Non-renormalizable Yukawa Interactions and Higgs Physics

We explore a scenario in the Standard Model in which dimension four Yukawa couplings are either forbidden by a symmetry, or happen to be very tiny, and the Yukawa interactions are dominated by effective dimension six interactions. In this case, the Higgs interactions to the fermions are enhanced in a large way, whereas its interaction with the gauge bosons remains the same as in the Standard Model. In hadron colliders, Higgs boson production via gluon gluon fusion increases by a factor of nine. Higgs decay widths to fermion anti-fermion pairs also increase by the same factor, whereas the decay widths to photon photon and gamma Z are reduced. Current Tevatron exclusion range for the Higgs mass increases to ~ 142-200 GeV in our scenario, and new physics must appear at a scale below a TeV.

The Standard Model (SM) based on the gauge symmetry SU (3) C × SU (2) L × U (1) Y is in excellent agreement with all the current experimental results. However, there are sectors of the SM which are still untested, such as the Higgs sector and the Yukawa sector. In the SM, we have only one Higgs doublet, and we allow the Higgs self interactions up to dimension four to maintain the renormalizability of the theory. In this case, the cubic (h 3 ) and the quartic (h 4 ) interactions of the remaining neutral scalar Higgs field, h is determined in terms of the Higgs mass, M h and the known vacuum expectation value (VEV), v. Although we know v experimentally to a very good accuracy, the Higgs mass is still unknown. Hence its presence, as well as the magnitude of its cubic and quartic self interactions are completely untested. The other untested sector of the SM is the Yukawa sector. In the SM, we introduce dimension four Yukawa interactions which give masses to the fermions, and also generate the Yukawa interactions between the Higgs field h and the fermions. The strength of these Yukawa interactions are completely determined in terms of the fermion masses and v. However, we do not have any experimental evidence for these interactions being the source of the fermion masses, and the presence of these dimension four Yukawa interactions. Another point to emphasize is that we do not know whether the Higgs boson is elementary or composite. Theories have been formulated in which the Higgs boson is a fermion anti-fermion composite; or more specifically a condensate of the third family quark and anti-quark [1]. Other possibilities for composite Higgs have also been advocated [2,3]. Whether the Higgs boson is an elementary particle or composite, the operators of dimension higher than four suppressed by some scale, M are expected. It has also been pointed out that the presence of dimension six operator in the Higgs potential allows us to have baryogenesis via sphaleron [4], still satisfying the current LEP limit on the Higgs mass.
In this letter, we propose an alternate scenario for the Yukawa sector, and explore how to test our predictions experimentally at the Tevatron and LHC. The effects of general dimension six operators in the Higgs sector have been considered and studied before [5]. Also other dimension six operators may appear in SM and a complete list of such operators is collected in Ref. [6]. We consider the case in which the usual dimension four Yukawa interactions are either forbidden by a symmetry, or the corresponding coupling happens to be too tiny to generate the observed values of the fermion masses. In this case, the dominant contribution to the fermion masses, as well as the interactions between the fermions and the Higgs boson will arise from the dimension six effective Yukawa interactions of the form (f /M 2 )ψ L ψ R H(H † H), where M is the mass scale for the new physics through which such effective interactions are generated. As in the SM, fermion masses are still parameters in the theory, but the Yukawa couplings of the fermions to the Higgs boson are a factor of three larger than the SM. This enhances the production of the Higgs boson, as well as affect its decay branching ratios to various final states. This will have interesting consequences for Higgs signals at the Tevatron and LHC, as well as in the possible future lepton collider.
Our model is based on the SM gauge symmetry, We denote the left handed electroweak (EW) quark doublets by q Li ≡ (u, d) T Li , and the right handed EW quark singlets by u Ri and d Ri , where the index i (i = 1, 2, 3) represent three fermion families. Then the Yukawa interactions of the fermions with the Higgs boson up to dimension six are given by where the fermion fields represent three families, and f d , f u and f l represent three corresponding Yukawa coupling matrices for the dimension four Yukawa interaction while y d , y u and y l represent three corresponding Yukawa coupling matrices for the dimension six Yukawa interactions. M is the mass scale for a new physics which generates these dimension six interactions. Our proposed scenario is the case in which the dimension four Yukawa couplings, f d , f u and f l are either forbidden by a symmetry, or happen to be very tiny to generate the observed fermion masses, and this sector is dominated by dimension six interactions given above. Thus, choosing the couplings f to be zero, for the fermion mass and the Yukawa coupling matrices, we obtain and similar expressions for the up quark and lepton sec-tor. In contrast, in the usual SM, where we do not include the effective dimension six interactions, we have In our scenario, one can see from Eq. 2 that the mass matrices and the corresponding Yukawa coupling matrices are proportional. Hence as in the usual SM, we do not have any Higgs mediated flavor changing neutral current interactions. The important point to note is that in our scenario (for simplicity, we call it the new model), the Yukawa couplings of the Higgs boson to the fermions are three times larger than those in the SM, whereas the gauge interaction of the Higgs boson remains the same. This will make important differences for Higgs production, and its decay branching ratios as we discuss below. Branching Ratio  In the low Higgs mass range (M h ≤ 125 GeV), the Higgs boson dominantly decays to bb in the SM. This mode is even more dominant in the new model, since the hbb coupling is enhanced by a factor of three compared to the SM. In the SM, the bb to W W crossover takes place at M h ∼ 135 GeV (see fig. 1a), while in our model, this crossover happens at M h ∼ 155 GeV, (see fig. 1b). Also, as can be seen from these figures, the γγ branching fraction in our model is suppressed by about a factor of ten compared to the SM. milab Tevatron. For the SM Higgs boson, recent combined analysis by the CDF and D0 collaborations (using 6.7 f b −1 of data) has excluded the SM Higgs mass range from 158 to 175 GeV at 95% confidence level (C.L.) [8,9]. The dominant production mechanism for the Higgs boson is gluon gluon fusion via the top quark loop. Since in our model, the coupling of the Higgs to the top quark is three times larger, the Higgs production cross sections will be nine times larger than the SM. Higgs production via the gauge interactions to W h and Zh in our model remains the same as in the SM. Combined Tevatron analysis includes the Higgs signals for all channels, and the corresponding backgrounds. Their experimental curve for the observation of the Higgs signals at 95% C.L. over the SM expectation curve as a function of the Higgs mass is shown by the solid curve in fig. 2 [9]. The corresponding SM expectation is shown by the horizontal dash-dotted line. As shown by the Tevatron analysis (solid curve), the SM Higgs mass in the range of 158−175 GeV is excluded. The corresponding exclusion in the low mass range is M h ≥ 109 GeV which falls short of the LEP exclusion of M h ≥ 114.4 GeV [10]. To apply this combined CDF-D0 analysis to our model, we have calculated the σ pp→h × BR(h → all) included by the Tevatron, and compared those with the SM. The dashed curve in fig. 2 shows our results for the ratio of the σ pp→h ×BR(h → all) in our model to the σ pp→h × BR(h → all) in the SM as a function of the Higgs mass. The intersection of the dashed curve with the solid curve indicates an estimate of the Higgs mass range (M h 142 GeV) that would be excluded by the present Tevatron analysis in our model.
In the low Higgs mass range, the lower exclusion range increases slightly from M h > 109 GeV in the SM to M h > 112 GeV in our model. As the Tevatron luminosity accumulates further, its increased sensitivity to our model will help it study a bigger mass range of the Higgs boson than in the SM. Also, we note that for light Higgs (M h < 130 GeV), the width of the Higgs boson in our model is larger by a factor of 9 compared to the SM. This can be tested in a possible future muon or e + e − collider.
At the LHC, in the SM for large Higgs mass, M h > 150 GeV, the most promising signals to observe the Higgs boson is via its dominant production through gluon gluon fusion (or W W fusion), and then its subsequent decays to W W or ZZ. In our model, since the dominant Higgs productions via gluon gluon fusion is nine times larger, the Higgs signals will be much stronger. The expectation for the Higgs signals in few of the relevant modes in our model is shown in fig. 3 (solid curve), and are compared with the SM expectations (dash-dotted curves) at the LHC for √ s = 7 TeV. Note that the cross section times the branching ratio of h → W W in our model is larger than the SM by a factor of ∼ 3 − 9 for the Higgs mass range of 150 − 200 GeV. The same is true for the ZZ mode. For the low mass range of the Higgs boson, M h ∼ 115 − 130 GeV, the γγ mode is the most promising in the SM. In our model though, as shown in fig. 3, the signal for the γγ mode is reduced by a factor of ∼ 3 − 5 compared to the SM. However, the signal in the τ τ mode is enhanced almost by a factor of nine. Thus in our model, signal in the τ τ mode may be observable at the LHC for the low Higgs mass range with good τ ID for the ATLAS and CMS detectors. Inclusion of dimension six operators in the Yukawa sector also leads to enhancement in the other modes of Higgs production at colliders. The associated production of a Higgs boson with a heavy quark pair (e.g. tth) is enhanced by a factor of 9. The increased event rate would help in improving the sensitivity for the top-Yukawa coupling in this channel at LHC [11,12]. Another important implication of our model is on double Higgs production at the LHC which can probe the triple Higgs vertex in SM. In the SM, double Higgs production at LHC proceeds through gluon gluon fusion at one-loop level through the top quark dominated triangle and box diagrams [13][14][15]. Due to additional contributions coming from the terms involving the dimension six operators, there is an enhancement in all the vertices involving the Higgs boson in our model. The box contribution is enhanced by a factor of 9 in its amplitude because of two Yukawa vertices, while the triangle contribution is enhanced by a factor of 5, after combining the new Yukawa and triple Higgs vertices (arising from the Higgs potential where we neglect the dimension 4 operator). There is an additional contribution to the amplitude through a new interaction term (f L f R h 2 ) with a coupling strength of ( ) where m f is the mass of the fermion which leads to a large enhancement of the double Higgs production cross section at LHC. The analytical formula for the double Higgs production in SM can be found in Ref. [14,15]. To put our results in context we can rewrite the contributions in our model as We plot the double Higgs production cross section 1 as a function of the Higgs mass in fig. 4 for both the SM as well as our model. Although Eq. 4 shows a large enhancement in the individual contributions, there still is large cancelation between the box and triangle contributions and so the enhancement in the cross section compared to the SM is only at the level of a factor of ∼ 10 for low Higgs masses as shown in fig. 4 which increases as we go higher in the Higgs mass. Nevertheless it is a substantial increase for the light Higgs mass range and gives a cross section of around ∼ 300 fb at LHC with √ s = 14 TeV and ∼ 40 fb with √ s = 7 TeV, respectively for M h ≤ 220 GeV. This can give large enough event rates to study the double Higgs production at LHC.
Finally, let us comment on the scale of new physics, M . Up to dimension six, we can write the Higgs potential as Choosing λ to be zero, the condition for the global minima gives Using the LEP bound for the Higgs mass, M h > 114 GeV, from Eq. 5, we obtain M ≤ 1 TeV. Note the interesting see-saw type relation between the M h and M in Eq. 6. Thus if our point of view is correct, we expect the new physics to appear below the TeV scale.
We are grateful to A. Khanov of the D0 collaboration for many helpful discussions, especially regarding the combined CDF-D0 Higgs mass exclusion ranges in the SM and in our new model. This work is supported in part by the United States Department of Energy, Grant Numbers DE-FG02-04ER41306 and DE-FG02-04ER46140.