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Gauge mediation with heavy doublet superparticles

It is challenging for supersymmetry if the 125 GeV Higgs boson is confirmed by the LHC. In the case of small squark mixing it is inevitable to introduce heavy top squarks to lift the Higgs mass that is hard to be produced by the LHC. Here we consider the possibility that in gauge mediation the superparticles belonging to SU(2) doublets are much heavier than those do not carry the SU(2) quantum numbers. Under the assumption not only the Higgs mass can be large enough but also there are light right handed top squarks below the TeV scale that can be observed in future.


I. INTRODUCTION
Supersymmetry is one of the most favored candidates for new physics beyond the Standard Model [1,2]. One of the main motivation for building the Large Hadron Collider (LHC) at CERN is to find the supersymmetric particles. If supersymmetry really describes nature the recent LHC results imply that the superpartners for known Standard Model particles, the sparticles, are heavy. It agrees with the Higgs mass if we treat the excess of events around 125 GeV in ATLAS [3] and CMS [4] as the signals of the Higgs bosons. In the Minimal Supersymmetric Standard Model (MSSM) heavy sparticles are needed to generate a heavy Higgs boson [5][6][7]. It is challenging to theories, comes from the following aspects.
Observability. A detailed calculation shows that in the absence of squark mixing the higgs boson can not be 125 GeV in a large area in the parameter space for the top squark lighter than 3 TeV [8,9]. It will beyond the the ability of the LHC to create them. It is significant to find a theory in which there are light colored sparticle that can be produced by the LHC and the there are still enough quantum corrections to the Higgs mass.
Naturalness. Heavy top squrks will introduce large corrections to the Higgs mass parameter which proportional to their mass square where M is the new physics scale. There must be other contributions to the Higgs potential to compensate such a large corrections in order to break the electroweak symmetry at right scale. Under the present condition it is inevitable to do a fine-tuning to obtain the weak scale.
In the usual theories with low energy supersymmetry breaking the fine-tuning is sensitive to the top squark mass. A natural question is that if there is a fine-tuned supersymmetric theory but the sensitivity of the fine-tuning to the top squark mass is lower.
Predictivity. There are over 100 free parameters in the MSSM, most of them are soft supersymmetry breaking parameters. In principle they can be predicted if the underlying theory of supersymmetry breaking and mediation is known. It is important to find and identify the supersymmetry breaking and mediation mechanism.
Theories with gauge mediated supersymmetry breaking [10][11][12][13] is attractive to predict these breaking parameters. There are only ten free parameters for the MSSM. Six of them are enough to determine all the soft breaking masses [14] and the other four are parameters in the Higgs sector, soft masses of H u,d , Dirac mass µ and its corresponding bilinear breaking Bµ [15]. The Bµ is generally much larger than the weak scale if there is no specified structure in the Higgs sector [16].
Recall that the Higgs mass matrix in gauge mediation is where m 2 e L is the gauge mediated left handed slepton mass. Superparticles will obtain the same soft masses in gauge mediation if they have the same Standard Model quantum numbers. The quantum numbers of the Higgs doublets H u,d are the same as the left handed sleptons up to the sign of the weak hypercharges, so the gauge mediated soft breaking masses for H u,d are m 2 e L . δm 2 u,d are the soft masses from the mechanism which generates µ and Bµ. In eq. (2) the general estimation in theories with low energy supersymmetry breaking and mediation Bµ is assumed. It is seen that both large Bµ and heavy top squarks tend to make one of the eigenvalue of eq. (2) to be negative with large absolute value. There must be large positive contributions to obtain the weak scale.
There are many excellent works on electroweak symmetry breaking under large Bµ [17,18], here a new possibility is given. Assuming that there is a large hierarchy between sparticles according to their quantum numbers, superpartners of left-handed fields are much heavier than those are SU(2) L singlets. The large left-handed superparticles' mass are used to compensate the above two negative contributions. We will see that the electroweak symmetry breaking can happen under fine-tuning which is less dependent on the top squark mass, the right-handed squarks and sleptons remain light below the TeV scale that will be observed in the future LHC experiment.
The basic structure and predictions of this scenario is given in the next section. In the last section, we will give brief discussions and conclusions of this article.

II. DOUBLET DOMINANT GAUGE MEDIATION
For simplicity it is assumed that the parameters in the Higgs sector are generated by simple dynamics. For theories with low energy supersymmetry breaking Bµ/µ 2 ≫ 1. There must be fine-tuning for correct electroweak symmetry breaking.
The most general sfermion masses in gauge mediation are given by where C f r is the quadratic Casimir of the sparticles and A r 's are the gauge mediated supersymmetry breaking effects which are determined by the correlation functions of the underlying dynamics [14]. They have mass dimension 2.In principle there is no prior reason that the three A r 's are of the same order of magnitude, they can be separated indeed.
Assuming that A 2 ≫ A 1,3 , the sparticles of left-handed fermions are much heavier then others. The sfermion spectrum has the following patten The simplest mechanism to realize such a patten is For simplicity we assume that M 1 ∼ M 2 ∼ M 3 and F 2 ≫ F 1,3 . It is easy to see that the superparticles in doublets are heavier than singlets. Under this patten the top squark correction to the Higgs mass matrix (2) it is less important than other quantities.
The four parameters in the Higgs sector in the assumed limit are [18] The gauge mediated left-handed selectron e L mass is To the first order that neglect contributions from the other two gauge interactions, the Higgs mass matrix (2) proportional to ( F 2 M 2 ) 2 . We can always choose λ u,d to make one of the eigenvalue of eq. (2) is at the weak scale no matter how large ( F 2 M 2 ) 2 is. It is easy to see this fact. Two of the eigenvalues of eq. (2) are all positive for λ u = λ d = 0 since m 2 e L is always positive and the small top squark correction (8). On the other hand for large λ u,d in which δm 2 u,d ≫ m 2 e L one of the eigenvalues is always negative with large absolute value which is of the order of λ 2 16π 2 ( F 2 M 2 ) 2 [18]. Due to the continuousness of the eigenvalues, there must be some λ u,d to make the negative eigenvalue is at the weak scale.
The most possible orders of magnitude of the couplings λ u,d can be inferred by the cancelation between the dynamical generated soft masses for the Higgs fields and the gauge mediated mediated heavy doublet masses. The requirement implies the estimation of order It can be seen that the one loop generating soft masses for H u,d should be of the same order of the two loop generated soft masses for doublet sfermions. Since λ u,d are very small numbers, large enough F 2 /M 2 is generally required for phenomenological reasons.
Assume that in the absence of the contributions of the top squarks the above fine tuning has been performed in which for given F 2 /M 2 the couplings λ u,d have been selected to make the correct electroweak symmetry breaking, for finite top squark mass m t L the element of the mass matrix (2) have to be changed for where ∆(δm from the estimation (14). The major fine tuning does not depends on top squark mass.
It is known that the Higgs mass in gauge mediation is hard to be 125 GeV because of the smallness of squark mixing terms which are generated at higher loops [9,19,20]. The large splitting in masses (5) and µ-term (10) induced mixing term gives us a possibility to generate a heavy Higgs bosons in gauge mediation. Neglecting the all of the trilinear soft supersymmetry breaking terms, the corrections to the lightest Higgs mass is where the first and second terms on the right hand side come from the mass splitting and mixing, respectively. The dominant contribution to the Higgs mass is from the logarithmic corrections of the top squark mass, the heavier the top squark the heavier the Higgs boson.
From eq. (14) we have Neglecting higher order term, the µ-term induced correction can be estimated by For sufficient heave doublet sparticles, together with the sizable µ correction, the Higgs boson can be as heavy as 125 GeV.
Notice that the above model (6) is only an example, it is weakly coupled and easy to show the basic features of the scenario of heavy doublet sparticles. In fact the hidden sector physics can be much more complicate or even strongly coupled. The ten parameters in the gauge mediation are all free parameters unless the underlying physics is detcovered.
Unlike the left handed sparticles, the right handed squarks and sleptons are not necessary to be heavy to contribute the electroweak symmetry breaking. They can be light to be able Where m g and m b are gluino and bino masses, respectively. M 3 and M 1 are gauge mediated masses for SU(3) and U(1) gauge groups, they are defined by Although the SU(2) gaugino mass m W does not contribute to the Higgs mass square matrix (2), it is also believed to be as large as the doublet sparticle masses as in the example (6).
For the Higgs mixing parameter µ, it can be above or below the TeV scale in different cases.
For simplicity it is assumed that the Higgsinos are heavy. Due to the largeness of the left handed sparticle masses, the mixings between left and right handed sfermions can be neglected.
The light sfermions are superpartners of right handed fermions u iR , d iR and l iR . Their masses are given by There is a simple relation among these masses though supersymmetric U(1) gauge interaction. The decay width is determined by the mass of slepton and bino, neglecting the lepton masses the decay width is given by Similarly the decay width of the right handed down type squarks for m g > m d R in the small quark mass limit is Precise measurement of the masses and widths of the l R and d R can justify if the scenario is correct or not using the derived identity from eqs. (27,28) It can also determine the mass of the LSP if the first equality is confirmed by experiments.

III. DISCUSSIONS AND CONCLUSIONS
The particles in the SU(2) doublets are special in the Standard Model and its extensions.
They violate the parity and participate the SU(2) gauge interactions. In addition the Higgs fields which break the electroweak gauge symmetry are also in the SU(2) doublet. It is very possible that there are internal connections between the properties of the doublets and the electroweak symmetry breaking. An example of such a connection is established in this article.
In gauge mediation masses of superparticles are determined by their gauge quantum numbers. Assuming that the supersymmetry breaking in the SU(2) gauge group is much larger than the other gauge interactions, many problems can be solved. There are light squarks especially the right handed top squarks that may be discovered by the LHC. In the usual mass patten in gauge mediation in which colored superparticles are considered to be heavier than those without colors, the LHC observable squarks can not contribute enough quantum corrections to lift the Higgs mass. In additional to the light t R we also have heavy enough t L to contribute the corrections.
Even though the electroweak symmetry breaking is achieved by a considerable fine tuning, but it is less dependent on the top squark mass as analyzed in the previous section. We can