Azimuthal Dependence of Intrinsic Top in Photon-Quark Scattering and Higgs Production in Boson-Gluon Fusion DIS

Transcription

1 Commun. Theor. Phys Vol. 68, No. 5, November, 7 Azimuthal Dependence of Intrinsic Top in Photon-Quark Scattering and Higgs Production in Boson-Gluon Fusion DIS G. R. Boroun, A. Khanehzar, and M. Boustanchi Kashan Physics Department, Razi University, Kermanshah 6749, Iran Received June 6, 7; revised manuscript received August 4, 7 Abstract In this paper, we study the top content of nucleon by analyzing azimuthal asymmetries in lepton-nucleon deep inelastic scattering DIS, also we search for the Higgs boson associated production channel, t th, at the large hadron-electron collider LHeC caused by boson-gluon fusion BGF contribution. We use azimuthal asymmetries in γ Q cross sections in terms of helicity contributions to semi-inclusive deep inelastic scattering to investigate numerical properties of the cos ϕ distribution. We conclude that measuring azimuthal distributions caused by intrinsic heavy quark production can directly probe heavy quarks inside nucleon. Moreover, in order to estimate the probability of producing the Higgs boson, we suggest another approach in the framework of calculating t t cross section in boson-gluon fusion mechanism. Finally, we can confirm that this observed massive particle is referred to Higgs boson produced by fermion loop. PACS numbers:.38.-t,.38.aw, 3.66.Fg, 4.65.Ha DOI:.88/53-6/68/5/654 Key words: deep inelastic scattering, azimuthal asymmetries, intrinsic top, boson-gluon fusion, Higgs coupling Introduction Study of heavy quarks production and their decay mechanisms at lepton-nucleon colliders, especially at LHeC, gives a deep intuition from strong interactions. These quarks can only be observed via heavy baryons and mesons because of strong interaction confinement properties in theory of QCD. Mesons are produced more than baryons, thus we focus on mesons. Now, we want to know why particle physicists are interested in top quarks? Top is the heaviest known elementary particle that observed at Fermilab s proton anti-proton collider, Tevatron, in 995 by D and CDF experiments. [ ] Exact measurement of the top quark gives us valuable data for analyzing electroweak force. Since, the top quark is a massive particle, it can decay before hadronization process, therefore, we can consider it as a quasi free particle and study its properties. For instance, the top quark spin is accessible due to angular distribution of its decay productions while this information will disappear during hadronization process for other quarks. Producing at a very short distance /m t, introduces the top quark as a perturbative object. The strong coupling constant at top production is about α s., consequently the perturbative series converge immediately. Accordingly, study of the top quark is a convenient tool in testing QCD. Among all fermions, Higgs boson has strong coupling with the top quark, and it is possible that Higgs produced Corresponding author, grboroun@gmail.com ahmad.khanezar@gmail.com mohsen.boustanchi@gmail.com c 7 Chinese Physical Society and IOP Publishing Ltd by top quark anti-quark cooperation. The activities accomplished at large hadron collider LHC in order to calculate Higgs production rate to the top quark anti-quark have low accuracy due to high rates of producing particles in colliding background, [3 4] therefore, to obtain higher accuracy we searched for Higgs at lepton-hadron collider in CERN via that process. The reason we focus on these calculations is that they have higher accuracy, because they have less hadronic state and there is higher luminosity at LHeC. Events consist of top, due to heavy mass and its association with Higgs are modern physics theme that we hope to discover it. If we represent the proton state as a superposition of quarks and gluons at Fock space, there might be two mechanisms for heavy quarks production: intrinsic and extrinsic heavy quarks. Intrinsic charm, bottom and top content of nucleon are a fundamental property of wave functions of hadronic bound states. While the extrinsic contributions to partonic distribution functions PDFs are most important at low x and logarithmically depend on heavy quark mass M Q, the contributions to intrinsic heavy quark are dominant at high x and depend on /M Q. The concept of intrinsic heavy quarks particularly the presence of intrinsic charm IC and intrinsic bottom IB fluctuations in the proton bound state, has been introduced over 35 years ago in Ref. [5]. Although, nucleons are usually considered as a bound state of three valence quarks p = n=3 ψ n x i, k i, λ i n; x i, k i, λ i,

2 No. 5 Communications in Theoretical Physics 655 but in fact they have more complex structure in Fock state in QCD: p = uud, uudg,... including a hidden heavy quark Fock component uudq Q here, Q is the heavy quark. The fact that hadronic eigenstates has fluctuations with an arbitrary number of constituents, is a consequence of quantum mechanics and relativity. This component describes intrinsic heavy quarks production where the gluons are coupled to different valence quarks see Fig.. Since quarks tend to travel at same rapidity and coherently in the uudq Q here, Q is the heavy quark bound state, the heaviest constituents carry the largest momentum fraction. Therefore, we expect that the intrinsic heavy quarks contribution dominate in the heavy quarks production cross sections at sufficiently large Bjorken-x. Thus the main concept of quark density in proton [6] has nonperturbative nature and known as nonperturbative intrinsic heavy quark. Although, this proton state is rare but existence of the heavy quarks in the proton bound state leads us to useful results. In contrast with the case of intrinsic charm, there is no existing global analysis that investigates intrinsic bottom or top content of nucleon. The main reason is the lack of experimental data that could impose this issue. There are various models that predict the existence of intrinsic bottom or top in the context e.g. Refs. [7 8, 7]. For instance, this phenomenon can be extended to the consideration of intrinsic top IT as the cross section of higgs production from intrinsic charm and intrinsic bottom has evaluated in Ref. [7] and it has also obtained a relation for cross section of higgs production from intrinsic perturbative top component of the proton if the higgs mass is restricted by MH < 4m t. In the present paper, we use the notion in Ref. [7] to predict intrinsic top by means of azimuthal asymmetries in the nucleon. Fig. The proton five quark fock state uudq Q and intrinsic sea origin. [8] Measuring the top content of proton requires observables that are well-defined in perturbative QCD. One of those observables is azimuthal asymmetry. Investigation of azimuthal asymmetries in unpolarized deep inelastic scattering DIS are introduced by Georgi and Plolitzer as an explicit test of perturbative QCD. [9] Afterwards, Cahn expanded this issue with the intuition that the azimuthal angle dependence is due to intrinsic transverse momenta of bound partons inside the proton. [] Eventually, Ivanov calculated the azimuthal dependence of the intrinsic charm contributions to lepton-nucleon DIS. [ 3] In the present paper, we focus on cos ϕ in intrinsic top production cross sections. Unlike production cross sections, azimuthal asymmetries are well-defined quantitatively in heavy flavor productions in pqcd. The main mechanism for intrinsic heavy quarks production is photon-quark scattering process. In the case of extrinsic top production, the dominant mechanism in lepton-nucleon collisions is via boson-gluon fusion. In extrinsic heavy quarks production, only gluons and light quarks appear in initial state of partonic processes, hence the probability of appearing heavy quarks in the proton wave function goes to zero and the top quark can be observed in final state from light partons at large scales Q M t. The paper is organized as follows. In Sec. we investigate azimuthal dependence of heavy quark production as a probe of intrinsic top in photon-quark scattering DIS. In Sec. 3 we calculate t th channel cross section in bosongluon fusion mechanism for detecting Higgs production. The conlusion is expressed in Sec. 4. Azimuthal Dependence of Intrinsic Top DIS cross section, dσ is proportional to product of leptonic tensor L µν and hadronic tensor W µν, dσ L µν W µν, while L µν can be explicitly calculated in QED: L µν = l µ l ν + l µl ν l l g µν, W µν is unknown. This tensor can be expressed by independent components known as structure functions. In the parton model, the structure functions are related to parton distribution functions PDFs. In standard model, the azimuthal asymmetries originated from QCD effects. ϕ, the azimuthal angle in Breit frame [5] is the angle between lepton scattering plane, which is defined by incoming lepton and the scattered lepton and the heavy quark production plane defined by virtual photon q = l l, and the detected quark Q See Fig.. Azimuthal dependence for unpolarized DIS at leading order LO has the following form, dσ = A + B cosϕ + C cosϕ dϕ + D sinϕ + E sinϕ, this equation results from the exchanged virtual photon polarization. The coefficients of sinϕ and sinϕ are disappeared due to time reversal invariance and the absence of final state interactions in quark-gluon level at LO.

3 656 Communications in Theoretical Physics Vol. 68 The coefficients B and C are related to the helicity of final state partons and the partonic transverse momenta. The term cosϕ is expected from interference of the amplitudes, which arises by + and helicity components of polarized transverse exchanged boson, while the interference between transverse longitudinal components gives rise to the term cosϕ. The total DIS cross section in terms of the angle ϕ, Q where Q is the negative of the virtuality of the exchanged boson, and the partonic kinematic variable z, is completely explained in Ref. [4] in the helicity basis. Fig. The azimuthal angle ϕ in the nucleon rest frame. The azimuthal angle ϕ can be written as [6] cos ϕ = sin ϕ = ˆq l ˆq l ˆq p Q ˆq p Q, l p Q ˆq ˆq l ˆq p Q, where ˆq = q/ q. The azimuthal asymmetry components are defined as [7] Ax, Q = σ A σ x, Q = x F A F x, Q, A I x, Q = σ I σ x, Q = 4 x F I F x, Q, where σ k k =, A, L, I is the partonic cross section and F k k =, A, L, I is its corresponding structure function that they are both illustrated in Refs. [3 4, 7] at LO and NLO. Like σ x, Q cross section for ϕ-independent state, Ax, Q and A I x, Q parameters can effectively measure azimuth-dependent production. Unlike boson-gluon fusion process, intrinsic heavy quark mechanism is practically cos ϕ-independent because photon-quark scattering contribution to σ A x, Q cross section is absent at LO due to kinematic reason and is negligible at NLO of the order of %. The heavy-quark-initiated contributions to ϕ-dependent intrinsic charm IC in DIS have been calculated by Ananikyan and Ivanov in Ref. [4] and we expand their calculations for ϕ-dependent intrinsic top quark for γ Q cross sections in DIS. For analyzing the concept of cos ϕ numerical distributions to photon-quark scattering component, we can not compare ˆσ A z, λ and ˆσ I z, λ with ϕ-independent contributions directly. For this reason, we use Mellin moments of these quantities as follows, ˆσ i N, λ = ˆσ i z, λz N dz. 3 The Mellin transform of Born level cross sections is obvious: ˆσ N, λ = ˆσ B + 4λ. The Mellin moments of results at NLO are calculated numerically. Hence, variable λ is a partonic kinematic for these cross sections, which is defined as λ = m /Q Q = q in Ref. [4]. As one can see, λ varies by heavy quark mass and therefore, we require more energies in hadron colliders in order to observe intrinsic top quark. For the one-loop approximation α s µ F, we use Λ 6 =. MeV, µ F = m + Q, m t = 73 GeV for top quark. The ratio of longitudinal cross section with respect to the total cross section, σ L N, λ/σ N, λ is shown in Fig. 3. One can find out that in the intrinsic heavy quark production mechanism, the contribution to this ratio decreases in higher energies. Fig. 3 The quantity ˆσ L N, λ/ˆσ N, λ in several values of λ. The quantities, ˆσ A N, λ/ˆσ N, λ and ˆσ I N, λ, for top quark are shown in Figs. 4a N, λ/ˆσ and 4b. We compare these quantities for the three heavy quarks t, b, c at λ = and Q m in Figs. 4c and 4d. We can see that the asymmetry quantity, A, in heavier quarks has less deviation and their contribution decreases immediately at higher N. These quantities are proportional to /m scale where m is the heavy quark mass.

4 No. 5 Communications in Theoretical Physics 657 Fig. 4 The quantities ˆσ A N, λ/ˆσ N, λ and ˆσ I N, λ/ˆσ N, λ for top quark at several values of λ a, b and the comparison of these quantities for heavy quarks c, d. 3 Higgs Production in BGF 3. Boson-Gluon Fusion Mechanism In theoretical calculations, top quark is an ideal object for studying of Higgs boson, because of its strong coupling to Higgs boson. Therefore, we probe Higgs and top quark anti-quark and the production cross section in electronproton DIS at LHeC in the following section. In photon-quark scattering, a single intrinsic heavy quark produced, but in boson-gluon mechanism, the extrinsic heavy quark is produced with its anti-quark, which are originated from a photon, which is radiated from the electron and a gluon is emitted from the proton, so we can use this mechanism for Higgs production. i Calculating t th cross section in electron-proton DIS In order to calculate the cross section of Fig. 5, we first need to write down it s scattering amplitude. This loop contains all massive colored particles in the model, but we only consider top quark contribution, since Higgs boson tends to coupled with top more than other quarks. First, we should generally consider the loop as a fermion propagator, then the amplitude of this loop by using the loop rules can be written as, i l + m i l+ p + m i l q + m ia = ig e l m γµ l + p m l q m γ ν im ig s v d d l π d ε µε ν, 4 this equation can be reduced to, imt ia = ig s ig e v d d l T µν π d Den i3 ε µ pε ν q, 5 where, d is the number of space dimensions, ε µ pε ν q are related to gluon and photon polarizations, v is the vacuum expectation value for Higgs production, and g s g e is responsible for QCD QED coupling. The first minus sign is due to the close fermion loop. m t in Eq. 5 is the top quark mass. Now, we need to estimate T µν and Den and inserting them into Eq. 5, Den = l m t [l + p m t ][l q m t ], 6 using Feynman factorization for the fermion loop to combine the denominators in Eq. 5 and the above relation, [9] gives, ABC = dx x dy [Ax + By + C x y] 3, 7 we obtain, l m t [l + p m t ] = dxdy [l m t + l px qy] 3, 8

5 658 Communications in Theoretical Physics Vol. 68 by transmitting momentum l to l = l + px qy the total loop momentum, [8] the above equation changes into, Den = dxdy [l m t + MH, 9 xy]3 now, in the integral loop, T µν is defined as, T µν = l + m l+ p + m l q + m, this equation has a trace consisting 8 parts, which 9 of them are zero odd gamma functions and the remaining parts can be written as, T µν = 4m t [g µν m t 3l +p l l q+6l µ l ν +p ν q µ ], knowing the rule that a b = a µ b ν = g µν a ν b µ we obtain, T µν = 4m t [g µν m t l +p l l q+4l µ l ν +p ν p µ ]. In these equations the Higgs mass is defined by MH = 4p l l q, so we have, [ T µν = 4m t g µν m t l M H + 4l µ l ν + p ν q µ]. 3 Substituting Eqs. 9, 3 into Eq. 5 gives, imt ia = ig s ig e dxdy dd l 4m t [g µν m t l MH / + 4lµ l ν + p ν q µ ] v π d [l m t + MH i 3 ε µ pε ν q. 4 xy]3 Finally, we can write the scattering amplitude by transmitting momentum to l which is the total loop momentum and using the following relation for close fermion loop, [9] d d k k µ k ν π d [k C + iε] m = d d k k d gµν π d [k C + iε] m, 5 therefore, ia = m t d d v g l sg e π d { dxdy g µν[ m t + l 4 d d + MH xy ] } + p ν q µ 4xy l m t + M H xy3 ε µpε ν q. 6 This equation is the Feynman diagram scattering amplitude in Fig. 5 that can be estimated from relations that are related to loops rules in calculating the scattering cross sections, [9] so the amplitude can be written as, Aγ g H = m t 4πv g sg e g µν M H pν q µ 4xy dxdy m t MH xy ε µ pε ν p. 7 The function Ia = M H /m t is defined by, Ia dx x dy 4xy axy, 8 as a consequence, Eq. 7 turns into, Aγ g H = 4πv g sg e g µν M H pν q µ Iaε µ pε ν p. 9 The cross section for head-on collisions and Higgs production in the standard model are estimated as, [8] ˆσγ g H = d 3 P s A π 3 E π4 δ 4 p + q P = s A πδs M H, in the above equation, s is the square central mass energy of the collision, P is the Higgs boson momentum, and the following relations is needed for Higgs production, [8] g µν M H pν q µ M 4 = H, A = 4 Nc A. In Eq., the factor /4 originates from averaging over photon and gluon spin initial states, and the factor /Nc is due to averaging over gluon color state, which is N c = 3 generally. Now, we can calculate the square scattering amplitude from Eq. 9, A = g s g e g µν M H 4πv pν q µ [ 4xy ] dxdy. 3 MH /m t xy According to definitions in this paper, A = gsg e m 4 H M H, 4 6π v also, we can express strong and electromagnetic coupling constant in terms of, m t g e = 4πα e, g s = 4πα s, 5 therefore, A 6 = v α eα s MH 4 M I H. 6 Finally, the cross section for boson-gluon fusion and the coupling of top quark anti-quark with Higgs boson gets, ˆσγ g H= π 64v α M H M eα s I H s δ, 7 s m t m t M H

6 No. 5 Communications in Theoretical Physics 659 in the equation above, the Dirac delta guarantees the energy conservation of Feynman diagram in Fig. 5. Fig. 5 H. [8] The Feynman diagram for the process γ g We need to calculate the central mass energy for comparison with hadronic collisions, s = P e + P p = P e + P p + P p P e = m e + M p + P e P p P e Pp, 8 neglecting particles mass in collision their energy is much more than their masses, we can write down this central mass energy as follows, s = P e P p P e P p cos θ, 9 since the collision is head-on, the angle is 8 and we have, s = P e P p + P e P p = 4P e P p = 4E e E p, 3 the strong coupling constant decreases by increasing energy. Finally, we use the central mass energy s = 4E e E p where the electron energy is of the order of 6 GeV and the proton energy is 7 TeV, also we need the vacuum expectation value for Higgs production, which is v = 46 GeV and the top quark mass, 73 GeV, Higgs boson mass, 5 GeV in calculations. [] We consider the strong α s and electromagnetic α em coupling constant as. [] and /37 respectively and the Bjorken scale as x = 8 in terms of LHeC energies, [] the BGF cross section and Higgs production via top quark anti-quark loop propagation is obtained, ˆσγ g H t th = 3.35 fb. 3 In gluon-gluon fusion mechanism, [3] the predicted cross section for emission rate of Higgs through top quark antiquark with central mass energy of s = 7 TeV is, ˆσgg H t th = 86 fb. By comparing our result to this number, one can realize that because of lower central mass, the Higgs production cross section in BGF via single fermion loop including top quark anti-quark is less than this cross section in gluongluon fusion. In lepton-hadron collisions, there are less hadrons in final state than hadron-hadron collisions, so measuring a specific state in lepton-hadron collision is easier and the luminosity at LHeC project is high, therefore, the estimations have more accuracy. The Higgs cross section at leading order in terms of Bjorken scale has the form of Fig. 6. In this figure, we can see that the Higgs cross section via paired top quark production in BGF is very small near Bjorken scale about zero because the top mass is large, which we need high collision energy to access this quark. With decreasing Bjorken scale we get enough energy for producing such massive quarks like top, so the probability of Higgs detection via this process increases. Finally, the Higgs cross section increases, since there is a sizable coupling between Higgs and top quark. As one can see in Fig. 6, the Higgs cross section increases more rapidly in the region s of energies from the order of top mass. By studying the Eq. 8 and plotting the function Ia in the limits of a and a, we find that this function goes to limited values rapidly. Numerically, mass of heavy fermion limit is a good approximation even for m M H. As the result, we can conclude that light quarks are irrelevant in photon gluon fusion and higgs boson. Indeed, we have Ia a a log a. 3 Therefore, in standard model, only the top quark is important in producing higgs boson via photon gluon fusion. [8,] Fig. 6 The cross section γ g H t th diagram in electron-proton DIS in term of Bjorken variable. For the first time, the proton, neutron and partonic density of nucleus has measured with high accuracy at LHeC. Because of the high energy provided by this accelerator, the accuracy in calculations of top and higgs properties extremely increases. For this amount of luminosity that exists at hadron-electron collider, which is of the order of fb the event rate of single top quark about 6 5 is better than event rate for paired top production about Consequently, the top quark anti-quark production can be observed in this collider. As for other processes like gg H, γγ H,

7 66 Communications in Theoretical Physics Vol. 68 which higgs is produced via one loop from top quark antiquark [4] and the reports exhibited in this reference, we could comprehend that higgs can be produced by the cooperation of paired top quark anti-quark in photon gluon fusion process as well. 4 Conclusion In the present paper, we first have studied azimuthdependence of photon-quark DIS caused by intrinsic transverse momentum of partons bind inside the proton at NLO. This asymmetry arises by polarization of accelerated beams at the accelerator ring that let us separate longitudinal and transverse structure functions. Azimuthal asymmetry is quantitatively well-defined in heavy flavor leptoproduction in pqcd. The ratio σ A /σ is the explicit intrinsic heavy quark contribution. According to our results, the ratio σ A /σ is negligibly small at all values of Q > m of the order of %, since the partonic cross section σ A is small. It means that the contribution of intrinsic quark is practically cos ϕ-independent. In the second part of this paper, we have calculated Higgs production cross section at t th channel in BGF mechanism. We compare our results of the coupling of top quark antiquark and higss cross section to existing data at hadronhadron colliders in gluon-gluon fusion mechanism. Although this process cross section via BGF is lower, but the accuracy of calculations is higher for comprehending the Higgs physics. Acknowledgments G. R. Boroun thanks Prof. M. Mangano for discussions, which completed this study and the Department of Physics of the CERN-TH for their warm hospitality. References [] S. Abachi, et al., Phys. Rev. Lett [] F. Abe, et al., Phys. Rev. Lett [3] S. Dittmaier, et al., Handbook of LHC Higgs Cross Sections:, Differential Distributions, arxiv[hep-ph]: [4] Daniel de Florian and Massimiliano Grazzini, Phys. Lett. B 78 7; H. Khanpour and M. M. Najafabadi, Phys. Rev. D [5] Stanley J. Brodsky, Cr Peterson, and N. Sakai, Phys. Rev. D ; Stanley J. Brodsky, et al., Phys. Lett. B 93 98: 45. [6] M. Franz, Maxim V. Polyakov, and K. Goeke, Phys. Rev. D [7] Brodsky, Stanley J., et al., Phys. Rev. D [8] S. J. Brodsky, et al., Advances in High Energy Physics 5 5; Lyonnet, Florian, et al., J. High Energy Phys [9] Georgi Howard and H. David Politzer, Phys. Rev. Lett [] R. N. Cahn, Phys. Lett. B [] N. Ya. Ivanov, A. Capella, and A. B. Kaidalov, Nuclear Phys. B [] N. Ya. Ivanov, Nuclear Phys. B [3] N. Ya. Ivanov, et al., Nuclear Physics B [4] L. N. Ananikyan and N. Ya Ivanov, Phys. Rev. D [5] N. Dombey, Rev. Mod. Phys [6] A. Bacchetta, et al., J. High Energy Phys [7] L. N. Ananikyan and N. Ya Ivanov, Nuclear Phys. B [8] F. Maltoni, pp Higgs: a Case Study, CERN School 4. [9] Jorge C. Romao, Phys. Dept. Inst. Sup. Tec. Lisboa. [] C. Bertella, Probing Top Quark and Higgs Boson Production in Multi-Jet Events at the LHC with the ATLAS Detector, Diss. Aix-Marseille University 3; H. Khanpour, et al., Probing Higgs Boson Couplings in H + γ Production at the LHC, arxiv[hep-ph]: [] J. L. Abelleira Fernandez, et al., J. Phys. G: Nuclear and Particle Physics [] O. Bruening and Max Klein, Mod. Phys. Lett. A [3] A. Accardi, et al., Euro. Phys. J. C [4] A. O. Bouzas and F. Larios, Phys. Rev. D ; G. R. Boroun, Phys. Lett. B ; G. R. Boroun, Phys. Lett. B