The Randall-Sundrum model with all Standard Model (SM) fields in the bulk,
including the Higgs, can be probed by precision measurements at the ILC. In
particular, the couplings of the Higgs to the gauge bosons of the SM can be
determined with high accuracy at the ILC. Here we examine the deviations in
these couplings from their SM values within the framework of the Universal
Randall-Sundrum Model (URSM) as well as the corresponding couplings of the
first Higgs Kaluza-Klein excitation.Comment: 3 pages, 2 figs, contributed to the 2005 ALCPG and ILC Workshops,
  Snowmass, CO, 8/14-8/27 2005; small typos remove

Davoudiasl, H.

Lillie, B.

Rizzo, T. G.

English

arXiv

The Randall-Sundrum model with all Standard Model (SM) fields in the bulk, including the Higgs, can be probed by precision measurements at the ILC. In particular, the couplings of the Higgs to the gauge bosons of the SM can be determined with high accuracy at the ILC. Here we examine the deviations in these couplings from their SM values within the framework of the Universal Randall-Sundrum Model (URSM) as well as the corresponding couplings of the first Higgs Kaluza-Klein excitation

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Work supported in part by Department of Energy contract DE-AC02-76SF00515MADPH-05-1441SLAC-PUB-11472Probing the Universal Randall-Sundrum Model at the ILCH. DavoudiaslDept. of Physics, University of Wisconsin, Madison, WI, 53706,USAB. Lillie and T. G. RizzoSLAC, Stanford, CA 94025, USAThe Randall-Sundrum model with all Standard Model (SM) fields in the bulk, including the Higgs, can be probed byprecision measurements at the ILC. In particular, the couplings of the Higgs to the gauge bosons of the SM can bedetermined with high accuracy at the ILC. Here we examine the deviations in these couplings from their SM valueswithin the framework of the Universal Randall-Sundrum Model (URSM) as well as the corresponding couplings of thefirst Higgs Kaluza-Klein excitation.The Randall-Sundrum (RS) model provides an interesting explanation of the hierarchy problem[1]. In the originalRS model, the only 5-d ﬁeld is the graviton. Since that time numerous works have extended the RS setup to includebulk fermions and gauge ﬁelds[2]. However, even though the SM can be promoted to a 5-d theory, the fundamentalHiggs ﬁeld responsible for electroweak symmetry breaking (EWSB) has been kept on the TeV-brane. The reasonfor this has been to avoid problems associated with extreme ﬁne-tuning and conﬂict with known experimental data.There have also been attempts to build RS models without fundamental Higgs bosons where the role of the Higgsdoublet as a source of Goldstone bosons is played by the ﬁfth components of the gauge ﬁelds themselves.We have recently shown[2] that by appropriate choices of the Higgs sector parameters in the bulk and on boththe TeV and Planck branes, one can generate a single tachyonic Kaluza-Klein (KK) mode of the Higgs ﬁeld in thelow energy 4-d theory. This tachyonic mode can be identiﬁed as the SM Higgs ﬁeld. Given a quartic bulk term forthe Higgs, the tachyonic mode will lead to the usual 4-d Higgs mechanism and endow the electroweak gauge bosonswith mass. A particularly interesting realization of this “Oﬀ-the-Wall” Higgs EWSB employs the gravitational sectorof the RS model to provide the necessary bulk and brane mass scales. These scales are then related to the 5-dcurvature of the RS geometry. Consequently, new relations and constraints among the parameters of the Higgs andgravitational sectors are obtained. In this gravity-induced EWSB scenario, the higher curvature Gauss-Bonnet termsplay an important role. Typical generic signatures of our scenario are the emergence of a tower of Higgs KK modesas well as a modiﬁcation of the WWH coupling which can be directly probed through precision measurements atthe ILC.In order to understand the basic model let us focus on the free Higgs case (i.e., ignoring gauge and self-couplingsas well as other particles such as the Goldstone bosons) which involves only the various mass terms. Studying thistruncated action for the free Higgs ﬁeld allows us to perform the KK decomposition φ→∑n φn(x)χn(y) = φTχT + ...where χT is the wavefunction for the tachyon and represents the shape of the Higgs vev proﬁle in the bulk. We haveStrunc =∫d5x√−g[(∂Aφ)†(∂Aφ) −m2φ†φ + 1kφ†φ [µ2P δ(y)− µ2Hδ(y − πrc)]]. (1)To scale out dimensional factors we deﬁne m2 = 20k2ξ and µ2P,H = 16k2ξβP,H since k is the canonical scale for RSmasses. Recall that the RS metric is given by ds2 = e−2k|y|ηµνdxµdxν −dy2 where we use −πrc ≤ y ≤ πrc as the 5-dcoordinate and k is the curvature parameter whose value is comparable to that of the fundamental scale M . Notethat the parameters ξ, βP,H are dimensionless and are expected to be O(1) but may, in principle, be of arbitrary sign.What we looking for in the (ξ, βP,H) parameter space is to obtain EWSB in a manner consistent with the SM; ourbasic criterion is to ﬁnd regions where there exists one, and only one, TeV scale tachyonic mode that we can identifyContributed to 2005 International Linear Collider Physics and Detector Workshop and 2nd ILC Accelerator Workshop, 8/14/2005-8/27/2005, Snowmass , CO, USAwith the SM Higgs. The remaining Higgs KK tower ﬁelds must also be normal, i.e., non-tachyonic. To this end wesolve the equation of motion for the Higgs KK wavefunctions:∂y(e−4k|y|∂yχn)−m2e−4k|y|χn + 1ke−4σ[µ2P δ(y)− µ2Hδ(y − πrc)]χn + m2ne−2k|y|χn = 0 , (2)and apply the appropriate boundary conditions on both the TeV and Planck branes[2]; one can show that βP playsno essential role in the solutions of interest to us. We ﬁnd that if the combination ξβH > 0 then either no tachyonexists or that the resulting Higgs vev is Planck scale. Clearly, we must instead choose the parameters such thatξβH < 0. In this case their are two remaining regions: (I)ξ > 0, βH < 0 or (II)ξ < 0, βH > 0. Furthermore, weﬁnd that within both of these regions further constraints on the parameters must apply in order that a tachyon rootexist: ξ ≥ (≤)ξ1,2 in region I(II). ξ1,2 are given by the expressions ξ1 = − 14βH and ξ2 =5−8βH16β2H. We note that regionII is favored by the “gravity-induced” EWSB mechanism since in that region it is easy to avoid ghosts in the radionand graviton sectors. Clearly the detailed nature of the solutions for the bulk Higgs proﬁle χT will depend on theparticular values of the parameters ξ, βH . One ﬁnds that the Higgs proﬁle is highly peaked near the TeV brane,χT ∼ e(2+ν)k|y| where ν2 = 4+ 20ξ. The masses of the Higgs boson and its KK excitations are found to be given bythe roots, xn, of a transcendental equation involving Bessel functions of order ν and depend on the values of both ξand βH .Let us now turn to the gauge boson couplings of the Higgs in URSM. In the SM the W boson gets its mass directlyfrom the vev of the Higgs boson. In the case of the URSM, the W has an additional, geometric, mass source arisingsolely from back reaction, i.e., wavefunction curvature. This implies that the HWW (and, hence, HZZ) couplingwill be somewhat smaller than that obtained in the SM. The relevant coupling can be expressed as an integral overy:Seff =∫d4x HW †µWµ 14πrcg2v∫dy e−2k|y|χ2T f20 , (3)where v is the Higgs vev, g is the usual 4-d coupling assuming that the light SM fermions are localized near thePlanck brane, and f0(y) is the W = W0 boson KK wavefunction. (It is important to note at this point that v neednot be vSM  246 GeV.) These are obtained by KK expanding the 5-d W ﬁeld W =∑n Wn(x)fn(y) and solvingthe mode equation∂y(e−2k|y|∂yfn)− 14g25v2χ2T e−2k|y|fn + m2nfn = 0 , (4)where g5 = g/√2πrc is the 5-d SU(2)L gauge coupling, with suitable boundary conditions. In this language the Wboson mass is given byM2W =18πrcg2v2∫dy e−2k|y|f20χ2T +∫dy e−2k|y|(∂yf0)2 . (5)How do the WWH couplings in the URSM compare to their SM values, i.e., what are ratios gWWH/gSMWWH as wescan over the ξ−βH parameters in the two regions? The results of such a scan are shown in Fig. 1 for both regions Iand II in units of v/vSM which we expect to be O(1); these results have been subjected to the additional requirementthat the tachyon root, xT , satisfy the bound xT < 2 so that the resulting Higgs mass lies below a TeV and, hence, isvisible at LHC/ILC. Here we see that results in the two regions are quite diﬀerent with much larger deviations fromthe SM seen in region I. It is important to note that not only are these deviations signiﬁcant but they are restrictedto a rather unique, narrow ranges in either region. With precision measurements at the ILC these predictions can bedirectly tested. The ratio v/vSM itself can be independently determined by combining the Higgs mass measurementwith that of the 4-d quartic coupling via the relation λ4d = m2H/(2v2). The ﬁrst KK Higgs excitation may be lightenough to be produced at a 1 TeV ILC so that it is important to examine these couplings as well which can beobtained in a manner similar to the above. The corresponding results can be seen in Fig. 2 for both regions wherewe see the previous pattern repeated. The reduced values of these couplings will lead to a substantial reduction inthe production cross section for this state making it diﬃcult to produce at LHC/ILC. 0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0  0.5  1  1.5  2  2.5g WWH/gWWH,SMξ 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7-0.2 -0.195 -0.19 -0.185 -0.18 -0.175 -0.17g WWH/gWWH,SMξFigure 1: Values of the coupling ratio gWWH/gSMWWH in regions I (left) and II (right) as functions of ξ for various βH . In regionI, from top from top to bottom, the curves correspond to βH = 1.4, 1.6, 1.8, 2.0. A cut on the Higgs boson mass as describedin the text has been imposed. 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0  0.5  1  1.5  2  2.5g WWH1 /gWWH,SMξ 0.125 0.13 0.135 0.14 0.145 0.15-0.2 -0.195 -0.19 -0.185 -0.18 -0.175 -0.17g WWH1 /gWWH,SMξFigure 2: Same as the previous figure but now for the first Higgs KK excitation.In the “gravity-induced” version of the URSM there are additional predictions which may be testable at the ILC.In this framework the parameter ξ controls the size of Higgs-radion mixing which is now directly correlated with theHWW coupling in the weak eigenstate basis. Measurements of radion properties will provide further tests of theURSM scenario.AcknowledgmentsThe authors wish to thank the Aspen Center of Physics for their hospitality. Work supported by Department ofEnergy contracts DE-AC02-76SF0051 and DE-FG02-95ER40896.References[1] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) [arXiv:hep-ph/9905221].[2] For details of the present work and original references, see H. Davoudiasl, B. Lillie and T. G. Rizzo, arXiv:hep-ph/0508279.

Probing the Universal Randall-Sundrum Model at the ILC

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Probing the Universal Randall-Sundrum Model at the ILC

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