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arXiv:0806.0386v3 [hep-ph] 1 Nov 2008 a osdrteatraiepsiiiyo sinn the assigning of possibility One alternative . the spin-0 consider are supermul- can chiral their to and belong left- tiplets the differ both top that models right-handed supersymmetric unex- spins and in with be Usually particles not 1/2. a relates by should is SUSY possibility loop as a top pected, Such the cancelling . for spin-1 responsible partner top There these with [3]. associated phenomenology models. exotic folded very be and can [2] model Higgs ynwprilsa h e cl ihthe one-loop with scale the TeV the [1], at particles cancelled theories new are by particles Higgs SM the little from divergences quadratic In were mass-squared discovered. 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SM corresponding the nti etrw ilepoetepsiiiyta the that possibility the explore will we Letter this In nrcn er,svrlohrpsiiiiso cancelling of possibilities other several years, recent In new for candidate promising and popular most The nteSadr oe S) h ig mass-squared Higgs the (SM), Model Standard the In o ur suie ihteHgs h o uaaaie from arises Yukawa top the Higgs, the supe with their unified hence and is supermultiplet quark vector top a of the ecntutasprymti oe hr h ethne t left-handed the where model supersymmetric a construct We SU 3 ag ru,a ntetwin the in as group, gauge (3) eateto hsc,Uiest fClfri,Dvs CA Davis, California, of University Physics, of Department ayn a,Hi-haCeg n onTerning John and Cheng, Hsin-Chia Cai, Haiying pn1TpQakSuperpartner Quark Top Spin-1 A same ∼ pn as spins TeV. 2 c- - ag ru.Te locarry also They group. gauge h e cl ont h ignlS ag group gauge SM diagonal the to down SU scale TeV the ainvle VV)o h ed Φ fields the of (VEVs) values tation e noacia uemlilttasomn ne the under uni- transforming be supermultiplet should SU chiral Higgs a the implies into and which fied top interaction, right-handed the a that coupling Yukawa from top the left- come gaugino, the should a identifying as By quark superpart- quark. top the top handed as left-handed them the identify of to ner try can we and group, SU h w ig obesbln to belong doublets Higgs two The rnfriga ( as transforming h edcneti ie nTbeI. 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H , Y 2 V µ H 5,i otisguebosons gauge contains it (5), µ H ytenneovcu expec- vacuum nonzero the by × 3 H + Φ U SU 3 H ( = Y Φ 1 hre nodrt ar- to order in charges (1) SU Eij + 3 5.I sboe at broken is It (5). T + 5 Y (3) SU L c H , Uij µ and i 3 e , 2 × (3) j Φ 2 Φ Q Φ ) SU 2 . 5 3 ¯ i 2 Φ × Φ , H. u fthe of 2 A (2) j SU trsand -terms Φ 2 , H × 2 SU 2 sub- (2) H Φ U and 2 SU (3) We . (1) (1) (2) (5) H H × . 2

H V 24 SU(3) SU(2) U(1) U(1) SU(5) H + V + aT U(1)Y gauge group are given by 1 1 1 Qi 6 0 6 1 1 1 1 1 1 1 2 2 = + , = + + , (5) ui 1 0 1 2 2 2 2 2 2 2 − 3 − 3 g2,3 gˆ2,3 gˆ5 g1 gˆ1H gˆ1V 15ˆg5 1 1 1 1 di 3 0 3 whereg ˆ andg ˆ5 are the gauge couplings of the original 1 1 i Li 1 0 1 − 2 − 2 SU(3), SU(2), U(1)H , U(1)V and SU(5) gauge groups ei 1 1 1 0 1 1 respectively. There are two broken U(1) gauge bosons 1 1 1 1 2 1 whose masses are fixed by H 2 10 ( 3 , 2 ) 1 1 1 1 2 1 1 1 5 H 2 10 ( 3 , 2 ) 1 2 2 gˆ H gˆ V gˆ 2 − − − − 6(f3 + f¯3 )( B1H B1V B24) 1 1 1 1 L⊃ 2 6 − 10 − √15 Φ3 6 10 (0, 6 )  − − 1 1 1 2 2 gˆ1V √15 2 Φ2 0 10 ( 6 , 0) +4(f2 + f¯2 )( B1V gˆ5B24) . (6) 10 − 10 1 1 1 1 Φ3 6 - 10 (0, 6 )  1 1 1 The masses of the other heavy gauge bosons after sym- Φ2 0 10 ( 6 , 0) − − metry breaking are given by, 2 2 2 2 ¯2 TABLE I: The field content of the model. The last column mG′ = (ˆg3 +ˆg5)(f3 + f3 ), (7) 2 2 2 2 2 is the hypercharge of the diagonal hypercharge U(1)Y , where ¯ mW ′ = (ˆg2 +ˆg5)(f2 + f2 ), (8) Y = H + V + aT24, with a = 1/√15. 2 1 2 2 2 2 2 m = gˆ5(f3 + f¯3 + f2 + f¯2 ). (9) Q~ 2 SUSY-breaking terms as it is not essential for the dis- The Q~ will be the dominant superpartner cussion here. We assume that due to SUSY break- of the left-handed top and doublet Q as ing the potential for Φj , Φj is unstable at the origin we will see later. We denote it with an arrow above the so that they get the following nonzero VEVs, breaking particle name to emphasize that it is a spin-1 superpart- SU(3) SU(2) U(1)H and SU(5) U(1)V down to the ner as opposed to the usual tilde used for superpartners. × × × diagonal SM gauge group, In SU(5) grand unified models these gauge bosons are often denoted by X and Y . For other particles beyond f3 0 000 f 3 0 000 the MSSM, we use the notation that the particles with T Φ3 = 0 f3 0 00 , Φ3 = 0 f 0 00 , odd R-parity in a supermultiplet have a tilde above the h i   h i  3  0 0 f3 0 0 0 0 f 3 0 0 particle name, and the particles with even R-parity do         not. 0 0 0 f2 0 T 0 0 0 f 2 0 The Yukawa couplings for the light SM fermions arise Φ2 = , Φ2 = .(3) h i 0000 f2! h i 000 0 f 2! from the last three terms of the superpotential (2). Af- ter substituting in the VEVs of the Φ2 and Φ2 fields, The alignment of the VEVs of Φ3 and Φ2 is ensured by they become the usual Yukawa terms. The fact that the y1Q3Φ3Φ2 term in the superpotential. The VEVs f3, they come from nonrenormalizable interactions can ex- f¯3, f2, and f¯2 are not equal in general as they depend on plain why they are small. Note that the scalar compo- 2 2 the soft SUSY breaking terms and µ2, µ3. The unequal nents of the Φ and Φ fields that get VEVs must have 2 2 the same R-parity assignments as the Higgs fields, i.e. VEVs can generate a U(1)H D-term, (ˆg1H /2)(f¯3 f3 ), 2 2 2 − 2 +. We will come back to the issue of the R-parity as- and a U(1)V D-term, (ˆg1V /10)(3(f3 f¯3 )+2(f2 f¯2 )). which in turn gives additional contributions− to the− scalar signments later. masses of fields charged under the U(1)s. We assume For the , Q3 and u3 mix with other states of that these are small enough not to affect the spectrum the same quantum numbers under the SM gauge symme- dramatically. try through the y1, y2, and µ terms. The mass matrix 3 2 With the above VEVs, the Φ fields split into the fol- for the fermions in the ( , , 1/6) sector is lowing representations under SU(3)C SU(2)L U(1)Y : × × λ Φ2t Φ3t Q3 λ¯ M5 gˆ5f2 gˆ5f¯3 0 Φ3 (1, 1, 0)+(8, 1, 0)+(3¯, 2, 1/6) , (10) → − Φ3t gˆ5f3 0 µ3 y1f¯2 Φ3 (1, 1, 0)+(8, 1, 0)+(3, 2, 1/6) → Φ2t gˆ5f¯2 µ2 0 y1f3 Φ2 (3, 2, 1/6)+(1, 1, 0)+(1, 3, 0) → Φ2 (3¯, 2, 1/6)+(1, 1, 0)+(1, 3, 0) (4) where λ, and λ¯ are the gauginos corresponding to the → − broken generators in SU(5) which are in the vector su- ∗ The gauge couplings for the SM SU(3)C SU(2)L permultiplets with Q~ and Q~ ; M5 is the SUSY-breaking × × 3 gaugino mass for all SU(5) gauginos; Φ2t, Φ3t are the twisted R-parity plays the same role as the usual R-parity color triplet fermions from Φ2, Φ3, and Φ3t, Φ2t are the in MSSM and it is conserved in all the interactions. More color anti-triplet fermions. The massless left-handed top explicitly the bosonic and fermionic components of H are quark is a linear combination of λ,Φ2 , Φ3 , and Q3. For t t ˜ M5 gˆ5f2,g ˆ5f3 µ3 (ˆg5f¯2), andg ˆ5f¯2 µ2, the mass- H (T , H1)+ θ(T , H˜1) . (14) ⊃ less≪ left-handed top≪ quark state is mostly≪ made of the Similarly if we use a subscript s and a to denote the gaugino λ. For example, if we take f¯2 = 1.5 TeV, f2 = 3 1.7 TeV, f¯3 = 0.6 TeV, f3 = 0.4 TeV, M5 = 0.7 TeV, SU(3)C singlet and adjoint pieces of Φ , and s and a for 2 µ2 = 5 TeV, µ3 = 2 TeV,g ˆ5 = 1.2, and y1 = 1.5, then the SU(2)L singlet and adjoint pieces of Φ we have the massless combination is Φj (Φjs, Φja, Φ˜ jt)+ θ(Φ˜ js, Φ˜ ja, Φjt) . (15) ⊃ Q (t, b)L 0.93λ 0.31Φ2t 0.02Φ3t 0.18Q3.(11) ≡ ≈ − − − Similarly, there is a new number symmetry which is a linear combination of the original baryon number For the right-handed top quark, u3 mixes with the col- (with Φ3, Φ3 carrying original baryon number 1/3, ored fermion component of H through the y2 term in the − superpotential Eq.(2). The mass matrix is: +1/3 respectively) and a gauge transformation 2(V + aT24). It is left unbroken by the VEVs, so there is no T u3 dangerous decay or -anti-neutron oscilla- c tion induced. T µH y2f¯3. The couplings of W ′, B′, and B′′ to the light One can see that for y2f¯3 µH , the massless combina- SM fermions are suppressed byg ˆ2/gˆ5,g ˆ1 /√15ˆg5 and ≫ H tion is mostly T . For example, if we take µH =0.3 TeV, gˆ1H /gˆ1V relative to the SM W and B gauge bosons re- y2 =1.5, and f¯3 =0.6 TeV, then spectively. The experimental constraints on Z′ put a lower bound on mW ′ at about 800 GeV. The more strin- t¯R =0.95 T 0.32 u3. (12) ′ − gent constraints come from the mixing of W , B and W , B′, B′′ due to the Higgs VEVs because the two Higgs As the left-handed and right-handed top quarks lie doublets and the light fermions transform under different mostly in λ and T respectively, the top Yukawa coupling gauge groups. In terms of the usual S, T parameters [4], predominantly comes from the gaugino interaction, the strongest constraint comes from T forg ˆ1V & 2 3 and † 2 ¯2 − gˆ5H λT . (13) it depends only on f2 +f2 . For a light Higgs ( 115 GeV) 1 2 2 2 ∼ f2 +f¯2 is required to be & (3 TeV) . For a heavier Higgs 2 2 This explains why the top Yukawa coupling is (1). Note the bound is weaker and f2 + f¯2 might be as low as O 2 that the top quark gets its mass mostly from H1, which (2 TeV) . Another constraint comes from the correc- ∼ is the same Higgs field that gives masses to the down tions to the Z b¯b vertex. The bL quark in this model type quarks and the charged leptons, while the up and is a linear combination→ of several fields and is mostly the charm quarks get masses from H2. This is because unlike gaugino of SU(5). It couples to the heavy gauge bosons the holomorphic superpotential, the gaugino interaction differently from dL, sL. It induces a correction to ZbL¯bL ′ ′ ′′ involves the conjugate of the Higgs field. The top quark coupling after Higgs VEVs mix Z with W3, B , and B . also receives a small contribution to its mass from the y2 Requiring that δgLb/gLb < 0.6% puts a lower bound of term and nonrenormalizable terms, which can account 1.6 TeV for mW ′ . Note, however, that these are indi- for the small mixings with light quarks. ∼rect constraints. It is possible that these contributions It is also interesting to note that if Φj , Φj fields have are cancelled by some additional contributions. It is still additional interactions, for instance, in the case that µ2, quite possible that Q~ has a mass below 2 TeV. µ3 may come from the VEV of some other field, the Higgs The model predicts the existence of new gauge bosons quartic coupling can receive a large tree-level correction, G′, W ′, B′,B′′ and several new fermions t′, b′ around the 2 proportional tog ˆ5, compared with the MSSM value after same scale as the spin-1 top superpartner Q~ . The masses integrating out the heavy states. of the gauge bosons are closely related through Eqs. (7)– Since we unify the right-handed top quark with the (9). For heavy t′ and b′ quarks, there are three doublets Higgs field in the same SU(5) multiplet, one may ask and one singlet. Their masses depend on the model pa- whether R-parity is conserved in this model. We have rameters. For the set of the parameters considered earlier already seen that the scalar pieces of Φ2 and Φ2 that above Eq. (11), (12) andg ˆ3 =2.0,g ˆ2 =0.75,g ˆ1H =0.36, have VEVs must have even R-parity. We have implicitly gˆ1V =3.5 at 2 TeV (to produce the measured values of ∼ assumed above that the color triplet fermions in Φj , Φj , SM gauge couplings), the sample spectrum for the heavy and H have even R-parity and therefore that the scalar gauge bosons and fermions is listed below. partners have odd R-parity. It is easy to check that a ′ modified R-parity with a twist P = ( 1, 1, 1, 1, 1) in G′ W ′ B′ B′′ QQ~ ′ Q′′ Q′′′ T − − − (16) the SU(5) sector will satisfy the above constraints. This M/TeV 1.7 3.2 0.83 2.6 2.0 0.65 3.0 5.8 0.95 4

The spectrum of superpartners depends on the soft- The total cross-sections of the top partners have been SUSY-breaking terms. The superpartners of the light used as a way to distinguish little Higgs models from fermions can have masses in the multi-TeV range with- SUSY models as the total cross-section of the fermionic out affecting the naturalness of electroweak symmetry top partner is much larger than that of a scalar partner breaking because of the small Yukawa couplings. The for the same mass [5]. However, we see that the spin-1 SUSY-breaking masses of Φ2,3, Φ2,3 should also be in the top partner can have an even larger total cross-section TeV range in order to induce symmetry breaking VEVs for the same mass. of the TeV scale. We assume that all soft-SUSY-breaking With a similar spectrum the Q~ decay is similar to the scalar masses except those of H and H are large (& a few usual top squark decay . If the gauginos are light, it TeV). In this case, most of the scalar superpartners are will decay to a gaugino and a top or bottom quark, and beyond the reach of the LHC. On the other hand, the eventually end up with a lightest R-parity odd particle soft masses of H and H are relevant for stabilizing the through cascade decays. One such possible decay channel electroweak scale as they contain the Higgses and the is shown in Fig. 2. It may have a different angular dis- right-handed top quark. They need to be at 1 TeV or tribution for its decay products compared with the usual ∼ below. Electroweak gauginos also give significant contri- top squark, but it would be very challenging to tell at butions to the Higgs masses. We assume that the SUSY- the LHC. breaking gaugino masses are of the order a few hundred ˜ GeV, smaller than (most of) the soft scalar masses. This B0 ~ ˜ + can be naturally achieved if there is an approximate R Q W symmetry in the SUSY breaking sector. b W + With the spectrum assumed above, the superpartners L µ of the SM particles that can be seen at the LHC are the spin-1 partner of the left-handed top-bottom doublet, the scalar partner of the right-handed top, gauginos of the FIG. 2: A decay chain for the spin-1 top partner. SM gauge group, and . In addition, we expect to see new gauge bosons, t′, b′, and some of their super- In conclusion, we have shown that a spin-1 top part- partners. We will focus on the spin-1 partner of the top ner requires an extended gauge symmetry which can ex- and bottom doublet. At the LHC, the main production plain why one quark is much heavier than the others, mechanism is GG Q~ Q~ ∗. The processes with qq¯ initial and provide a larger Higgs quartic coupling than in the states are suppressed→ by destructive interference between MSSM. The spin-1 top partner thus provides a interesting G and G′ exchanges because q, q¯ and Q~ transform under (and experimentally challenging) new scenario for LHC different UV gauge groups. The dominant production physics. cross-sections of the spin-1 and spin-0 top partners of We thank K. Agashe and C. Csaki for pointing out this model from are shown in Fig. 1 as functions an extra U(1) symmetry in this model. This work was of their masses. In comparison, the cross-sections of the supported in part by U.S. DOE grant No. DE-FG02- (right-handed) top squark in MSSM and fermionic top 91ER40674. partner in little Higgs models are also shown.

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