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Published for SISSA by Springer

Received: July 10, 2014 Accepted: August 7, 2014 Published: August 26, 2014

N. Chamoun,a,b H.K. Dreiner,b F. Staubb and T. Stefaniakb

aPhysics Department, HIAST,

P.O. Box 31983, Damascus, Syria

bPhysikalisches Institut and Bethe Center for Theoretical Physics, University of Bonn, Nussallee 12, 53115 Bonn, Germany

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: In order to accommodate the observed Higgs boson mass in the CMSSM, the stops must either be very heavy or the mixing in the stop sector must be very large. Lower stop masses, possibly more accessible at the LHC, still give the correct Higgs mass only if the trilinear stop mixing parameter [notdef]At[notdef] is in the multi-TeV range. Recently it has

been shown that such large stop mixing leads to an unstable electroweak vacuum which spontaneously breaks charge or color. In this work we therefore go beyond the CMSSM and investigate the e ects of including baryon number violating operators [prime][prime] D D on the

stop and Higgs sectors. We nd that for [prime][prime] [similarequal] O(0.3) light stop masses as low as 220 GeV

are consistent with the observed Higgs mass as well as avour constraints while allowing for a stable vacuum. The light stop in this scenario is often the lightest supersymmetric particle. We furthermore discuss the importance of the one-loop corrections involving R-parity violating couplings for a valid prediction of the light stop masses.

Keywords: Supersymmetry Phenomenology

ArXiv ePrint: 1407.2248

Open Access, c

[circlecopyrt] The Authors.

Article funded by SCOAP3. doi:http://dx.doi.org/10.1007/JHEP08(2014)142

Web End =10.1007/JHEP08(2014)142

Resurrecting light stops after the 125 GeV Higgs in the baryon number violating CMSSM

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Contents

1 Introduction 1

2 The MSSM with baryon number violation 2

3 Light stop, the Higgs mass and vacuum stability 43.1 Dominant (s)top corrections to the Higgs mass 43.2 Vacuum stability and R-parity violation 53.3 Loop corrections to the stop mass 7

4 Results 74.1 Numerical setup 74.2 Light stops in the CMSSM withDD operators 10

5 Conclusion 14

A Benchmark points 15

B D D corrections to stop masses 15

C Minimising the scalar potential of the MSSM with D D operators 18

1 Introduction

Run I of the the Large Hadron Collider (LHC) is complete. To date, there is no evidence for superpartner particles as predicted in supersymmetry (SUSY) [1] or experimental indications of any other physics beyond the Standard Model (SM).1 The simplest SUSY scenarios like the constrained minimal supersymmetric standard model (CMSSM) [2] are under pressure by the ongoing non-discovery, leading to the exclusion of large areas of parameter space [36]. The observed Higgs boson mass of mh 126 GeV [7, 8] is within the

previous predicted allowed range for supersymmetric models, including the CMSSM [9]. In order to have at least part of the SUSY spectrum moderately light and accessible at the LHC, i.e. stop masses of m~t1 [lessorsimilar] 500 GeV, it is necessary to maximise the mixing parameter in the stop sector, Xt [10]. However, it has been pointed out that large stop mixing in the (C)MSSM with rather light stop masses su ers from an unstable electroweak vacuum, such that charge or colour would be broken in a cosmologically short time [1114]. A stable electroweak vacuum together with the correct Higgs mass implies a lower limit on the stop

1See for example the talk given by O. Buchmller at the EPS 2013 conference in Stockholm https://indico.cern.ch/event/218030/ session/28/contribution/869/material/slides/

Web End =https: https://indico.cern.ch/event/218030/ session/28/contribution/869/material/slides/

Web End =//indico.cern.ch/event/218030/session/28/contribution/869/material/slides/ .

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mass of at least 800 GeV. At the same time the stop should not be too heavy, in order to avoid the ne-tuning related to the hierarchy problem, see for example ref. [15].

These conclusions are restricted to the (C)MSSM. More recently, non-minimal SUSY models have gained more attention. For instance, singlet extensions which give additional tree-level contributions to the Higgs mass, soften signicantly the little hierarchy problem of the MSSM and can accommodate a much smaller stop mixing while obtaining the correct Higgs mass [1624]. However, there are also non-minimal SUSY models with the MSSM particle content with appealing properties. It has been pointed out that the MSSM together with R-parity violation (RpV) [2528] can signicantly weaken the collider mass limits [29 32] and provide a rich phenomenology [3336]. It is the purpose of this paper to extend the (C)MSSM to allow for the R-parity baryon-number violating operators [prime][prime]ijki Dj Dk and in this framework to determine the allowed stop mass regions, which give (a) the correct Higgs mass, (b) a charge and colour stable vacuum, and (c) full all experimental constraints from avour observables. We show that in this case it is possible to have light stop masses of a few hundred GeV together with a Higgs mass consistent with the LHC observations, but without introducing charge and colour breaking (CCB) minima.

The paper is organised as follows: in section 2 we introduce the model under consideration. In section 3 we explain the connection between the Higgs mass, light stops and the occurrence of charge and colour breaking minima in the baryon number violating CMSSM. In section 4 we present our numerical results, before we conclude in section 5. In the appendices we provide our benchmark points, section A, the one-loop RpV corrections to the squark masses, section B, as well as the minimum of the scalar potential, the vacuum, of the MSSM in the presence of [prime][prime]ijki Dj Dk operators, section C.

2 The MSSM with baryon number violation

R-parity is a discrete Z2 symmetry of the MSSM which is dened as [2528, 37]

RP = (1)3(BL)+2s , (2.1) where s is the spin of the eld and B, L are its baryon respectively lepton number. We consider in the following the R-parity conserving superpotential of the MSSM

WR = Y ije LijHd + Y ijd Qi DjHd + Y ijuQijHu + [notdef] HuHd , (2.2)

and extend it only by the renormalizable baryon number violating operators [38, 39]

B = 12 [prime][prime]ijk

i Dj Dk, (2.3)

which also violate R-parity. Here i, j, k = 1, 2, 3 are generation indices, while we suppressed SU(3) colour and SU(2) isospin indices. In both of the previous equations Li,j, Qi,i, Di, Hd, Hu denote the left chiral superelds of the MSSM in the standard notation [28].

We thus have for the total superpotential

Wtot = WR + W/

B . (2.4)

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This superpotential arises for example from the unique discrete gauge anomaly-free hexality ZR6. This is a discrete R-symmetry2 and is derived and discussed in ref. [42]. The low-energy [notdef] term given in eq. (2.2) is generated dynamically [43, 44].

For the superpotential in eq. (2.4) the proton is stable, since lepton number is conserved, and the proton thus has no nal state to decay to. However, heavier baryons can decay via double nucleon decay and virtual gluino or neutralino exchange [45], if [prime][prime]

couplings to light quarks are non-vanishing. However, we concentrate in the following exclusively on RpV couplings which involve the top quark. These are presently just bounded by perturbativity constraints [46], but could contribute at the one-loop level to avour violating processes if the SUSY masses are not too heavy. For SUSY masses in the TeV range these e ects are usually very small and do not provide better limits [47]. The main reason is that it is usually only possible to constrain products of [prime][prime] couplings by avour observables. However, we are going to consider in the following the case of only one non-vanishing [prime][prime] at the GUT scale. Other couplings get induced via the RGE running because of the quark avour violation but those remain small.

The corresponding standard soft supersymmetry breaking terms for the scalar elds

eL, eE, eQ, eU, eD, Hd, Hu and the gauginos

eB,

fW ,

eg read

LSB,R=m2Hu[notdef]Hu[notdef]2+m2Hd[notdef]Hd[notdef]2+

eQm2[tildewide]Q [tildewide] Q+

eLm2[tildewide]L [tildewide] L+

eDm2[tildewide]D [tildewide] D+

eUm2[tildewide]U [tildewide]

U +

eEm2[tildewide]E [tildewide] E

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+12

eB + M2

fWa

fW a + M3

eg + h.c.

[parenrightBig]

eQTu

eUHu +

eQTd

eDHd +

eLTe

eEHd + BHuHd + h.c.) (2.5)

B = 12T [prime][prime] ,ijk

eDk + h.c. . (2.6)

Here we have suppressed all generation indices, except in the last RpV term. The m2~F are 3[notdef]3 matrices and denote the squared soft masses of the scalar components

eUi

eDj

~F of the

corresponding chiral superelds F . The Tu,d,e are 3[notdef]3 matrices of mass-dimension one. They are trilinear coupling constants of the scalar elds, and can be written in terms of the standard A-terms [48] if no avour violation is assumed, T fii = AfiY iif, with i = 1, 2, 3, and no summation over repeated indices, and f = e, u, d. Similarly, for the baryon number violating term we have T [prime][prime] ,ijk = A[prime][prime]ijk [prime][prime]ijk, again with no summation.

Already the general, R-parity conserving MSSM with massless neutrinos has 105 parameters beyond those of the SM [49]. In the R-parity violating sector, as shown, there are 36 additional parameters. Note that [prime][prime]ijk and T [prime][prime] ,ijk are anti-symmetric in the last two indices and can be complex. In order to signicantly reduce the number of free parameters, we study a constrained model similar to the R-parity conserving CMSSM. As usual, we demand that all soft-breaking masses are universal at the grand unication (GUT) scale, MGUT = O(1016 GeV). In addition, we treat the soft-breaking RpV couplings T [prime][prime] ,ijk in

the same way as the trilinear soft-breaking couplings of the MSSM, i.e. we assume that it is proportional to the corresponding superpotential term at MGUT, with a universal

2For a discussion of R-symmetries see for example refs. [40, 41].

Figure 1. On the left: approximation of the light Higgs mass at one-loop as a function of Xt with m~t1 = 750 GeV (dotted), m~t1 = 1000 GeV (dashed), m~t1 = 1500 GeV (full). On the right: mh as a function of m~t1 with Xt = 2.5 TeV (dotted), Xt = 3 TeV (dashed), Xt = 3.5 TeV (full). In

both plots we set m~t2 = 2 TeV.

proportionality constant A0. Thus, our boundary conditions at MGUT are

m20 m2Hd = m2Hu , 1m20 m2[tildewide]Q

= m2[tildewide]D

= m2[tildewide]U

= m2[tildewide]E

= m2[tildewide]L

(2.7)

M1/2 M1 = M2 = M3 (2.8) T [prime][prime] A0 [prime][prime] , Ti A0Yi with i = e, d, u . (2.9)

The parameters [notdef] and B are xed by the minimisation conditions of the vacuum ground state and we always set [notdef] > 0. We furthermore assume that all CP-violating phases vanish.

3 Light stop, the Higgs mass and vacuum stability

3.1 Dominant (s)top corrections to the Higgs mass

The main corrections to the light Higgs mass in the MSSM at one-loop stem from the (s)top contributions. They can be written in the decoupling limit MA MZ as [1, 9, 10, 5052]

m2h = 3

X2t 12M2S [parenrightbigg][bracketrightbigg]

with MS pm~t1m~t2, mt being the running DR top mass and Xt At [notdef] cot . Our con

vention for the electroweak vacuum expectation value (vev) is v [similarequal] 246 GeV. If one wants

to keep m~ti moderately low (around or even below 1 TeV) the loop corrections required to explain the measured Higgs mass can be achieved by maximising the contributions proportional to the stop mixing Xt. m2h becomes maximal for Xt = p6MS. In the following, we want to discuss the dependence of the light Higgs mass on Xt and m~t1 in more detail. For this purpose we show in gure 1 the approximate values of the light Higgs mass at the one-loop level as function of these two parameters, respectively, keeping the other two xed. The plots are based on the approximate formula given in eq. (3.1). One can see that the light stop mass can be reduced by a few hundred GeV, for xed values of Xt, without a ecting

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m4t v2

log M2Sm2t+ X2t M2S

(3.1)

Figure 2. Left: the minimal value of A0 in GeV compatible with a stable EW vacuum as a function of m0 for M1/2 = 0.5 TeV (dashed), 1.0 TeV (dotted), 1.5 TeV (dot-dashed), 2.0 (full) and tan = 15. Right: for the corresponding value of A0(m0) of a given point in the left gure we compute the lightest stop mass. This is shown on the right as a function of m0 for the same choices of M1/2. We set tan = 15 in all cases.

the one-loop corrections to the light Higgs mass substantially. However, it is not possible in the CMSSM to change m~t1 without a ecting Xt and/or m~t2, because all three parameter depend on m0, A0 and tan . This is problematic because it has recently been pointed out that the maximal mixing scenario, Xt = p6MS, in the context of a light SUSY spectrum is ruled out by the instability of the electroweak (EW) vacuum: the required large values of [notdef]A0[notdef]

compared to m0 lead to minima in the scalar potential below the EW vacuum, where colour and charge are broken by vacuum expectation values of stops or staus [1113]. Furthermore, the EW vacuum would decay in a cosmologically short time. The condition of a stable EW vacuum can be used to put a lower limit on the light stop mass in the R-parity conserving CMSSM: one can determine the maximal value of [notdef]A0[notdef] allowed by vacuum stability for

xed values of [notdef]m0, M1/2, tan [notdef]. This value can be translated into the minimal allowed

stop mass for a given combination of [notdef]m0, M1/2, tan [notdef]. These limits have been derived in

ref. [11] and we present examples in gure 2. For m0 > 1 TeV, M1/2 > 1 TeV it is not pos

sible to get a light stop mass below 1 TeV. Lighter stops are possible for smaller values of

M1/2. However, this is often in conict with current lower limits from gluino searches [53]. The constraint from the Higgs mass measurement has not yet been applied at this point.

3.2 Vacuum stability and R-parity violation

The situation described above changes if one allows for non-vanishing R-parity violating couplings. These a ect at one-loop for example the running of Tu,33 = AtY ttu and m2u,33 = m2~tR [28]:

(1)Tu,ij = (1),MSSMTu,ij + 2 [prime][prime] abcYu,ajT [prime][prime] ibc + [prime][prime] cab [prime][prime]iabTu,cj, (3.2)

(1)m2,ij = (1),MSSMm2u,ij + 2T [prime][prime] jabT [prime][prime] iab

+ 4 [prime][prime] jac [prime][prime]iabm2~D,cb + [prime][prime] cab [prime][prime]iabm2~U,cj + [prime][prime] jbc [prime][prime]abcm2~U,ia. (3.3)

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Figure 3. First row: the lightest stop mass, m~t1, (left) and light Higgs mass, mh, (right) as a function of the R-parity violating coupling [prime][prime]313 evaluated at MGUT. Here, we set m0 = 1500 GeV, tan = 12, A0 = 3500 GeV and [notdef] > 0. The solid lines are for M1/2 = 1000 GeV, the dotted lines

are for M1/2 = 1250 GeV, and the dashed lines are for M1/2 = 1500 GeV. Second row: dependence of m~t1 (left) and mh (right) on A0 (we consider only A0 < 0 here) in the R-parity conserving case, [prime][prime]313 = 0. The remaining parameters are chosen as in the rst row. The blue lines correspond to a stable and the red lines to a meta-stable EW vacuum.

To demonstrate the consequences of these additional terms, we show as an example the a ect of [prime][prime]313(MGUT) on the weak scale values of m~t1 and mh in gure 3. We already distinguish here between points with a stable and an unstable EW vacuum. For these plots we have used our full numerical setup, explained in detail below in section 4.1.

Here, we start with a xed set of CMSSM parameters [notdef]m0, M1/2, tan , A0[notdef] with a

stable EW vacuum and then turn on [prime][prime]313. We see that the light stop mass can be reduced by several hundred GeV without spoiling the vacuum stability or a ecting the light Higgs mass too much. For comparison, we show also the impact of a variation of A0 while keeping [prime][prime]313 = 0. This reduces also the light stop mass as expected and has a much larger impact on the Higgs mass. However, values of A0 below 3.7 TeV are forbidden because the vacua where charge and colour are broken become deeper than the EW vacuum. Thus, baryon number violating couplings are a very attractive possibility to obtain light stop scenarios in the CMSSM which are not in conict with vacuum stability.

3.3 Loop corrections to the stop mass

We have seen that light stops and the correct Higgs mass can be obtained for large values of [prime][prime]31i if the operator couples directly to the top quark. However, the R-parity violating coupling will not only change the RGE running, as discussed in refs. [28, 54], but also contribute to the radiative corrections to the stop masses at the one-loop level. Since these corrections to the stop masses to our knowledge have not been considered so far in the literature, we discuss the e ect here. The analytical calculation is summarised in appendix B. We nd that the corrections to the right-stop mass squared are approximately given by

m2~tR [similarequal]

182 [notdef] [prime][prime]3ij[notdef]2M2SUSY . (3.4)

Here, MSUSY is taken to be the mass scale of the down-like squarks running in the loop. If these masses are much heavier than the stop they can give large positive contributions to the light stop mass.

To show the importance of these corrections we present in gure 4 the mass of the light stop as function of [prime][prime]313 and m0 at tree and one-loop level. We present in the top gures [prime][prime]313 evaluated at both MGUT and MSUSY. At one-loop we give the results with and without the R-parity violating corrections to the stop self-energies. These results are based on a full numerical calculation which does not rely on the simplifying assumptions made in appendix B. All e ects of avour mixing, mass di erence between squarks, and of the external momentum are taken into account. The numerical calculation is based on the general procedure to calculate one-loop mass spectra with the Mathematica package SARAH, presented in refs. [55, 56].

We can see that for light stops the loop corrections are very important. They are dominated by the s corrections if the D D contributions are neglected. These corrections are negative and quickly reduce the tree-level mass in the limit m~g m~t1 [57]. In contrast, the D D corrections are positive and stabilise the stop mass at the one-loop level. We see that these corrections can easily shift the stop mass by more than 100 GeV compared to the case of an R-parity conserving one-loop calculation. Thus, these corrections have to be taken into account for any meaningful prediction of light stop masses in the context of large R-parity violating couplings.

4 Results

We are interested in parameter regions in the CMSSM extended by baryon number violating operators, which provide a light stop. As constraints, we take the Higgs mass measurement, the limits on new physics from avour observables and the stability of the EW vacuum. Before we present the preferred regions, we give the main details of our numerical setup.

4.1 Numerical setup

We have used SARAH [55, 5861] to obtain a SPheno [62, 63] version of the MSSM with trilinear RpV. This SPheno version calculates the renormalisation group equations (RGEs) taking into account the full RpV e ects at the one and two-loop level. The RGEs have

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Figure 4. First row: the lightest stop mass, m~t1, as a function of the R-parity violating coupling [prime][prime]313, evaluated either at MGUT (bottom axis labels) or at MSUSY (top axis labels). We set m0 =

1500 GeV, M1/2 = 1250 GeV, tan = 12, A0 = 3500 GeV, and [notdef] > 0. On the left we show the

tree-level mass (dotted line), the one-loop mass without D D corrections (dashed line) and the mass with full one-loop corrections (full line). On the right we show the mass di erence between the tree-level and the one-loop mass ( m~t1 = m(1L)~t

1 m(T)~t1) with (full line) and without (dotted

line) D D corrections. Note that the contributions of the D D operators to the RGE running are included in all cases. Second row: m~t1 as function of m0. Here we xed

[prime][prime],GUT313 = 0.2. The

other parameters are chosen as in the rst row.

been cross checked against refs. [28, 54]. In addition, the program calculates the entire mass spectrum at the one-loop level. Thus, also the one-loop corrections to the stop masses stemming from [prime][prime]31i discussed in section 3.3 are included. Furthermore, the known two-loop corrections to the light Higgs mass are taken into account [6468]. We have compared the mass spectrum calculation of this SPheno version with SoftSusy 3.3.8 [69, 70]. We found good agreement if we remove the radiative RpV corrections to the mass spectrum, which are not included in SoftSusy. The remaining di erences are of the same size as the known discrepancies in the MSSM [71, 72] and provide an estimate of the theoretical uncertainty.

Moreover, SPheno calculates the decay widths and branching ratios of the Higgs boson(s), as well as the Higgs couplings normalised to the SM expectations. We employ this information through HiggsBounds [7376] and HiggsSignals [77, 78] to confront the Higgs sector for a given parameter point with existing measurements and exclusion limits. This has almost no inuence on our results, as the stops we obtain are too heavy [79].

There are also a wide range of avour observables calculated by SPheno with a high precision even for SUSY models beyond the MSSM, thanks to the FlavorKit interface [80], which is an automatisation of the approach presented in ref. [81]. We consider in the following the observables B ! Xs , B0q ! [notdef]+[notdef], and MBq (q = s, d), which provide

the best limits. To accept or discard parameter points based on the avour observables we consider the ratio R(X) dened as

R(X)

XSM . (4.1)

Here X is the predicted value of each avour observable for a given parameter point, and XSM is the corresponding SM theoretical expectation. If we assume a 10% uncertainty in the SUSY calculation and combining the experimental limits together with the corresponding SM predictions, we get the following constraints at 95% C.L. on the R(X):

B ! Xs [8286] 0.89 < R(BR(b ! s )) < 1.33 (4.2)

Bq ! l+l [47, 8688]

0.43 < R(BR(Bs ! [notdef]+[notdef])) < 1.35 (4.3)

R(BR(Bd ! [notdef]+[notdef])) < 8.3 (4.4)

MBq [85, 8991]

0.54 < R( MBs) < 1.44 (4.5)

0.25 < R( MBd) < 1.84 (4.6)

To check the vacuum stability of each parameter point we use the computer program Vevacious [92], for which we have created the corresponding model les with SARAH. For this step, we had to restrict ourselves to a set of particles, which can in principle get a non-vanishing vev. Since the required computational e ort grows quickly with the number of allowed vevs, we employ a two step approach: rst, we assume that only the staus and stops can have non-vanishing vevs (vL,vR, vtL, vtR), besides those for the neutral Higgs scalar elds. All points which pass this check, i.e. they do not have a charge or colour breaking minimum, are again checked for the global vacuum taking into account the vevs of those generations of down-squarks which are involved in the [prime][prime]3ij coupling (vtL, vtR, vDiL ,

vDiR , vDjL ,vDjR ). Here it is necessary to allow also for vevs of the left-handed counterparts

of the right down-like squarks to nd D-at directions in the scalar potential, even though they do not couple directly to D D. The scalar potential at tree-level is discussed in more detail in appendix C. As discussed there, the additional checks for CCB vacua with down-like squark vevs should have only a minor impact on the number of points which are ruled out by the vacuum considerations. This is conrmed by our numerical study: only 5% of the points with stop masses below 1 TeV, which seem to be stable when checking only for stau and stop vevs, are in fact only meta-stable when including the sdown and

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Figure 5. Vacuum stability in the (

[prime][prime],GUT313 , m~t1) (left) and (

[prime][prime],GUT312 , m~t1) (right) planes based on a random scan using the parameter ranges of eqs. (4.7) and (4.8). The blue points have a stable

EW vacuum while for the red points deeper CCB vacua exist. For the lled dots we required mh 2 [124, 128] GeV, and for the large empty circles we applied mh 2 [122, 130] GeV as a cut. The

small empty grey circles are without any cut on the Higgs mass but have a stable vacuum.

sbottom vevs in addition ( [prime][prime]313-case). For [prime][prime]312 no points are a ected by the additional check for vacua with sdown and sstrange vevs.

In the following, we only accept points which do not exhibit a deeper CCB vacuum. In principle, it might be possible that the EW vacuum is only meta-stable, but long-lived on a cosmological time scale. However, it is been shown that vacua which seem to be long-lived at zero temperature are likely to have tunnelled in the early universe into the CCB vacuum if temperature e ects are taken into account [14].

4.2 Light stops in the CMSSM with D D operators

To nd regions with light stops in the CMSSM in the presence of D D operators in agreement with all constraints, we performed random scans with the tool SSP [93] restricted to the following ranges of CMSSM parameters

m0 2[0, 2] TeV , M1/2 2[0, 2] TeV , tan 2[5, 60] , A0 2[10, 0] TeV , [notdef] > 0 . (4.7) For the D D parameters we have chosen the range

[prime][prime]31i 2 [0, 0.7] with i = 2, 3 , (4.8)

as the input at the GUT scale. The results are summarised in gure 5. Here, we have applied two di erent cuts on the Higgs mass: mh = (126 [notdef] 4) GeV or the stricter case

mh = (126 [notdef] 2) GeV. The second cut is motivated by the theoretical uncertainty for the

light Higgs mass of 23 GeV, which is usually assumed when using the known two-loop results. However, the [prime][prime]3ij couplings give rise to new corrections to the Higgs mass at two-loop. These contributions are unknown and increase therefore the theoretical uncertainty.

In gure 5, the blue points have a stable EW vacuum while for the red points deeper CCB vacua exist. For the lled dots we required mh 2 [124, 128] GeV, while for the large

empty (red and blue) circles we applied the weaker constraint mh 2 [122, 130] GeV. The

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[prime][prime],GUT313 . The blue points have a stable EW vacuum while for the red points deeper CCB vacua exist. No cut is imposed on the light Higgs mass.

Figure 6. Allowed values for A0 as function of

small empty grey circles are without any cut on the Higgs mass, but have a stable vacuum. The gure on the left di ers from that on the right slightly, due to the lighter sbottom mass to be applied in eq. (3.4). The corresponding plot for [prime][prime]323 is indistinguishable from that presented here for [prime][prime]313.

We can see the general trend: for increasing [prime][prime]31i a lighter and lighter stop mass is compatible with all constraints. One central result of this paper is that we can have a stop mass as low as 220 GeV while satisfying the strict Higgs mass constraint and also having a stable EW vacuum, for [prime][prime]31j [greaterorsimilar] 0.3.

We see that the Higgs mass limit has a large impact on the preferred regions in the ( [prime][prime]31i, m~t1) plane: if no cut on the light Higgs mass is applied, the full planes shown in gure 5 are populated with (small empty grey) circles which have a stable EW vacuum.

However, using mh 2 [122, 130] GeV makes it much more di cult to nd viable points

with [prime][prime]31i > 0.4, and stop masses below 1 TeV. This can be understood from gure 6, where we show the correlation between A0 and [prime][prime]313: if [prime][prime]313 increases, the upper limit of

|A0[notdef] allowed by a non-tachyonic spectrum decreases. For [prime][prime]313 > 0.4 a spectrum without

tachyons requires A0 > 3000 GeV. For larger values of [notdef]A0[notdef], the T [prime][prime] contributions to the

running of m2~U shown in eq. (3.3) cause a negative soft SUSY breaking mass squared term

for the right-handed stop. However, these values of [notdef]A0[notdef] are not su cient to lift the light

Higgs mass above the lower limit of 122 GeV, if the stop is too light. As a consequence, the maximal value for the light Higgs mass that we nd decreases with increasing [prime][prime]31i, because

of the simultaneously decreasing stop mass. This behaviour can also be seen in gure 7.

For small or vanishing [prime][prime]31i couplings and a Higgs mass above 124 GeV the minimal stop mass with a stable EW vacuum is above 800 GeV. This is in agreement with our expectations based on gure 2. In contrast, we nd for [prime][prime]313 0.3 points with stop masses below 400 GeV which do not su er from a deeper CCB vacuum.

If we relax the bound on the heavy Higgs mass and use as the lower limit 122 GeV, we nd in the R-parity conserving limit ( [prime][prime]31i 0.1) already points with stop masses

below 350 GeV. However, for these small [prime][prime]31i couplings a theoretical uncertainty of 4 GeV on the light Higgs mass might be overestimated. In addition, these points usually have a

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[prime][prime],GUT313 (left) and A0 (right). All points full m~t1 < 1 TeV. The blue points have a stable EW vacuum while for the red points deeper CCB vacua exist. In the scan, no constraint has been imposed on the Higgs mass here. We do require m~t1 < 1 TeV.

Figure 7. Dependence of the light Higgs mass mh on

Figure 8. Vacuum stability in the (

small value of M1/2, as seen in gure 2. This implies a light gluino mass which would be in conict with current mass limits [94], for [prime][prime]31i = 0. Furthermore, in the case of non-zero [prime][prime]31i, constraints from LHC searches for three-jet resonances from gluinos apply [95, 96]. Thus it is questionable if these points should be considered at all. Nevertheless, also for this very conservative limit on the Higgs mass, one can nd parameter points with even lighter stops if sizeable RpV couplings are present. In general, we nd in our scans that [prime][prime]313 [similarequal] 0.3 turns out to be the optimal value to nd parameter points with a light stop with m~t1 (220

250) GeV, a Higgs mass in agreement with the measurement and a stable EW vacuum.

In gure 8 we show the same planes as in gure 5, but only for points where the lightest supersymmetric particle (LSP) is the stop. In principle, it is possible to have a stop LSP in the CMSSM without RpV operators [97]. However, these regions are usually very ne-tuned and need very large values of M1/2 in order to raise the ~

[notdef]01 mass and to

[prime][prime],GUT313 , m~t1) plane (on the left) and (

[prime][prime],GUT312 , m~t1) plane (on the right) showing only points with a stop lightest supersymmetric particle (LSP). The blue points have a stable EW vacuum while for the red points deeper CCB vacua exist. For the lled dots we required mh 2 [124, 128] GeV, while for the empty circles we only required mh 2 [122, 130] GeV.

JHEP08(2014)142

[prime][prime],GUT313 ) plane

(right). Here, we required mh 2 [122, 130] GeV. The blue points have a stable EW vacuum while for

the red points deeper CCB vacua exist. The mass of the light stop is indicated by the plot marker: m~t1 < 1 TeV (open circles), m~t1 < 0.5 TeV (lled circles), m~t1 < 0.3 TeV (lled squares).

obtain a light Higgs mass in the experimentally preferred range. Therefore, we found no

points with a stop LSP and a moderately small RpV coupling [prime][prime]31i < 0.14 in our scan. In

contrast, for larger values of the RpV couplings it is much easier to nd a stop LSP. Also here we nd that the minimal stop mass is obtained for [prime][prime]31i [similarequal] 0.3. We emphasise that the

points in gure 5, which feature very light stop masses, are exactly the same points as in gure 8, which have a stop LSP. This is a non-trivial observation, because M1/2 must be large to lift the ~

[notdef]01 mass above the ~t1 mass. However, at the same time, a large value of M1/2 also raises the ~t1 mass via the RGEs.

One might wonder how strong the bias from our parameter choice in eqs. (4.7) and (4.8) is: it might be possible to nd very light stops fullling all considered constraints for even larger values of [prime][prime]31i, if the maximal value of m0 or M1/2 is increased. However, this is not the case because this would also increase the size of the radiative corrections to the light stop, as the squarks of the rst and second generation also get heavier. To demonstrate that our points with very light stops are not on the edge of our parameter range, we show the correlation between the mass of the light stop and m0, M1/2 and [prime][prime]31i, respectively, in gure 9. The red and blue lled squares denote a stop mass m~t1 < 0.3 TeV. These are not clustered at the edge of our allowed ranges. In fact, in the R-parity violating coupling the low-mass stops are clustered around [prime][prime]313 0.3.

We conclude with a brief comment on the collider aspects of the presented scenario. To this a ect, we have selected four benchmark points (BP313A, BP313B, BP312A, BP312B) which show the main characteristics of the mass spectra in our preferred parameter regions with very light stops. We give in table 1 only the most important values but list the entire spectrum and input values in appendix A.

In table 1, we have summarised all squark masses not given explicitly by m~q. While the stop mass can be reduced due to the large RpV couplings, all other SUSY scalars are heavy and typically in the multi-TeV range. Also, the gluino is very heavy, and just the electroweakinos can have masses below 1 TeV. Thus for these benchmarks ~t1 is the LSP.

Figure 9. The mass of the lightest stop in the (m0, M1/2) plane (left) and (m0,

BP313A BP313B BP312A BP312B mh1 [GeV] 124.5 122.3 124.4 122.9 m~t1 [GeV] 325.8 247.9 364.6 222.9 m~t2 [GeV] 2473.3 1670.9 2227.0 1719.6 m~b1 [GeV] 2015.1 1353.5 2215.7 1703.7 m ~dR [GeV] 2075.4 1420.8 1896.0 1437.3 m~sR [GeV] 2792.8 1908.1 1896.0 1437.3 m~q [GeV] > 2800 > 1900 > 2500 > 1950 m~1 [GeV] 1441.1 1139.3 1446.7 976.1 m~~01 [GeV] 568.2 334.9 480.5 373.3 m~~+

1 [GeV] 1073.2 639.1 911.3 710.6 m~g [GeV] 2834.9 1794.0 2461.0 1955.9

Table 1. Main features of our benchmark points. The full information is given in appendix A. The benchmarks BP313 have [prime][prime]313 [negationslash]= 0, while the benchmarks BP312 have [prime][prime]312 [negationslash]= 0. m~q refers to all not

explicitly listed squark masses. ~t1 is the LSP.

This mass hierarchy together with the large RpV couplings, yields prompt di-jet decays of the stop LSP, and makes it di cult to look for the light stops at the LHC [32, 96, 98 105]. Therefore, we leave the exploration of possible search strategies for such light stops together with large RpV couplings for future studies.

5 Conclusion

We have discussed the possibility of light stops in a constrained version of the MSSM extended by large R-parity violating couplings [prime][prime]31i, i = 2, 3. It has been shown that in this

model it is possible to nd parameter regions providing light stops with masses as low as 250 GeV which are consistent with the Higgs mass measurement, avour observables and the stability of the electroweak vacuum. This is di erent from the CMSSM without D D operators where large stop mixing or heavy stops are needed to accommodate the Higgs mass. There the presence of light stops is highly constrained by the stability of the electroweak vacuum. Thus stop masses below 800 GeV can hardly be obtained in the R-parity conserving CMSSM. In the CMSSM with large R-parity violation, an interesting observation is that the lightest stop mass is usually found for [prime][prime]31i [similarequal] 0.3. In these scenarios the light

est stop is usually the LSP. We have shown that for this size of RpV couplings it is necessary to calculate the additional RpV one-loop corrections to the stop mass. These corrections can alter the prediction of the light stop mass by more than 100 GeV compared to an incomplete one-loop calculation that takes into account only R-parity conserving interactions.

JHEP08(2014)142

Figure 10. One-loop correction to the stop mass due to down-like (s)quarks.

Acknowledgments

We thank Ben Allanach for his fast replies to our questions regarding SoftSUSY and Ben OLeary for many interesting discussions about vacuum stability. NC is supported by the Alexander von Humboldt foundation. HD, FS and TS are supported by the BMBF PT DESY Verbundprojekt 05H2013-THEORIE Vergleich von LHC-Daten mit supersymmetrischen Modellen.

A Benchmark points

In table 2 we list the explicit parameters, the full sparticle mass spectrum and the predictions for the relevant avour observables of our four benchmark scenarios. The RpV coupling is evaluated at the GUT scale and is about 0.3. This results in the lowest possible stop masses in our scan. The sparticle masses are all above 1 TeV, except those of the lightest neutralino ~

[notdef]01 and the lightest stop ~t1. The latter is the LSP for all four benchmark points. Thus we expect the dominant stop decay to be to two jets: ~t! ddi, with possibly

a b-jet for i = 3.

B D D corrections to stop masses

In the following we give a brief analytical estimate of the one-loop corrections to the stop masses in the presence of large [prime][prime] couplings. The necessary Feynman diagrams are shown in gure 10. This also denes our notation for the two-point functions ([notdef]).

JHEP08(2014)142

BP313A BP313B BP312A BP312B m0 [GeV] 1437.8 1182.0 1466.8 1075.7

M1/2 [GeV] 1299.1 780.5 1104.4 867.6 tan 12.8 17.2 14.4 22.1 sign([notdef]) + + + +

A0 [GeV] -3555.5 -2152.8 -2972.3 -2347.6 [prime][prime],GUT

313 0.310 0.329 0 0 [prime][prime],GUT

312 0 0 0.317 0.335 mh1 [GeV] 124.5 122.3 124.4 122.9 mh2 [GeV] 2523.7 1655.1 2238.6 1571.6 mA [GeV] 2554.0 1668.4 2253.1 1613.3 mH+ [GeV] 2523.7 1656.3 2238.9 1573.4 m~t1 [GeV] 325.8 247.9 364.6 222.9 m~t2 [GeV] 2473.3 1670.9 2227.0 1719.6 m~b1 [GeV] 2015.1 1353.5 2215.7 1703.7 m~b2 [GeV] 2463.7 1658.4 2469.4 1867.8 m ~dL [GeV] 2892.5 1961.3 2609.9 2038.0 m ~dR [GeV] 2075.4 1420.8 1896.0 1437.3 m~uL [GeV] 2891.6 1959.9 2608.9 2036.7 m~uR [GeV] 2803.8 1914.1 2539.2 1981.3 m~sR [GeV] 2792.8 1908.1 1896.0 1437.3 m~1 [GeV] 1441.1 1139.3 1446.7 976.1 m~1 [GeV] 1640.5 1256.7 1603.6 1159.7 m~lR [GeV] 1512.7 1215.0 1519.8 1120.1 m~lL [GeV] 1670.4 1288.0 1634.7 1218.2 m~~01 [GeV] 568.2 334.9 480.5 373.3 m~~02 [GeV] 1073.1 639.0 911.2 710.5 m~~03 [GeV] 2019.9 1227.1 1702.0 1334.3 m~~04 [GeV] 2023.1 1231.8 1705.6 1338.6 m~~+

1 [GeV] 1073.2 639.1 911.3 710.6 m~~+

2 [GeV] 2023.5 1232.6 1706.2 1339.3 m~g [GeV] 2834.9 1794.0 2461.0 1955.9

R(b ! s ) 0.98 0.90 0.96 0.86

R(B ! [notdef] ) 0.99 0.98 0.99 0.98

R(Bs ! [notdef]+[notdef]) 1.14 1.18 1.13 1.25

R(Bd ! [notdef]+[notdef]) 1.14 1.16 1.13 1.24

R( MB,s) 1.01 1.02 1.01 1.02 R( MB,d) 1.01 1.02 1.01 1.02

R([epsilon1]K) 1.01 1.02 1.02 1.02

Table 2. Full sparticle mass spectrum and avour observables predicted for our benchmark points. The benchmarks BP313 have [prime][prime]313 [negationslash]= 0, while the benchmarks BP312 have [prime][prime]313 [negationslash]= 0.

JHEP08(2014)142

We start with the corrections which only involve superpotential couplings: since ~fL

(see gure 10) has no contribution from baryon number violating operators, we do not consider it in the following. ~fR ~fR only has contributions proportional to the soft-terms T [prime][prime] , which will be discussed below. The amplitudes for the remaining diagrams can be expressed by

162 ff = ([notdef] L(~tR, di, dj)[notdef]2 + [notdef] R(~tR, di, dj)[notdef]2)G(p2, m2di, m2dj)

2( L(~tR, di, dj) R(~tR, di, dj)

+ L(~tR, di, dj) R(~tR, di, dj))mdimdjB0(p2, m2di, m2dj) , (B.1)

162 ~f~f = [notdef] (~tR,

~dRi, ~dLj)[notdef]2B0(p2, m2~dRi , m2~dLj ) + (i $ j) , (B.2)

162 ~f = (~tR, ~tR,

~dRi, ~dRi)A0(m2~dR

i ) + (i $ j) . (B.3)

with ~f~f ~fL ~fR + ~fR ~fL. Here, we have introduced

G(p2, m21, m22) A0(m21) A0(m22) + (p2 m21 m22)B0(p2, m21, m22) . (B.4)

A0 and B0 are the standard Passarino-Veltman integrals [106]. The s represent the involved vertices. These are given in the limit of diagonal Yukawa couplings by:

1. (Chiral) stop-quark-quark vertex:

L(~tR, di, dj) [prime][prime]3ij ,

R(~tR, di, dj) = 0 .

2. Stop-squark-squark vertex:

(~tR, ~dRi, ~dLj) [prime][prime]3ijY jjd[angbracketleft]Hd[angbracketright] = mdj [prime][prime]3ij . (B.5)

3. Four squark vertex:

(~tR, ~tR, ~dRi, ~dRj) [prime][prime]3ik [prime][prime]3jk . (B.6)

One can check easily that in the limit of unbroken SUSY, m ~dRi = m ~dLi = mdi, the sum of all diagrams vanishes exactly

ff + ~f~f + ~f = 0 . (B.7)

If we assume for simplicity that all SUSY masses are degenerate (m ~dRi = m ~dLi = MSUSY ,

8i) and take the limit p2 ! 0, MSUSY mdi we obtain a very simple expression for the

sum of all diagrams

ff + ~f~f + ~f = 182 [notdef] [prime][prime]3ij[notdef]2M2SUSY

[prime][prime] . (B.8)

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Here, we have used

B0(0, m2, m2) = A0(m2)

m2 1 , (B.9)

A0(m2) = m2 m2 log

Q2 , (B.10)

and set as the renormalisation scale Q = MSUSY .

As mentioned above there is also another one-loop contribution due to the trilinear soft-breaking terms:

162 ~fR ~fR = [notdef]T [prime][prime]3ij[notdef]2B0(p2, m2~dRi , m2~dRj ) . (B.11)

However, this contribution vanishes exactly in the limit of degenerate down-like squark masses m ~dRi = m ~dRj = Q = MSUSY . Hence, it can only play a role in the case of a large mass splitting between the squarks in the loop. To see this, we can use m ~dRi = Q = MSUSY together with m ~dRj = MSUSY + and obtain

~fR ~fR =

2 162M2SUSY [notdef]

T [prime][prime]3ij[notdef]2 . (B.12)

Here, we have made use of

B0(0, m21, m22) = log

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m22

Q2 +

1m22 m21 [parenleftbigg]

m22 m21 + m21 log

m21 m22

[parenrightbigg]

. (B.13)

We can now use the derived expressions for the one-loop self-energies to calculate the stop mass at one-loop. If we neglect avour mixing in the squark sector, the one-loop stop masses are the eigenvalues of the one-loop corrected stop mass matrix m2,(1L)~t given by

m2,(1L)~t = m2,T~t + m2,MSSM + (

[prime][prime] + ~fR ~fR) 0 0 0 1

[parenrightBigg]

. (B.14)

Here, m2,T~t is the stop mass matrix at tree-level,

m2,T~t =

m2~tL 124[parenleftBig]

g213g22[parenrightBig][parenleftBig]

v2dv2u[parenrightBig]

+ v

2 u

|Yt[notdef]2

1 p2

vuT t vd[notdef]Y t[parenrightBig]

, (B.15)

and m2,MSSM is the matrix for the well known corrections which do not involve R-parity violating couplings, see e.g. ref. [107].

C Minimising the scalar potential of the MSSM with D D operators

We discuss in the following the scalar potential in the MSSM in the presence of [prime][prime]3ij cou

plings and vevs for stops, staus, as well as the down-type squarks at tree-level. The checks performed by Vevacious include also the one-loop corrections to the e ective potential. However, these expressions are not shown here because of their length. To simplify the expressions we assume here that the Yukawa couplings and the soft-breaking parameters in the R-parity conserving sector are diagonal:

Y = Ye,33, Yb = Yd,33, Yt = Yu,33 ,

T = Te,33, Tb = Td,33, Tt = Tu,33 ,

1 p2

vuTt vdYt[notdef] [parenrightBig]

m2~tR + v2 u 2

|Yt[notdef]2+ 16g21[parenleftBig] v2dv2u[parenrightBig]

m2~tL = m2~Q,33, m2~tR = m2~U,33 ,

m2~L = m2~L,33, m2~R = m2~E,33 ,

m2~qi = m2~Q,ii, m2~di = m2~D,33 .

The full expression in the limit of diagonal Yukawa and R-parity conserving soft terms read

V treeHd,Hu =

132 g21(v2d v2u)2 + g22(v2d v2u)2

[parenrightbig]

Bvdvu + 12 [notdef][notdef][notdef]2(v2d + v2u) + m2Hdv2d + m2Huv2u

[parenrightbig]

, (C.1)

V treeHd,Hu,~L,~R =

132 g21(v2L 2v2R)2 + g22(v2L)2

[parenrightbig]

+14 Y 2(v2dv2L + v2dv2R + v2Lv2R

[parenrightbig]

2m2~tR + v2uY 2t

[parenrightBig]

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+ 1

p2vLvR (Tvd Y[notdef]vu)

+12 m2~Lv2L + m2~Rv2R

[parenrightbig]

, (C.2)

V treeHd,Hu,~tL,~tR =

288

4 6 v2tL

2m2~tL + Y 2t(v2tR + v2u)

[parenrightBig]+ v2tR

+2p2vtLvtR (vuTt vdYt[notdef])

[parenrightbig]

+ g23(v2tL v2tR)2

[parenrightbig]

3g22 2v2uv2tL + 2v2dv2tL + v4tL

[parenrightbig] [parenrightBig]

+ g21 v2tL 4v2tR

[parenrightbig]

(v2tL 4v2tR + 6v2u)

6v2d(v2tL 4v2tR)

[parenrightbig][bracketrightBig]

, (C.3)

V treeH

d,Hu, ~diL, ~diR =

288

4 6 v2DiR

2m2~di + Y 2di(v2DiL + v2d)

[parenrightBig]+ v2DiL 2m2~qi + v2dY 2di

+2p2vDiLvDiR (vdTdi vuYdi[notdef])

[parenrightbig]

+ g23(v2DiL v2DiR )2

[parenrightbig]

v4DiL + 2v2DiL (v2u v2d)[parenrightBig] [parenrightBig]+ g21 6v2u(v2DiL + 2v2DiR )

+(v2DiL + 2v2DiR )(v2DiL 6v2d + 2v2DiR )

[parenrightbig][bracketrightBig]

, (C.4)

V treeH

d,Hu, ~djL, ~djR = V treeHd,Hu, ~diL, ~diR [notdef] (i ! j) , (C.5)

V tree~t

L,~tR, ~diL, ~diR =

1 144

hg21(v2DiL + 2v2DiR )(v2tL 4v2tR) 9g22v2DiL v2tL

6g23(v2DiL v2DiR )(v2tL v2tR)[bracketrightBig]

, (C.6)

+3g22

V tree~t

L,~tR, ~djL, ~djR = V tree~tL,~tR, ~diL, ~diR [notdef] (i ! j) , (C.7)

V tree~di

L, ~diR, ~djL, ~djR =

1 144

hg21(v2DjL + 2v2DjR )(v2DiL + 2v2DiR ) + 9g22v2DjL v2DiL

6g23(v2DjL v2DjR )(v2DiL v2DiR ) + 72vDjL vDjR vDiL vDiR YdiYdj[bracketrightBig]

, (C.8)

V tree~t

R,~tR, ~diR, ~djR =

1 4

h [prime][prime],2 3ij

v2DjR (v2DiR + v2tR) + v2DiR v2tR

[parenrightBig]

2 [prime][prime]3ij

vDjL vdvDiR vtRYdj + vDjR vDiL vdvtRYdi + vDjR vDiR vtLvuYt

[parenrightBig]

2p2T [prime][prime]3ij vDjR vDiR vtR

[bracketrightBig]

. (C.9)

The D-term contributions are minimised for

vDiL = vDiR , vDjL = vDjR , vtL = vtR, vu = vd . (C.10)

In addition, for j = 3 we neglect the terms involving Ydi and Tdi which correspond to rst or second generation Yukawas, respectively, trilinear terms. In this limit all terms involving down-squark vevs read

V treev

[parenrightBigg]

,vDjR

= v2DiR

2(m2~di + m2~qi) +

[prime][prime],2

3ij v2tR4

+v2DjR 0

2(m2~dj + m2~qj) +

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vdTdj p2 +

[prime][prime],2

3ij v2tR

4 +

2v2dY 2dj

vdYdj[notdef] p2 +

v2DjR

4 Y 2dj1

vDjR vDiR 4

[prime][prime],23ij vDjR vDiR 2 [prime][prime]3ijvdvtR(Ydj + Yt) 2p2T [prime][prime]3ij vtR[parenrightBig]

+g21 + g22

[parenleftBig][parenleftBig]

v2DjR + v2DiR

[parenrightBig] [parenleftBig]

v2DjR + v2DiR 2v2tR[parenrightBig][parenrightBig]

. (C.11)

The rst line on the right hand side is always positive. Especially since the -function of m2~qi has no terms proportional to [prime][prime] or to a third generation Yukawa coupling at one-loop it is positive and usually much larger than the other soft-parameter involved. This makes it rather unlikely that vDiR [negationslash]= 0 are preferred at the minimum of the potential. However,

in the limit vDiR ! 0 the entire rst and third line vanish. The form of the potential then

has a similar form to the potential when considering only stop and Higgs vevs. However, usually m2~qi > m2~tL and m2~di > m2~tR holds. This makes it unlikely that the down-squarks

gain a vev before the stops do. Thus, one can expect that the check for the additional down-squark vevs put only weak constraints in addition for points with very large tan . While the discussion has been so far rather hand-waving the general statement has been conrmed in our numerical studies: only 5% of the points with stop masses below 1 TeV which pass the stability check including only stop vevs fail the additional test that includes sbottom vevs. Including sdown and sstrange vevs does not put any additional constraint. For comparison: about 1/3 of the entire points in the scan fail the check for a stable vacuum when checking for stop and stau vevs. In the interesting parameter range of stop masses below 1 TeV even 2/3 are ruled out.

Open Access. This article is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/

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(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

Abstract

In order to accommodate the observed Higgs boson mass in the CMSSM, the stops must either be very heavy or the mixing in the stop sector must be very large. Lower stop masses, possibly more accessible at the LHC, still give the correct Higgs mass only if the trilinear stop mixing parameter |A ^sub t^| is in the multi-TeV range. Recently it has been shown that such large stop mixing leads to an unstable electroweak vacuum which spontaneously breaks charge or color. In this work we therefore go beyond the CMSSM and investigate the effects of including baryon number violating operators ...... on the stop and Higgs sectors. We find that for ...... light stop masses as low as 220 GeV are consistent with the observed Higgs mass as well as flavour constraints while allowing for a stable vacuum. The light stop in this scenario is often the lightest supersymmetric particle. We furthermore discuss the importance of the one-loop corrections involving R-parity violating couplings for a valid prediction of the light stop masses.

Details

Title

Resurrecting light stops after the 125 GeV Higgs in the baryon number violating CMSSM

Author

Chamoun, N; Dreiner, H K; Staub, F; Stefaniak, T

Pages

1-27

Publication year

2014

Publication date

Aug 2014

Publisher

Springer Nature B.V.

e-ISSN

10298479

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/JHEP08(2014)142

ProQuest document ID

1708016206

SISSA, Trieste, Italy 2014

Resurrecting light stops after the 125 GeV Higgs in the baryon number violating CMSSM

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