On the possibility to detect the Higgs decay H→b b ¯ in the associated Z+b b ¯ production at the LHC
aa r X i v : . [ h e p - ph ] A p r On the possibility to detect the Higgs decay H → b ¯ b in the associated Z + b ¯ b production at the LHC A.V. Lipatov , , N.P. Zotov July 16, 2018 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991Moscow, Russia Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia
Abstract
We investigate the possibility to detect the scalar Higgs boson decay H → b ¯ b in theassociated Z and b ¯ b production at the LHC using the k T -factorization QCD approach.Our consideration is based on the off-shell (i.e. depending on the transverse momenta ofinitial quarks and gluons) production amplitudes of q ∗ ¯ q ∗ → ZH → Zq ′ ¯ q ′ , q ∗ ¯ q ∗ → Zq ′ ¯ q ′ and g ∗ g ∗ → Zq ′ ¯ q ′ partonic subprocesses supplemented with the Catani-Ciafoloni-Fiorani-Marchesini (CCFM) dynamics of parton densities in a proton. We argue that the H → b ¯ b signal could be observed at large transverse momenta near Higgs boson peak despite theoverwhelming QCD background, and point out an important role of angular correlationsbetween the produced Z boson and b -quarks.PACS number(s): 12.38.Bx, 14.65.Fy, 14.70.Hp, 14.80.Bn1n 2012, during the search performed by the CMS and ATLAS Collaborations at theLHC, the scalar Higgs boson H with a mass m H near 125 GeV has been discovered [1, 2],giving us the confidence in the physical picture of fundamental interactions which followsfrom the Standard Model Lagrangian. Some time later, the ATLAS Collaboration hasreported first measurements of the Higgs boson differential cross sections in the γγ decaymode [3]. The measured cross sections were found a bit higher than the central next-to-next-to-leading order (NNLO) expectations [4–9] and those matched with soft-gluonresummation carried out up to next-to-next-to-leading logarithmic accuracy (NNLL) [10,11], although no significant deviations from theoretical predictions are observed withinthe uncertainties [3]. The significant signal was detected also in channels where the Higgsboson decays into the ZZ or W W pairs [12, 13]. The interaction of the Higgs particlewith the massive Z and W bosons indicates that, as it was expected, it plays a role inelectroweak symmetry breaking. However, the interaction with the fermions and whetherthe Higgs field serves as the source of mass generation in the fermion sector still remainsto be established. Since Higgs boson with mass m H ∼
125 GeV decays mainly into abeauty quark-antiquark pair [14], the observation and study of the H → b ¯ b decay (whichinvolves the direct coupling of the Higgs boson to beauty quarks) is therefore essential indetermining the nature of the newly discovered boson.The most sensitive channel for the H → b ¯ b events at the LHC is the production ofHiggs particle in association with the Z boson [15]. Despite the largest branching fraction( ∼ H → b ¯ b final state is a more difficult for the experimental observationcompared to the signatures provided by the diphoton or diboson decay modes due tosmall signal over background ratio. One of main backgrounds for the associated Higgsand Z boson production is the associated production of Z boson and two b -quark jets. Thecorresponding cross sections, calculated at the NNLO level (see [14]), are several ordersof magnitude larger than the Higgs boson signal. However, recently CMS Collaborationreported [16] an excess of events above the expected background with a local significanceof 2 . −
140 GeV mass range, consistent with the mass of theHiggs boson observed at the LHC.The experimental searches [15,16] are stimulated us to investigate the associated Higgs(decaying into a b ¯ b pair) and Z boson production as well as corresponding main back-ground process, associated production of Z boson and two b -quark jets , using the k T -factorization approach of QCD [17, 18]. A detailed description of this formalism can befound, for example, in reviews [19]. We only mention that the main part of higher-orderQCD corrections (namely, NLO + NNLO + N LO + ... contributions which correspondto the log 1 /x enhanced terms in perturbative series) is effectively taken into account inthe k T -factorization approach already at leading order, and it provides solid theoreticalground for the effects of initial parton radiation and transverse momenta of initial quarksand gluons. Recently, the k T -factorization QCD approach was successfully applied [20,21]to describe the ATLAS data [3] on the inclusive Higgs production in the diphoton decaymode .Let us start from a short review of calculation steps. Our consideration is based on the Other background processes, like as t ¯ t pair, diboson or QCD multijet production are out of ourpresent consideration. In our opinion, the results [21] suffer from the problem of double counting and contain the wrongnumerical factor. q ∗ ( k ) + ¯ q ∗ ( k ) → Z + H → Z ( p ) + q ′ ( p ) + ¯ q ′ ( p ) , (1) q ∗ ( k ) + ¯ q ∗ ( k ) → Z ( p ) + q ′ ( p ) + ¯ q ′ ( p ) , (2) g ∗ ( k ) + g ∗ ( k ) → Z ( p ) + q ′ ( p ) + ¯ q ′ ( p ) , (3)where the four-momenta of all corresponding particles are given in the parentheses (seeFig. 1). The subprocesses (2) and (3) correspond to the main QCD background to theassociated Higgs and Z boson production. Note, to calculate the production amplitudes,we apply the reggeized parton approach [22, 23], which is based on the effective actionformalism [24], currently explored at next-to-leading order [25], and take into account thevirtualities of both initial quarks and gluons. In this point our consideration differs fromthe one based on the collinear QCD factorization, where these virtualities are not takeninto account. The use of effective vertices [22, 23] ensures the exact gauge invariance ofcalculated amplitudes despite the off-shell initial partons.The off-shell amplitude of subprocess (1) reads: M = ee q ǫ µ ( p ) ¯ v s ( p )Γ Hq ¯ q u s ( p ) 1( p + p ) − m H − im H Γ H ×× Γ µνZZH (cid:20) g νλ − ( k + k ) ν ( k + k ) λ m Z (cid:21) s − m Z − im Z Γ Z ¯ v r ( x l )Γ λq ∗ ¯ q ∗ Z u r ( x l ) , (4)where e and e q are the electron and incoming quark (fractional) electric charges, ǫ µ is thepolarization 4-vector of produced Z boson, ˆ s = ( k + k ) , k i = x i l i + k iT (with i = 1or 2), l and l are the 4-momenta of colliding protons, x and x are the correspondingmomentum fractions and Γ H is the full decay width of Higgs boson, m Z and Γ Z are themass and full decay width of Z boson. We will take the propagators of intermediate Z and Higgs bosons in the Breit-Wigner form to avoid any artificial singularities in thenumerical calculations. The fermion and gauge boson to Higgs vertices are usual:Γ Hq ¯ q = − e sin 2 θ W m q ′ m Z , (5)Γ µνZZH = e sin 2 θ W g µν m Z , (6)where m q ′ is the mass of produced quark or antiquark, θ W is the Weinberg mixing angle.We will neglect the masses of initial quarks compared to the masses of final state par-ticles but keep their non-zero transverse momenta: k T = − k T = 0, k T = − k T = 0.The effective vertex Γ µq ∗ ¯ q ∗ Z which describes the effective coupling of off-shell quark andantiquark to Z boson reads [22, 23] (see also [26]):Γ µq ∗ ¯ q ∗ Z = (cid:20) γ µ − ˆ k l µ ( l · k ) − ˆ k l µ ( l · k ) (cid:21) (cid:0) C qV − C qA γ (cid:1) , (7)where C qV and C qA are the corresponding vector and axial coupling constants. The effectivevertex Γ µq ∗ ¯ q ∗ Z satisfy the Ward identity Γ µq ∗ ¯ q ∗ Z ( k + k ) µ = 0. The off-shell amplitude ofsubprocess (2) reads: M = ee q ′ g t a δ ab t b ǫ µ ( p ) ¯ v s ( p ) F µν u s ( p ) g νλ ( k + k ) ¯ v r ( x l )Γ λq ∗ ¯ q ∗ g u r ( x l ) ++ ee q g t a δ ab t b ǫ µ ( p ) ¯ v s ( p ) F µλ u s ( p ) g νλ ( p + k ) ¯ v r ( x l ) γ ν u r ( x l ) , (8)3here e q ′ is the produced quark (fractional) electric charge, g is the strong charge, a and b are the eight-fold color indexes, and F µν = Γ µqqZ ˆ p + ˆ p + m q ′ ( p + p ) − m q ′ γ ν + γ ν − ˆ p − ˆ p + m q ′ ( − p − p ) − m q ′ Γ µqqZ , (9) F µλ = Γ (+) λq ∗ qg ( k , p + p ) ˆ k − ˆ p ( k − p ) Γ ( − ) µq ∗ qZ ( k , p ) ++ Γ (+) µq ∗ qZ ( k , p ) − ˆ k − ˆ p ( − k − p ) Γ ( − ) λq ∗ qg ( k , p + p ) + ∆ µλ ( k , − k , p, p + p ) . (10)The on-shell quark coupling to the Z boson is taken in a standard form:Γ µqqZ = γ µ ( C qV − C qA γ ) . (11)The effective vertices can be written as [22, 23]:Γ µq ∗ ¯ q ∗ g = γ µ − ˆ k l µ ( l · k ) − ˆ k l µ ( l · k ) . (12)Γ (+) µq ∗ qg ( k, q ) = γ µ − ˆ k l µ ( l · q ) , (13)Γ ( − ) µq ∗ qg ( k, q ) = γ µ − ˆ k l µ ( l · q ) . (14)The corresponding couplings of the off-shell quark or antiquark to usual on-shell quarkand Z boson are constructed as it was done earlier [26]:Γ ( ± ) µq ∗ qZ ( k, q ) = Γ ( ± ) µq ∗ qg ( k, q )( C qV − C qA γ ) . (15)The induced term ∆ µν ( k , k , q , q ) has the form [27]:∆ µν ( k , k , q , q ) = ˆ k l µ l ν ( q · l )( q · l ) + ˆ k l µ l ν ( q · l )( q · l ) . (16)The summation on the produced Z boson polarizations is carried out with the usualcovariant formula: X ǫ µ ( p ) ǫ ∗ ν ( p ) = − g µν + p µ p ν m Z . (17)In according to the k T -factorization prescription [17, 18], the summation over the polar-izations of incoming off-shell gluons is carried with P ǫ µ ǫ ∗ ν = k µT k νT / k T . In the collinearlimit, when | k T | →
0, this expression converges to the ordinary one after averaging on theazimuthal angle. In according to the using of the effective vertices, the spin density matrixfor off-shell spinors in initial state is taken in the usual form P u ( x i l i )¯ u ( x i l i ) = x i ˆ l i + m (where i = 1 or 2 and we omited the spinor indices). Further calculations are straightfor-ward and in other respects follow the standard QCD Feynman rules. The evaluation oftraces was performed using the algebraic manipulation system form [28]. We do not listhere the obtained lengthy expressions because of lack of space. The off-shell amplitude ofgluon-gluon fusion subprocess (3) was derived in our previous paper [29] (see also [30]).The cross section of any process in the k T -factorization approach is calculated as aconvolution of the off-shell partonic cross section and the unintegrated, or transverse4omentum dependent (TMD), parton densities in a proton. The cross sections of sub-processes (1) and (2) read: σ = X q Z π ( x x s ) | ¯ M , | ×× f q ( x , k T , µ ) f q ( x , k T , µ ) d k T d k T d p T p T dydy dy dφ π dφ π dψ π dψ π , (18)where f q ( x i , k iT , µ ) is the TMD quark density in a proton, y is the rapidity of produced Z boson, s is the total energy, p T , p T , y , y , ψ and ψ are the transverse momenta,rapidities and azimuthal angles of final state quarks, respectively. The incoming quarkshave azimuthal angles φ and φ . The cross sections of subprocess (3) can be written as: σ = Z π ( x x s ) | ¯ M | ×× f g ( x , k T , µ ) f g ( x , k T , µ ) d k T d k T d p T p T dydy dy dφ π dφ π dψ π dψ π , (19)where f g ( x i , k iT , µ ) is the TMD gluon density in a proton, and M is the off-shell am-plitude of subprocess (3).Concerning the TMD parton densities in a proton, we concentrate on the approachbased on the CCFM evolution equation [31]. The CCFM parton shower, based on the prin-ciple of color coherence, describes only the emission of gluons, while real quark emissionsare left aside. It implies that the CCFM equation describes only the distinct evolution ofTMD gluon and valence quarks, while the non-diagonal transitions between quarks andgluons are absent. Below we use the TMD gluon and valence quark distributions whichwere obtained [32, 33] from the numerical solutions of the CCFM equation (namely, setA0). Following to [34], we calculate the TMD sea quark density with the approximation,where the sea quarks occur in the last gluon-to-quark splitting. At the next-to-leadinglogarithmic accuracy α s ( α s ln x ) n , the TMD sea quark distribution can be written asfollows [34]: f (sea) q ( x, k T , µ ) = Z x dzz Z d q T ∆ α s π P qg ( z, q T , ∆ ) f g ( x/z, q T , ¯ µ ) , (20)where z is the fraction of the gluon light cone momentum carried out by the quark, and ∆ = k T − z q T . The sea quark evolution is driven by the off-shell gluon-to-quark splittingfunction P qg ( z, q T , ∆ ) [35]: P qg ( z, q T , ∆ ) = T R (cid:18) ∆ ∆ + z (1 − z ) q T (cid:19) (cid:20) (1 − z ) + z + 4 z (1 − z ) q T ∆ (cid:21) , (21)where T R = 1 /
2. The splitting function P qg ( z, q T , ∆ ) has been obtained by generalizingto finite transverse momenta, in the high-energy region, the two-particle irreducible kernelexpansion [36]. It takes into account the small- x enhanced transverse momentum depen-dence up to all orders in the strong coupling constant, and reduces to the conventionalsplitting function at lowest order for | q T | →
0. The scale ¯ µ is defined [37] from the an-gular ordering condition which is natural from the point of view of the CCFM evolution:¯ µ = ∆ / (1 − z ) + q T / (1 − z ).Other essential parameters were taken as follows: renormalization scale µ R = m Z + p T ,factorization scale µ F = ˆ s + Q T (with Q T being the transverse momentum of initial5arton pair), beauty quark mass m b = 4 .
75 GeV, m Z = 91 . m H = 125 GeV,Γ Z = 2 . H = 4 . θ W = 0 . α s ( µ ) with n f = 4 active quark flavors at Λ QCD = 200 MeV, sothat α s ( m Z ) = 0 . K -factor, as it was done in [38, 39]: K = exp (cid:20) C F α s ( µ )2 π π (cid:21) , (22)where color factor C F = 4 /
3. A particular scale choice µ = p / T m / Z was proposed [38,39]to eliminate sub-leading logarithmic terms. Note we choose this scale to evaluate thestrong coupling constant in (22) only. Everywhere the multidimensional integration havebeen performed by the means of Monte Carlo technique, using the routine vegas [40].The corresponding C++ code is available from the authors on request .We now are in a position to present our numerical predictions. The differential crosssections of associated Zb ¯ b production in pp collisions as a function of M , the invariantmass of final beauty quarks, and Z boson transverse momentum at √ s = 8 and 14 TeVare shown in Figs. 2 and 3. The solid, dashed and dash-dotted histograms correspond tothe contributions from the subprocesses (1), (2) and (3), respectively. There is no any cutsapplied. One can see that the associated Higgs (decaying into the b ¯ b pair) and Z bosonproduction cross section lies below the QCD backgrounds by several orders of magnitudein a whole p T range, but peaks near Higgs mass. To increase the relative contributionfrom Higgs signal, we repeated the calculations in the restricted region of M , namely120 < M <
130 GeV (see Fig. 4). We found that here the associated Higgs and Z bosonproduction gives a sizeble contribution to the Zb ¯ b cross section at high Z boson transversemomenta. So, at √ s = 8 TeV it practically coincides with the leading contribution fromthe gluon-gluon fusion subprocess at p T >
200 GeV. At √ s = 14 TeV, it lies below thelatter. However, these contributions are almost comparable at p T >
300 GeV. With theexpected LHC luminosity of about 40 fb − , our estimation gives 400 — 500 events (withbeauty quarks originating from the Higgs boson decays) for both energies, 8 and 14 TeV.Therefore, the possibility for the experimental detection of Higgs signal appears in thekinematical region defined above.A special opportunity to detect the decays of scalar Higgs bosons can be providedby the investigations of different angular correlations between the final state particles.As an example, we calculated the distributions on the angle θ between the produced Z boson and b -quark in the Collins-Soper frame (where z axis is defined with respect to thebisector of colliding protons in the b ¯ b rest frame), and on the azimuthal angle difference∆ φ between the final beauty quarks in the pp center-of-mass frame. The results of ourcalculations performed near Higgs boson peak (with 120 < M <
130 GeV) are shown inFigs. 5 and 6, where an additional cut p T > √ s = 8(14) TeV.As it was expected, the isotropic decay of scalar Higgs particle H → b ¯ b greatly differs fromthe angular distributions predicted by the off-shell amplitudes of subprocesses (2) and (3).Moreover, the beauty quarks, originating from the Higgs boson decay, populate mostly atlow ∆ φ (see Fig. 6), whereas the leading QCD background, as given by the gluon-gluonfusion subprocess (3), has more flat ∆ φ distribution. So, the different angular correlationsbetween the final state particles in the associated Zb ¯ b production are very sensitive to thesource of b ¯ b pairs, and therefore future experimental investigations of such observables atthe LHC with increased luminosity can give a clear information about Higgs signal.Finally, we study the size of theoretical uncertainties of our calculations connectedwith the hard scale. As usual, in order to estimate these uncertainties we vary the scales [email protected]
6y a factor of 2 around their default values. Also, we use the CCFM set A0+ and A0 − instead of the default TMD gluon density A0. These two PDF sets represent a variationof the hard scale involved in (18) and (19). The A0+ stands for a variation of 2 µ , whileset A0 − reflects µ/
2. We observe a deviation of about 50% with both A0+ and A0 − sets (see Fig. 7) for the QCD background (as given by the sum of gluon-gluon fusionand quark-antiquark annihilation subprocesses considered above). Despite the relativelylarge band of uncertainties, the latter does not change our conclusions. Additionally, toinvestigate the role of higher-order QCD corrections, in Fig. 7 we presented the results forthe QCD background obtained in the framework of collinear QCD factorization at LO.We find that in the kinematical region where the possible Higgs signal could be observedthese corrections are important.To conclude, in the present note we applied the k T -factorization approach of QCD tostudy the possibility to detect the scalar Higgs boson decay H → b ¯ b in the associated Z and b ¯ b production at the LHC. Our consideration was based on the off-shell productionamplitudes of q ∗ ¯ q ∗ → ZH → Zq ′ ¯ q ′ , q ∗ ¯ q ∗ → Zq ′ ¯ q ′ and g ∗ g ∗ → Zq ′ ¯ q ′ partonic subprocessessupplemented with the CCFM dynamics of parton densities in a proton. The main partof higher-order QCD corrections (corresponding to the log 1 /x enhanced terms in pertur-bative series) is effectively taken into account in our consideration. We demonstrated thatthe H → b ¯ b signal can be observed at large transverse momenta near Higgs boson peakdespite the overwhelming QCD background, and pointed out an important role of angularcorrelations between the produced Z boson and b -quarks. The gauge invariant off-shellamplitudes of q ∗ ¯ q ∗ → ZH → Zq ′ ¯ q ′ and q ∗ ¯ q ∗ → Zq ′ ¯ q ′ partonic subprocesses, calculatedfor the first time, can be implemented in a different Monte Carlo event generators, likeas, for example, cascade [41]. Acknowledgements.
The authors are grateful to H. Jung for very useful discussionswhich give us the idea of present study. We thank also S. Baranov for helpful discussionconcerning the role of angular distributions and M. Malyshev for additional check of theoff-shell amplitude of q ∗ ¯ q ∗ → ZH → Zq ′ ¯ q ′ subprocess. This research was supported bythe FASI of Russian Federation (grant NS-3042.2014.2). We are also grateful to DESYDirectorate for the support in the framework of Moscow—DESY project on Monte-Carloimplementation for HERA—LHC. References [1] CMS Collaboration, Phys. Lett. B , 30 (2012).[2] ATLAS Collaboration, Phys. Lett. B , 1 (2012).[3] ATLAS Collaboration, JHEP , 112 (2014).[4] M. Spira, A. Djouadi, D. Graudenz, P. Zerwas, Nucl. Phys. B
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50 100 150 200 250 300 d σ / d M [ pb / G e V ] M [GeV] -2 x 10 -2 -7 -6 -5 -4 -3 -2 -1
50 100 150 200 250 300 d σ / d M [ pb / G e V ] M [GeV]
14 TeVx 10 -2 x 10 -2 Figure 2: The associated Z + b ¯ b cross sections in pp collisions calculated as a function ofinvariant mass of b ¯ b quarks at √ s = 8 TeV (left panel) and √ s = 14 TeV (right panel).The solid, dashed and dash-dotted histograms correspond to the contributions from the q ∗ ¯ q ∗ → ZH → Zb ¯ b , q ∗ ¯ q ∗ → Zb ¯ b and g ∗ g ∗ → Zb ¯ b subprocesses, respectively. No cuts isapplied. 10 -6 -5 -4 -3 -2 -1 d σ / dp TZ [ pb / G e V ] p TZ [GeV] -5 -4 -3 -2 -1 d σ / dp TZ [ pb / G e V ] p TZ [GeV]
14 TeV
Figure 3: The associated Z + b ¯ b cross sections in pp collisions calculated as a functionof Z boson transverse momentum at √ s = 8 TeV (left panel) and √ s = 14 TeV (rightpanel). Notation of all histograms is the same as in Fig. 2. No cuts is applied. -6 -5 -4 -3 -2 -1 d σ / dp TZ [ pb / G e V ] p TZ [GeV] -6 -5 -4 -3 -2 -1 d σ / dp TZ [ pb / G e V ] p TZ [GeV]
14 TeV
Figure 4: The associated Z + b ¯ b cross sections in pp collisions calculated as a functionof Z boson transverse momentum at √ s = 8 TeV (left panel) and √ s = 14 TeV (rightpanel) at 120 < M <
130 GeV. Notation of all histograms is the same as in Fig. 2. -3 -2 -1 -0.5 0 0.5 1 d σ / d c o s θ [ pb ] cos θ -3 -2 -1 -0.5 0 0.5 1 d σ / d c o s θ [ pb ] cos θ
14 TeV
Figure 5: The associated Z + b ¯ b cross sections in pp collisions calculated as a functionof angle θ between the produced Z boson and beauty quark in the Collins-Soper frameat √ s = 8 TeV (left panel) and √ s = 14 TeV (right panel) at 120 < M <
130 GeV.An additional cut p T > √ s = 8(14) TeV. Notation of allhistograms is the same as in Fig. 2. 11 -4 -3 -2 d σ / d ∆ φ [ pb ] ∆φ [rad] -4 -3 -2 d σ / d ∆ φ [ pb ] ∆φ [rad]
14 TeV
Figure 6: The associated Z + b ¯ b cross sections in pp collisions calculated as a function ofazimuthal angle difference ∆ φ between the produced beauty quarks in the pp center-of-mass frame at √ s = 8 TeV (left panel) and √ s = 14 TeV (right panel) at 120 < M <
130 GeV. An additional cut p T > √ s = 8(14) TeV. Notationof all histograms is the same as in Fig. 2. 12 -6 -5 -4 -3 -2 -1 d σ / dp TZ [ pb / G e V ] p TZ [GeV] -6 -5 -4 -3 -2 -1 d σ / dp TZ [ pb / G e V ] p TZ [GeV]
14 TeV -3 -2 -1 -0.5 0 0.5 1 d σ / d c o s θ [ pb ] cos θ -3 -2 -1 -0.5 0 0.5 1 d σ / d c o s θ [ pb ] cos θ
14 TeV -4 -3 -2 d σ / d ∆ φ [ pb ] ∆φ [rad] -4 -3 -2 -1 d σ / d ∆ φ [ pb ] ∆φ [rad]
14 TeV
Figure 7: The associated Z + b ¯ b cross sections in pp collisions calculated as a func-tion of Z boson transverse momentum p T , angle θ and azimuthal angle difference ∆ φ at √ s = 8 TeV (left panel) and √ s = 14 TeV (right panel) at 120 < M <
130 GeV. The solidand dash-dotted histograms correspond to the QCD background (sum of the gluon-gluonfusion and quark-antiquark annihilation subprocesses) calculated in the framework of k T -factorization approach and collinear approximation of QCD at LO, respectively. The up-per and lower dashed histograms correspond to the scale variations in the k T -factorizationpredictions, as it is described in the text. The dotted histograms correspond to the con-tributions from the q ∗ ¯ q ∗ → ZH → Zb ¯ b subprocess. An additional cut p T > √ s = 8(14) TeV in the θ and ∆ φφ