Radion production in exclusive processes at CERN LHC
aa r X i v : . [ h e p - ph ] J u l Radion production in exclusive processes at CERN LHC
V. P. Gon¸calves ∗ and W. K. Sauter † High and Medium Energy Group,Instituto de F´ısica e Matem´atica,Universidade Federal de PelotasCaixa Postal 354, CEP 96010-900, Pelotas, RS, Brazil (Dated: May 29, 2018)In the Randall-Sundrum (RS) scenario the compactification radius of the extra dimension isstabilized by the radion, which is a scalar field lighter than the graviton Kaluza-Klein states. Itimplies that the detection of the radion will be the first signature of the stabilized RS model. In thispaper we study the exclusive production of the radion in electromagnetic and diffractive hadron -hadron collisions at the LHC. Our results demonstrate that the diffractive production of radion isdominant and should be feasible of study at CERN LHC.
PACS numbers: 11.10.Kk, 14.80.-jKeywords: Theories in extra dimension; Radion production; Exclusive processes
I. INTRODUCTION
The search for particles beyond the Standard Model is one of the key issues of the ATLAS and CMS experiments atLHC. In particular, these experiments could test the theories with extra dimensions, which aim to solve the hierarchyproblem by bringing the gravity scale closer to the eletroweak scale (For a review see, e.g., [1]). In recent years, thescenario proposed by Randall and Sundrum (RS) [2], in which there are two (3+1)-dimensional branes separated ina 5th dimension, has attracted a great deal of attention. This model predicts a Kaluza-Klein tower of gravitons anda graviscalar, called radion, which stabilize the size of the extra dimension without fine tuning of parameters and isthe lowest gravitational excitation in this scenario. The mass of radion is expected to be of order of O (TeV), whichimplies that the detection of the radion will be the first signature of the RS model.Several authors have discussed the search of the radion in inclusive processes at Tevatron and LHC [3–9]. In thispaper we extend these previous studies for exclusive processes, in which the hadrons colliding remain intact afterthe interaction, losing only a small fraction of their initial energy and escaping the central detectors [10]. The signalwould be a clear one with a radion tagged in the central region of the detector accompanied by regions of low hadronicactivity, the so-called ”rapidity gaps”. In contrast to the inclusive production, which is characterized by large QCDactivity and backgrounds which complicate the identification of a new physics signal, the exclusive production willbe characterized by a clean topology associated to hadron - hadron interactions mediated by colorless exchanges. Inwhat follows, we will calculate the radion production considering photon - photon or Pomeron - Pomeron interactionsfor pp , pP b and P bP b collisions at LHC energies. In particular, we will extend for radion production the perturbativeKMR model [11] (For a recent review see [12]), which has been extensively used to calculate the exclusive diffractiveproduction in hadron colliders considering Pomeron - Pomeron interactions, with predictions which are in agreementwith the rates observed at the Tevatron [13].This paper is organized as follows. In the next section we present a brief review of the formalism necessary forcalculate the radion production in electromagnetic and diffractive interactions in hadron - hadron collisions. Moreover,we discuss the extension of the survival probability gap for nuclear collisions. In Section III we present our results forthe radion production in pp , pA and AA collisions for LHC energies. Finally, in Section IV we present a summary ofour main conclusions. II. RADION PRODUCTION
In exclusive processes the radion can be produced in photon - photon and Pomeron - Pomeron interactions (See Fig.1). In both cases, rapidity gaps between the radion and the hadrons colliding are expected. Let us start our analysis ∗ Electronic address: [email protected] † Electronic address: [email protected]
Φ Φ h S i (a) (b)FIG. 1: (Color online) Exclusive radion production in (a) γγ and (b) Pomeron - Pomeron interactions. considering the radion production in photon-photon interactions which can occur in coherent hadronic processes (For areview see, e.g., [14]). At large impact parameter ( b > R h + R h ) and ultra-relativistic energies, we expect dominanceof the electromagnetic interaction. In heavy ion colliders, the heavy nuclei give rise to strong electromagnetic fieldsdue to the coherent action of all protons in the nucleus, which can interact with each other. Similarly, this also occurswhen considering ultra- relativistic protons in pp (¯ p ) colliders. The photon emitted from the electromagnetic field ofone of the two colliding hadrons can interact with one photon of the other hadron (two-photon process) or directlywith the other hadron (photon-hadron process). The total cross section for a given process can be factorized in termsof the equivalent flux of photons of the hadron projectile and the photon-photon or photon-target production crosssection [14]. In particular, the total cross section for the radion production will be given by σ [ h h → h ⊗ Φ ⊗ h ] = Z ∞ dω ω Z ∞ dω ω F ( ω , ω ) σ γγ → Φ ( W γγ = √ ω ω ) , (1)where ⊗ means the presence of a rapidity gap, F ( ω , ω ) is the folded photon spectra and σ γγ → Φ is the cross-sectionof the fusion of two photons to produce the radion. The folded photon spectra is given by [15] F ( ω , ω ) = 2 π Z ∞ R db b Z ∞ R db b Z π dφ N ( ω , b ) N ( ω , b )Θ( b − R − R ) , (2)where R i are the projectile radii and b = b + b − b b cos θ . The theta function ensures that the hadrons do notoverlap. The Weizs¨acker-Williams photon spectrum for a given impact parameter of two colliding hadrons is given by[14] N ( ω, b ) = α em Z π (cid:18) ξb (cid:19) (cid:26) K ( ξ ) + 1 γ K ( ξ ) (cid:27) , (3)with K , modified Bessel function of second kind, ξ = ωb/γβ , β is the speed of the hadron, γ is the Lorentz factorand α em is the electromagnetic coupling constant. This approximation is valid for heavy ion only, with the radiigiven by R ≃ . A / fm. For protons, the equivalent photon spectrum can be obtained from its elastic form factorsin the dipole approximation (See e.g. [16]). An alternative is to use Eq. (3) assuming R p = 0 . γγ → Φ cross section can be expressed as follows σ γγ → Φ = 8 π m φ Γ(Φ → γγ ) . (4)The partial decay width of radion into two photons was calculated in [4, 5] and is given by:Γ(Φ → γγ ) = α em m π Λ (cid:26) − − [2 + 3 x W + 3 x W (2 − x W ) f ( x W )] + 83 x t [1 + (1 − x t ) f ( x t )] (cid:27) , (5)with m Φ is the radion mass, Λ Φ = h Φ i ≈ O ( v ) ( v the VEV of the Higgs field) determines the strength of the couplingof the radion to the standard model particles, x i = 4 m i /m (with i = W, t denoting the W boson and the top quark)
100 200 300 400 500 600 700 800 900 1000m φ [GeV]10 -12 -10 -8 -6 -4 -2 σ t o t [ pb ] |P |P (Tevatron, = 5%) γγ (Tevatron) |P |P (LHC, = 3%) γγ (LHC) FIG. 2: (Color online) Total cross section for radion production in proton-proton collisions as function of radion mass fordifferent mechanism of production, center of mass energies and values of the survival probability hS i . and the auxiliary function f being given by f ( z ) = h sin − (cid:16) √ z (cid:17)i , z ≥ − h log √ − z −√ − z − iπ i . z < gg → Φ, similarly to theSM Higgs boson production [4, 5]. However, it gets further enhancement from the trace anomaly for gauge fields,which implies that the radion cross section is expected to be a factor ≈ IP IP ) interactions. A QCD mechanism for the exclusive diffractive production of a heavy centralsystem has been proposed by Khoze, Martin and Ryskin (KMR) [11] with its predictions in broad agreement withthe observed rates measured by CDF Collaboration [13] (For a recent study see Ref. [18]). In this model, the totalcross section for radion production can be expressed in a factorizated form as follows σ tot = Z dy hS iL excl π m Γ(Φ → gg ) (7)where hS i is the survival probability gap (see below), Γ stand for the partial decay width of the radion Φ in a pairof gluons and L excl is the effective luminosity, given by L excl = (cid:20) C Z dQ t Q t f g ( x , x ′ , Q t , µ ) f g ( x , x ′ , Q t , µ ) (cid:21) , (8)where C = π/ [( N C − b ], with b the t -slope ( b = 4 GeV − in what follows), and the quantities f g being the skewedunintegrated gluon densities. Since ( x ′ ≈ Q t / √ s ) ≪ ( x ≈ M Φ / √ s ) ≪ f g ( x , x ′ , Q t , µ ),to single log accuracy, in terms of the conventional integral gluon density g ( x ), together with a known Sudakovsuppression T which ensures that the active gluons do not radiate in the evolution from Q t up to the hard scale µ ≈ M Φ /
2. Following [19] we will assume that f g ( x, Q T , µ ) = R g ∂∂ ln Q T hp T ( Q t , µ ) xg ( x, Q T ) i (9)where R g = 2 λ +3 √ π Γ( λ + 5 / λ + 4)
100 200 300 400 500 600 700 800 900 1000m φ [GeV]10 -8 -6 -4 -2 σ t o t [ pb ] γγ |P |P ( = 3%)|P |P ( = (3/A ) %)|P |P (Levin-Miller) 100 200 300 400 500 600 700 800 900 1000m φ [GeV]10 -8 -6 -4 -2 σ t o t [ pb ] γγ |P |P ( = 3%)|P |P ( = (3/A) %)|P |P (Levin-Miller) (a) (b)FIG. 3: (Color online) Total cross section for radion production in (a) PbPb and (b) pPb collisions as function of radion massfor different mechanism of production and values of the survival probability hS i . accounts for the single log Q skewed effect, being R g ∼ . .
4) for LHC (Tevatron), and the Sudakov factor is givenby T ( Q t , µ ) = exp ( − Z µ Q t dk t k t α s ( k t )2 π Z − ∆0 dz " zP gg ( z ) + X q P qg , (10)with ∆ = k t / ( µ + k t ) and P ( z ) the leading order DGLAP splitting functions. Moreover, the partial decay width ofone radion into two gluons is [4, 5]Γ[Φ → gg ] = α s m π Λ φ (cid:12)(cid:12)(cid:12)(cid:12)
153 + x t [1 + (1 − x t ) f ( x t ))] (cid:12)(cid:12)(cid:12)(cid:12) . (11)In this paper we will calculate f g in the proton case considering that the integrated gluon distribution xg ( x, Q T ) isdescribed by the CTEQ6L parameterization [20]. In the nuclear case we will include the shadowing effects in f Ag considering that the nuclear gluon distribution is given by the EKS98 parameterization [21], where xg A ( x, Q T ) = AR Ag ( x, Q T ) xg p ( x, Q T ), with R g describing the nuclear effects in xg A . Moreover, we assume in our calculationsΛ φ = 1 TeV.In order to obtain realistic predictions for the radion production by pomeron-pomeron fusion using the KMRmodel, it is crucial to use an adequate value for the survival probability gap, hS i . This factor is the probability thatsecondaries, which are produced by soft rescatterings do not populate the rapidity gaps (For a detailed discussion see[12]). In the case of proton-proton collisions, we will assume that hS i = 3 (5)% for LHC (Tevatron) energies [19].However, the value of the survival probability for nuclear collisions still is an open question. An estimate of hS i fornuclear collisions was calculated in [22] using the Glauber model, which have obtained hS i = 8 × − (8 . × − )for pAu (AuAu) collisions at LHC energies. Another conservative estimate can be obtained assuming that hS i A A = hS i pp / ( A .A ) (For a discussion about nuclear diffraction see [23]). In what follows we will consider these two modelsfor hS i A A when considering radion production by pomeron-pomeron fusion. It is important to emphasize that, incontrast, the value of the survival probability is of the order of unity for the γγ → Φ process in pp/pA/AA collisions.
III. RESULTS
In Figs. 2 and 3 we present our results for the dependence of the total cross section for radion production onthe radion mass considering γγ and IP IP interactions. In Fig. 2 we calculate the cross section for pp collisions andTevatron ( √ s = 2 . √ s = 14 . P bP b and (b) pP b collisions for LHC energies: √ s = 5 . γγ → Φ mechanism providesa natural lower limit for the radion exclusive production rate. Moreover, as the photon flux scales as the squaredcharged of the beam, Z , two photon cross sections are extremely enhanced for ion beams. However, they are eversmaller than the predictions for radion production by IP IP interactions in
P bP b and pP b collisions, independently γγ IP IPpp . pP b . × − × − P bP b . × − . × − TABLE I: The events rate/year for the radion production in pp/pP b/P bP b collisions at LHC energies considering the γγ and IP IP mechanisms and m Φ = 200 GeV. of the model considered for the survival probability hS i . In the case of pp collisions, they only are similar for largevalues of the radion mass. In comparison to the pp case, the IP IP predictions for AA ( pP b ) nuclear collisions areenhanced by a factor A ( A ). However, they are strongly reduced by the survival probability. In the P bP b casethe predictions obtained using the model proposed in [22] and our naive model are very similar. In contrast, for pP b collisions, they differ by a factor 5. Assuming the
IP IP predictions obtained using our model for hS i as being a lowerbound and that m Φ = 200 GeV, one obtain that the radion production by this mechanism is a factor 180 (36) largerthan the γγ predictions for P bP b ( pP b ) collisions. In comparison to the exclusive Higgs production in pp collisions[19] we predict cross sections that are a factor ≈
10 larger. This enhancement is directly associated to the traceanomaly for gauge fields, which leads to additional effective radion coupling to gluons or photons.Let us now to compute the production rates for LHC energies considering the distinct mechanisms. The resultsare presented in Table I. At LHC we assume the design luminosities L = 10 / / . − s − for pp/pP b/P bP b collisions at √ s = 14 / . / . (10 ) s for collisions with protons (ions). Moreover, wealso consider the upgraded pP b scenario proposed in Ref. [16], which analyse a potential path to improve the pP b luminosity and the running time. These authors proposed the following scenario for pP b collisions: L = 10 mb − s − and a run time of 10 s. The corresponding event rates are presented in the third line of the Table I. Our resultsindicate that for the default settings and running times, the statistics are marginal for P bP b collisions. Consequently,the possibility to carry out a measurement of the radion in γγ and IP IP interactions is virtually null in these collisions.On the other hand, in pp collisions the event rates are reasonable, in particular for IP IP interactions. In comparison tothe inclusive radion production [5], our predictions for exclusive production are a factor ≤ − smaller. Despite theirmuch smaller cross sections, the clean topology of exclusive radion production implies a larger signal to backgroundratio. Therefore, the experimental detection is in principle feasible. However, the signal is expected to be reduced dueto the event pileup which eliminates one of the main advantages of the exclusive processes. In contrast, in pA collisionsit is expected to trigger on and carry out the measurement with almost no pileup [16]. Therefore, the upgraded pA scenario provides the best possibility to detect the radion in an exclusive process.Some comments are in order. The exclusive cross sections for radion production are inversely proportional to Λ ,which still is a free parameter. Here we assume Λ Φ = 1 TeV as in [4, 5]. Moreover, our predictions are stronglydependent of the radion mass. In Table I we have considered m Φ = 200 GeV. Larger values imply that the radionmeasurement in exclusive processes would not be possible at LHC. Finally, the value of the survival probability forprocesses involving nuclei still is an open question. In this paper we calculated the cross sections considering twophenomenological models for hS i and estimated the event rates assuming a pessimistic scenario. However, thesepoints deserve a more detailed study which we postpone for a future publication. IV. SUMMARY
Exclusive processes have already been observed at the Tevatron with rates in broad agreement with the theoreticalpredictions. It is expected that at LHC the addition of forward proton taggers [24] to enhance the discovery andphysics potential of the ATLAS, CMS and ALICE detectors [25–27]. One of the possible scenarios which could beanalyzed is that proposed by Randall and Sundrum (RS) [2], which predicts the radion as the lowest gravitationalexcitation in order to stabilize the size of the extra dimension. As the mass of radion is expected to be ≈ TeV, thedetection of the radion will be the first signature of the RS model. In this paper we study the exclusive production ofthe radion in electromagnetic and diffractive hadron - hadron collisions at the LHC. We predict larger cross sectionsin comparison to the Higgs production in exclusive processes. Our results demonstrate that the diffractive productionof radion is dominant and should be feasible of study at CERN LHC.
Acknowledgements
This work was partially financed by the Brazilian funding agencies CNPq and CAPES. [1] J. L. Hewett and M. Spiropulu, Ann. Rev. Nucl. Part. Sci. , 397 (2002).[2] L. Randall and R. Sundrum, Phys. Rev. Lett. , 3370 (1999).[3] U. Mahanta and A. Datta, Phys. Lett. B , 196 (2000).[4] S. Bae, P. Ko, H. S. Lee and J. Lee, Phys. Lett. B , 299 (2000).[5] K. m. Cheung, Phys. Rev. D , 056007 (2001).[6] G. C. Nayak, arXiv:hep-ph/0211395.[7] G. Azuelos, D. Cavalli, H. Przysiezniak and L. Vacavant, Eur. Phys. J. direct C (2002) 16.[8] M. Battaglia, S. De Curtis, A. De Roeck, D. Dominici and J. F. Gunion, Phys. Lett. B , 92 (2003).[9] P. K. Das, S. K. Rai and S. Raychaudhuri, Phys. Lett. B , 221 (2005).[10] M. G. Albrow, T. D. Coughlin and J. R. Forshaw, arXiv:1006.1289 [hep-ph].[11] V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C , 525 (2000).[12] A. D. Martin, M. G. Ryskin and V. A. Khoze, Acta Phys. Polon. B , 1841 (2009).[13] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. Lett. , 242002 (2007); Phys. Rev. D , 052004 (2008); Phys. Rev.Lett. , 242001 (2009).[14] G. Baur, K. Hencken, D. Trautmann, S. Sadovsky, Y. Kharlov, Phys. Rep. , 359 (2002); C. A. Bertulani, S. R. Kleinand J. Nystrand, Ann. Rev. Nucl. Part. Sci. , 271 (2005); K. Hencken et al. , Phys. Rept. , 1 (2008).[15] G. Baur and L. G. Ferreira Filho, Nucl. Phys. A , 786 (1990).[16] D. d’Enterria and J. P. Lansberg, Phys. Rev. D , 014004 (2010)[17] J. Ohnemus, T. F. Walsh and P. M. Zerwas, Phys. Lett. B , 369 (1994)[18] T. D. Coughlin and J. R. Forshaw, JHEP , 121 (2010)[19] V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C , 311 (2002); Eur. Phys. J. C , 581 (2002).[20] J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. M. Nadolsky and W. K. Tung, JHEP , 012 (2002).[21] K. J. Eskola, V. J. Kolhinen and P. V. Ruuskanen, Nucl. Phys. B , 351 (1998); K. J. Eskola, V. J. Kolhinen andC. A. Salgado, Eur. Phys. J. C , 61 (1999).[22] E. Levin and J. Miller, arXiv:0801.3593 [hep-ph].[23] A. B. Kaidalov, V. A. Khoze, A. D. Martin and M. G. Ryskin, Acta Phys. Polon. B , 3163 (2003)[24] M. G. Albrow et al. [FP420 R and D Collaboration], JINST , T10001 (2009).[25] G. L. Bayatian et al. [CMS Collaboration], J. Phys. G , 995 (2007); D. G. . d’Enterria et al. [CMS Collaboration], J.Phys. G , 2307 (2007); R. Adolphi et al. [CMS Collaboration], JINST , S08004 (2008).[26] G. Aad et al. [The ATLAS Collaboration], arXiv:0901.0512 [hep-ex].[27] F. Carminati et al. [ALICE Collaboration], J. Phys. G , 1517 (2004); B. Alessandro et al. [ALICE Collaboration], J.Phys. G32