Fermiophobia in a Higgs triplet model
16
0
0
Texto completo
(2) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). Higgs Triplet Model and in Sec. III the scenario of fermiophobia with Majoron suppression is described. In Sec. IV the decays of the fermiophobic Higgs boson are discussed, with phenomenology studied in Sec. V. Conclusions are contained in Sec VI. II. HIGGS TRIPLET MODEL The Higgs triplet model (HTM) which we will study [9] includes a complex triplet Higgs field with lepton number L ¼ 2 and hypercharge Y ¼ 2, a complex doublet Higgs field , with lepton number L ¼ 0 and hypercharge Y ¼ 1, pffiffiffi # " " 0# 0 þ = 2 ¼ ; ¼ ; (1) pffiffiffi þ þþ = 2 and a complex singlet Higgs field , with lepton number L ¼ 2 and hypercharge Y ¼ 0. The model without the singlet field has received much attention recently [10], and we note the phenomenology of the charged scalars (doubly and singly) at the LHC is essentially identical in both models. A. Higgs potential and mass spectrum The scalar potential can be written as follows: Vð; ; Þ ¼ 21 y þ 22 y þ 23 trðy Þ þ 1 ðy Þ2 þ 2 ½trðy Þ2 þ 3 y trðy Þ þ 4 trðy y Þ þ 5 ðy y Þ þ 1 ðy Þ2 þ 2 ðy Þðy Þ þ 3 trðy Þy ðT þ H:c:Þ;. (2). where 2i , i ¼ 1, 2, 3, are mass squared parameters, i , i ¼ 1; . . . ; 5 are dimensionless couplings not related to the singlet, i , i ¼ 1, 2, 3. are dimensionless couplings related to the singlet, and is a dimensionless coupling that mixes all three Higgs fields. The electroweak symmetry is spontaneously broken when the neutral components of the Higgs fields acquire 2 6 6 M2R ¼ 6 4. vacuum expectation values vi , i ¼ 1, 2, 3. We shift the Higgs fields in the following way, v R þ iI ¼ p1ffiffiffi þ 1 pffiffiffi 1 2 2 v R þ iI 0 ¼ p3ffiffiffi þ 3 pffiffiffi 3 ; 2 2. v R þ iI 0 ¼ p2ffiffiffi þ 2 pffiffiffi 2 2 2 (3). finding minimization conditions, or tree-level tadpole equations, given by Vlineal ¼ t1 R1 þ t2 R2 þ t3 R3 ¼ 0; where. 1 1 1 t1 ¼ v1 21 þ 1 v21 þ 2 v22 þ 3 v23 v3 v22 2 2 2 1 1 t2 ¼ v2 22 þ 1 v22 þ 3 v23 þ 5 v23 2 2 1 1 þ 2 v21 v1 v3 2 2 1 1 1 t3 ¼ v3 23 þ 2 v23 þ 3 v22 þ 4 v23 þ 5 v22 þ 3 v21 2 2 2 1 v1 v22 : (5) 2 In Ref. [9] cases, where different vacuum expectation values are equal to zero are analyzed, but these scenarios are not relevant for our purposes. In the following we assume all VEV’s are nonzero. The quadratic potential can be written as follows, 2 3 R1 6 7 1 26 Vquadratic ¼ ½R1 ;R2 ; R3 MR 4 R2 7 5 2 R3 2 3 I1 " þ# 6 7 1 26 7 2 þ ½I1 ;I2 ;I3 MI 4 I2 5 þ ½ ; Mþ 2 þ I3 þ m2þþ þþ :. (6). The CP-even neutral Higgs mass matrix is given by, 3. 21 v21 þ 12 v22 vv31 þ vt11. 2 v1 v2 v2 v3. 3 v1 v3 12 v22. 2 v1 v2 v2 v3. 21 v22 þ vt22. ð3 þ 5 Þv2 v3 v1 v2. 3 v1 v3 . 1 2 2 v2. (4). ð3 þ 5 Þv2 v3 v1 v2. 2ð2 þ. 4 Þv23. þ. 1 2 v1 2 v2 v3. þ. t3 v3. 7 7 7 5;. (7). where we have eliminated the mass parameters 2i using the tadpole equations. This mass matrix is diagonalized by an orthogonal matrix OR , which can be parametrized with three angles, 2. 1. 0. 0. 32. c13 0 s13. 32. c12 s12 0. 3. 2. c13 c12. c13 s12. s13. 3. 76 76 7 7 6 6 OR ¼ 6 56 56 5; 5¼6 4 0 c23 s23 7 4 0 1 0 7 4 c23 s12 s23 s13 c12 c23 c12 s23 s13 s12 s23 c13 7 4 s12 c12 0 7 0 s23 c23 s23 s12 c23 s13 c12 s23 c12 c23 s13 s12 c23 c13 s13 0 c13 0 0 1. 095003-2. (8).
(3) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. PHYSICAL REVIEW D 83, 095003 (2011). where s12 ¼ sin12 , c12 ¼ cos12 , and similarly for the other two angles 13 and 23 . The CP-odd neutral Higgs mass matrix is, 3 2 1 2 v3 t1 1 2 v2 v3 2 v2 v1 þ v1 2 v2 7 6 v2 v3 2v1 v3 þ vt22 v1 v2 7 7 6 M2I ¼ 6 5: (9) 4 t3 1 1 2 2 v1 v1 v2 2 v2 2 v2 v3 þ v3 Clearly, this mass matrix has two zero eigenvalues, of which one is unphysical and corresponds to the neutral Goldstone boson. The other one is physical and corresponds to the Majoron J. The third eigenvalue is the CP-odd neutral Higgs A, and has a mass given by v1 v22 v22 v3 m2A ¼ þ þ 4v1 v3 : (10) 2 v3 v1 As one can see, a value for 0 is essential in our model in order to have a massive CP-odd Higgs boson. In the limit ! 0 the CP-odd mass matrix has three zero eigenvalues; one of them is unphysical and the other two are related to spontaneously broken symmetries. To identify them, let us concentrate on the scalar potential in Eq. (2). All the terms, with the exception of the one proportional to , are invariant under global symmetries which we could call triplet and singlet number (T and S). If this is true, also conserved are the symmetries T S and T þ S, where we can identify the last one with lepton number. The term proportional to conserves lepton number, but not T-S. When the term is present, the spontaneously broken lepton number produces one Majoron. When the term is absent from the potential, the spontaneous breaking of both symmetries, lepton number and T-S, produces two massless physical states. This latter case is experimentally ruled out because only one of those Majorons will be mainly singlet and therefore safe. Consequently, it will be not possible to avoid a large contribution to the invisible Z decay width by the other one. In this article we work with 0. The charged Higgs mass matrix, given by pffiffiffi # " 2v3 =v2 2 1 1 2 Mþ ¼ v1 v2 5 v2 v3 (11) pffiffiffi 2 2 2 v2 =v3 also has a zero eigenvalue, corresponding to the charged Goldstone boson. It is diagonalized by an orthogonal matrix Oþ such that Oþ M2þ OTþ ¼ diagðm2Hþ ; 0Þ. The rotation matrix is " # " pffiffiffi # cþ sþ 2v3 v2 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; (12) Oþ ¼ pffiffiffi sþ cþ 2v3 v2 þ 2v2 v2 2. 3. where sþ ¼ sinþ , cþ ¼ cosþ , and þ is the angle of rotation. The massive eigenvalue is the singly-charged Higgs boson, with a mass 1 v 1 m2Hþ ¼ 1 5 ðv22 þ 2v23 Þ: (13) 2 v3 2. Finally, the doubly-charged Higgs boson has the following mass 1 v v2 1 m2þþ ¼ 1 2 5 v22 4 v23 : 2 v3 2. (14). B. Gauge sector The kinetic terms of the Higgs fields are L kinetic ¼ ðD Þy ðD Þ þ Tr½ðD Þy ðD Þ þ @ y @ ;. (15). where the covariant derivatives can be written as 1 D ¼ @ þ igTa Wa þ i g0 YB ; 2. (16). where the action of the isospin and hypercharge operators T and Y on the Higgs doublet and triplet is 1 ; 2 a Y ¼ ;. Ta ¼. 1 2 Y ¼ 2:. Ta ¼ . a. 1 2. a. (17). Gauge bosons receive contributions to their masses from the the doublet and triplet. After these scalar fields acquire vacuum expectation values, we find 1 m2W ¼ g2 ðv22 þ 2v23 Þ; 4. 1 m2Z ¼ ðg2 þ g02 Þðv22 þ 4v23 Þ; (18) 4. which leads to the following -parameter at tree level ¼1. v22. 2v23 : þ 4v23. (19). The experimental measurement of is given by ¼ þ0:0007 1:0002 0:0004 , and this restricts the value of the triplet VEV to be smaller than a few GeV. Nevertheless, in order to satisfy stringent bounds from astrophysics, we will work with v3 < 0:35 GeV [9]. From Eq. (10) we see that the small value for v3 implies in turn a small value for the coupling in order to have a CP-odd Higgs mass mA below 1 TeV. Another consequence of the small value for v3 is that the vacuum expectation value of the Higgs doublet v2 will be very close to 246 GeV, as indicated by the masses of the gauge bosons in Eq. (18). III. FERMIOPHOBIA AND MAJORON SUPPRESSION Fermiophobia was first introduced in [12], where it was stressed that the mechanism for the generation of fermion masses could be independent of the mechanism for the generation of the masses of the gauge bosons (e.g., a 2HDM in which the fermions receive mass from just one vacuum expectation value, while the gauge bosons receive mass from both).. 095003-3.
(4) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). We investigate the possibility that the lightest CP-even Higgs boson is fermiophobic, in which case the conven þ , are suppressed. In tional decay modes, H10 ! bb, addition, we study the singlet content of this Higgs boson, looking for cases in which the fermiophobic Higgs has a suppressed mixing with the singlet field, a situation which we call ‘‘Majoron suppression’’. If the fermiophobic Higgs has a large mixing with the singlet, it will decay mainly into two Majorons, which leads to a missing energy signature. In this paper we focus on signatures of fermiophobia which are visible in detectors. We start by doing a general scan of the parameter space as follows: 0:5 GeV < v1 < 1 TeV; 0 < < 0:1;. v2 ¼ 246 GeV;. j1;2;3 j < 4;. v3 < 0:35 GeV;. j1...5 j < 4:. TABLE II. Fraction of points in the general scan of the parameter space that are within a given region around the point of exact fermiophobia and Majoron suppression defined by jO13 R j ¼ 1. Min. jO13 R j value. 41.5% 41.0% 36.6% 27.8% 14.0%. 0.9 0.999 0.99999 0.999999 0.9999999. TABLE I. Fraction of points in the general scan of the parameter space that are within a given region around the point of exact fermiophobia defined by jO12 R j ¼ 0.. (20). Our aim is to see how large the parameter space is for fermiophobia and Majoron suppression for the lightest CP-even Higgs boson. In addition to Eq. (20), we respect the current experimental limits for the masses of A0 , H , and (mA > 90 GeV, mHþ > 80 GeV, mþþ > 136 GeV), and we also require 90 < mH1 < 300 GeV. In the left frame of Fig. 1 we show a frequency histogram from which one can see the values of the matrix element O12 R (see Eq. (8)), with no other restriction on the parameters in the Lagrangian, except for a correct minimization of the scalar potential. In this plot we see the rather unexpected result that a sharp maximum is obtained at O12 R ¼ 0, indicating a high concentration of points in the fermiophobic region. Therefore we conclude that fermiophobia is not a fine-tuned scenario in this model. In Table I we show the fraction of points from the general scan of the parameter space (defined by Eq. (20)) that lie in a given region around the exact fermiophobic point jO12 R j ¼ 0. Clearly it is not necessary to deviate too much from jO12 R j ¼ 0 in order to encapsulate an important number of the points in parameter space. In other words, the model has a ‘‘preference’’ for fermiophobia. The. Fraction of Scan. Fraction of Scan. Max. jO12 R j value. 45% 40% 30% 20% 10%. 0070 00086 00014 000056 000019. reason for this is that the CP-even neutral mass matrix in Eq. (7) has diagonal elements which are much larger than the nondiagonal elements in a large region of parameter space, making O12 R naturally small. This feature is present in our model due to both the hierarchy of the three vacuum expectation values and the smallness of the coupling. In the right frame of Fig. 1 we show a two-dimensional 12 frequency histogram in the plane O11 R -OR , within the same 11 scan as before. The peak around OR ¼ O12 R ¼ 0 (or equi¼ 1) corresponds to a fermiophobic Higgs valently O13 R with suppressed couplings to the Majoron, implying that the visible decay modes of this Higgs boson are not suppressed. The concentration of parameter space points around O13 R ¼ 1 is again due to the hierarchy of vacuum expectation values.. 10 4 10. 4. 10 10. 3. 3. 10 2 -1. 10. O11. 2. -1. -0.5. 0. 0.5. 1. O12. -0.5. 0. 0.5. 1. -1. -0.5. 0. 0.5. 1. O12. 11 12 FIG. 1 (color online). Frequency histogram for O12 R (left frame) and OR -OR (right frame) in a general scan of parameter space.. 095003-4.
(5) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. In Table II we display the fraction of points within a given region around the exact fermiophobic and Majoron suppressed case, defined by jO13 R j ¼ 1. It is surprising how little deviation from this point is necessary to find a large fraction of the scan points around the fermiophobic and Majoron suppressed situation, indicating that it is not a fine-tuned case in this model. A. Imposing fermiophobia in the CP-even Higgs Sector We are interested in the possibility of having a light CP-even neutral Higgs boson with suppressed couplings to fermions (fermiophobia). A light fermiophobic Higgs boson is characterized by O12 R ¼ c13 s12 ¼ 0, since it is mainly the Higgs doublet which couples to fermions (the triplet coupling to the fermions is suppressed). With the condition s12 ¼ 0 we find general fermiophobia. The diagonalizing matrix in this case is 2. c13. 0. s13. 3. 6 OR ¼ 6 4 s23 s13. c23. 7 s23 c13 7 5;. c23 s13. s23. c23 c13. (21). where corresponds to signðc12 Þ. The diagonalized CP-even Higgs mass matrix is given by ðM2R Þdiag ¼ OR M2R OTR , and implies the following consistency conditions, . s13 c13 M2R13 þ M2R33 c13 s13 s M2R12 ¼ 13 M2R23 c13 s s c 1 2 M2R22 ¼ 13 M2R13 23 23 M þ M2R33 ; c13 c23 s23 c13 R23 M2R11 ¼ . PHYSICAL REVIEW D 83, 095003 (2011). 1 1 v M2R11 v22 3 2 2 v1 2v1 1 ðM2R12 þ v2 v3 Þ 2 ¼ v1 v2 1 ¼. . 1 ¼. 1 M2 ; 2v22 R22. (22). v2 ¼ 246 GeV;. 0:5 GeV < v1 < 1 TeV; 0 < < 0:1; 12 ¼ 0;. j3 j < 4;. 0 < 13 < 2 ;. v3 < 0:35 GeV;. j2...5 j < 4; 0 < 23 < 2 ;. 1 m2Hþ m2A 5 v22 4. 1 m2þþ m2A 5 v22 : 2. (25). This indicates that the singly-charged Higgs boson mass lies in a narrower region than the doubly-charged Higgs mass, and this effect can be seen in the figures. Note that this implies (26). which is a very good approximation up to order Oðv3 Þ. The correlation between the CP-odd Higgs mass mA and the lightest CP-even Higgs mass mH1 seen in the right frame of Fig. 2 is explained by inspecting the CP-even Higgs boson mass matrix in Eq. (7), and the CP-odd mass in Eq. (10). Because of the hierarchy of VEV’s we see that. 350. 300. mA (GeV). 350. 250. (24). checking that 1 , 2 , and 1 have all an absolute value smaller than 4. In order to study the masses of the scalars in the pure fermiophobic limit, in Fig. 2 we show a scatter plot of mHþ and mþþ (left frame), and a scatter plot of mA and mH1 (right frame), resulting from the scan. The correlation between the singly- and doubly-charged Higgs boson masses is understood from the small value of the triplet VEV, which implies that the charged Higgs bosons satisfy. 400. 300. (23). with the above expressions found from Eq. (7). We do a scan of parameter space, imposing fermiophobia in the way just described. The free parameters are varied according to. 1 m2Hþ ðm2A þ m2þþ Þ; 2. which allow us to eliminate three parameters of the potential in favor of the three angles in Eq. (8). These three parameters are chosen as. mH ± (GeV). . 250. 200. 200 150 150 100 100 100. 150. 200. 250. 300. 350. 400. 450. 100. m∆±± (GeV). 150. 200. 250. 300. mh (GeV). FIG. 2 (color online). Charged Higgs and doubly-charged Higgs boson masses as a function of the fermiophobic Higgs mass.. 095003-5.
(6) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). ðM2R Þ33 m2A . v1 v22 m2H1 ; 2v3. 2v O13 þ v2 O12 ðh1 W þ W Þ R ¼ c2W 3 R13 4v3 OR þ v2 O12 ðh1 ZZÞ R. (27). where the last relation comes from the fact that most of the time the CP-even Higgs mass matrix is nearly diagonal, with the ðM2R Þ33 element being the smallest. Another point we wish to emphasize here is the relation between the couplings of the fermiophobic Higgs boson to charged scalars and to gauge bosons. In the left frame of Fig. 3 we show the relation between the couplings hf þþ and hf H þ H (see the appendix for Feynman rules), when we vary all parameters as indicated in Eq. (24). The couplings are clearly proportional to each other, as can be inferred from the Feynman rules, which in the fermiophobic case satisfy ðhf þþ Þ ¼ 1 þ Oðv3 Þ: ðhf H þ H Þ. (28). These couplings can have a magnitude as large as 4 TeV, although in most of the parameter space they are & 300 GeV. Similarly, in the right frame of Fig. 3 we plot the relation between the couplings hf W þ W and hf ZZ.. (29). and if we take the exact fermiophobic limit we get ðhf W þ W Þ 1 ! c2W ; ðhf ZZÞ 2. (30). which is half the value for a SM Higgs boson. This has implications that will be evaluated in the next sections. Note that this limit changes drastically with a small but nonzero value for O12 R . Notice also that the couplings hf W þ W and hf ZZ are much smaller in this fermiophobic limit than the equivalent SM couplings. Within the same scan of parameter space in the fermiophobic scenario given by Eq. (24) we explore in Fig. 4 the magnitude of couplings with and without a Majoron. In the left frame of Fig. 4 we have the relation between the ðhf ZJÞ and ðhf ZAÞ couplings. The ðhf ZAÞ coupling can be large, but it is not relevant for the decay of a fermiophobic Higgs, since mhf is rarely larger than mZ þ mA , as indicated in Fig. 2. On the contrary, the coupling ðhf ZJÞ is very small and irrelevant for. 4000. 0.15. 3000. hWW (GeV). h ∆ ± ∆ ± (GeV). 0.1. 2000 1000 0 -1000. 0.05 0 -0.05. -2000 -0.1. -3000. -0.15. -4000 -4000 -3000 -2000 -1000 ±. 0 ±. 1000 2000 3000 4000. -0.4. -0.3. -0.2. -0.1. 0. 0.1. 0.2. 0.3. 0.4. hZZ (GeV). h H H (GeV). FIG. 3 (color online). Fermiophobic Higgs boson couplings to a pair of charged Higgs (left) and to a pair of gauge bosons (right). 0.005. 0.15 0.004. 0.1. 0.003. hWW (GeV). 0.002. hZJ. 0.001 0 -0.001. 0.05 0 -0.05. -0.002. -0.1. -0.003 -0.004. -0.15 -0.8. -0.6. -0.4. -0.2. 0. 0.2. 0.4. 0.6. 0.8. -400 -300 -200 -100. 0. 100. 200. 300. 400. hJJ (GeV). hZA. FIG. 4 (color online). Relation between couplings with and without Majoron in the Fermiophobic scenario.. 095003-6.
(7) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. PHYSICAL REVIEW D 83, 095003 (2011). production of a fermiophobic Higgs boson. Nevertheless, the decay hf ! ZJ is possible and it is characterized by missing energy. We evaluate its branching ratio in the next section. In the right frame of Fig. 4 we see the relation between the ðhf JJÞ and ðhf WWÞ couplings. The coupling ðhf WWÞ is diminished compared to the value in the SM, implying that the decay rate hf ! WW is small. Nevertheless its branching ratio, together with the comparable BR for hf ! ZZ, will dominate unless the invisible decay hf ! JJ is large. This decay is controlled by the coupling ðhf JJÞ, also displayed in the right frame of Fig. 4. We see that this coupling can be large, in which case the fermiophobic Higgs will be invisible. In this scenario, one has to look for the second lightest Higgs boson. B. Imposing fermiophobia and majoron suppression We impose exact fermiophobia and Majoron suppression by fixing the value of cos13 ¼ c13 ¼ 0 in Eq. (8). The diagonalizing matrix in this case is 3 2 0 0 1 7 6 OR ¼ 6 0 7 5 4 c23 s12 s23 c12 c23 c12 s23 s12 2. s23 s12 c23 c12 0 0. 6 ¼6 4 sin. cos. cos sin. s23 c12 c23 s12 3 1 7 0 7 5;. 0 (31). 0. where corresponds to signðs13 Þ, and 12 23 is introduced as a new independent parameter. The last definition indicates that only one angle controls the rotation matrix in this scenario. The diagonalized CP-even Higgs mass matrix ðM2R Þdiag ¼ OR M2R OTR , implies, M2R13 ¼ 0. 0:5 GeV < v1 < 1 TeV; j1 j < 4;. v2 ¼ 246 GeV;. j1...5 j < 4;. v3 < 0:35 GeV;. 0<<2 :. (34). checking that 2 , 3 and have values smaller than 4. First we notice the clear dependence of the doublycharged Higgs mass mþþ on 3 , shown in Fig. 5. This dependence is easily understood from the expression for the mass mþþ in Eq. (14), which after replacing from Eq. (33) transforms into 1 m2þþ 3 v22 4 v23 ; 2. (35). with the equality holding in the exact fermiophobic and Majoron suppression scenario. Since v3 v2 , this relation would enable a direct determination of 3 from experiments. Note also that the relation in Eq. (26) is valid also in the fermiophobic plus Majoron suppression scenario (since it is a special case of the fermiophobic case), thus providing a measurement that could validate or refute the model. In the left frame of Fig. 6 we plot the relation between the fermiophobic Higgs couplings to a pair of charged Higgs ðhf H þ H Þ and to a pair of doubly-charged Higgs bosons ðhf þþ Þ. Clearly, the suppression of the Majoron component in the fermiophobic Higgs reduces dramatically the value of these couplings (compare with the left frame of Fig. 3), which are important for the decay rate for the hf ! mode. In the right frame of Fig. 6 we study couplings that involve one or two Majorons. To be more specific, we see the relation between ðhf ZJÞ and ðhf JJÞ, the first one corresponding to hf decay with missing energy, and the second one corresponding to an invisible decay. The coupling ðhf ZJÞ maintains its magnitude compared with the previous scenario, but ðhf JJÞ is much smaller, an expected effect since this scenario is defined by a null singlet component in hf .. M2R23 ¼ 0. 1 M2R12 ¼ ðM2R11 M2R22 Þ tan2: 2. (32). From these equations we eliminate the following parameters from the list of independent parameters given in Eq. (20) v22 v ¼ ð3 þ 5 Þ 3 2v1 v3 v1 v 1 1 v 2 ¼ 3 þ 21 v21 þ v22 3 21 v22 tan2: 2 v1 2v1 v2 v1 3 ¼. (33) We do a scan of the parameter space, imposing fermiophobia and Majoron suppression. The free parameters are varied according to,. FIG. 5 (color online). Doubly-charged Higgs mass dependence on 3 coupling in the Fermiophobic and Majoron suppressed scenario.. 095003-7.
(8) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). FIG. 6 (color online). Relation between couplings with and without Majoron in the Fermiophobic and Majoron suppressed scenario.. IV. FERMIOPHOBIC HIGGS BOSON DECAYS. mW ðhf Hþ H Þ; gm2Hþ mW ¼ ðhf þþ Þ; gm2þþ. g~hHH ¼. A fermiophobic Higgs boson will have four main decay modes, two of them into a pair of massive gauge bosons, hf ! W þ W and hf ! ZZ, where one or two of the gauge bosons may be off-shell depending on the Higgs mass, and the other two into one or two photons hf ! and hf ! Z, decays which are generated at one-loop [17]. In the later case, W gauge boson contribute to the oneloop generated decay with the graphs. g~h. where in the fermiophobic case with O11 R 0 we find ðhf H þ H Þ ðhf þþ Þ O11 R 3 v1. 1 gO13 R v3 ðhf W þ W Þ ¼ : mW gmW. (40). This implies tha, in the case of fermiophobia with Majoron suppression, all the contributions from W loops to ðhf ! Þ are suppressed.. The decay rate for hf ! is given by. V. PHENOMENOLOGY OF A HTM FERMIOPHOBIC HIGGS BOSON. ðhf ! Þ m3hf. 2 2. F1 ð. (39). which translate into a diminished influence of the charged scalars in the decay rate for hf ! . The other contribution to hf ! is from the W loop, controlled by the dimensionless coupling g~hWW , which satisfies in both scenarios: g~ hWW ¼. g ¼ 1024. (38). up to terms of Oðv3 Þ. In the fermiophobic case with Majoron suppression scenario, where O11 R ¼ 0, the terms that were subleading in the previous case, dominate now ðhf H þ H Þ 22 v3 1 ðhf þþ Þ 2 2 þ 4 5 v3 ; 2. present already in the SM. These graphs are complemented in our model with singly and doubly-charged Higgs bosons. (37). 3. m2W. jF0 ð. ghWW j W Þ~. 2;. ghHH H Þ~. þ 4F0 ð. gh Þ~ (36). where F0 and F1 are loop functions associated with scalar and vector bosons, and explicit expressions can be found in Ref. [18]. They are a function of i ¼ 4m2i =m2f , where i ¼ H; ; W. The dimensionless couplings g~hHH and g~h are. In the SM the main Higgs boson decay channels are h ! bb and h ! þ (for mh 130 GeV). In fermiophobic models, though, like the ones based on the 2HDM Type I or the HTM, the fermionic decays are suppressed. As a consequence, decay channels into gauge bosons become the most important ones, including the one-loop generated decays h ! and h ! Z. Here we study the decay rates of a fermiophobic Higgs boson into gauge bosons in our HTM, including decay modes with Majorons. For an analysis in the 2HDM see [19,20]. In. 095003-8.
(9) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. PHYSICAL REVIEW D 83, 095003 (2011). the left frame of Fig. 7 we show the fermiophobic Higgs boson branching ratios Bðhf ! XYÞ as a function of its mass mf , which include four gauge bosons modes: , ZZ, WW, and Z, and modes with one or two Majorons: JJ and JZ. We do not consider the decay hf ! , induced via the Higgs triplet coupling to leptons and responsible for neutrino masses, because it only has a non-negligible branching ratio for typically v3 104 GeV. Such small values of v3 are rare in our scan of the parameter space, and are obtained only after a fine-tuned cancellation between parameters in the tadpole equations in (5). We randomly vary the parameters in the potential as indicated in Eq. (24), imposing exact fermiophobia with Majoron suppression via Eq. (35). We also use the following experimental restrictions for the Higgs masses, mH > 80 GeV; mh > 90 GeV. m > 136 GeV; and. mA > 90 GeV:. We highlight from the left frame of Fig. 7 three distinctive features: (i) decay modes with Majorons are very important for low Higgs masses; (ii) decay modes with two massive gauge bosons can dominate for large masses, with a distinctive ratio Bðhf ! WWÞ=Bðhf ! ZZÞ as compared with the SM; (iii) radiative decays are suppressed with the exception of at very low masses. In the right frame of Fig. 7 we restrict a few of the free parameters in order to better visualize the above features. The dispersion of allowed points in parameter space is reduced by imposing 700 < v1 < 1000 GeV and 3 < 0:3. In the case of the aforementioned feature (i), we see in the left frame that the decay mode hf ! JJ can dominate at masses mf < 160 GeV, while it becomes smaller than 10% for mf * 110 GeV in the restricted case in the right frame. This decay is invisible, since the Majoron escapes detection. Its effect would show up as a diminished production cross section for the visible decays of hf . The. decay mode hf ! JZ is also very important, and manifests itself as a Z decaying into two fermions plus missing energy. In the restricted case in the right frame, hf ! JZ dominates for masses 102 < mf < 155 GeV, being reduced to a few percent for large Higgs masses. Regarding feature (ii), both decay modes hf ! WW, ZZ are above 5% for masses mf > 190 GeV, while in the restricted case (right frame) the two branching ratios are larger than 5% for even smaller masses (mf > 130 GeV). It is also very interesting to note that the decay hf ! ZZ can have a branching ratio larger than hf ! WW, in contrast with the SM where Bðhf ! WWÞ=Bðhf ! ZZÞ 2:5. This situation appear for mf > 190 GeV in the right frame of Fig. 7. In the restricted case, the two branching ratios interchange dominance around mf 190 GeV. This is a very important feature of the model since it can differentiate it from other models. The reason for this behavior lies in the Higgs boson couplings to gauge bosons, and can be understood from Eq. (29). For feature (iii) we see in the left frame of Fig. 7 that the radiatively generated decay hf ! can be potentially important at the LHC ( * 6%) only for very low Higgs masses mh & 107 GeV, while the Z mode is irrelevant with a largest value of 0:1% at intermediate masses 105 & mf & 160 GeV. These results can also be seen in the restricted case in the right frame. As we mentioned, one characteristic of our model is that the ratio Bðhf ! ZZÞ=Bðhf ! WWÞ can be larger than unity, while in fermiophobic 2HDM and in the SM, it is smaller than unity. From Eq. (29) we see that if the triplet VEV vanishes we recover the SM ratio. On the other hand, with exact fermiophobia where O12 R ¼ 0, we get an inverted ratio with respect to the SM one. The obvious question is how much deviation from exact fermiophobia is needed to reestablish the SM limit. A similar question is by how much the visible branching ratios change when we. FIG. 7 (color online). Branching ratios for the two-body fermiophobic Higgs decays fermiophobic Higgs decays hf ! XY as a function of mf in the fermiophobic scenario with the Majoron suppression approximation. In the left frame parameters are varied freely, while in the right frame they are restricted as indicated in the text.. 095003-9.
(10) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). deviate from the scenario of exact Majoron suppression. We explore these issues in the following figures. We define five scenarios in order to explore the effects from deviating from exact fermiophobia and Majoron suppression. The choice of parameters is random with the following exception: the first three scenarios are chosen such that the decay hf ! is enhanced, and the last two are chosen such that Bðhf ! ZZÞ > Bðhf ! WWÞ for large Higgs masses, in contrast to the SM prediction. The first three scenarios are characterized by a small fermiophobic Higgs mass, while the last two are characterized by a large one. Another difference between them is that in the first three scenarios mH < m as opposed to the last two where mH > m . This can be easily explained using Eq. (25). The five scenarios are defined in Table III. 11 Each scenario, defined by O12 R ¼ OR ¼ 0, is analyzed in the next five figures. In the left frames we explore the effects of deviation from exact fermiophobia, taking O12 R * 0. In the right frames we explore the effects of deviation from exact Majoron suppression, taking O11 R * 0. In Fig. 8 we consider scenario 1. The enhancement of the decay hf ! is achieved by choosing a light Higgs boson, which in scenario 1 is mh ¼ 96:55 GeV. The relevant BR are Bðhf ! Þ and Bðhf ! JZÞ, and they are close to 10% for exact fermiophobia and Majoron suppression, with the invisible mode Bðhf ! JJÞ dominating. Deviation from exact fermiophobia is seen in the left frame: both Bðhf ! Þ and Bðhf ! JZÞ grow up to 40% because the hf JJ coupling vanishes when O12 R 0:0001. After that, they decrease sharply. The effect of deviation from exact Majoron suppression is seen in the right frame: TABLE III. Parameter v1 v3 1 2 3 4 5 1 tanð2Þ mh mH m mA hH H h hWW hZZ hJJ hZJ. Scenario 1 639.54 0.29 0.85 3.98 0.68 2.72 0:37 0.45 0:3 96.55 122.18 143.29 96.44 3:98 2:30 0:12 0:31 0:33 102 0:33 103. Scenario 2 931.26 0.13 2.53 3.45 2.90 2.54 2:62 0.17 1:25 92.40 219.57 296.46 94.27 1.97 0.93 0:57 101 0.15 0:66 103 0:11 103. all visible decay modes diminish rapidly with increasing O11 R . In Fig. 9 we have scenario 2, also with a low Higgs mass of mf ¼ 92:4 GeV. In this case the coupling hf JJ does not vanish and all bosonic decay modes decrease monotonically, while the fermionic ones increase. In particular, Bðhf ! Þ 7% for O12 R ¼ 0:0001. The behavior of the BR as a function of O11 R is similar to the previous case. Scenario 3 is analyzed in Fig. 10. This is the third scenario with a low Higgs mass, mh ¼ 95:18 GeV, which enhances the decay hf ! . This scenario is characterized by the fact that all Higgs couplings to a pair of gauge bosons vanish at some point in the displayed parameter space. One effect is that the Higgs decay into gauge bosons survives up to higher values of 12 O12 R , for example hf ! 2% for OR ¼ 0:01, too small for the LHC, but useful for the International Linear Collider. In the right frame we see that the coupling hf JJ 7 vanishes for O11 R 7 10 , with the effect that visible decay modes increase their branching ratio. After this point the decay channels to the visible channels rapidly decrease. In the following two figures we analyze scenarios 4 and 5, characterized by a large Higgs mass, where the decay modes hf ! ZZ and hf ! WW are very important. In Fig. 11 we have scenario 4, characterized by mf ¼ 244:78 GeV. In the left frame we see that the decay modes hf ! ZZ and hf ! WW remain between 30% and 70% when we deviate from fermiophobic limit, even up to O12 R & 0:01. In addition, we see that Bðhf ! ZZÞ > Bðhf ! WWÞ up to O12 R 0:001, while for larger values the ratio returns to the SM one. In the right frame, of O12 R we see that the deviation from exact Majoron suppression causes the BR of the decay mode hf ! JJ to increase until. HTM parameters for four scenarios. Scenario 3 919.58 0.026 2.81 2.86 1.81 0.90 1:52 0.20 1.1 95.18 178.89 234.40 94.81 2:33 0:14 0:11 101 0:27 101 0:14 103 0:21 104. 095003-10. Scenario 4 950.94 0.34 1.78 0.72 1.11 1:68 0.87 0.27 0:34 244.78 216.06 182.89 244.78 0.95 0:26 0:49 0:14 0:36 1:12 102 2:61 104. Scenario 5 862.93 0.072 2.24 0:86 1.36 0:38 1.10 3.58 0:015 272.33 239.98 202.53 272.33 0:26 0:12 3:05 102 7:78 102 3:60 103 6:15 105. Units GeV GeV. GeV GeV GeV GeV GeV GeV GeV GeV GeV.
(11) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. PHYSICAL REVIEW D 83, 095003 (2011). FIG. 8 (color online). Higgs branching ratios for scenario 1, with mf ¼ 96:55 GeV. Deviation from exact fermiophobia in the left frame, and deviation from exact Majoron suppression in the right frame.. FIG. 9 (color online). Higgs branching ratios for scenario 2, with mf ¼ 92:4 GeV. Deviation from exact fermiophobia in the left frame, and deviation from exact Majoron suppression in the right frame.. FIG. 10 (color online). Higgs branching ratios for scenario 3, with mf ¼ 95:18 GeV. Deviation from exact fermiophobia in the left frame, and deviation from exact Majoron suppression in the right frame.. 095003-11.
(12) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). FIG. 11 (color online). Higgs branching ratios for scenario 4, with mf ¼ 244:78 GeV. Deviation from exact fermiophobia in the left frame, and deviation from exact Majoron suppression in the right frame.. FIG. 12 (color online). Higgs branching ratios for scenario 5, with mf ¼ 272:33 GeV. Deviation from exact fermiophobia in the left frame, and deviation from exact Majoron suppression in the right frame.. it becomes the largest one for O11 R * 0:002. However, Bðhf ! ZZÞ and Bðhf ! WWÞ never go below 10% in the displayed parameter space. The last scenario 5, characterized by mf ¼ 272:33 GeV, is shown in Fig. 12. We see in the left frame that the deviation from exact fermiophobia causes the couplings 12 hf WW and hf ZZ to vanish for O12 R 0:0003 and OR 0:0006, respectively. The invisible decay peaks up to 2% between these zeros, but both Bðhf ! ZZÞ and Bðhf ! WWÞ never fall simultaneously below 30%. In the right frame we see that Bðhf ! ZZÞ and Bðhf ! WWÞ remain fairly stable at 60% and 30%, respectively, when one deviates from exact Majoron suppression, until 5 hf ! JJ becomes equally important at O11 R 5 10 . After that point, WW and ZZ modes fall fast, reaching 5% at O11 R 0:0002. We remind the reader that Table I shows that 30% of the allowed parameter space satisfies fermiophobia to a level of jO12 R j < 0:0014, and that Table II indicates that 36:6% of parameter space satisfy fermiophobia and Majoron sup-. pression to a level of jO13 R j > 0:99999. These numbers tell us that the model ‘‘prefers’’ fermiophobia and/or Majoron suppression, which in turn comes from the hierarchy of the three vacuum expectation values. VI. CONCLUSIONS We have studied the Higgs sector of a model with scalar fields in singlet, doublet and triplet isospin representations. In this model the singlet scalar field acquires a vacuum expectation value, which spontaneously breaks lepton number and leads to a vacuum expectation value for the scalar triplet field, the latter providing a mass for the neutrinos. The lightest neutral CP-even scalar (H) can be a fermiophobic Higgs boson (i.e. a scalar with very suppressed couplings to fermions). We have studied distinctive signals of fermiophobia which can be probed at the LHC, and we have shown that fermiophobia is not a finetuned situation, unlike in two higgs doublet models. Characteristic signals are possible for both the cases of small and heavy Higgs boson mass. For a light. 095003-12.
(13) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. PHYSICAL REVIEW D 83, 095003 (2011). fermiophobic Higgs boson a distinctive signal would be a moderate BðH ! Þ accompanied by a large BðH ! JJÞ (where J is a Majoron), the latter being an invisible decay. For the case of a large Higgs boson mass the decay modes H ! ZZ, WW can be dominant, while the channel H ! JJ is suppressed. In this situation, BðH ! ZZÞ is larger than BðH ! WWÞ, which differs from the SM prediction and provides a test for the model. ACKNOWLEDGMENTS A. G. A. was supported by the ‘‘National Central University plan to develop first-class universities’’, and. by a Marie Curie Incoming International Fellowship, FP7-PEOPLE-2009-IIF, Contract No. 252263. M. A. D. was supported by Fondecyt Regular Grant # 1100837. M. A. R. was supported by Fondecyt grant No. 3090069. D. R. M. was supported by CONICYT. APPENDIX A Here we present the relevant Feynman rules which involve the lightest Higgs boson in our HTM. The notation used here is the same as that used in Sec. II. Higgs-Higgs-Higgs Interactions. Higgs-gauge boson-Higgs Interactions. 095003-13.
(14) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). Higgs-gauge boson-gauge boson Interactions. 095003-14.
(15) FERMIOPHOBIA IN A HIGGS TRIPLET MODEL. PHYSICAL REVIEW D 83, 095003 (2011). Higgs-Higgs- gauge boson-gauge boson Interactions. [1] R. Barate et al. (LEP Working Group for Higgs boson searches and ALEPH Collaboration), Phys. Lett. B 565, 61 (2003). [2] CDF Collaboration and D0 Collaboration, arXiv:0903.4001. [3] G. Aad et al. (The ATLAS Collaboration), arXiv:0901.0512. [4] R. Adolphi et al. (CMS Collaboration), JINST 0803, S08004 (2008); 3, S08004 (2008). [5] E. Accomando et al., arXiv:hep-ph/0608079. [6] H. Georgi and M. Machacek, Nucl. Phys. B262, 463 (1985); M. S. Chanowitz and M. Golden, Phys. Lett. B 165, 105 (1985). [7] W. Konetschny and W. Kummer, Phys. Lett. B 70, 433 (1977); T. P. Cheng and L. F. Li, Phys. Rev. D 22, 2860 (1980); J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); R. N. Mohapatra and G. Senjanovic, Phys. Rev. D 23, 165 (1981). [8] J. Schechter and J. W. F. Valle, Phys. Rev. D 25, 774 (1982); P. Fileviez Perez and S. Spinner, Phys. Lett. B 673, 251 (2009). [9] M. A. Diaz, M. A. Garcia-Jareno, D. A. Restrepo, and J. W. F. Valle, Nucl. Phys. B527, 44 (1998). [10] E. J. Chun, K. Y. Lee, and S. C. Park, Phys. Lett. B 566, 142 (2003); A. G. Akeroyd and M. Aoki, Phys. Rev. D 72, 035011 (2005); A. G. Akeroyd, M. Aoki, and H. Sugiyama, Phys. Rev. D 77, 075010 (2008); J. Garayoa and T. Schwetz, J. High Energy Phys. 03 (2008) 009; M. Kadastik, M. Raidal, and L. Rebane, Phys. Rev. D 77,. [11]. [12]. [13]. [14]. 095003-15. 115023 (2008); P. Fileviez Perez, T. Han, G. y. Huang, T. Li, and K. Wang, Phys. Rev. D 78, 015018 (2008); F. del Aguila and J. A. Aguilar-Saavedra, Nucl. Phys. B813, 22 (2009); A. G. Akeroyd, C. W. Chiang, and N. Gaur, J. High Energy Phys. 11 (2010) 005. J. F. Gunion, J. Grifols, A. Mendez, B. Kayser, and F. I. Olness, Phys. Rev. D 40, 1546 (1989); K. Huitu, J. Maalampi, A. Pietila, and M. Raidal, Nucl. Phys. B487, 27 (1997). T. J. Weiler, Proceedings of the 8th Vanderbilt Int. Conf. on High Energy Physics, Nashville, TN, 1987, edited by J. Brau and R. Panvini (World Scientific, Singapore, 1988), p 219; A. Stange, W. J. Marciano, and S. Willenbrock, Phys. Rev. D 49, 1354 (1994); M. A. Diaz and T. J. Weiler, arXiv:hepph/9401259; V. D. Barger, N. G. Deshpande, J. L. Hewett, and T. G. Rizzo, arXiv:hep-ph/9211234; H. Pois, T. J. Weiler, and T. C. Yuan, Phys. Rev. D 47, 3886 (1993); A. G. Akeroyd, Phys. Lett. B 368, 89 (1996); A. Barroso, L. Brucher, and R. Santos, Phys. Rev. D 60, 035005 (1999); L. Brucher and R. Santos, Eur. Phys. J. C 12, 87 (2000); S. Mrenna and J. Wells, Phys. Rev. D 63, 015006 (2000); A. G. Akeroyd, M. A. Diaz, and F. J. Pacheco, Phys. Rev. D 70, 075002 (2004); A. G. Akeroyd, Nucl. Phys. B544, 557 (1999) ; A. G. Akeroyd, A. Alves, M. A. Diaz, and O. J. P. Eboli, Eur. Phys. J. C 48, 147 (2006). M. S. Carena and H. E. Haber, Prog. Part. Nucl. Phys. 50, 63 (2003)..
(16) AKEROYD et al.. PHYSICAL REVIEW D 83, 095003 (2011). [15] M. C. Gonzalez-Garcia and Y. Nir, Phys. Lett. B 232, 383 (1989). [16] G. B. Gelmini and M. Roncadelli, Phys. Lett. B 99, 411 (1981). [17] D. Phalen, B. Thomas, and J. D. Wells, Phys. Rev. D 75, 117702 (2007); E. Boos, J. C. Brient, D. W. Reid, H. J. Schreiber, and R. Shanidze, Eur. Phys. J. C 19, 455 (2001).. [18] J. F. Gunion, H. E. Haber, G. L. Kane, and S. Dawson, The Higgs Hunter’s Guide (Perseus Publishing, Cambridge, MA,2000). [19] A. G. Akeroyd, M. A. Diaz, and M. A. Rivera, Phys. Rev. D 76, 115012 (2007). [20] A. Arhrib, R. Benbrik, R. B. Guedes, and R. Santos, Phys. Rev. D 78, 075002 (2008).. 095003-16.
(17)
Documento similar
In the preparation of this report, the Venice Commission has relied on the comments of its rapporteurs; its recently adopted Report on Respect for Democracy, Human Rights and the Rule
Although some public journalism schools aim for greater social diversity in their student selection, as in the case of the Institute of Journalism of Bordeaux, it should be
In the “big picture” perspective of the recent years that we have described in Brazil, Spain, Portugal and Puerto Rico there are some similarities and important differences,
Modern irrigation is transforming traditional water irrigation norms and therefore it is critical to understand how the access mechanisms to assets (natural, financial, social),
Keywords: Metal mining conflicts, political ecology, politics of scale, environmental justice movement, social multi-criteria evaluation, consultations, Latin
In the previous sections we have shown how astronomical alignments and solar hierophanies – with a common interest in the solstices − were substantiated in the
It might seem at first that the action for General Relativity (1.2) is rather arbitrary, considering the enormous freedom available in the construction of geometric scalars. How-
This effect is enough to stabilize the potential and allow to extend the scenario of Higgs inflation to the experimentally preferred range of Higgs and top masses provided the mass
