Charged scalars from $\mathrm{SU}(3)^3$ theories

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by  José Eliel Camargo-Molina

7 Charged scalars from SU(3)3 theories
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E-mail: [email protected]
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[ InspiredbyarecentlyproposedGUTmodelbasedonthetrinification(SU(3)3)gaugegroupwith

a global family (SU(3) ) symmetry, we consider an effective low-energy three Higgs doublet
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v model that may shed light on what underlies the observed fermion mass hierarchies and CKM
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mixing. Wediscusspossibilitiesforchargedscalarscomingfromthismodeltoshowincollider
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ProspectsforChargedHiggsDiscoveryatColliders
3-6October2016
Uppsala,Sweden
Speaker.
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(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommons
Attribution-NonCommercial-NoDerivatives4.0InternationalLicense(CCBY-NC-ND4.0). http://pos.sissa.it/
ChargedscalarsfromSU(3)3theories JoséElielCamargo-Molina
1. Introduction
In[1,2],asetofGrandUnifiedTheories(GUTs)basedonthetrinificationSU(3)3gaugegroup
was proposed. The theories have very promising features that might lead to low energy scenarios
that can predict e.g. the Cabibbo structure for quark mixing and pave the way for an explanation
tothemasshierarchies intheSM.Thefirstversion [2],leads touniversality ofYukawaandgauge
couplings forchiralquarksandleptonsinasupersymmetric (SUSY)scenario. Thesectorsoflight
Higgsbosons andleptons areunifiedintoasinglechiralsuper-multiplet dramatically reducing the
parameter space ofthemodelwhileleading torealistic lowenergy scenarios. In[1], itwasshown
thatforanon-SUSYGUTwithaverylownumberoffreeparameters,itisstillpossibletogenerate
thetheory’s differentscalesbymeansofradiativesymmetrybreaking. Oneofthemostinteresting
lowenergy scenarios ofthetheories isathree Higgsdoublet model(3HDM).Inthisworkwewill
understand how a specific low energy 3HDM scenario arises from the model proposed in [1] and
whethercharged scalarsfromthemodelwouldbevisible inthemostcommonsearches atcollider
experiments.
2. From trinification to 3HDM
Herewewillbrieflyintroducethenon-SUSYtrinificationscenariodiscussedin[1]. Themodel
consists of three scalar (L˜,Q˜ ,Q˜ ) and three fermion multiplets (L,Q ,Q ) of the trinification
L R L R
gauge group (and the associated gauge bosons) enhanced with a SU(3) global symmetry. The
F
finalsymmetrygroupofthetheoryisthus:
G =[SU(3) SU(3) SU(3) ]⋉Z SU(3) U(1) U(1) , (2.1)
T L R C 3 F A B
× × ×{ × × }
wherethebracketsindicateglobal(includingaccidental) symmetriesofthetheoryandthediscrete
Z leads to gauge coupling unification. Scalar and fermion multiplets share the same quantum
3
numbersasgiveninTable. 1. Theglobalminimumofthetheoryis1
v
(L˜i)l =d id ld 3 T , (2.2)
h ri 3 3 r √2
where the l,r,i indices correspond to the SU(3) groups respectively and Q˜ = Q˜ = 0.
L,R,F L R
h i h i
Thiscanbeshowntospontaneously breakG as
T
G G SU(3) SU(2) SU(2) U(1) SU(2) U(1) U(1) U(1) . (2.3)
T LR C L R L+R F X Z B
→ ≡ × × × ×{ × × × }
SU(3) SU(3) SU(3) SU(3)
L R C F
{ }
L˜,L 333 333¯ 111 333
Q˜ ,Q 333¯ 111 333 333
L L
Q˜ ,Q 111 333 333¯ 333
R R
Table 1: Field content of the GUT-scale trinification model. The fermionic fields are left-handed
Weylfermions.
1In[1]itwasshowedthatthisistheglobalminimumwheneveritexistsasalocalminimun
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ChargedscalarsfromSU(3)3theories JoséElielCamargo-Molina
Dependingonthemassspectrum ofthetheoryafterSSB,differenteffectivefieldtheories can
arisefromthisbreaking. Thedecompositionoftrinificationscalarfieldsintermsofrepresentations
ofthegroupG canbewrittenas(notethatuppercase indicestakevalues1and2)
LR
(L˜i)l =d i d ld R(H˜I)L+d ld 3(l˜ I)L+d ld R(l˜ I) +d ld 3F˜I
r I L r R L r L 3 r R R 3 r
h vi (2.4)
+d i d ld Rh˜L+d ld 3l˜sL+d Ld Rl˜s +d ld 3 F˜s+ 3 ,
3 L r R L r L 3 r RR 3 r √2
(cid:20) (cid:18) (cid:19)(cid:21)
where the gauge Goldstone bosons in L˜ have been removed. Similar decompositions hold for
(Q˜ ),(Q˜ )andtheirfermioncounterparts. In[1],weconsideredalowenergyscenariowhereonly
L R
h˜L and (l˜i ) are light and thus present in the EFT. In this work we will study an alternative case
R R R
inwhich,aftertrinification breaking, thefield(H˜I)L arekeptlightinsteadofh˜L. Aftertrinification
R R
breaking, theSSBchaincontinues bymeansofaVEVinl˜ :
R
w
(l˜ I) =d Id 2 (2.5)
h R Ri 2 R√2
As also shown in [1] this can happen through radiative breaking triggered by RG running. With
thisVEV,thesymmetrygroupisfurther brokenas
G G =[SU(3) SU(2) U(1) ] U(1) U(1) U(1) U(1) , (2.6)
LR→ EW C× L× Y ×{ Y2× Y3× D× B}
AsSU(2) SU(2) isbroken, (H˜1,2)L arenowdistinctfieldsandinparticular, theyareallowed
R× F 1,2
tohavedifferentmasses. Inthefollowing,wewillexplorethelowenergyscenario(inotherwords,
we will focus on a region of the LR symmetric theory parameter space) where after l˜ acquires a
R
VEV,onlythreescalarswillremainlight,namely:
H1L (H˜1)L1 (L˜1)L1 , H2L (H˜2)L1 (L˜2)L1 , H3L e LL′(H˜1∗)2L e LL′(L˜∗1)2L (2.7)
≡ ≡ ≡ ≡ ≡ ≡ ′
(Y,Y ,Y ,D,B) (Y,Y ,Y ,D,B) (Y,Y ,Y ,D,B)
2 3 2 3 2 3
L ( 1, 3, 1, 1,0) q (+1,+5,+13, 1,+1) H (1, 1, 2,0,0)
1 −2 −2 −6 − L1 6 3 18 −3 3 1 2 − −3
L ( 1, 7, 7, 1,0) q (+1, 1, 5 , 1,+1) H (1,1,1,0,0)
2 −2 −2 −6 − L2 6 −3 −18 −3 3 2 2 3
L ( 1, 2, 2,0,0) q (+1,+7,+2,+2,+1) H (1,0,1,0,0)
3 −2 − −3 L3 6 6 9 3 3 3 2 3
e (1,3,4,0,0) u ( 2, 1,+1, 2, 1)
R1 3 R1 −3 −6 9 −3 −3
e (1,1,1,0,0) u ( 2, 13, 8, 2, 1)
R2 3 R2 −3 − 6 −9 −3 −3
e (1,5,5,1,0) u ( 2, 2, 7 ,+1, 1)
R3 2 6 R3 −3 −3 −18 3 −3
d (+1, 7, 5, 2, 1)
R1 3 −6 −9 −3 −3
d (+1,+1, 1 ,+1, 1)
R2 3 3 −18 3 −3
d (+2, 11,+4,+4, 1)
R3 3 − 6 9 3 −3
Table2: Lepton(left),quark(middle)andhiggs(right)U(1) charges.
3. The Model
Wedescribe here thethree Higgs Doublet Model (3HDM)inspired byflavour enhanced non-
SUSY trinification. That is, we take the Standard Model (SM) fermion content and the fields in
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ChargedscalarsfromSU(3)3theories JoséElielCamargo-Molina
eq. (2.7), and give them corresponding quantum numbers under the symmetries of G shown
EW
eq. (2.6). Thelowenergy scenario presented herecorresponds tothelargestcontinuous symmetry
possibleontopoftheSMgaugegroup,U(1) U(1) [3]. Byfixingthechargesofthescalarsto
Y2× Y3
that in [3](right-most panel in Table2), wefindthecharges ofthe fermion fields (left and middle
panel ofTable2). Thesecharges can allbewritten aslinear combinations ofthe generators ofG
T
in Eq. (2.1), which are left unbroken by v and w. The scalar potential with all the symmetries
T
accounted forisquitesimple,
l l H+
V = m 2 H 2+ ij H 2 H 2+ i′j H†H 2 with H = i (3.1)
− i | i| 2 | i| | j| 2 | i j| i √12 vi+Hi0+iA0i .!
We can take all parameters real and l =l , l =l and l =l =(cid:0) l =0 with(cid:1)out loss of
ij ji i′j j′i 1′1 2′2 3′3
generality. Assumingv =0,theextremalconditionsaresolvedbysettingm 2= 1 l +l v2
1,2,36 i 2 ij i′j j
whichleadsto (cid:16) (cid:17)
1
V H0(M2) H0+H (M2) H+ (3.2)
∋ 2 i N ij j i− C ij j
where (M2) = 2(l +l )vv , (M2) = l vv d (cid:229) l v2 and H (H+) . The pseudo-
N ij ij i′j i j C ij i′j i j− ij k i′k k i− ≡ i ∗
scalarsA0 allbecomeGoldstonemodesandarethereforemassless. Thetrinificationfermionfields
i
correspond totheSMonesinthefollowingway
LiL≡(Li)L3, eRi≡(Li)31, qLiL≡e LL′(QLi)L′, uRi =(QRi)1, dRi= (QR2)2,(QR3)2,(QR3)3 i,
(3.3)
(cid:0) (cid:1)
leading totheU(1) charges inTable2. Thefollowing Yukawainteractions areallowedbythelow
energy theorysymmetries:
L ylH†L e +ylH†L e +ylH†L e +ylH†L e (3.4)
∋ 1 1 1 R3 2 1 3 R1 3 2 2 R3 4 2 3 R2
+yuH q u +yuH q u +yuH q u +yuH q u
1 1 L2 R3 2 1 L3 R2 3 2 L1 R3 4 2 L3 R1
+ydH†q d +ydH†q d +h.c.
1 3 L2 R2 2 3 L3 R1
Its important tonote that although the Yukawa sector looks somewhat complicated in comparison
to that of the SM,in eq.(3.4), ya are complex numbers and not 3 3matrices. In total, the model
i ×
has25freeparameters: m 2,l ,l ,yu,l ,yd andg .
i i′j i′j 1,2,3,4 1,2 1,2,3
3.1 CabibbostructureofCKM-matrix
Inthelow-energy 3HDM,thequarkmasstermsintheLagrangian are
0 0 v yu 0 0 v yd
L =MUiju¯iRuLj+MDijd¯RidLj+c.c. where MU= √12 0 0 v12yu24, MD= √120 v3yd1 302, (3.5)
v yu v yu 0 0 0 0
 2 3 1 1   
   
givingamasslessfirstgeneration. We’llarrangethemasseigenstates as
u˜i =(u ,c ,t )i, d˜i =(d ,s ,b )i. (3.6)
R,L R,L R,L R,L R,L R,L R,L R,L
Thesearerelatedtothecharge eigenstates byunitarytransformations,
ui =(Vu)iju˜i , ui =(Vu)iju˜j , di =(Vd)ijd˜j , di =(Vd)ijd˜j. (3.7)
L L L R R R L L L R R R
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ChargedscalarsfromSU(3)3theories JoséElielCamargo-Molina
FromthestructureoftheYukawasectorofthemodel,wefindthatVu,d aresuchthattheCKM
L
matrixautomatically takestheCabibboformbytakingtanq = v2yu3,namely,
C v1yu1
cq sq 0
C C
VCKM=VLu†VLd=−sqC cqC 0. (3.8)
0 0 1
 
 
4. Charged scalarsatcolliders
The purpose of this work is to explore whether charged scalars coming from the above de-
scribed 3HDM could be visible at current collider experiments in the mostcommon channels and
to trigger the discussion for possible ways of testing the model with available data. The study
of neutral scalars and other possible signals is left for further work. In this light, we calculated
branching ratios for the channels usually looked at the LHC in charged scalar searches for five
benchmark points(shownintable3). Thebenchmarkpointswerefoundthroughagridscanofthe
model parameter space requiring a Higgs-like boson with amas of 125 5 GeV, a stable vacuum
±
at tree level and the correct gauge boson masses in agreement with experiment2. In addition we
calculated, forthesamebenchmark points, theinclusive hadronic cross sections shownintables 4
and5forassociated production ofcharged scalarswithW bosonsandup-typequarksrespectively.
4.1 Branchingratios
mH+=162 mH+=165 mH+=164 mH+=118 mH+=138
1 1 1 1 1
mH+=120 mH+=100 mH+=95 mH+=88 mH+=135
2 2 2 2 2
BR(t H+b) 1.972 10 11 5.176 10 9 8.338 10 9 3.505 10 7 1.091 10 8
→ × − × − × − × − × −
5.310 10 8 4.892 10 8 3.761 10 7 2.536 10 7 3.106 10 7
× − × − × − × − × −
BR(H+ cs¯) 0.997 0.999 0.991 0.999 0.973
→
0.999 0.999 0.999 0.999 0.780
BR(H+ W+H0) 0.002 0.001 0.008 Kin.Forb. 0.026
→ i
Kin.Forb. Kin.Forb. Kin.Forb. Kin.Forb. 0.220
BR(t H+b) BR(H+ cs¯) 1.094 10 11 5.169 10 9 8.264 10 9 3.505 10 7 1.061 10 8
→ × → × − × − × − × − × −
5.306 10 8 4.891 10 8 3.761 10 7 2.536 10 7 2.424 10 7
× − × − × − × − × −
BR(t H+b) BR(H+ cb¯) 4.336 10−18 1.630 10−15 4.007 10−15 1.286 10−13 2.200 10−19
→ × → × × × × ×
7.221 10 12 3.670 10 14 2.238 10 14 3.036 10 15 2.362 10 15
× − × − × − × − × −
BR(t H+b) BR(H+ t n ) 5.474 10 15 2.517 10 13 2.967 10 13 1.144 10 11 3.212 10 13
→ × → ∗ × − × − × − × − × −
2.655 10−11 2.381 10−12 1.350 10−11 8.278 10−12 7.336 10−12
× × × × ×
Table3: Branchingratiosforbenchmark points. MassesareinGeV.
In table 3 we show the branching ratios most commonly used in charged scalar searches at
the LHC. As an example, both ATLAS[4] and CMS [5] have presented limits for the production
of H+ t n . The current limits set BR(t H+b) BR(H+ t n ) to around 10 3 – 10 2
∗ ∗ − −
→ → × →
2Thegridscanfound5pointsinaroundtwoweeks,whichhavemotivatedustosearchformoreefficientmethods
toscantheparameterspace.Futureworkwilldescribeonesuchmethodbasedonageneticalgorithm.
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ChargedscalarsfromSU(3)3theories JoséElielCamargo-Molina
(dependingonthechargedscalarmass),muchabovethevaluescalculatedforthe3HDMpresented
in this work. The same holds true for H+ cs¯,cb¯ (se e.g. [6,7]) and thus for the remaining
→
branching ratiosintable33.
4.2 Inclusivehadroniccrosssections
An interesting quantity to look for is the inclusive hadronic cross sections for associated
charged scalar production at collider experiments. Being a highly model dependent quantity, it
might provide some insight into possible model-exclusive signals and how it compares to other
popular models. In tables 5 and 4 we show the cross sections for associated production with up-
type quarks and W bosons respectively. Comparing with similar studies performed e.g. in [8]
and [9], we find that the signal from charged scalars in this model is several orders of magnitude
belowMSSMandNMSSMpredictions andStandardModelbackground attheLHC.
mH1+=162 mH1+=165 mH1+=164 mH1+=118 mH1+=138 mH1+=162 mH1+=165 mH1+=164 mH1+=118 mH1+=138
mH2+=120 mH2+=100 mH2+=95 mH2+=88 mH2+=135 mH2+=120 mH2+=100 mH2+=95 mH2+=88 mH2+=135
0.104×10−10 0.109×10−7 0.130×10−7 0.367×10−7 0.177×10−8 0.124×10−9 0.138×10−6 0.162×10−6 0.358×10−6 0.191×10−7
0.568×10−8 0.456×10−8 0.352×10−7 0.240×10−7 0.452×10−7 0.561×10−7 0.399×10−7 0.294×10−6 0.190×10−6 0.487×10−6
Table 4: Inclusive hadronic cross sections Table 5: Inclusive hadronic cross sections
(in pb) for H /W+ associated production (inpb)forup-typequarkassociatedH pro-
− −
(Fig.1) duction(Fig.2)
d Hj−
Hi0
d¯ W+ d Hi−
d Hi−
d Hi−
d Hi− u d
u γ,Z
G u G u
d¯ W+ d¯ W+
Figure 2: Diagrams included in the cross
Figure 1: Diagrams included in the cross section sectioncalculationforH /uassociatedpro-
−
calculation forH /W+ associated production. duction.
−
5. Conclusions anddiscussion
Bylookingattheresults,itisclearthatthecommonchannels forchargedscalarsearcheswill
notdetectorexcludethechargedscalarscomingfromtheproposed model. Duetothe
unconventional Yukawasector, aconsequence ofthehigh-scale trinification symmetry,the
coupling ofcharged scalarstoquarks(controlling thedominantdecaychannels ine.g.the
StandardModel)leadstoverylowcrosssections andatypicaldominantdecaychannels (e.g.
H+ cs¯). Thiscallsforamorethorough phenomenological analysis andthedetermination of
→
interesting channels tolookforincurrentandfuturecolliderexperiments.
3TheH+ tbchanneliskinematicallysuppressedinallbenchmarkpoints
→
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ChargedscalarsfromSU(3)3theories JoséElielCamargo-Molina
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