The CERN LHC Sensitivity on measuring Production and Anomalous Coupling
Abstract
In this paper we present for the first time a detailed Monte Carlo study of measuring production with pure leptonic decays and probing anomalous quartic gaugeboson couplings at the TeV LHC, with parton shower and detector simulation effects taken into account. We find that with an integrated luminosity of 100 and proper selection cuts, the Standard Model signal significance can be improved to as much as . After reviewing previous parametrization on anomalous couplings (see e.g. or as shown in Ref. Belanger:2000 ), we propose a more general parametrization scheme with 4 free inputs leading only to genuine aQGC couplings. Finally, our numerical results show that one can reach constraints at 95% confidence level of GeV GeV and GeV GeV, which are more stringent than LEP’s results by three orders of magnitude.
Keywords:
Triple Gauge Boson Production, Anomalous Quartic Gauge Boson Couplings, MC Simulation, LHCPeking University, Beijing, 100871, China
1 Introduction
The Standard Model (SM) has so far undergone considerable experimental tests and proved to be quite successful, especially after the recent discovery of the 125126 GeV Higgslike boson FGianotti ; JIncandela ; plb:2012gu ; plb:2012gk . However, there are strong hints suggesting possible existence of new physics at or beyond TeV scale, arising from, e.g., the compelling astrophysical evidences on dark matter, and the large hierarchy between electroweak and Planck scale. Thus searching for new physics beyond the SM remains both a theoretical and experimental pursuit.
One possible way to explore new phenomena in particle physics is to investigate bosonic anomalous couplings. Under the framework of SM, gauge symmetry completely determines gauge boson interactions, while presence of any anomalous coupling vertex may generate observable deviation from SM prediction. Study on these vectorboson interactions, therefore, can either confirm the SM and the spontaneously symmetry breaking mechanism, or give hint on the form of new physics.
So far, explorations of anomalous trilinear gauge boson couplings (aTGCs) have already been carried out extensively at the LEP Achard:2002vd ; Abreu:2001rpa , Tevatron Gounder:1999wq ; Abbott:1999aj , and later at the LHC Aad:2011xj ; Chatrchyan:2012bd via vector boson pair production, while less effort has been made on probing anomalous quartic gauge boson couplings (aQGCs). It is important to note that aQGCs, although involving more complicated event topology and may be less sensitive at high energy colliders, are not mere substitution of aTGCs but should be regarded as an independent way of uncovering new physics, since, for example, the exchange of heavy bosons can generate treelevel contribution to quartic coupling while its effect on trilinear vertex appears only at oneloop and is consequently suppressed Belanger:1992qh ; Eboli:0310141 . Historically, T. Han et al. in 1989 calculated the scattering cross sections of various triple gauge boson productions at and later colliders Han:1989 ; Han:1995 . Monte Carlo (MC) studies were also performed later by Éboli et al. at colliders and colliders through the processes ( and ) and (), giving constraints on relevant aQGCs Eboli:9306306 ; Eboli:9503432 . Further MC work on aQGCs during that period were performed at collider, and can be found in Belanger:2000 ; Stirling:2000 ; Dawson:1996aw ; Denner:2001vr . Direct constraints from experiments came mainly from the LEP at CERN, through Abbiendi:1999aa ; Abdallah:2003xn ; Acciarri:2000en , Acciarri:2000rz and Abbiendi:2004bf channels. Due to limitations of center of mass energy, LEP’s constraints at 95 confidence level on anomalous coupling constant are approximately at GeV level, still two orders of magnitude larger than those from the oblique parameters and as argued in Ref. Eboli:0009262 ().
It is expected, comparatively, that the operation and its proposed upgrade within next few years of the Large Hadron Collider (LHC) at CERN will set more strict constraints on aQGCs. As shown in e.g., Eboli:0310141 ; Eboli:0009262 ; Royon:2010tw , LHC can reach limits at about on the aQGCs, via the channel , vector boson fusion (VBF) production of , and . A more elaborated research by D. Yang et al. on production with full leptonic decay also confirmed the potential of LHC on probing aQGCs Yang:2012vv .
In the paper, we are interested in measuring final states with full leptonic decay at the TeV LHC and probing anomalous coupling. This work extends our previous study on and aQGCs measurement Yang:2012vv as a further independent examination on tripe gauge boson physics at the LHC. Moreover, we believe process has additional advantages as following: (1) process suffers from less background due to the requirement of a leptonically decayed boson reconstructed; (2) Being sensitive to vertex exclusively, serves as a direct examination on aQGC.
Our paper is organized as follows. In Sec. 2 we describe the photonic aQGCs effective Lagrangian and a novel parametrization to genuine aQGC. This is then followed by Sec. 3, showing our MC simulation framework and event selection details. Subsequently, Sec. 4 features numerical results, including the LHC sensitivities on production with pure leptonic decays and the aQGC. Finally, we conclude in Sec. 5.
2 Effective Lagrangian for Photonic aQGCs
The quartic interaction can be constructed in a modelindependent way with respect to the chiral Lagrangian approach Eboli:0310141 ; Belanger:2000 . Assuming that new physics beyond the SM keeps gauge invariance and custodial symmetry, we may write down the lowest order genuine aQGC operators in the form of independent Lorentz stuctures Eboli:0310141 ; Belanger:2000 ; Yang:2012vv . We list below two previously commonly used expressions of effective Lagrangian, both of which will be studied in this paper:

(i) violating Lagrangian
(1) 
where is the electroweak coupling constant, characterizes the strength of anomalous coupling, stands for new physics scale, represents the field strength tensor given by , and is the weak isospin triplet:
(2) 
with symbolizing the Weinberg mixing angle. The expression was widely used in references, but Bélanger et al. Belanger:2000 argued that it essentially violates symmetry. However we emphasize that invariance is not in general required by the first principle, thus we keep this form of effective Lagrangian for the purpose of comparison with previous experimental and MC outcomes Eboli:9306306 ; Stirling:2000 ; Denner:2001vr ; Abbiendi:1999aa ; Abdallah:2003xn ; Acciarri:2000en .

(ii) conserving Lagrangian
Following the notation in Ref. Eboli:0310141 (see Eq. (5) therein), there are 14 effective photonic operators relevant to aQGCs, specified by 14 independent coupling parameters . After recombining and sorting various terms into similar Lorentz structures, one can see that among them five are related to anomalous vertex:
(3) 
(4) 
(5) 
(6) 
(7) 
where , , and we adopt the abbreviated symbol , .
Accordingly, the effective interactions can be expressed by the above operators as
(8) 
where the coefficient parameters can be written as
(9) 
(10) 
(11) 
as shown in Eboli:0310141 . Here .
One would expect these s are correlated with those coupling constants that characterize , and interactions Eboli:0310141 . A practicable way for decorrelation is to seek for proper subspace of these 14 parameters (), namely, to impose extra restrictions on , leaving only vertex nonvanishing. A simple parametrization is proposed in Ref. Belanger:2000 , requiring and others vanished, and then one has:
(12) 
One alternative solution involving four independent parameters , and is given in Appendix. A, which can be expressed as:
(13) 
(14) 
(15) 
(16) 
(17) 
The 4dimensional solution automatically includes Eq. (12), if we set other three parameters than to zero. In the following, we stick to this 4dimensional parametrization, and in our analysis we first vary each parameter separately while setting others equal to zero, and then we also investigate the correlation of two individual parameters and draw contours at 95% confidence level.
Finally, we want to mention that, for sufficiently high energy collision, the effective Lagrangian leads to treelevel unitarity violation and is usually regulated by introducing appropriate form factor (ff) as following Eboli:0310141 :
(18) 
where is the the partonic centerofmass energy and represents the new physics scale. In Ref. Yang:2012vv we see that a reasonable choice of form factor can indeed satisfy the unitarity requirement. In this paper we choose , or TeV. The latter choice of equals to no form factor at all.
3 Event Simulation and Selection
We carry out our MC simulations within MadGraph/MadEvent v5 Alwall:2007st ; MadGraph:2012 ; Maltoni:2002qb . The effective Lagrangian of aQGCs is implemented into MadGraph based on the FeynRules Christensen:2008py UFO Degrande:2011ua ALOHA deAquino:2011ub framework. The signal and background concerned are initially generated at parton level by MadGraph and MadEvent, and are then passed through the interface to Pythia 6 for parton showering and hardronization Sjostrand:2003wg . The detector simulations are then done using Delphes 2.0 Ovyn:2009tx package, where we focus on the CMS detector at the LHC. Finally, all events are delivered to ExRootAnalysis ExRootAnalysis and analyzed with ROOT ROOT . The work flow has also been used in our previous studies Yang:2012vv ; Liu:2012rv .
The characteristic signal we are interested in contains three welldefined leptons with total electric charge , in association with large missing transverse energy . Besides, there is one and only one pair of oppositely charged lepton with same flavor originated from boson decay. Some example Feynman diagrams are plotted in Fig. 1, for production at the LHC, in the dileptontic final state , with and . Note decays into at the ratio of about 35% and is handled with TAUOLA tauola .
In Fig. 1, two types of diagrams, Figs. 1(a) and 1(b), involve TGCs and are not sensitive to aQGCs, while Fig. 1(d) can also be seen as the initial and final state radiations (ISR and FSR) from the production process, generated by Pythia. However, the ISR and FSR approximations in Pythia should break down for hard or wide scattering photon, e.g., when the transverse momentum of , is large. Note also this subset of contributions to is not related to QGCs, thus it would be interesting and important to show the overall results subtracting the contributions of the ISR/FSR approximations of Fig. 1(c), which we denote as :
(19) 
Aside from ISR/FSR, another six backgrounds are taken into account: , , , , and . Note that multilepton () final state can be possible backgrounds with additional leptons misidentified. Here we do not consider backgrounds with photons from jet fragmentation, in which the photons tend to be close to jets and the contributions can be suppressed efficiently via photon isolation cuts (see e.g. Ref. Frixione:1998 ).
We choose the following preselection cuts to generate unweighted events at parton level with MadGraph/MadEvent to interface later with Pythia and Delphes ,

(1) GeV,

(2) ,

(3) ,
where denotes the separation in which being the azimuthal angle and the pseudorapidity of a particle. Note, however, for the backgrounds involving misidentified leptons, we do not require any of the above cuts on leptons in order not to make bias.
Moreover, in the hard process generation with MadGraph/MadEvent we adopt the CTEQ6L1 parton distribution functions (PDFs) Pumplin:2002vw and set the renormalization and factorization scales as the transverse mass of the core process.
Further reconstruction cuts are then imposed on the reconstructed objects in the Delphes settings cards,

GeV, and .

Jets are clustered according to the anti algorithm with a cone radius . Moreover, (25 GeV by default) and are required.
Tighter cuts are set in the analysis steps posterior to detector simulation,

(1) The leading photon should exceed the threshold, , the value of which will be optimized,

(2) GeV,

(3) To distinguish from background processes (e.g., ) with more hard jets, require and at most 1 jet is allowed,

(4) Three and only three leptons with total charge,

(5) Exclude tagged jets to suppress top quarkrelated production,

(6) ,

(7) One and only one pair of oppositely charged lepton with same flavor comes from boson decay, with GeV.
In Delphes, photons and charged leptons may overlap with the jet collections: Delphes first reconstructs photons and leptons based on MC information, and then jets which can be seeded from the already reconstructed photons or leptons. In our analysis, we clean the lepton collections from jets by requiring the Delphes’s calculated “EhadOverEem” (the energy deposition in the Hadron Calorimeter over the one in the Electromagnetic Calorimeter) smaller than 1. Moreover, we remove any jet with as it would be indeed most like a photon.
4 Numerical Results
4.1 Production
As a first step, we are interested in estimating the feasibility of observing triple gauge boson production at the LHC, before going into aQGCs. As mentioned before, we are also interested in comparing overall results with the ones subtracting ISR/FSR contributions from processes (see Eq. (19)).
To optimize our results, we introduce further the following 3 requirements (similar as in our previous study Yang:2012vv ), in addition to all the cuts as mentioned in Sec. 3: (A) Maximize sensitivities by varying photon threshold cut ; (B) Keep the best , optimize over ; (C) Keep the best and values, vary threshold cut, and further require that within the interval at most 1 jet exists. The significance is defined by stat:atlas
(20) 
where , stand for number of signal and number of backgrounds, and .
We list the event numbers for the signal and backgrounds in Table 1, with the optimized parameters (optimized for contributions) from the above 3 steps: () GeV, () GeV, () GeV. Related Kfactors for the signal and backgrounds are also listed with references in Table 1. Correspondingly, the significances are shown in Fig. 2, calculated with Eq. (20).
Processes  (LO)  Kfactor  Events  

[fb]  [Ref.]  () GeV  () GeV  () , GeV  
0.89  2.0 Kwza  3.78  3.48  3.41  
I(F)SR  349.4  1.8 Kwz  0.76  0.50  0.44 
0.24  1.4 Kzza  0.19  0.18  0.17  
99.4  1.6 Kwz  0.16  0.16  0.16  
0.059  1.5 Kzzz  0.008  0.007  0.007  
1.72  1.8 Kzzz  0  0  0  
0.96  1.9 Kwwz  0.085  0.079  0.073  
6.16  1.4 Kttz  0.35  0.16  0.086 
More details can also be checked in Fig. 2 for cuts optimization. Note we also give the curves to show the results after subtracting ISR/FSR contributions from processes, as mentioned above. One can see that higher only slightly changes the significance as it removes both signal and backgrounds in a similar way, on the other hand, pure aQGCs significance is enhanced quickly as more ISR/FSR background is killed. cuts a bit more toprelated backgrounds but the overall effects on significance is small. Increasing jet reconstructing cut , increases the 0jet contributions while decreases the 1jet ones, as expected. The overall 0+1 jet significances shrink slightly, as signal events are also discarded.
Above all, a significance about 3 can be achieved to observe production at the 14 TeV LHC, and does not depend so much on the cuts as mentioned above. Note a large portion of events can come from the QED ISR/FSR which is not related to QGCs, as shown by the curves in Fig. 2, however, sticking to large lower cut ( GeV), one can still get a total significance about 2 from contributions.
4.2 Anomalous Couplings
The signal process can be sensitive to aQGCs . As shown in Fig. 3, the aQGCs lead to excesses on the hard tails in various kinematic region. One thus can refine the cuts in Sec. 3 to enhance the sensitivity to aQGCs as following, e.g. :

(1) GeV,

(2) GeV.
After all these selection cuts, the significances are calculated and displayed in Fig. 4 as functions of the aQGCs within conserving Lagrangian (Eq. (12)) or violating Lagrangian (Eq. (1)), at the 14 TeV LHC, with an integrated luminosity of 30, 100 and 200 , respectively. The horizontal dash lines here correspond to the 95% confidence level limit. Note here the signal is defined as .
Performing linear interpolation, 95% C.L. limits on aQGCs are obtained (the constraints of and are derived assuming independence among them, , varying one parameter while setting others zero, with the parametrization given in Appendix. A) at the 14 TeV LHC, with an integrated luminosity of 30(100)[200] , respectively:

(1) TeV
GeV,
GeV,
GeV,
GeV,

(2) TeV:
GeV,
GeV,
GeV,
GeV,

(3) GeV GeV.
Fig. 5 illustrates the correlation between two coupling constants. The left subplot is for the case of and , as they always appear as the sum , the 2 contour is simply bandlike. The right subplot is for and , where the contour is more complex as a circle . Other correlations can be deduced from these two examples, for more details see Appendix A.
Our results can be directly compared with the former experimental results and MC expectations. In Ref. Eboli:0310141 and Belanger:2000 , bounds on were derived through the MC simulations via VBF channel at the LHC and processes, respectively. While in Ref. Abbiendi:1999aa ; Abdallah:2003xn ; Acciarri:2000en (LEP experiments results) and Sahin (MC expectations at colliders), limits were given on . Summary of those results are listed in Table. 2 and Table. 3. At the 14 TeV LHC, we can set more stringent limit by at least three orders of magnitude compared to LEP results. Although a bit worse than the VBF channel, the leptonic decay mode of has simpler event topology and may be less contaminated by the QCD and VBF systematics.
parameter  95% confidence interval  

(GeV)  MC VBF Eboli:0310141 (GeV)  MC at LEP2 Belanger:2000 (GeV)  
parameter  95% confidence interval  

(GeV)  OPAL Abbiendi:1999aa  DELPHI Abdallah:2003xn  L3 Acciarri:2000en  MC at collider Sahin  
5 Conclusion and Discussion
The future upgrade of LHC with higher center of mass energy and luminosity enables measurement of triple gauge boson production and anomalous quartic gauge couplings, and production will be a potential channel which can be exploited to test the SM predictions and probe anomalous coupling exclusively with lower background contamination.
In summary, our study shows that at the 14 TeV LHC with an integrated luminosity of 100 , one can reach a significance of about 3 to observe the SM production, and can constrain at 95% C.L. the anomalous coupling parameters, e.g., and at , respectively. The expected limits are far beyond the existing LEP results, and can be comparable with the ones from VBF MC simulation studies Eboli:0310141 .
Acknowledgements.
This work is supported in part by the National Natural Science Foundation of China, under Grants No. 10721063, No. 10975004, No. 10635030 and No. 11205008, and National Fund for Fostering Talents in Basic Science, under Grant No. J1103206.Appendix A Appendix: a more general parametrization to genuine aQGCs
Taking account all the coefficients that characterize each anomalous coupling, we have the following set of equations Eboli:0310141 :
(21) 
(22) 
(23) 
(24) 
(25) 
(26) 
(27) 
Here the first four set of equations, (21)  (24), are the coupling constants of , , and thus are irrelevant to coupling, and we would like to find a solution for which they vanish. Here we seek for restrictions on these parameters that can lead to zero of Eqs. (21)  (24), which are:
(28) 
(29) 
(30) 
(31) 
(32) 
(33) 
The conditions Eqs.(3133), lead to . We have here in total 10 independent restrictions, hence leaving 4 independent variables. And we choose them to be , and . It is then easy to verify that the couplings constants can be expressed exactly as those in Eq. (13)  Eq. (17).
Having obtained the paramterization of genuine aQGC, we may further investigate the correlations between two paramters while setting the remaining two zero, which involve a total of six combinations. We take the following two combinations as examples, and the other cases can be inferred in a similar manner:

(1) .
It is easy to verify that we have and . Observe that this special case is equivalent to Eq. (12), if we subsititute in (12) with . Thus restrictions on and can be expressed as (for 100 LHC and with ff n=5, for instance):
(34) 
One may as well check that when only and are left nonzero, the confidence region can be extracted directly if we make substitution in the inequalities given in Sec. 4.2.

(2) .
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