used in ref. [11] as | ∆ η jj | = 2 | η ∗ | .For the comparison of the experimental and theoretical results we use the variable χ r (,,reduced” χ ) defined as χ r = 1 n N X i ( σ expi − σ thi ) (∆ σ expi ) , where σ expi denote the experimental value of d σ ( pp → jet jet ) dm jj d | y ∗ | in the case of the ATLAS data(or dσ ( pp → jet jet ) dm jj in the case of the CMS data) in the i -th bin, σ thi is the correspondingtheoretical value, ∆ σ expi is the experimental error of this value, n = N − N p is the numberof degrees of freedom, N is the number of the bins under consideration and N p is thenumber of the free parameters of the model. In the further analysis we use the values N p = 0 for the SM and N p = 2 for the gauge chiral color symmetry model.The ATLAS dijet double-differential cross-sections were measured [10] for pp collisionsat √ s = 7 TeV with 4 . − as functions of the dijet mass m jj and half the rapidityseparation y ∗ = | y − y | / y ∗ of ref. [10] relates toour variable (32) as y ∗ = | y ∗ | ). The measurements are performed in six ranges of y ∗ ininterval 0 < y ∗ < . .
5. The ATLAS collaboration provides the resultsas tables of measured dijet cross-section in N = 21 dijet mass bins for all six ranges of y ∗ .In order to compare our results with the ATLAS measurements we have calculatedthe double-differential cross-sections (30) for the same dijet mass bins and the ranges of y ∗ as the ATLAS ones and use in our calculations the ATLAS kinematic cuts on the finalstates | y i | < i = 3 , ,p T i >
100 GeV , where y i and p T i are the rapidity and transverse momentum of each jet. We set also thefactorization ( µ F ) and renormalization ( µ R ) scales as µ = µ R = µ F = p maxT e . y ∗ where p maxT is the p T of the leading jet. In the ATLAS analysis [10] the jets are clustered by the7nti- k t algorithm using two values of the radius parameter, R = 0 . R = 0 .
6. Fordefiniteness we perform our calculations and analysis of the ATLAS data with the value R = 0 .
6. To demonstrate the dependence of the results on the parton distribution func-tions we use in our theoretical evaluations two PDF sets, CT10 [17] and MSTW 2008 [16].We have calculated the double-differential cross-sections (30) by means of the programsMEKS and CalcHEP with using the CT10 and MSTW 2008 PDF sets with account ofthe contributions of the SM NLO QCD and G ′ -boson in each dijet mass bin and in allthe ranges of y ∗ for the model parameters m G ′ > ◦ < θ G < ◦ . The resultsaccounting only the SM NLO QCD contribution are in good agreement with the cross-sections measured by the ATLAS (in all the bins the theoretical cross-sections consistwith the experimental ones within the experimental errors). For example, for the range0 ≤ y ∗ < . χ rSM = 6 . /
21 = 0 . χ rSM = 15 . /
21 = 0 .
74 in the case of theMSTW 2008 PDF set. θ , ◦ ATLAS, TeV, . fb − CT10 PDF a) excluded ATLAS, TeV, . fb − MSTW2008 PDF b) excluded2 4 6 8 10 12 m G ′ , T eV θ , ◦ CMS, TeV, . fb − CT10 PDF c) excluded 2 4 6 8 10 12 m G ′ , T eV CMS, TeV, . fb − MSTW2008 PDF d) excluded excludedexcluded at probability levelintermediate region consistent at CL= consistent at CL= Figure 2: The exclusion (at 95% probability level) and consistency (at CL = 68% and CL = 90%) m G ′ − θ G regions resulting from the ATLAS ( √ s = 7 TeV with 4 . − ) andCMS ( √ s = 8 TeV with 19 . − ) data on dijet cross sections with using the CT10 andMSTW 2008 PDF sets.We have compared the results accounting simultaneously the contributions of the SMNLO QCD and G ′ -boson with the ATLAS data to find the regions of the parameters m G ′ and θ G which are excluded by the ATLAS data at the appropriate level as well as theallowed ones. 8n the upper sections of the Fig. 2 we show the excluded and allowed m G ′ − θ G regionsresulting from the ATLAS data on the double-differential dijet cross sections for therange 0 ≤ y ∗ < . m G ′ − θ G region excluded at the probability level of 95% and the dashed and dottedlines show the bounds of m G ′ − θ G regions which are consistent with the data at CL = 68%and CL = 90% respectively.As seen from the Fig. 2 a), b) in the case of using the CT10 (MSTW 2008) PDF setthe G ′ -boson for θ G = 45 ◦ (i.e. the axigluon) with the masses m G ′ < . .
6) TeV (34)is excluded at the probability level of 95% by the ATLAS dijet data and for the othervalues of θ G the corresponding exclusion limits are more stringent. At the same time independence on θ G the G ′ -boson with masses m G ′ > .
55 (5 .
8) TeV (35)is consistent with these data at CL = 68% and with masses m G ′ > .
65 TeV (36)at CL = 90% in the case of using the CT10 PDF set.The CMS search [11] for dijet resonances was done at √ s = 8 TeV with 19 . − ofthe data and the dijet differential cross-section as function of the dijet mass was measuredand is accessible at the HepData [12]. For comparison with CMS data we used in ournumerical calculations the CMS dijet search criteria | η i | < . i = 3 , , | ∆ η jj | < . ,H T >
650 GeV , where η i is the pseudorapidity of each jet, | ∆ η jj | = 2 | η ∗ | is the pseudorapidity separationof the two jets and H T is the scalar sum of the jet p T , and the values of the renormalizationand factorization scales µ = µ R = µ F = p maxT and of the radius parameter R = 1 . G ′ -boson in each dijet mass bin for the modelparameters m G ′ > ◦ < θ G < ◦ .The comparison of the theoretical results with the CMS dijet data occurs to be slightlymore complicated then that in the case of the ATLAS data.In the upper left (right) section of the Fig. 3 we show the CMS data [11, 12] withtheir experimental errors by the solid lines and the dijet differential cross-section (33)calculated with accounting the SM NLO QCD contribution for the case of using the CT10(MSTW2008) PDF sets by the dashed lines, for the jet radius parameter R = 1 .
1. In thecorresponding lower sections of the Fig. 3 we show the relations r i = ( σ expi − σ thi ) / ∆ σ expi ,where σ expi ( σ thi ) denote the experimental (theoretical) value of dσ ( pp → jet jet ) dm jj in the i -th binand ∆ σ expi is the experimental error of this value, the dashed lines correspond also to thecase of accounting only the SM NLO QCD contribution to σ thi .9 − − − − − − d σ d m jj , p b G e V CMS data, TeV, , fb − SM NLO QCD, CT10 PDF m G ′ = 3 . TeV, θ = 45 ◦ CMS data, TeV, , fb − SM NLO QCD, MSTW2008 PDF m G ′ = 3 . TeV, θ = 30 ◦ m jj , T eV -4-2024 r i m jj , T eV Figure 3: The dijet differential cross-section dσ ( pp → jet jet ) dm jj calculated using the CT10(MSTW2008) PDF set for the jet radius parameter R = 1.1 with account of the contribu-tions of the SM NLO QCD and G ′ -boson with m G ′ = 3 . θ G = 45 ◦ ( m G ′ = 3 . θ G = 30 ◦ ) in comparison with the CMS dijet data.As seen from the Fig. 3 in the bins from the region 2 . < m jj < . N = 22 bins of the Fig. 3 from the range m jj > . χ rSM = 23 . /
22 = 1 . χ rSM = 106 . /
22 = 4 .
8) in the case ofusing the CT10 (MSTW2008) PDF set. As seen, this agreement is not sufficiently good,especially in the case of using the MSTW2008 PDF set.In the case of the simultaneous account of the contributions of the SM NLO QCD and G ′ -boson we vary two free parameters of the gauge chiral color symmetry model ( m G ′ and θ G ) to minimize χ r . It is found that in the case of using the CT10 (MSTW2008) PDFset the minimum of χ r is at the values m G ′ = 3 . .
7) TeV , θ G = 45 ◦ (30 ◦ ) . (37)The dijet differential cross-section (33) calculated with simultaneous accounting thecontributions of the SM NLO QCD and G ′ -boson with parameters (37) and the corre-sponding relations r i are shown in the Fig. 3 by the dotted lines. This cross-section agreeswith the corresponding CMS data (solid lines) with χ r min = 7 . /
20 = 0 .
39 (7 . /
20 = 0 . χ rSM = 1 . .
8) in the case of accounting only the SM NLO QCD contribution(dashed lines).We have found and analysed the exclusion and consistency m G ′ − θ G regions resultingfrom the CMS dijet data. In the lower sections of the Fig. 2 we show the excluded andallowed m G ′ − θ G regions resulting from the CMS data on the differential dijet cross sections10or R = 1.1 in the cases of using the CT10 (section c)) and MSTW 2008 (section d)) PDFsets. In these sections the crosses refer to the points (37) and the other notations are thesame as those in the upper ones.As seen from the Fig. 2 c), d) in the case of using the CT10 (MSTW 2008) PDF setthe G ′ -boson for θ G = 45 ◦ (i.e. the axigluon) with the masses m G ′ < .
35 (3 .
25) TeV (38)is excluded at the probability level of 95% by the CMS dijet data and for the other valuesof θ G the corresponding exclusion limits are more stringent. In the up-right part of theFig. 2 d) there is an additional exclusion region but this region is caused mainly by thementioned above not sufficiently good agreement between the CMS dijet data and theSM NLO QCD calculations with using the MSTW2008 PDF set. It is also seen that inthe both cases c) and d) there are the m G ′ − θ G regions which are consistent with theCMS dijet data at CL = 68% and CL = 90%.It should be noted that our results are obtained with account only the G ′ -bosoncontribution to the dijet cross-sections and generally speaking the presence of the newparticle (the exotic quarks an additional scalar particles) in the model could influence onthese results.Through their OCD interaction with gluons and interaction (13) with G ′ -boson theexotic quarks can contribute to the dijet cross-sections as well as give the analogousto (6), (7) additional contributions to the G ′ -boson hadronic width. We have calculatedthe contributions of the exotic quarks to the dijet cross-sections analogously to the case ofthe usual quarks and found that the CMS data [11, 12] are consistent within experimentalerrors with the existence of the exotic quarks with masses m ˜ q ′ ia &
900 GeV. It is worthy tonote that the current experimental low mass limits for additional heavy quarks are of abouta few hundreds GeV. For example the ATLAS Collaboration excludes the t ′ quark with themass m t ′ <
790 GeV [18] and the CMS exclusion limit for T / is of m T / <
800 GeV [19].Accounting in (6), (7) also the contributions of three generations of the exotic quarkswith m ˜ q ′ ia = 900 GeV we obtain that the G ′ -boson peak becomes more wide and low,which slightly effects the results. For example instead of (38) we obtain in this case themass limit m G ′ < .
25 (3 .
23) TeV, as seen the deviations are ∆ m G ′ = −
100 ( −
20) GeV.Because of (20), (18) the exotic quarks can be more heavy. For m ˜ q ′ ia = 1 . m G ′ ≈ − (5 −
20) GeV and for m ˜ q ′ ia > m G ′ / G ′ -boson peak becomes negligible.As mentioned above the model under consideration reproduces in the scalar sector theSM Higgs doublet Φ ( SM ) a and predicts new colorless doublets Φ ′ a and Φ ′′ a and two doubletsof color octets Φ (1 , ia . Although the SM Higgs doublet Φ ( SM ) a interacts with the SMfermions and W ± and Z bosons in the standard way the new doublets could contributeto the signal-strengths of the Higgs decays through the loop corrections. These loopcontributions depend on the details of the interactions of the Higgs doublet with the newscalar doublets (coupling constants, mixings, masses). At the present time the signal-strengths of the partial Higgs decays are measured with accuracy of about 20 - 30 % [20].For example the signal-strength is equal to µ H → γγ = 1 . ± .
27 for the decay H → γγ and has the global value µ = 1 . +0 . − . . All the measured signal-strengths are compatiblewith the SM predictions. It seems that the uncertainty in the Higgs doublet interactionswith the new scalar doublets allows at the present time to satisfy the current experimentalvalues of the signal-strengths of the Higgs decays.In conclusion, we summarize the results of this paper.11he possible contributions of G ′ -boson predicted by the chiral color symmetry ofquarks to the differential dijet cross-sections in pp -collisions at the LHC are calculatedand analysed in dependence on two free parameters of the model, the G ′ mass m G ′ andmixing angle θ G .Using the ATLAS [10] and CMS [11, 12] data on dijet cross-sections we find the G ′ -boson mass limits (in dependence on θ G ) imposed by these experimental data. In particu-lar, it is found that in the case of using in theoretical calculations the CT10 (MSTW 2008)PDF set the G ′ -boson for θ G = 45 ◦ (i.e. the axigluon) with the masses m G ′ < . .
6) TeVand m G ′ < .
35 (3 .
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