# Differentiating the Higgs boson from the dilaton and the radion at hadron colliders

###### Abstract

A number of candidate theories beyond the standard model (SM) predict new scalar bosons below the TeV region. Among these, the radion, which is predicted in the Randall-Sundrum model, and the dilaton, which is predicted by the walking technicolor theory, have very similar couplings to those of the SM Higgs boson, and it is very difficult to differentiate these three spin-0 particles in the expected signals of the Higgs boson at the LHC and Tevatron. We demonstrate that the observation of the ratio gives a simple and decisive way, independently of the values of model parameters: the VEVs of the radion and dilaton fields.

###### pacs:

14.80.Bn 14.80.EcA number of candidate theories beyond the Standard Model (SM) predict new scalar bosons below the TeV region. When a scalar boson signal is detected in the Higgs search at the LHC, it is very important to determine whether it is really a SM Higgs boson or another exotic scalar. Among these, the radion(), predicted in the Randall-Sundrum (RS) modelRS (); RS1 (); RS6 (); GRW (); CHL (); RS2 (); RS3 (); RS4 (); RS5 (); ADMS (); ACP (); CGPT (); CGK (); Han (); Dav (); Dav2 (); Toharia (); BI (), and the dilaton(), predicted in spontaneous breakingGGS (); Fujii (); WT0 (); WT2 (); WT3 (); WT4 (); Sannino (), have very similar couplings to those of the standard model Higgs boson (), and it is very difficult to differentiate these three particles, , in the signals. A distinctive differenceGGS (); Toharia (); BIK (); Logan () is in their couplings to massless gauge bosons. We demonstrate that the ratios are different from each other, and their observation gives a decisive method to distinguish these three spin-0 particles. Our main result is given in Fig. 2. It is important that the ratio is independent of the model-paramneters; the VEVs of the radion and dilaton fields. The test applies to both LHC and Tevatron experimental searches.

For definiteness we consider the dilaton coupling given in ref.GGS (), which is the same as the dilaton coupling in 4-dimensional walking technicolor theoryWT0 (); WT2 (); WT3 (); WT4 (); Sannino () where all SM fields are composites of strongly interacting fields in conformal field theory (CFT). In AdSCFT correspondence this dilaton is dual to the radionRS1 (); RS6 (); GRW () in the original Randall-Sundrum (RS1) modelRS (), where all the SM fields are localized at the infrared (IR) brane in the 5-dimensional Anti-de Sitter(AdS) space background. We consider the radion coupling of the Randall-Sundrum (RS2) model given in ref.CHL () where all the SM fields are in the bulkRS2 (); RS3 (); RS4 (); RS5 (); ADMS (); ACP (); CGPT (); CGK (); Han (); Dav (); Dav2 (); Toharia (); BI (). The radion has bulk couplings to the gauge bosons. It is dualCHL () to the dilaton in CFT. We do not consider flavor changing neutral current (FCNC) processes; however, we note that a dilaton in a particular CFT with SM fields that are elementary and weakly coupled can generically have FCNCrefe1 (); refe2 (), as can the radion of the RS2 modelToha2 () considered here. We will study collider signatures from the gauge coupling differences of in the following.

Effective Lagrangians We treat the SM Higgs boson , the radion , and the dilaton , which are also denoted as . The vacuum expectation values (VEV) of these fields are denoted as

(1) |

for , , and , respectively. The determine overall coupling strengths of these particles, and GeV.

The Lagrangian of the interactionsRS6 (); GRW (); GGS (); Han (); CHL (); Dav2 () with the SM particles is given by

(2) | |||||

(3) | |||||

(4) | |||||

(5) | |||||

(6) | |||||

(7) |

where denotes the separation of the branes in the RS2 model and is a parameter that governs the weak scale-Planck scale hierarchy. The term is absent for the dilaton and the Higgs boson. specifies the couplings to the massless gauge bosons, and represents the field strength of gluon(photon). gives the couplings to the weak bosons, and etc. In the fermion-coupling Lagrangian , the factors are and for all fermions , while the depend upon the bulk wave functions of the fermion in the RS2 model. We take for one value of couplingDav () as our example. represents the couplings to the Higgs boson. is also applicable to the . In the radion effective interaction, the brane kinetic terms are taken to be zeroDav2 ().

A distinction in Eq. (3) is the and couplings . Their expressions are given in Table 1. is given by the sum of the triangle-loop contributions of top quark and boson and the function coefficient appearing in the trace-anomaly of the SM energy-momentum tensor RS1 (); GRW (); Sannino (); GGS (). The trace-anomaly term contributes for and but not for . Here we should note that the function contributions (the second column) always count all favors ”light or heavy”. But, the mass-coupling-term of the triangle-loop diagram operates in a way to cancel the heavy countings if the (or ) masses are lower than the corresponding threshold. As a result, for with the number of effective flavors . A similar argument is also applicable to .

; | ||||

; |

The real part of the couplings are given in Fig. 1. The destructive interference between the bulk coupling term and the term is due to the opposite sign, and this yields the very different shape of versus : The cusp at , which comes from the threshold effect, constructively contributes for and , and destructively for . This behavior is seen in Fig. 2.

describes the decays. The effective couplings are given by

(8) |

where have both and terms from the triangle-loop contributions of and SM fermions, respectively. Their explicit forms are given in refs.Hunter (); Anatomy (). is negligible compared to . The third term comes from the trace anomaly of and it contributes to , but not to . We can check that particles with heavier thresholds than or decouple also in . To a good approximation the bulk-field coupling of gives no contribution to Ren ().

ratio From in Eq. (2), we can calculate the partial widths of and . They are proportional to the inverse squares of the overall constants , but the values of and are presently unknown. However, the ratiosbook () are independent of these VEVs. Figure 2 shows the ratios (upper figure), the ratios (middle figure), and the ratios (lower figure), for and of the same mass. They are compared with those of of the same mass.

As can be clearly seen in Fig. 2, we can differentiate the three scalars, , by observing the ratio . In Fig. 2 the slope changes around since steeply decreases below the threshold. The gives an almost constant ratio in becuse of the contribution from the bulk coupling term which is energy-independent. The drastic change in slope of the ratio of near occurs from the interference between this bulk coupling and the trace anomaly term. See, Fig. 1.

The ratio of can differ from and , because of the parameter , so measuring this quantity is also helpful to distinguish from the other two scalars.

The ratio of and can differ from , because of the trace anomaly contributions. This channel is helpful to determine the coupling form of the signal. It may be possible to detect it by focusing on the monochromatic photon spectrum from .

Total widths and decay branching fractions (BF)

The total widths of are given in Fig. 3. scale with where TeV are taken, and the and widths are about two orders of magnitudes smaller than the with the same mass.

The branching fractions () of the decays to are compared in Fig. 4, where the -factor in NNLOKfact () is considered for . BF() shows very delicate structures. is the largest at , since the has the smallest couplings to and the main decay mode in this energy region is .

Concluding Remarks The measurement of the ratioratio () provides a decisive way to differentiate the radion , the dilaton , and the SM Higgs . It is only necessary to count the event numbers of and decays of an observed signal. This method is independent of the values of the model-parameters, the VEVs and . It applies to both the LHC and Tevatron experimental searches.

The scalars are also expected to be produced in associated production, and . The production cross section and are smaller than , respectively, by the factors and , which are in the TeV case. This small cross section of associated production also can be used to differentiate the and from Logan ().

The production of and via the fusion subprocess is much smaller than that of , due to their relatively smaller decay widths to and .

We may also consider the scenario that both and (or and ) exist with comparable masses in the region GeV, where the on-going Higgs search data show some excess over the expected SM cross section. At this mass both and have very narrow widths, and their resonance peaks will be smeared by experimental resolution into one with twice the production cross section, even with the mixing of scalars taken into account. In this case the ratio will be intermediate between the single-state values. Another possible scenario is that or mixGRW (); mix1 (); mix2 (); mix3 () with . Then, the lighter scalar can have a mass below 100 GeV and its production will be suppressed compared to that of the SM Higgs.

For dilaton or radion masses much larger than , the narrow width makes discovery in and easier than for the SM HiggsLogan ().

Finally, our study applies also to generic singlet modelsNMSSM (). The singlet decouples from SM particles and the phenomenology is dependent on the amount of mixing of with the singlet scalar. The production cross section can be significantly smaller by the mixing effect, and thus, a low-mass Higgs boson with GeV also become possible.

Acknowledgements

We thank Professors Bill Bardeen and Prof. Misha Stephanov for discussions. M.I. is very grateful to the members of phenomenology institute of University of Wisconsin-Madison for hospitalities. This work was supported in part by the U.S. Department of Energy under grants No. DE-FG02-95ER40896 and DE-FG02-84ER40173, in part by KAKENHI(2274015, Grant-in-Aid for Young Scientists(B)) and in part by grant as Special Researcher of Meisei University.

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