<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.06569958pt" id="M1" height="15.1614pt" version="1.1" viewBox="-0.0657574 -15.0957 17.0609 15.1614" width="17.0609pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-91" d="M669 636L663 650H260C230 650 221 652 208 675H186C177 621 162 548 144 481L173 479C195 534 211 560 226 578C248 604 266 615 373 615H544C460 511 114 112 23 16L31 0H561C577 34 611 135 622 170L594 182C566 125 544 88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z"/></g><g transform="matrix(.012,0,0,-0.012,11.875,-7.578)"><path id="g50-31" d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"/></g></svg> Resonance and Associated <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2723999pt" id="M2" height="12.533pt" version="1.1" viewBox="-0.0657574 -12.2606 20.9385 12.533" width="20.9385pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g113-91"/></g><g transform="matrix(.017,0,0,-0.017,11.875,0)"><path id="g113-105" d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"/></g></svg> Production at Future Higgs Boson Factory: ILC and CLIC

Gutiérrez-Rodríguez, A.; Hernández-Ruíz, M. A.

doi:https://doi.org/10.1155/2015/593898

Advances in High Energy Physics

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Research Article | Open Access

Volume 2015 | Article ID 593898 | https://doi.org/10.1155/2015/593898

Resonance and Associated Production at Future Higgs Boson Factory: ILC and CLIC

A. Gutiérrez-Rodríguez¹and M. A. Hernández-Ruíz²

Academic Editor: Sally Seidel

Received21 Apr 2015

Revised23 Jun 2015

Accepted24 Jun 2015

Published13 Jul 2015

Abstract

We study the prospects of the model with an additional boson to be a Higgs boson factory at high-energy and high-luminosity linear electron positron colliders, such as the ILC and CLIC, through the Higgs-strahlung process , including both the resonant and the nonresonant effects. We evaluate the total cross section of and we calculate the total number of events for integrated luminosities of 500–2000 fb⁻¹ and center of mass energies between 500 and 3000 GeV. We find that the total number of expected events can reach 10⁶, which is a very optimistic scenario and it would be possible to perform precision measurements for both and Higgs boson in future high-energy colliders experiments.

1. Introduction

The discovery of a light scalar boson of the ATLAS [1] and CMS [2] collaborations at the Large Hadron Collider (LHC) compatible with a SM Higgs boson [3–7] and with mass around has opened a window to new sectors in the search for physics beyond the Standard Model (SM). The Higgs boson might be a portal leading to more profound physics models and even physics principles. Therefore, another Higgs factory besides the LHC such as the International Linear Collider (ILC) [8–13] and the Compact Linear Collider (CLIC) [14–16] that can study in detail and can precisely determine the properties of the Higgs boson is another important future step in high-energy and high-luminosity physics exploration.

The existence of a heavy neutral () vector boson is a feature of many extensions of the Standard Model. In particular, one (or more) additional gauge group provides one of the simplest extensions of the SM. Additional gauge bosons appear in Grand Unified Theories (GUTs) [17], Superstring Theories [18], Left-Right Symmetric Models (LRSM) [19–21], and other models such as models of composite gauge bosons [22]. In particular, it is possible to study some phenomenological features associated with this extra neutral gauge boson by considering a (baryon number minus lepton number) model.

The symmetry plays an important role in various physics scenarios beyond the SM. (a) The gauge symmetry group is contained in a GUT described by a group [23]. (b) The scale of the symmetry breaking is related to the mass scale of the heavy right-handed Majorana neutrinos mass terms providing the well-known see-saw mechanism [24] to explain light left-handed neutrino mass. (c) The symmetry and the scale of its breaking are tightly connected to the baryogenesis mechanism through leptogenesis [25].

The model [26, 27] is attractive due to its relatively simple theoretical structure, and the crucial test of the model is the detection of the new heavy neutral gauge boson. The analysis of precision electroweak measurements indicates that the new gauge boson should be heavier than about 1.2 [28]. On the other hand, recent bounds from the LHC indicate that the gauge boson should be heavier than about 2 TeV [29, 30], while future LHC runs at 13-14 TeV could increase the mass bounds to higher values or may be lucky and find evidence for its presence. Further studies of the properties will require a new linear collider [31], which will also allow us to perform precision studies of the Higgs sector. Detailed discussions on the model can be found in the literature [26, 32–38].

The Higgs-stralung [39–43] process is one of the main production mechanisms of the Higgs boson in the future linear colliders experiments, such as the ILC and CLIC. Therefore, after the discovery of the Higgs boson, detailed experimental and theoretical studies are necessary for checking its properties and dynamics [44–47]. It is possible to search for the Higgs boson in the framework of the model; however the existence of a new gauge boson could also provide new Higgs particle production mechanisms, which could prove its nonstandard origin. In this work, we analyze how the gauge boson of the model could be used as a factory of Higgs bosons.

Our aim in the present paper is to study the sensitivity of the boson of the model as a Higgs boson factory through the Higgs-strahlung process , including both the resonant and the nonresonant effects at future high-energy and high-luminosity linear colliders, such as the International Linear Collider (ILC) [8] and the Compact Linear Collider (CLIC) [14]. We evaluate the total cross section of and we calculate the total number of events for integrated luminosities of 500–2000 and center-of-mass energies between 500 and 3000 GeV. We find that the total number of expected events for the colliders is very promising and that it would be possible to perform precision measurements for both the and the Higgs boson in the future high-energy colliders experiments. In addition, we also studied the dependence of the Higgs signal strengths on the parameters and of the model for the Higgs-stralung process .

This paper is organized as follows. In Section 2, we present the theoretical framework. In Section 3, we present the decay widths of the boson in the context of the model. In Section 4, we present the calculation of the process , and, finally, we present our results and conclusions in Section 5.

2. Theoretical Framework

We consider an model consisting of one doublet and one singlet and briefly describe the lagrangian including the scalar, fermion, and gauge sector. The Lagrangian for the gauge sector is given by [36, 48–50]where , , and are the field strength tensors for , , and , respectively.

The Lagrangian for the scalar sector of the model iswhere the potential term is [34]with and as the complex scalar Higgs doublet and singlet fields, respectively. The covariant derivatives for the doublet and singlet are given by [32–34]where the doublet and singlet scalars arewith , , and being the Goldstone bosons of , , and , respectively.

After spontaneous symmetry breaking the two scalar fields can be written aswith and being real and positive. Minimization of (3) gives

To compute the scalar masses, we must expand the potential in (3) around the minima in (6). Using the minimization conditions, we have the following scalar mass matrix:

The expressions for the scalar mass eigenvalues areand the mass eigenstates are linear combinations of and and written aswhere is the SM-like Higgs boson. The scalar mixing angle can be expressed as

In the Lagrangian of the model, the terms for the interactions between neutral gauge bosons and a pair of fermions of the SM can be written in the form [36, 37]From this Lagrangian we determine the expressions for the new couplings of the bosons with the SM fermions, which are given bywhere and is the mixing angle. The current bound on this parameter is [51]. In the decoupling limit, that is to say, when and , the couplings of the SM are recovered.

3. The Decay Widths of in the Model

In this section we present the new decay widths of the boson [28, 52–54] in the context of the model which we need in the calculation of the cross section for the process . The partial decay widths involving vector bosons and the scalar boson arewhereThe vacuum expectation value is taken as TeV, while for the Higgs mixing parameter in correspondence with [1, 2, 48, 55]. In our analysis we take GeV and constrain the other scale, , by the lower bounds imposed on the mass of the extra neutral gauge boson . The mass of the and of the heavy neutrinos depends on and should be related to it, while the Higgs masses depend on the angle , the value of which is completely arbitrary.

Finally, the decay width of the boson to fermions is given bywhere is the color factor ( for leptons, for quarks) and the couplings and of the boson with the SM fermions are given in (14).

4. The Total Cross Section of in the Model

In this section, we calculate the Higgs production cross section via the process in the context of the model at future high-energy and high-luminosity linear electron-positron colliders, such as the ILC and CLIC.

The Feynman diagrams contributing to the process are shown in Figure 1. The expressions for the total cross section of the Higgs-strahlung process for the different contributions, that is to say SM, , and SM − (), respectively, can be written in the following compact form:whereis the usual two-particle phase space function, while , , , , , and are given in (13), (14), and (16), respectively.

The expression given in the first term of (18) corresponds to the cross section with the exchange of the boson, while the second and third terms come from the contributions of the model and of the interference, respectively. The SM expression for the cross section of the reaction can be obtained in the decoupling limit, that is to say, when and ; in this case the terms that depend on and in (18) are zero and (18) is reduced to the expression given in [39, 43] for the standard model.

5. Results and Conclusions

5.1. Resonance and Associated Production in the Model

In this section we evaluate the total cross section of the Higgs-strahlung process in the context of the model at next generation linear colliders such as the ILC and CLIC. Using the following values for numerical computation [51], , MeV, GeV, GeV, GeV, GeV, GeV, and , and considering the most recent limit from LEP [56]in our numerical analysis, we obtain the total cross section . Thus, in our numerical computation, we will assume , and as free parameters.

We do not consider the process [35] in our study since in major parts of the model parameter space the Higgs boson is quite heavy, and it is difficult to detect the process when the relevant mechanism is .

In Figures 2 and 3 we present the total decay width of the boson as a function of and the new gauge coupling , respectively, with the other parameters held fixed to three different values. From Figure 2, we see that the total width of the new gauge boson varies from a few to hundreds of over a mass range of , depending on the value of . In the case of Figure 3, a similar behavior is obtained in the range and depends on the value of . The branching ratios versus mass are given in Figure 4 for different channels, that is to say, , , and , respectively. In this figure the is the sum of all BRs for the decays into fermions. We consider , , and .

To illustrate our results on the sensitivity of the gauge boson of the model as a Higgs boson factory through the Higgs-strahlung process , including both the resonant and the nonresonant effects at future high-energy and high-luminosity linear colliders, such as the International Linear Collider (ILC) and the Compact Linear Collider (CLIC), we present the total cross section in Figures 5–11.

(a)

(b)

In Figure 5, we show the cross section for the different contributions as a function of the center-of-mass energy for and : the solid line corresponds to the first term of (18), where in the model the couplings and of the SM gauge boson to electrons receive contributions of the model. The dashed line corresponds to the second term of (18), that is to say, is the pure contribution. Finally, the dot-dashed line corresponds to the total cross section of the process . From Figure 5, we can see that the cross section corresponding to the first term of (18) decreases for large , whereas, in the case of the cross section of the model and the total cross section, respectively, these are increased for large values of the center-of-mass energy, reaching its maximum value at the resonance boson; that is to say, .

To see the effects of , the free parameter of the model on the process , we plot the relative correction as a function of for and in Figure 6. We can see that the relative correction reaches its maximum value between and remains almost constant as increases.

The deviation of the cross section in our model from the SM one is depicted in Figure 7 as a function of for and three values of the , new gauge coupling. Figure 7 shows that the relative correction is very sensitive to the gauge boson mass and for the gauge parameter the peak of the total cross section emerges when the heavy gauge boson mass approximately equals , respectively. Thus, in a sizeable parameter region of the model, the new heavy gauge boson can produce a significant signal, which can be detected in future ILC and CLIC experiments.

We plot the total cross section of the reaction in Figure 8 as a function of the center-of-mass energy, for the values of the heavy gauge boson mass of and , , respectively. In this figure we observed that, for , the resonant effect dominates the Higgs particle production. A similar analysis was performed in Figure 9, but in this case and . In both figures we show that the cross section is sensitive to the free parameters. Comparing Figures 8 and 9, we observe that the height of the resonances is the same in both figures, but the resonances are broader for larger values, as the total width of the boson increases with , as it is shown in Figure 2.

Finally, in Figure 10 we use the currents values of and , as well as the value of the coupling constant and center-of-mass energy of the collider to obtain contour plot 3D for the total cross section of the process for and . In this figure the resonance peaks for the boson are evident for the entire range of allowed parameters of the model.

From Figures 5–10, it is clear that the total cross section is sensitive to the value of the gauge boson mass , center-of-mass energy , and ; the new gauge coupling increases with the collider energy, reaching a maximum at the resonance of the gauge boson. As an indicator of the order of magnitude, we present the number of events in Table 1, for several gauge boson masses, center-of-mass energies, and values and for a luminosity of . We find that the possibility of observing the process is very promising as shown in Table 1, and it would be possible to perform precision measurements for both the and the Higgs boson in the future high-energy linear colliders experiments. We observed in Table 1 that the cross section rises once the threshold for production is reached, with the energy, until the is produced resonantly at , , and 2500 GeV, respectively, for the three cases. Afterwards it decreases with rising energy due to the and propagators. Another promising production mode for studying the boson and Higgs boson properties is [57].

5.2. The Higgs Signal Strengths in the Model

Considering the Higgs boson decay channels, the Higgs signal strengths can be defined aswhere denotes a possible final state of the Higgs boson decay, for example, , and .

Fixing the Higgs boson mass to the measured value and considering the decays , , , , and , the ATLAS collaboration reports [58] a signal strength ofThe corresponding CMS collaboration result [59] isGood consistency is found, for both experiments, across different decay modes and analyses categories related to different production modes.

In the model, the modifications of the (the SM fermions pair) and couplings can give the extra contributions to the Higgs boson production processes. On the other hand, the loop-induced couplings, such as and , could also be affected. Finally, besides the effects already seen in the Higgs-strahlung channel due to the couplings equations (13) and (14) and the functions given by (16), the exchange of -channel heavy neutral gauge boson also affected the production cross section. All effects can modify the signal strengths in a way that may be detectable at the future ILC/CLIC experiments.

In Figure 11, we show the dependence of the Higgs signal strengths on the parameters and for the Higgs-strahlung process , where (a) and (b) denote the Higgs signal strengths and , respectively.

Using for the mixing angle and for the Higgs boson mass, the following bound on the signal strength is obtained:which is consistent with that obtained for the ATLAS [58] and CMS [59] collaborations, (22) and (23), respectively.

In conclusion, we consider the heavy gauge boson of the model as a Higgs boson factory, through the Higgs-strahlung process . We find that the future linear colliders experiments such as the ILC and CLIC could test the model by measuring the cross section of the process , and it would be possible to perform precision measurements of the gauge boson and of the Higgs boson, as well as of the parameters of the model and , complementing other studies on the model and on the Higgs-strahlung process. The SM expression for the cross section of the reaction can be obtained in the decoupling limit; that is to say, when and , in this case the terms that depend on and in (18) are zero and (18) is reduced to the expression given in [39, 43] for the standard model. We also studied the dependence of the Higgs signal strengths on the parameters and of the model for the Higgs-stralung process . We obtain a bound on , which is consistent with that obtained for the ATLAS [58] and CMS [59] collaborations. In addition, the analytical and numerical results for the total cross section have never been reported in the literature before and could be of relevance for the scientific community.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The authors acknowledge support from CONACyT, SNI, PROMEP, and PIFI (Mexico).

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Copyright © 2015 A. Gutiérrez-Rodríguez and M. A. Hernández-Ruíz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

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