Anomalous quartic WWγγ and ZZγγ couplings in γp collision at the LHC
aa r X i v : . [ h e p - ph ] S e p Anomalous quartic
W W γγ and
Z Z γγ couplings in γp collision atthe LHC A. Senol ∗ Kastamonu University, Department of Physics, 37100, Kastamonu, Turkey
Abstract
We analyze the anomalous quartic gauge boson couplings
W W γγ and
ZZγγ , described bydimension-6 effective quartic Lagrangian at the LHC. The sensitivities to anomalous quartic gaugecouplings a W,Z ,c / Λ by examining the two different photon-induced processes pp → pγp → pW γqX and pp → pγp → pZZqX with W and Z s decaying leptonically are investigated. We show that γp mode of photon-induced reactions at the LHC are able to probe these couplings to the order of10 − -10 − GeV − at 95% confidence level with √ s = 14 TeV and for proton-proton luminositiesin the range of 30-200 fb − . PACS numbers: 13.85.Hd, 12.15.-y ,12.60.Cn ∗ Electronic address: [email protected] . INTRODUCTION The structure of triple and quartic interactions of the gauge bosons in the electroweaksector of the Standard Model (SM) are represented by the non-Abelian SU (2) L × U (1) Y local gauge symmetry. Possible deviations of the triple and quartic gauge boson couplingsfrom SM predictions within the experimental precision can give valuable information aboutnew physics beyond the SM. A simple way to parameterize these new physics effects athigher energies is to assume that the SM is an effective theory at low energies. Genuinequartic gauge couplings arise from effective operators which do not lead to any trilineargauge boson couplings. Therefore, the SM can be extended via the trilinear gauge couplingsthat are equal to their SM values while quartic gauge couplings are modified by genuineanomalous interactions. In this way, quartic gauge boson couplings can be constrainedindependently of the bounds on the anomalous trilinear vertices. The two independent Cand P conserving dimension-6 effective quartic Lagrangian operators involving at least twophotons that give rise to genuine anomalous quartic couplings imposing local U (1) EM andcustodial SU (2) W eak symmetry are [1, 2] L = − e a W Λ F µν F µν W + α W − α − e
16 cos θ W a Z Λ F µν F µν Z α Z α (1)and L c = − e a Wc Λ F µα F µβ ( W + α W − β + W − α W + β ) − e
16 cos θ W a Zc Λ F µα F µβ Z α Z β , (2)where W ± α is the W ± boson field, F µν is the tensor for electromagnetic field strength, a W ( Z )0 and a W ( Z ) c are the dimensionless anomalous coupling constants of W (Z) parts of the La-grangian, and Λ is interpreted as the energy scale of the new physics. The anomalouscouplings are zero in the SM.The interaction Lagrangians L and L c generate anomalous contributions to two W W γγ vertices as given by [3] i πα Λ a W g µν [ g αβ ( p .p ) − p α p β ] (3)and i πα a Wc [( p .p )( g µα g νβ + g µβ g αν ) + g αβ ( p µ p ν + p µ p ν ) − p β ( g αµ p ν + g αν p µ ) − p α ( g βµ p ν + g βν p µ )] , (4)2 ABLE I: The 95% C.L. upper limits on anomalous quartic
W W γγ and
ZZγγ couplings withoutform factors.Parameters [GeV − ] CMS D0 OPAL a W / Λ [-4.0 × − ; 4.0 × − ] [-0.00043, 0.00043] [-0.020, -0.020] a Wc / Λ [-1.5 × − ,1.5 × − ] [-0.0015, 0.0015] [-0.052, 0.037] a Z / Λ - - [-0.007, 0.023] a Zc Λ - - [-0.029, 0.029] where the fine structure constant is α = e / (4 π ), p and p are the four-momenta of photons.The anomalous ZZγγ vertex is derived by multiplying above vertex functions Eq. (3) andEq. (4) by 1 / cos θ W and with the replacement W → Z . The ZZγγ vertex does not occurin SM at tree level.All anomalous couplings in the effective Lagrangian Eqs. (1) and (2) cause tree-levelunitarity violation at high energies. The standard procedure to regularise the cross sectionis to employ a dipole form factor: a W,Z ,c (ˆ s ) = a W,Z ,c (1 + ˆ s/ Λ cutoff ) (5)where ˆ s is the partonic center of mass energy and Λ cutoff is the scale of new physics.We obtained the limits on anomalous couplings to compare our results with the scenarioΛ cutoff → ∞ . The maximal Λ cutoff is calculated from the given value of anomalous cou-plings which can be in form factors. To protect the unitarity, in this study we calculatedthe maximal Λ cutoff to be about 3 TeV when order of 10 − is taken for a W,Z ,c / Λ .The anomalous a W,Z / Λ and a W,Zc / Λ couplings were experimentally limited at the 95%C.L. by the OPAL collaboration from measurements of W W γ , q ¯ qγγ , and ν ¯ νγγ production atCERN LEP collider [4]. Recently, the experimental 95% C.L. limits on anomalous couplings a W ,c have been provided by the D0 [5] collaboration at the Fermilab Tevatron from eventswith dielectron and missing energy, and by the CMS [6] collaboration at CERN LHC fromexclusive two-photon production of W + W − . All limits are given in Table I.LHC will allow probing of new physics via photon-induced interactions at energies beyondthe electroweak energy scale by allowing the use of complementary information to the parton-parton collisions at the LHC by adding forward proton detectors [7]. For instance, the useof forward proton tagging for the measurements of outgoing scattered proton momenta,3ould provide spin-parity information about exclusively produced particles in the photon-induced processes [8]. Photon-induced processes include a low virtuality quasi-real photonwhich is scattered with small angle from the beam pipe. Therefore, the photon emittingintact proton is scattered with small angle and thus escapes from the central detectors ofCMS and ATLAS without being detected. This intact scattered protons in the final stateleave a characteristic sign in the forward detectors which are suggested to be located atdistances of 220 m and 420 m from the interaction point according to the forward physicsprogram of CMS and ATLAS collaborations [9–11]. The photon-induced reactions providea suitable platform of searching for photonic-quartic anomalous gauge couplings thanks tothese distinctive experimental features. At the LHC, photonic quartic W W γγ and
ZZγγ vertices are probed in photon-induced reactions, i.e. pp → pγγp → pW + W − p [12, 13] for W W γγ couplings and pp → pγγp → pZZp [13, 14], pp → pγp → pγqZX [15] for ZZγγ couplings which were elaborately studied in the literature. Furthermore, particularly wellsuited phenomenological studies of anomalous vertices
W W γγ and
ZZγγ have already beenperformed at the LHC via traditional pp reactions [16–21], e + e − colliders [1, 22–30] and its γγ [2, 31–33], eγ [3, 34] modes. In this work, we study the anomalous quartic gauge bosoncouplings W W γγ and
ZZγγ by examining the two different photon-induced processes whichare pp → pγp → pW γqX and pp → pγp → pZZqX at the LHC. II. THE CROSS SECTIONS FOR THE PRODUCTION OF
W γ
AND ZZ IN γp COLLISION
The tree-level SM Feynman diagrams of the subprocess γq → W γq ′ in the main reaction pp → pγp → pW γqX are shown in Fig. 1. The first of these diagrams receive contributionsfrom the anomalous W W γγ couplings. In the case of examining anomalous
ZZγγ couplings,we consider the subprocess γq → ZZq of the main reaction pp → pγp → pZZqX . Theanomalous ZZγγ vertex contributions are shown in the first diagrams of Fig. 2, whereasthe others depict the tree-level SM Feynman diagrams. All calculations were evaluated usingthe tree-level event generator CalcHEP [35], by adding the vertex functions Eqs. (3) and(4). The total cross sections for pp → pγp → pW γqX and pp → pγp → pZZqX processescan be obtained by integrating the cross sections for the subprocess γq → W γq ′ (where q = u, c, ¯ d, ¯ s and q ′ = d, s, ¯ u, ¯ c ) and γq → ZZq (where q = u, ¯ u, d, ¯ d, c, ¯ c, s, ¯ s, b, ¯ b ) with the4 W+ W+(cid:13)q q0 (cid:13) W+W+q q0W+(cid:13) (cid:13) W+ W+W+ (cid:13)q q0 (cid:13) W+ W+q q0q (cid:13)(cid:13) W+ W+q q0 q0(cid:13) (cid:13) q0q0q W+q0(cid:13) (cid:13) q0 q0q0 (cid:13)q W+ (cid:13) q0 q0q W+q (cid:13)(cid:13) q0 q0q W+ W+(cid:13) (cid:13)q q W+q0 q0(cid:13) (cid:13)q q q0W+ W+(cid:13) (cid:13)q q (cid:13)q q0W+(cid:13) q qq (cid:13)q0W+
FIG. 1: Feynman graphs for the tree-level subprocess γq → W γq ′ (where q = u, c, ¯ d, ¯ s and q ′ = d, s, ¯ u, ¯ c ). (cid:13) (cid:13) ZZq q (cid:13)q q Zq qZ (cid:13)q q qH ZZ(cid:13) q qq ZqZ (cid:13) q qq Zq Z (cid:13) q qq H ZZ FIG. 2: Feynman graphs for the tree-level subprocess γq → ZZq (where q = u, ¯ u, d, ¯ d, c, ¯ c, s, ¯ s, b, ¯ b . σ pp → pγp → pW γqXpp → pγp → pZZqX = Z Q max Q min dQ Z x max x min dx Z x max x min dx (cid:18) dN γ dx dQ (cid:19) × (cid:18) dN q dx (cid:19) ˆ σ γq → W γqγq → ZZq (ˆ s ) (6)where x = E γ E (here E denotes the energy of the incoming proton beam and E γ is the photonenergy), x is the momentum fraction of the proton’s momentum carried by the quark, dN q dx isthe quark distribution function of the proton and dN γ dx dQ is the photon spectrum in equivalentphoton approximation (EPA). In numerical calculations, we use CTEQ6L [36] for partondistribution functions and the EPA [37–39] embedded in CalcHEP for the photon spectra.The photon spectrum of virtuality Q and energy E γ in EPA is defined by the followingformula [37, 39]: dN γ dE γ dQ = απ E γ Q [(1 − E γ E )(1 − Q min Q ) F E + E γ E F M ] (7)where Q min denotes the photon minimum virtuality is given by Q min = m p E γ E ( E − E γ )here, m p is the mass of the incoming proton. The magnetic and electric form factors F M and F E are defined by F E = 4 m p G E + Q G M m p + Q , F M = G M G E = G M .
78 = (1 + Q . ) − In our calculations, we have taken Q max =2 GeV for which the contribution to the integralabove this value is very small.The total cross sections of the processes pp → pγp → pW γqX and pp → pγp → pZZqX are given in Fig. 3 and Fig. 4 as functions of anomalous a W ,c / Λ and a Z ,c / Λ couplings atthe LHC with √ s = 14 TeV. In these figures, the cross sections depending on the anomalousquartic gauge coupling parameter were obtained by varying only one of the anomalouscouplings at a time while the other was fixed to zero.6 W ‘ L a cW ‘ L - - @ - GeV - D Σ H pb L FIG. 3: The total cross sections depending on anomalous a W / Λ and a Wc / Λ couplings for theprocess pp → pγp → pW γqX at the LHC with √ s = 14 TeV. W ‘ a Z ‘ L a cZ ‘ L - - @ - GeV - D Σ H pb L FIG. 4: The total cross sections as function of anomalous a Z / Λ and a Zc / Λ couplings for theprocess pp → pγp → pZZqX at the LHC with √ s = 14 TeV. III. SENSITIVITY TO THE ANOMALOUS
W W γγ
AND
ZZγγ
COUPLINGS
The bounds of anomalous a W,Z / Λ and a W,Zc / Λ couplings at 95% C.L. were obtainedby applying one and two-dimensional χ tests without considering systematic errors. χ is7 ABLE II: 95% C.L. constrains on anomalous quartic gauge couplings
W W γγ and
ZZγγ param-eters a W,Zc / Λ and a W,Z / Λ at LHC with √ s = 14 TeV.L(fb − ) a W / Λ ( × − GeV − ) a Wc / Λ ( × − GeV − ) a Z / Λ ( × − GeV − ) a Zc / Λ ( × − GeV − )30 [-8.67; 8.32] [-12.71; 12.33] [-5.82; 5.58] [-22.62; 21.24]50 [-7.65; 7.31] [-11.21; 10.83] [-5.13; 4.90] [-19.99; 18.61]100 [-6.46; 6.12] [-9.45; 9.08] [-4.33; 4.10] [-16.93; 15.54]200 [-5.46; 5.12] [-7.98; 7.61] [-3.66; 3.43] [-14.35; 12.97] defined as: χ = (cid:18) σ SM − σ AN σ SM δ (cid:19) (8)where σ AN is the cross section in the presence of anomalous couplings, δ = √ N is thestatistical error and here N is the number of events. The number of events for pp → pγp → pW γqX is given by N = E × S × σ SM × L int × BR ( W → lν ) where E is the jetreconstruction efficiency, S denotes the survival probability factor, σ SM is the correspondingSM background cross section, L int is the integrated luminosity and l = e − or µ − . Similarly,for pp → pγp → pZZqX process N = S × E × σ SM × L int × BR ( Z → l ¯ l ) . We also assume S = 0 . E = 0 . p j,γT >
15 GeV cutwas applied on the transverse momenta of final state photons and jets. We also imposedthe pseudorapidity cuts | η j,γ | < . | η | < .
5. We do not consider anyacceptance for the final state leptons because our calculations do not provide the leptonmomenta.To discern the photoproduction process from the usual proton-proton backgrounds andclose the intrinsic p T spread of the LHC beams, we apply a p T >
100 MeV cut on thetransverse momentum of outgoing protons that emit photons [9, 39, 41].The calculated one-dimensional limits (with the other anomalous coupling fixed to zero)on anomalous quartic gauge couplings a W,Zc / Λ and a W,Z / Λ at 95% C.L. sensitivity for someintegrated luminosities are given in Table II.Our obtained limits on a W,Z / Λ and a W,Zc / Λ are approximately four orders of magnitudemore restrictive than the best limits obtained from OPAL [4] as can be seen from thecomparison of Table I and Table II . On the other hand, the bounds for a W / Λ and a Wc / Λ √ s =7 TeV with L int =5 fb − [6] have similar sensitivity as ourlimits.In addition, we present 95% C.L. contours in the a W / Λ - a Wc / Λ plane in Fig.5 and the a Z / Λ - a Zc / Λ plane in Fig.6 at √ s =14 TeV for various integrated luminosities. As we can seefrom Fig.5, the best limits on a W / Λ and a Wc / Λ through the reactions pp → pγp → pW γqX are [ − . × − ; 6 . × − ] GeV − and [ − . × − ; 8 . × − ] GeV − , respectively forL int =200 fb − at the LHC. According to Fig.6, the attainable bounds on a Z / Λ and a Zc / Λ via reactions pp → pγp → pZZqX are [ − . × − ; 1 . × − ] GeV − and [ − . × − ; 3 . × − ] GeV − , respectively. L int =
30 fb - L int =
50 fb - L int =
100 fb - L int =
200 fb - - - - - - - a W (cid:144) L @ x10 - GeV - D a c W (cid:144) L @ x10 - G e V - D FIG. 5: 95% C.L. contours for anomalous a W / Λ and a Wc / Λ couplings for the process pp → pγp → pW γqX at the LHC with √ s = 14 TeV. int =
30 fb - L int =
50 fb - L int =
100 fb - L int =
200 fb - - - - - - a Z (cid:144) L @ x10 - GeV - D a c Z (cid:144) L @ x10 - G e V - D FIG. 6: 95% C.L. contours for anomalous a Z / Λ and a Zc / Λ couplings for the process pp → pγp → pZZqX at the LHC with √ s = 14 TeV. IV. CONCLUSIONS
The high energy photon-photon or photon-proton interactions at the LHC exhibit asuitable platform to probe genuine anomalous quartic gauge couplings. Especially, thephoton-photon reactions can provide much higher sensitivity than partonic reactions due toclean experimental conditions and mostly free from QCD backgrounds for anomalous quarticgauge couplings. On the other hand, photon-proton reactions have higher luminosities andhigher center of mass energies compared to photon-photon reactions. Since the anomalousquartic gauge boson couplings involve higher luminosity and higher center of mass energies,it is more proper to study them in photon-proton reactions. In this work, we have performedan analysis of the pp → pγp → pW γqX and pp → pγp → pZZqX processes with W and Z sdecaying leptonically in order to assess the sensitivities to anomalous quartic gauge couplings a W,Z ,c / Λ by using dimension-6 effective quartic Lagrangian at LHC assuming triple gauge10oson couplings W W γ to be at their SM values. We showed that our limits are severalorders of magnitude beyond the best limits obtained from LEP [4] and Tevatron [5]. Ourlimits have similar sensitivity with those obtained from CMS [6] at √ s =7 TeV with L int =5fb − . The results of pp → pγp → pW γqX and pp → pγp → pZZqX processes in ourstudy are less sensitive than the results of ref. [12] which are obtained by the fully exclusiveproduction. Acknowledgments
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