Higgs Sector in Extensions of the Minimal Supersymmetric Standard Model

Transcription

1 Univerity of Pennylvania ScholarlyCommon Deartment of Phyic Paer Deartment of Phyic Higg Sector in Extenion of the Minimal Suerymmetric Standard Model Vernon Barger Univerity of Wiconin - Madion Paul Langacker Univerity of Pennylvania Hye-Sung Lee Univerity of Florida Gabe Shaughney Univerity of Wiconin - Madion Follow thi and additional work at: htt://reoitory.uenn.edu/hyic_aer Part of the Phyic Common Recommended Citation Barger, V., Langacker, P., Lee, H., & Shaughney, G. (6). Higg Sector in Extenion of the Minimal Suerymmetric Standard Model. Retrieved from htt://reoitory.uenn.edu/hyic_aer/ Suggeted Citation: Barger, V., Langacker, P. Lee, H. and Shaughney, G. (6). Higg ector in extenion of the minimal uerymmetric tandard model. Phyical Review D 73, 5. 6 American Phyical Society htt://dx.doi.org/.3/phyrevd.73.5 Thi aer i oted at ScholarlyCommon. htt://reoitory.uenn.edu/hyic_aer/ For more information, leae contact reoitory@obox.uenn.edu.

2 Higg Sector in Extenion of the Minimal Suerymmetric Standard Model Abtract Extenion of the minimal uerymmetric tandard model (MSSM) with additional inglet calar field olve the imortant µ-arameter fine-tuning roblem of the MSSM.We comute and comare the neutral Higg boon ma ectra, including one-loo correction, of the following MSSM extenion: next-tominimal uerymmetric tandard model (), the nearly-minimal uerymmetric tandard model (nmssm), and the U()'-extended minimal uerymmetric tandard model () by erforming can over model arameter. We find that the ecluded U()'-extended minimal uerymmetric tandard model (MSSM) i identical to the nmssm if three of the additional calar decoule. The dominant art of the one-loo correction are model indeendent ince the inglet field doe not coule to MSSM article other than the Higg doublet. Thu, model-deendent arameter enter the mae only at tree level. We aly contraint from LEP bound on the tandard model and MSSM Higg boon mae and the MSSM chargino ma, the inviible Z decay width, and the Z - Z' mixing angle. Some extended model ermit a Higg boon with ma ubtantially below the SM LEP limit or above theoretical limit in the MSSM.Way to differentiate the model via mae, couling, decay and roduction of the Higg boon are dicued. Diciline Phyical Science and Mathematic Phyic Comment Suggeted Citation: Barger, V., Langacker, P. Lee, H. and Shaughney, G. (6). Higg ector in extenion of the minimal uerymmetric tandard model. Phyical Review D 73, 5. 6 American Phyical Society htt://dx.doi.org/.3/phyrevd.73.5 Thi journal article i available at ScholarlyCommon: htt://reoitory.uenn.edu/hyic_aer/

3 PHYSICAL REVIEW D 73, 5 (6) Higg ector in extenion of the minimal uerymmetric tandard model Vernon Barger, Paul Langacker, Hye-Sung Lee, 3 and Gabe Shaughney Deartment of Phyic, Univerity of Wiconin, Madion, Wiconin 5376, USA Deartment of Phyic and Atronomy, Univerity of Pennylvania, Philadelhia, Pennylvania 94, USA 3 Deartment of Phyic, Univerity of Florida, Gaineville, Florida 368, USA (Received 7 Aril 6; ublihed 6 June 6) Extenion of the minimal uerymmetric tandard model (MSSM) with additional inglet calar field olve the imortant -arameter fine-tuning roblem of the MSSM. We comute and comare the neutral Higg boon ma ectra, including one-loo correction, of the following MSSM extenion: next-tominimal uerymmetric tandard model (), the nearly-minimal uerymmetric tandard model (nmssm), and the U -extended minimal uerymmetric tandard model () by erforming can over model arameter. We find that the ecluded U -extended minimal uerymmetric tandard model (MSSM) i identical to the nmssm if three of the additional calar decoule. The dominant art of the one-loo correction are model indeendent ince the inglet field doe not coule to MSSM article other than the Higg doublet. Thu, model-deendent arameter enter the mae only at tree level. We aly contraint from LEP bound on the tandard model and MSSM Higg boon mae and the MSSM chargino ma, the inviible Z decay width, and the Z Z mixing angle. Some extended model ermit a Higg boon with ma ubtantially below the SM LEP limit or above theoretical limit in the MSSM. Way to differentiate the model via mae, couling, decay and roduction of the Higg boon are dicued. DOI:.3/PhyRevD.73.5 I. INTRODUCTION Suerymmetry (SUSY) i a leading candidate for hyic beyond the tandard model (SM). It i the only extenion of the boonic acetime Poincaré ymmetry to include a fermionic acetime. Suertring theory, the currently revailing aradigm of quantum gravity, generally include SUSY, though not necearily at the weak cale. The cancellation of the quadratic divergence in the Higg ma-quared radiative correction, requiring finetuning in the SM, trongly motivate SUSY at the TeV cale. TeV-cale SUSY alo unite the gauge couling contant at the GUT cale and rovide an attractive cold dark matter candidate, the lightet neutralino, when R-arity i conerved. The imlet uerymmetric extenion of the SM i the minimal uerymmetric tandard model (MSSM). The MSSM uffer from the -roblem []. The -arameter i the only dimenionful arameter in the SUSY conerving ector. Naively, in a to down aroach, one would exect the -arameter to be either zero or at the Planck cale, O 9 GeV. At tree level, the MSSM give the relation [] M Z m d m utan tan ; () where m d and m u are the oft ma arameter for the down-tye and u-tye Higg, reectively. With the oft arameter at the EW/TeV cale, mut be at the ame cale, while LEP contraint on the chargino ma require to be nonzero [3]. A imle olution i to romote the -arameter to a dynamical field in extenion of the MSSM that contain an additional inglet calar field that PACS number: 4.8.C,.6.Jv doe not interact with MSSM field other than the two Higg doublet. Extended model thereby circumvent the need for a fine-tuning of the -arameter to the electroweak cale. The dicovery of Higg boon i a rimary goal of the Tevatron and the Large Hadron Collider (LHC) exeriment. Although Higg boon ignal at collider have been extenively tudied, mot of thee tudie were baed on the aumtion that the Higg boon occur only in doublet field [4]. The few cae tudie of the Higg ector in the extenion of the MSSM have not been a comrehenive a the SM and MSSM Higg tudie [5,6]. With the addition of inglet calar field, the roertie of the Higg boon can be ubtantially different from thoe in the SM or the MSSM. Moreover, with SUSY, there are alo one or more extra neutralino and there may be an extra neutral gauge boon in ome model. In thi aer we conider model with an extra Higg inglet field that yield a dynamical olution to the -roblem. The dynamical field that get a vacuum exectation value (VEV) generate an effective -arameter that i aociated with a new ymmetry. Thee model have a third CP-even Higg boon and, in ome cae, an extra CP-odd Higg boon. The mixing with the extra calar tate alter the mae and couling of the hyical Higg boon. We evaluate the henomenological conequence of an extra calar for the Higg mae, couling, decay and roduction. We include one-loo radiative correction to the Higg mae, which to a good aroximation turn out to be common among the model at thi order for the neutral and charged Higg boon ector. While erforming our ytematic tudy on the Higg ector alone, we conider indirect conequence from the neutralino ector in =6=73()=5(3) 5-6 The American Phyical Society

4 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6) anticiation of a later full treatment including both ector. Detailed tudie of the neutralino ector in thee model have been done by examining the lightet neutralino [7]. We tranlate the contraint from LEP exeriment on the SM (lightet MSSM) Higg into limit on the CP-even (CP-even and CP-odd) Higg boon mae in the extended model and include contraint from the LEP chargino ma limit, the inviible Z width and the Z Z mixing angle. The extended model of reent interet are the next-tominimal uerymmetric tandard model () [], the minimal nonminimal uerymmetric tandard model (MNSSM) or the nearly-minimal uerymmetic tandard model (nmssm) [], the U -extended minimal uerymmetric tandard model () [], and the ecluded U -extended minimal uerymmetric tandard model (MSSM) [3]. A common -generating term, h ^H u ^H d ^S, i contained in the uerotential of thee model, which are lited in Table I. After the S field get a VEV, the effective -arameter i identified a eff h hsi: () where hsi denote the VEV of the inglet field. The defining feature of each model i the ymmetry that i allowed by the uerotential. The ha a dicrete Z 3 ymmetry, allowing the S 3 term [,4]. With any dicrete ymmetry, the oibility of domain wall exit. It ha been hown that domain wall can be viewed a a ource of dark energy [5]. In the, the equation of the tate, w, of dark energy i redicted to have w =3 which i difavored by a recent analyi of WMAP data that lace w :6 :8 :79 [6]. The domain wall may be eliminated if the Z 3 ymmetry i broken by higher dimenional oerator, but thee may lead to very large detabilizing tadole oerator [7]; one oibility for avoiding thi roblem i decribed in Ref. [8]. The nmssm with a Z R 5 or ZR 7 ymmetry ha a tadole term of ^S that break the dicrete ymmetrie and i thu free from domain wall [,9]. The harmful tadole divergence can detabilize the gauge hierarchy, but the dicrete ymmetrie Z R 5 or ZR 7 allow the divergence to exit only at ix and even-loo order, reectively [9]. At thee order, the divergence are ureed at cale below M Planck. An extra U gauge ymmetry, U, i motivated by many model beyond the SM, including grand unified theorie (GUT) [,], extra dimenion [], uertring [3], little Higg [4], dynamical ymmetry breaking [5], and the Stueckelberg mechanim [6]. The and MSSM each contain a U gauge ymmetry and it gauge boon, Z, that can mix with the SM after ymmetrie are broken Z [,7]. While the continuou U ymmetry i free from domain wall contraint, the may require exotic field [8 3] to cancel chiral anomalie related to the U ymmetry. There are contraint on the from the trict exerimental limit on Z Z mixing that are at the mil-level [3]. The Z ma mut be above 6-9 GeV to atify the Tevatron dileton earch reult, with the recie exerimental limit deendent on the U model [33]. With a letohobic Z, thee ma limit are evaded. The Higg field content of the above lited model i given in Table I. In the MSSM, the uual Higg doublet give two CP-even (H, H ), a CP-odd (A ), and a air of charged (H ) Higg boon 3. The extended model include additional CP-even Higg boon and CP-odd Higg boon or a Z gauge boon, deending on the model. The MSSM contain three additional inglet that allow ix CP-even and four CP-odd Higg tate. However, the additional Higg field decoule if i mall and the vacuum exectation value hs i; hs i; hs 3 i are large. The decouling limit eliminate the D-term in the maquared matrix for the S; Hd, and H u field and yield a model imilar to the nmssm with three CP-even and two CP-odd Higg boon. Thi i hown in Aendix A. We hall therefore refer to the nmssm a n/mssm ince the reult of the nmssm correond to the MSSM in the decouling regime. The charged Higg ector for all of thee model remain the ame a in the MSSM due to the aumtion that the number of Higg doublet i unchanged. We reent an overview of the Higg ma-quared matrice including radiative correction due to to and to loo in Sec. II. We dicu the exerimental and theoretical contraint alied in Section III and the detail of the arameter can in Sec. IV. In Sec. V, we dicu the Higg ectra and couling for variou model, while imlication for collider henomenology are reented in Sec. VI. Finally, we ummarize our reult in Sec. VII. We rovide detail of decouling of the MSSM in Aendix A. The derivation of the ma-quared matrice of each model are reented in Aendix B and the neutralino ma matrice are given in Aendix C. In Aendix D, imortant limit in the Higg ector are addreed, while additional information on the heavier tate i given in Aendix E. II. HIGGS MASS MATRICES A. Tree level The tree-level Higg ma-quared matrice are found from the otential, V, which i a um of the F-term, D-term and oft-term in the Lagrangian, a follow. Many of the idea of ome of the model aeared already in Ref. [8]. For a recent review of uerymmetric inglet model, ee Ref. [9]. Exotic fermion can be avoided in a family nonuniveral U model [3]. 3 We ignore the oibility of CP-violating mixing effect. 5-

5 HIGGS SECTOR IN EXTENSIONS OF THE MINIMAL... PHYSICAL REVIEW D 73, 5 (6) TABLE I. Higg boon of the MSSM and everal of it extenion. We denote the ingle CP-odd tate in the MSSM and by A for eaier comarion with the other model. Model Symmetry Suerotential CP-even CP-odd Charged MSSM ^H u ^H d H ;H A H Z 3 h ^S ^H u ^H d ^S 3 3 H ;H ; A ;A H nmssm Z R 5 ; ZR 7 h ^S ^H u ^H d F Mn ^S H ;H ; A ;A H U h ^S ^H u ^H d H ;H ; A H MSSM U h ^S ^H u ^H d ^S ^S ^S 3 H ;H ; ;H 4 ;H 5 ;H 6 A ;A ;A 3 ;A 4 H V F jh H u H d F M n S j jh Sj jh d j jh u j ; (3) V D G 8 jh dj jh u j g jh dj jh u j jh u H d j ; g Q H d jh d j Q Hu jh u j Q S jsj ; V oft m d jh dj m ujh u j m jsj (4) A h SH u H d 3 A S 3 S M 3 ns H:c:: (5) Here, the two Higg doublet with hyercharge Y = and Y =, reectively, are H H d d H H ; H u Hu : (6) and H u H d ij HuH i j d. For a articular model, the arameter in V are undertood to be turned off aroriately according to Table I :g ; M n ; nmssm:g ; ; A ; :M n ; ; A : The couling g ;g, and g are for the U Y ;SU L, and U gauge ymmetrie, reectively, and the arameter G i defined a G g g. The modeldeendent arameter are and A while the free nmssm arameter are F and S with M n being fixed near the SUSY cale. The model deendence of the i exreed by the D-term that ha the U charge of the Higg field, Q Hd ;Q Hu and Q S. In general, thee charge are free arameter with the retriction 4 that Q Hd Q Hu Q S to reerve gauge invariance. In any articular U contruction, the charge have ecified value. We aume the charge of a E 6 model that break via the chain E 6! SOU! SU5U U []. At ome high energy cale, the U U ymmetry 4 Additional retriction on the charge of the ordinary and exotic article come from the cancellation of anomalie. (7) i aumed to break into one U 5. The above breaking cenario reult in the charge Q Hd Q Hu co E6 in E6 ; 6 co E6 in E6 ; 6 where E6 i the mixing angle between the two U and i the only model-deendent arameter. The F-term and the oft term contain the model deendence of the and n/mssm. The oft term A of the and S M 3 n of the n/mssm are new to V oft. The B-term of the MSSM i exreed in V oft a A h SH u H d after we identify (8) B A eff : (9) The other term in V oft are the uual MSSM oft ma term. The minimum of the otential i found exlicitly uing the minimization condition found in Aendix B. The condition found allow u to exre the oft ma arameter in term of the VEV of the Higg field. At the minimum of the otential, the Higg field are exanded a Hd v d d i d ; Hu v u u i u ; S i: () with v v d v u 46GeV and tan v u =v d.we write the Higg ma-quared matrix in a comact form that include all the extended model under conideration. The CP-even tree-level matrix element in the H d ;H u;s bai are: 5 Thi i the ame breaking cheme a in the excetional uerymmetric tandard model (ESSM) [34]. In the ESSM, among three air of SU() doublet calar with MSSM Higg quantum number and three inglet calar, only one air of doublet and one inglet develo VEV due to an extra Z H ymmetry and imoed hierarchical tructure of the Yukawa interaction, yielding a model imilar to the. 5-3

6 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6) G M 4 Q H d g v d M v ug h 4 h A h h F Mn vu ; () A h v d h h F Mn vu ; (3) v d G M 4 h Q Hd Q Hu g v d v u h A h h F M n ; () M 3 h Q Hd Q S g v h A d h v u ; (3) G M 4 Q H u g v u h A h h F Mn vd ; (4) v u M 3 h Q Hu Q S g h A v u h v d ; (5) M 33 Q S g h A S M 3 n vd v u v d v u A : (6) The tree level CP-odd matrix element are: M h A h h F Mn vu ; (7) v d M h A M h A 3 M h A M h A 3 h h F Mn ; (8) h v u ; (9) h h F Mn vd ; () v u h v d ; () M h A 33 S M 3 n vd v h u v d v u 3A : () The tree-level charged Higg ma-quared matrix element are: M v dv u g h 4 M v d g h 4 A h h h F Mn A h h h F Mn ; (4) vd v u : (5) The hyical Higg boon mae are found by diagonalizing the ma-quared matrice, M D RMR, where M alo include the radiative correction dicued below. The rotation matrice for the diagonalization of the CP-even and CP-odd ma-quared matrice, R ij, and for the charged Higg matrix, R ij, may then be ued to contruct the hyical Higg field. H i R i d R i u R i3 ; (6) A i R i d R i u R i3 ; (7) H i R i H R i H : (8) where the hyical tate are ordered by their ma a M H M H M H3 and M A M A. Many feature of the model are aarent by inection of the ma-quared matrix element. We dicu thee aect in Sec. V. B. Radiative correction An accurate analyi of the Higg mae require loo correction. The dominant contribution at one-loo are from the to and calar to loo due to their large Yukawa couling. In the, the gauge couling are mall comared to the to quark Yukawa couling o the oneloo gauge contribution can be droed. Correction unique to the and n/mssm begin only at the two-loo level. Thu all contribution that are modeldeendent do not contribute ignificantly at one-loo order and the uual one-loo SUSY to and to loo are univeral in thee model. A imilar aroach ha been done in tudying extended Higg ector with many additional inglet field [35]. Thee one-loo correction to the otential can be found from the Coleman-Weinberg otential [36] and are reviewed in Aendix B. The ma-quared matrix element become M M M ; (9) where the radiative correction to the CP-even ma- 5-4

7 HIGGS SECTOR IN EXTENSIONS OF THE MINIMAL... PHYSICAL REVIEW D 73, 5 (6) quared matrix element are given by with Q being the DR renormalization cale and A t i the M em k m m G v d h h to trilinear couling. t A t vu F ; The correction to the CP-odd ma-quared matrice v d are given by et et (3) M ij h v d v u kh t A t F m~t vi v j ;m~t ; (4) M em k em m m G where we identify v v d ;v v u, and v 3. Thee et et one-loo correction agree with thoe of [4,9,7]. h t em h h t A m m Gv d v u t The one-loo correction to the charged Higg ma are F ; equivalent to thoe in the MSSM and can be ignificant for et et large tan. The charged Higg boon in the MSSM ha a (3) tree-level ma M M em 3 k em m m G h h M H W M Y ; (4) t F v d and the extended-mssm charged Higg boon ma i et et h h t A M t F v M H W M Y h v u ; (3) h F Mn ; in (4) where MY h A in i the tree-level ma of the MSSM M em k m m G h t em m m G et et et et h h t A k t h 4 t lnm et m et m 4 t vd F ; M v 3 k u M ~m 33 k m~t m~t G v u (33) em em m et m et G h t em m m G v u et et h h t A t F v d ; (34) h h t A t F where k 3 and the loo factor are 4 G m~t ;m~t m ~t m~t m~t m~t m~t log ; m ~t F log m ~t m ~t Q 4 Here we have defined Gm ~t ;m ~t : vd v u : (35) (36) em h t eff eff A t tan; (37) CP-odd Higg boon. The cae of large M Y (or M A in the MSSM) yield a large charged Higg ma and i conitent with the MSSM decouling limit yielding a SM Higg ector. Radiative correction in the MSSM hift the ma by M h A t kh t F M ; (43) H in H where after including tan deendent term, M i H given by the leading logarithm reult of the full one-loo calculation [37] M N cg m t m b H 3 MW in co m MW t in m b co 3 M4 W log M SUSY m ; t (44) where N c 3 i the number of color and M SUSY i the uerymmetric ma cale, taken to be TeV. Modeldeendent term come in at tree level, giving a charged Higg ma after radiative correction of M M H W M Y h v h F Mn in h A t kh t F M : (45) in H em h t A t A t eff cot; (38) em v d h t eff eff A t tan; (39) III. CONSTRAINTS Both theoretical and exerimental contraint are imortant in enuring that the model are realitic. In the 5-5

8 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6) following, we lit the contraint that we aly in obtaining the allowed Higg ma ectra. To generate the Higg boon mae, we can over the relevant arameter of each model. Theoretical contraint eliminate large region of the arameter ace. To avoid olution that contain untable addle-oint of the otential, we require that the ma-quared eigenvalue are oitive-definite, i.e. M A i ;M H i ;M H. We alo exclude olution which give m et i <. A. Direct contraint The direct contraint are rovided by collider data. Currently, LEP give the bet exerimental bound on the ma of the SM Higg boon, h, of 4.4 GeV at 95% C.L. [38]. We tranlate thi to limit the ma of the lightet Higg boon of the extended model by uing the ZZh couling limit from LEP, a reroduced in Fig. 3a of Sec. V B, that conider all SM article decay mode down to M h GeV [38] 6. The ZZH i couling relative to the SM couling i given by the factor ZZHi g ZZHi =g SM ZZh R i co R i in : (46) Since the ZZH i couling in extended model i reduced by doublet-inglet mixing effect, it i oible to have Higg boon lighter than the SM bound of 4.4 GeV. The reach of the ZZH i couling limit extend only to GeV, below which we do not enforce thi contraint. However, thi low ma region i well contrained by bound on M A and M h in the MSSM dicued below. The LEP bound i alo alied to H and ince a heavier Higg boon may violate the bound even if the lightet doe not. Another channel of relevance from LEP i Z! A i H j with A i! b b and H j! b b. Current limit lace the lightet oible CP-even and odd MSSM mae at M H 9:9 GeV and M A 93:4 GeV, reectively, and are calculated auming maximal to mixing, yielding the mot conervative limit on the lightet Higg mae in the MSSM [4]. An etimation of the correonding limit in extended model may be obtained by comaring the exected roduction cro ection of the extended-mssm model at the maximum LEP energy, 9 GeV, to that of the MSSM [43]. At thi energy the ma limit of 6 Thee limit actually aume tandard model branching ratio for the H i, which are dominantly into b b and in the relevant ma range. A dicued in Sec. VI B, for ome of the arameter value in the extended model the dominant decay are into (inviible) neutralino, or into two light CP-odd tate, and for thoe oint the contraint in Fig. 3(a) doe not trictly aly. However, there are alo quite tringent limit on the inviible H i decay mode [39], and (weaker) limit on the decay into two CP-odd tate which ubequently decay into b b or [4,4]. Thee have not been given for the entire kinematic range of interet here, o we will imly take the conervative aroach of allowing only thoe oint atifying the ZZH i couling limit in Fig. 3(a). the CP-even and CP-odd Higg boon rovide an uer bound of the cro ection at 4 fb. In ractice, we find that the LEP Z! A i H j contraint eliminate a ignificant fraction of the oint generated with a low CP-odd Higg ma. In Fig. 3(b), we how co, the refactor of the ZAh couling where i the rotation angle required to diagonalize the MSSM CP-even Higg ma-quared matrix, veru CP-odd Higg ma for the MSSM. A trong ZAh couling reult in an enhanced Ah roduction cro ection. In the extended-mssm model, we calculate the cro ection for e e! A i H j where A i i the lightet nonzero CP-even Higg for that model. If it i above the calculated LEP limit of 4 fb, the generated oint fail thi contraint. Mixing effect which maximize the ZA i H j couling in the MSSM alo reult in a lower value of M A, o that the LEP limit imlie a lower bound on M A. With the two comlementary limit on the neutral Higg boon and the charged Higg ma (M H 78:6 GeV from LEP [44]), the Higg ector in the MSSM and extended-mssm model are rather well contrained. B. Indirect contraint While we focu on the Higg ector in our analyi, indirect contraint from the neutralino and chargino ector alo need to be conidered. The lightet chargino ma i currently limited by LEP to be M > 4 GeV at 95% C.L. [3]. The chargino mae are determined by the diagonalization of M M MW in ; (47) MW co eff The SU L gaugino ma, M, that enter the chargino ector doe not have a direct effect on the Higg ector, but the lower bound on M doe contrain oible arameter value. Preciion electroweak data alo rovide an uer bound on the new contribution to the inviible Z decay width of.9 MeV at 95% C.L. 7 Contribution to thi decay width include Z! A i H j for M Ai M Hj M Z and Z! Z H i! f fh i for M Hi M Z. The decay width are given by Z!Ai H j 48x W x W M Z 3= MA i =MZ ;M H j =MZ R i R j R i R j ; (48) 7 Thi i baed on the contraint on new hyic contribution to the inviible Z width, new inv :65 :5 MeV [45], renormalizing the robability ditribution to require that the true value i oitive. Strictly eaking, uch decay may not be inviible, and lightly weaker contraint would be obtained uing the total or hadronic width. We ue the inviible width to be conervative and for imlicity, ince it i alo alied to decay of the Z into neutralino air. 5-6

9 HIGGS SECTOR IN EXTENSIONS OF THE MINIMAL... PHYSICAL REVIEW D 73, 5 (6) d Z!f fh i dx Z!SM Hi 4x W x W 3 y H i x Hi x q H i x Hi y H i x H i 4y H i : (49) where x; y x y xy x y, x Hi E Hi =M Z and y Hi M Hi =M Z and where the SM Z decay width i Z!SM :5 GeV [45]. Here we aume male fermion in the Z! f fh i decay, which i a good aroximation at low M Hi. Thi decay mode comlement the ZZH i couling contraint quite well a it i valid below the reach of the LEP limit on ZZHi. Since the mae of H ;, and A are tyically larger than M Z, we only conider Z! H A and Z! f fh decay mode 8. The neutralino ector alo rovide contraint on the allowed arameter ace via Z boon decay. If M M Z =, then Z decay into neutralino air and thi decay contribute to the inviible Z-decay width. Since the Z doe not coule to the inglino, the uerartner of the Higg inglet, the decay width formula in the extended model i imilar to that of the MSSM, excet for mixing effect [46]. The Z decay width to neutralino air, when kinematically acceible, i Z! g g 96MZ jn 3 j jn 4 j MZ M 3= : (5) The neutralino rotation matrix element, N ij, are found by diagonalizing the model-deendent neutralino maquared matrice in Aendix C. The Z Z mixing angle, ZZ M ZZ tan MZ ; (5) M Z i alo contrained by electroweak reciion data to be le than O 3, where the exact value i deendent on the U model. The Z ma arameter are MZ g Q H d v d Q H u v u Q S ; q MZZ g g g v d Q H d v uq Hu : (5) Equation (5) bound what tye of Z model and aociated Higg ector arameter are allowed; it tranlate into a high value of, tyically at the TeV cale. There do, however, exit iolated oint that allow a ureion of ZZ at low uch a the following (i) If Q Hd ;Q Hu haver the ame ign, a cancellation Q occur at tan Hd. Q H u 8 Singlet mixing may allow H or A to be lightly le than M Z but the decay i till kinematically inacceible. (ii) If Q Hu i mall and tan i large, the mixing term i ureed. The Z ma i alo contrained [3,33], but the limit are very model-deendent on the quark and leton couling and can be eliminated entirely in the letohobic Z cae [47]. In any cae, the large limit yield a Z with ma tyically large enough to avoid exiting exerimental contraint. Therefore, we only aly the Z Z mixing contraint in our tudy. Contraint due to the oibility of electroweak baryogenei have been reviouly exlored in the [], the MSSM [48] and the nmssm [49]. The cubic (A ) term in the tree-level otential make it much eaier to achieve the needed trongly firt-order hae tranition in thee model than in the MSSM [5]. However, we do not conider CP-violating hae in the Higg ector, which i alo a neceary condition for baryogenei. Furthermore, there are other oibilitie for baryogenei. Therefore, electroweak baryogenei contraint are not included here. IV. PARAMETER SCANS To generate the Higg boon mae, we erform both grid and random can over the allowed available arameter ace of each model. In the random can, we evaluate 5 oint in the available arameter ace for each model. Our grid can give a reroducible catalogue of the Higg mae of each model. However, due to the large number of arameter, a finely aced grid on individual arameter i not feaible. The reult from the grid can erve a a ueful guide of the allowed Higg boon mae but do not rovide definitive uer or lower ma limit. The model-indeendent arameter canned over are tan,, eff, A, A t, and M, where we alway aume gaugino ma unification M M 5g M 3g. The mae M U ~ and M Q ~ are the oft mae of the u-tye quark and doublet-tye quark, reectively, and are fixed at TeV; M i the ma of the Z -ino in the. The modeldeendent arameter are and A for the, F and S for the n/mssm, and E6 for the. In the arameter can, we veto oint that fail the direct and indirect contraint of Section III. We chooe the hae convention A >, eff >, with all the VEV real and oitive. We limit h to be real and oitive and allow the gaugino ma M and couling to be real with either ign, although more generally thee arameter could be comlex. With comlex arameter, CP violation could occur. If hae were included, the Higg ector would be further comlicated with u to five tate for the and n/mssm (four tate for the ) that can intermix. The Higg ector with an arbitrary number of additional inglet and CP violation wa tudied in Ref. [35]. The couling run a the energy cale i varied. Naturalne and the requirement that the couling remain 5-7

10 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6) TABLE II. Parameter range in can. (a) Model-indeendent arameter. (b) Modeldeendent arameter. Parameter not canned aume the value M Q ~ M U ~ TeV and Q 3 GeV. tan eff A A t M Range, 5 5, GeV 5, GeV, TeV,TeV 5, 5 GeV Ste ize GeV GeV GeV 5 GeV GeV A S F E6 Range :75,.75,TeV,, ; Ste ize.5 5 GeV.. erturbative at the GUT cale limit : h :75 or : h < :75 for the. The couling in the n/mssm are real and fixed in the interval S ; F with M n 5 GeV. We alo contrain eff to the range 5 eff GeV to avoid fine-tuning. A ummary of the can range over model arameter are given in Table II. For the grid can, the te ize for each arameter i given and we ecifically can tan ; :5; ; ; 5. V. DISCUSSION OF THE HIGGS MASS SPECTRA Throughout mot of the arameter ace, model ditinguihing feature are aarent in the Higg mae. However, different model can roduce imilar mae and mixing in certain limit. Characteritic that are a direct conequence of how the inglet tate mix affect the limit laced on the lightet Higg boon ma. A. Common characteritic If the model-deendent arameter in the Higg maquared matrice are et to zero, we obtain common maquared matrice and an additional ymmetry that alie for each model. For the n/mssm, thi i a Peccei-Quinn (PQ) ymmetry which rotect the ma of one CP-odd Higg. Deending on what arameter vanih, the may either have a PQ or a U R ymmetry [5], the global invariance of uerymmetry. Near thee limit, the A ma in thee extended model i mall, allowing decay mode involving light CP-odd Higg boon; thi i addreed in more detail in Sec. VI B. In the in the g! limit, the gauged U turn into a global U PQ ymmetry for the matter field. A male CP-odd tate, A, emerge, which i jut the Goldtone boon of the broken U while the other CP-odd tate, reent for g, remain maive. The Z decoule and remain male in thi limit. In Table III, we ummarize the common limit of the extended model. In the PQ limit (and for the for all g ), the CP-odd Higg ma-quared matrix factor into a treelevel matrix time the one-loo correction. Such a form i required by the U ymmetrie to require the exitence of two male CP-odd goldtone, one of which i eaten by the Z and the econd by the Z in the after radiative correction are included. Thu, M A i elevated by a factor of kh t A t A F, where the F term i the loo contribution, i.e., MA h A k h t A t vd v F u v u v d : (53) A v d v u Effectively the oft ma i increaed by A! A k h t A tf (54) to romote the tree-level ma of the CP-odd Higg boon to the radiatively corrected one. In the U R limit of the, the radiative correction to the CP-odd mae vanihe. Another limit, the -decouling limit,! while keeing eff h OEW, give imilar EW/TeV-cale Higg boon mae for all model. In thi limit there i little mixing among Higg tate. For the and, two CP-even Higg correond to the MSSM Higg tate, while the remaining Higg boon i dominantly inglet with the ma ordering deending on TABLE III. Common Higg ma-quared matrix limit of variou model and their effect. Note that in the, the U i a global ymmetry and not a remaining U ymmetry. In thee limiting cae, two of the CP-even Higg boon of each model are equivalent to the MSSM Higg boon if eff, while the third decoule and i heavy for the, or light for the n/mssm or. Model Limit Symmetry Effect MSSM B! U PQ M A! ; A! U PQ M A! A ;A! U R M A! n/mssm F, S! U PQ M A! g! U PQ M Z ;M A! 5-8

11 HIGGS SECTOR IN EXTENSIONS OF THE MINIMAL... PHYSICAL REVIEW D 73, 5 (6) A ;;A and g. In the n/mssm, the lightet Higg boon ha vanihing ma and i inglet dominated while H and correond to the MSSM Higg boon. Ma exreion in thi limit cay be found in Aendix D. The Higg boon that i dominantly inglet coule weakly to MSSM article. The trength of a articular Higg boon, H i, couling to field in the MSSM may be quantified a the MSSM fraction H X i MSSM R ij : (55) j Thi quantity i not to be confued with the caled ZZH i couling ZZHi. Since R i unitary, a um rule exit X 3 i H i MSSM ; (56) which imlie that at mot two CP-even Higg boon can be MSSM-like; equal mixing cenario have H ;;3 3.A imilar quantity can be found for the CP-odd Higg boon. In the and in the limit in Table III for the and n/mssm, the MSSM fraction of the maive CP-odd Higg boon i A MSSM v ; co in (57) conitent with the -decouling limit. Since the trace i invariant under rotation, a maquared um rule exit. The limit in Table III lead to a common um rule of the tree-level Higg mae: TrM M M M M M H H H3 A MZ ; (58) where the Z ma i given by MZ G 4 v d v u. The um rule for the MSSM i realized by taking the -decouling limit in the n/mssm, and additionally require g! in the and! in the. In the CP-even and CP-odd ma-quared matrice of Sec. II, we ee that the uer left ubmatrix i that of the MSSM while the third column/row vanihe. Then, the decouled M H and M A (M Z for the ) become male at tree level and the Higg ma-quared um rule become MSSM-like: M h M H M A M Z ; (59) where h H and H H 3 are the uual MSSM CP-even Higge. B. Ditinguihing characteritic The introduction of the inglet Higg field in MSSM extenion roduce Higg boon roertie that are ditinct from thoe of the MSSM. Each model ha additional defining characteritic that may be ued to ditinguih one model from another. In thi ection, we give bound on the lightet CP-even Higg ma and rovide exreion for the mae utilizing the hierarchy of matrix element given in Aendix D. We can over relevant model arameter to determine their effect on the Higg mae. Finally, we ummarize the reult of the comlete random and grid can.. Lightet CP-even Higg ma bound In any uerymmetric theory that i erturbative at the GUT cale, the lightet Higg boon ma ha an uer limit [5]. Since the ma-quared CP-even matrix M i real and ymmetric, an etimation of the uer bound on the mallet ma-quared eigenvalue may be obtained by the Rayleigh quotient MH ut M u u T ; (6) u where u i an arbitrary nonzero vector. With the choice u T co; in MSSM co; in; extended model; (6) the well-known uer bound of the lightet Higg maquared from the ma-quared matrice of Eq. () (6) and (3) (35) are given a (i) MSSM [53]: M H M Z co ~ M ; (6) where ~M M co M in M in: (63) (ii), n/mssm, and Peccei-Quinn limit [54]: M H M Z co h v in ~ M : (64) (iii) [55]: M H M Z co h v in g v Q Hd co Q Hu in ~ M : (65) Although the uer bound change with the choice of the u vector, thee reult indicate that extended model have larger uer bound for the lightet Higg due to the contribution of the inglet calar. The can have the larget uer bound due to the quartic couling contribution from the additional gauge couling term, g,in the U extenion. In the MSSM, large tan value are uggeted by the conflict between the exerimental lower bound and the theoretical uer bound on M H. Since the extended model contain additional term which relax the 5-9

12 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6) theoretical bound, they allow maller value for tan than the MSSM.. Numerical Evaluation of mae a. CP-even Higg mae In Fig. we how the variation of the lightet Higg ma in the different model a function of and tan with the other arameter fixed. (Similar lot for the heavier tate are hown in Aendix E) We only aly the theoretical contraint to thee ectra to ee the general trend of the model before exerimental contraint are alied. The would fail to a the ZZ contraint in mot of the lotted range of. Note that the MSSM doe not conform to the behavior of the extended model in the CP-even ector. Since the MSSM contain only two CP-even Higg boon, the heavier of the two ma-quare increae with eff A at tree level, imilar to the CP-odd and charged Higg mae. Since we fix h :5, thi Higg ma-quared cale a the inglet VEV,. The radiative correction do not contribute a ignificant deendence to the maquared matrix. The tree-level deendence on revent a level croing between the H and H tate. However, in the extended model there are three CP-even Higg boon. Level croing are oible here a there i a Higg boon of intermediate ma: ee Fig. (c). We alo ee a ignificant difference between the MSSM and the extended-mssm model in the tan can, which i exected ince a moderate value of 5 GeV i choen. The term that differentiate the matrix element in the extended model from that of the MSSM are not negligible at thi value of, giving different -deendence of the Higg ma. The MSSM tan can how a di in the Higg ma at tan and a maximal ma i aroached a tan increae. However, the extended-mssm model have a decreae in ma after tan of 4 due to the level croing with the additional moderate ma CP-even Higg reent in thee model. The reence of the di in the mae at tan for the and n/mssm i not a conequence of a level croing, but i due to the ma deendence on tan. When tan, the uer bound on the lightet CP-even Higg ma decreae a een in Eq. (6) (65). Overall, we ee ubtantial difference in the ectra of the lightet Higg in the extended model comared to the MSSM. b. CP-odd Higg Mae Since only one maive CP-odd Higg boon exit in the MSSM,, and the Peccei-Quinn limit of the extended model, the CP-odd CP Even CP Odd 5 5 MSSM n/mssm PQ Limit = 5 GeV 5 5 MSSM n/mssm PQ Limit = 5 GeV tan β (a) tan β (b) CP Even CP Odd 5 5 MSSM n/mssm PQ Limit tan β = MSSM n/mssm PQ Limit tan β = (GeV) (c) (GeV) (d) FIG. (color online). Lightet CP-even and lightet CP-odd Higg mae v tan and for the MSSM,, n/mssm,, and the PQ limit. Only the theoretical contraint are alied with 5 GeV (for tan-varying curve), tan (for -varying curve). Inut arameter of A 5 GeV, A t TeV, M Q ~ M U ~ TeV, :5, A 5 GeV, M n q 5 GeV, F :, S :, h :5, E6 tan 5 3, and Q 3 GeV, the renormalization cale, are taken. The U PQ limit allow one maive CP-odd Higg whoe ma i equivalent to that of the CP-odd Higg. 5-

13 HIGGS SECTOR IN EXTENSIONS OF THE MINIMAL... PHYSICAL REVIEW D 73, 5 (6) mae generally behave the ame over both can and conform to the general caling M A A cot tan. (The exact exreion in thee cae i given by Eq. (53), with the firt term omitted for the MSSM.) Further, we note that the CP-odd ma in the Peccei-Quinn limit i identical to that of the, which may be undertood by the abence of mixing and the reulting ma litting that occur in the MSSM or other extended model. However, the MSSM ma aroache the PQ/ ma a increae, a reult conitent with the -decouling limit. The lightet CP-odd Higg in the n/mssm and the, however, doe not hare the imilaritie of the other model. In thee model, there are two CP-odd Higg boon, reulting in a different deendence on and tan. Mixing effect tend to lower the lightet Higg mae in thee model, roviding intereting henomenological conequence. Thee are further dicued in Sec. VI. c. Higg ma range We ummarize the available range found in the grid and random can of the lightet CP-even, CP-odd, and charged Higg boon mae that atify the alied contraint in Fig.. For each model, the value of the maximum and minimum mae are given a well a the reaon for the bound. The lightet CP-even and CP-odd and the charged Higg boon ma range differ ignificantly among the model. The CP-even Higg ma range i quite retricted in the MSSM and atifie the uer theoretical ma bound and lower exerimental bound from LEP dicued in Sec. III. The uer limit for the CP-even Higg mae in the extended model aturate the theoretical bound and are extended by 3 4 GeV comared to the MSSM while the uer limit in the lightet CP-odd Higg mae are artificial in the MSSM and a they change with the ize of the can arameter uch a A and tan. The lower limit of the lightet CP-odd mae in the MSSM and reflect the LEP limit on M A ; the i imilar to the MSSM ince i required to be large by the trict ZZ contraint, decouling the inglet tate and recovering a largely MSSM Higg ector. However, finetuning the Higg doublet charge under the U gauge ymmetry and tan allow the Z Z mixing contraint on to be le evere, and can reult in a lower Higg ma with reect to the MSSM. Thee intance along with the value A A t GeV allow very low CP-even Higg mae at O GeV and a male CP-odd tate. Since thee oint are ditinct from the range of mae tyically found in the, we do not how thee oint in Fig. but imly note that they exit. However, the and n/mssm may have a male CP-odd tate due to global U ymmetrie dicued in Sec. VA while the uer limit on the lightet CP-odd Higg ma deend on the ecific of the tate croing with the heavier tate, A, that ha a can-deendent ma. In thee model, the CP-odd mae extend to zero ince the mixing of two CP-odd tate allow one CP-odd Higg to be comletely inglet and avoid the contraint dicued above. CP-Even Higg Ma Range CP-Odd Higg Ma Range MSSM Scan Scan n/mssm LEP 9 LEP & α ZZ 9 Th. 35 Th. 64 Th. 7 Th. 73 LEP MSSM 94 Th. State Croing 63 Th. State Croing n/mssm 7 LEP & α ZZ 93 Scan 367 Scan Charged Higg Ma Range LEP MSSM 79 LEP 83 LEP n/mssm 8 LEP 8 Scan 48 Scan 359 Scan 6873 Scan FIG. (color online). Ma range of the lightet CP-even and CP-odd and the charged Higg boon in each extended-mssm model from the grid and random can. Exlanation of extremal bound and their value are rovided for each model. Exlanation are Th. theoretical bound met, value not enitive to limit of the can arameter; Scan-value enitive to limit of the can arameter; State croing - value ha maximum when croing of tate occur (ecifically for A and A in the and n/mssm); LEP exerimental contraint from LEP; ZZ exerimental contraint in the on the Z Z mixing angle. 5-

14 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6).8 MSSM ξ ZZH.. MSSM n/mssm LEP limit 95% C.L M H (GeV) co (β α) M A (GeV) (a) (b) FIG. 3 (color online). (a) LEP limit [38] on ZZHi g ZZHi =g SM ZZh Z!ZHi = SM Z!Zh, the caled ZZH i couling in new hyic, v the light Higg ma. The olid black curve i the oberved limit with a 95% C.L. Point falling below thi curve a the ZZH i contraint. (b) co v M A in the MSSM. The hard cutoff hown by the olid green line at M A 93:4 GeV i due to the contraint on e e! A i H dicued in Sec. III A. The charged Higg mae are found to be a low a 79 GeV in the can, in agreement with the imoed exerimental limit of 78.6 GeV. In thee cae where M H 8 GeV, the charged Higg i often the lightet member of the Higg ectrum. However, thee cae require fine-tuning to obtain value of eff > GeV [9]. The uer limit of the charged Higg ma i deendent on the range of the can arameter a een in Eq. (45). The dicreancy in the uer limit of the charged and CP-odd Higg ma between the and MSSM i a conequence of a lower eff in the, reulting in a lower M Y. Large value of eff are more fine-tuned in the than the MSSM ince the additional gauge, g, and Higg, h, couling often drive MH <. Conequently, CP-odd and charged Higg mae comarable to the higher MSSM limit are not reent in the can. The uer bound on the charged Higg ma in the i relaxed due to the additional arameter of the model. d. Higg boon earche The focu of Higg earche i mot commonly the lightet CP-even Higg boon. In the model that we conider, the lightet CP-even Higg boon can have different couling than in the SM. In Fig. 3(a), we how the reent limit from LEP on the caled ZZH i couling. 9 Mixing effect can lower the ZZH i couling and, in the MSSM, thi occur if M A i low, a een in Fig. 3(b) where the ZZH i couling i lowet for co. However, an additional limit i laced on the mixing via the e e! A i H cro ection dicued in Sec. III A, eliminating low ma CP-even Higg boon in the MSSM, a een in Fig. 3(b). In extended-mssm model, additional mixing may occur with the inglet field. Becaue of thi mixing and the ubequent evaion of the LEP limit on the ZZH i couling, the lightet CP-even Higg may then have a ma maller 9 For clarity, in all the lot that follow we amle the aed oint in the reult from the random can. than the SM Higg ma limit. Indeed, attemt to exlain the :3 and :7 exce of Higg event at LEP for mae of 98 GeV and 4.4 GeV, reectively, with light CP-even Higg boon in the have been exlored [56]. Thi light exce ha alo been tudied in the where a light Higg with a SM couling to ZZ decay to CP-odd air [57]. The reduction in the CP-even Higg ma in extended model can be een in Fig. 4, where we lot the MSSM fraction veru the Higg boon ma. When there i little mixing between the inglet and doublet Higg field, the MSSM limit i reached and the LEP bound alie, a een by the MSSM cutoff at MSSM and M Hi 4:4 GeV. A common feature of each model i a CP-even Higg boon with a ma range concentrated jut above the LEP SM ma limit hown by the dark-green vertical line. Thee Higg boon have a large MSSM fraction, for which the ZZH i couling limit i effective in elimination of the generated oint. We note that there are cae where a Higg boon ma below 4.4 GeV but with relatively high MSSM fraction i allowed due to cancellation between the rotation matrice in Eq. (46). Thi cancellation ermit the lightet MSSM Higg boon to be below the SM limit, and ha been taken a a oible exlanation of the Higg ignal exce [58]. By meauring the lightet Higg boon couling to MSSM field, an etimation of the MSSM fraction may be obtained, roviding imortant information on the inglet content. In the and eecially the n/mssm the lightet CP-even Higg boon may have both low MSSM fraction and low ma a een in Fig. 4(d). Since eff i fixed at the EW cale, the matrix element M i3 are ureed in the n/mssm at large. Thi reult in a low ma CP-even Higg boon with high inglet comoition; the other Higg tate have a high MSSM fraction due to the um rule in Eq. (56). However in the n/mssm, the exitence of a lowma CP-even Higg boon deend on the value of S. In Aendix D g, we how that the tree-level ma-quare of the inglet-dominated CP-even 5-

15 HIGGS SECTOR IN EXTENSIONS OF THE MINIMAL... PHYSICAL REVIEW D 73, 5 (6) n/mssm ξ MSSM H H A A ξ MSSM H H A A.. (a) (b) Lightet Higg ξ MSSM H H A ξ MSSM n/mssm.. (c) (d) FIG. 4 (color online). Higg mae v MSSM in the (a), (b) n/mssm, (c), and (d) the lightet CP-even Higg of all extended model. The vertical line i the LEP lower bound on the MSSM (SM-like) Higg ma. and odd Higg boon in the n/mssm at large are MH MA S Mn 3 ; (66) which force the arameter S to be negative in thi limit. Therefore, a largely inglet CP-even Higg boon can have a ma lower than the LEP limit if S < 4 GeV :: (67) M 3 n In Fig. 5, we how the Higg ma deendence on thi arameter, which exhibit the croing of tate at S :. In the, the lightet Higg ma i concentrated near the LEP limit with MSSM near one, which i a direct conequence of the high contraint laced by the trict ZZ limit. Thi i alo een in Fig. 6, where we lot the Higg mae veru the inglet VEV. The lowet allowed oint in the ha above 8 GeV, comared to the other model which allow to be a low a a few hundred GeV. By examining Fig. 4(c) and 6(c) we ee that M H varie linearly with and i characteritically dominantly inglet. Without the ZZ contraint, the H and H tate cro near 4 GeV. Thi contraint may be evaded by the fine-tuning cae dicued in Sec. V B. At thi oint, the ma eigentate witch content, below which the lightet Higg i dominantly inglet, ha a ma below the LEP bound, and evade the ZZH i couling contraint. The Higg ma deendence on tan ha ome intereting feature, eecially that of the lightet Higg. We how ξ SH H A A n/mssm, M n = 5 GeV - FIG. 5 (color online). Higg ma deendence on S in the n/ MSSM. When S :, H and H witch content, allowing a light CP-even Higg below the LEP limit. 5-3

16 BARGER, LANGACKER, LEE, AND SHAUGHNESSY PHYSICAL REVIEW D 73, 5 (6) H H A A 5 5 (GeV) n/mssm H H A A 5 5 (GeV) (a) (b) Lightet Higg H H A n/mssm 5 5 (GeV) (c) 5 5 (GeV) (d) FIG. 6 (color online). Higg mae v in the (a), (b) n/mssm, (c), and (d) the lightet CP-even Higg of all extended model. The vertical line i the LEP lower bound on the ma of the SM Higg. thi deendence in Fig. 7 for all the Higg boon of each extended-mssm model and earately for the lightet Higg in all the model conidered. The lightet CP-even Higg boon ma v tan in each model hown in Fig. 7(d) ha a majority of generated oint in the band 4:4 GeV & M H & 35 GeV and tan *. Thi i one of the alient feature of the MSSM a hown in Fig. (a). The MSSM arameter ace ha a lower cutoff at tan due to the LEP limit at 4.4 GeV for a SM-like Higg and i hown in Fig. 7(d) a the interection of the theoretical MSSM Higg ma limit hown in blue and the LEP limit in green. However, the extended-mssm model may have value of tan that are below thi region. Since mixing effect can decreae the lightet Higg ma and thereby atify the LEP bound, a trict bound on tan cannot be given. Additionally, an increae in the Higg ma from the MSSM theoretical limit hown in Sec. V B can ermit low tan cenario which have mae above the LEP limit. Among thee model, the heaviet CP-odd Higg tate follow the ame deendence on tan that wa noted above in Sec. VB. The heaviet CP-even Higg and charged Higg boon alo follow thi trend with the charged Higg boon ma having the ame tan deendence a the CP-odd Higg ma, ee e.g. Eq. (45). The heaviet CP-even and CP-odd Higg mae are aroximately the ame even after radiative correction. An exlanation i rovided by the ma-quared um rule that each model obey, namely X MH i X MA j MZ M xmssm M ; (68) j i The um are over the maive Higg boon, and M xmssm i a model-deendent ma arameter with value M h v d v u A ; (69) M n=mssm ; (7) M M Z : (7) The term M in Eq. (68) i due to the radiative correction, and ha a value M TrM M ; (7) that give an etimate of the effect the radiative correction have on the Higg mae. Note that the CP-odd radiative correction, the F term, are cancelled by equivalent term in the CP-even ma-quared matrix. The radiative correction alter the um rule by at mot O GeV over mot of the canned range, a een in Fig. 8 where we lot the hift veru both tan and A t. The radiative correction contribution to the um rule are larget for large A t and mall tan. Since the to quark Yukawa couling increae when tan i mall, the radiative correction are enhanced at mall tan, cauing larger 5-4