Are supersymmetric models with minimal particle content under tension for testing at LHC?

In supersymmetric models with minimal particle content and without large left-right squarks mixing, the conventional knowledge is that the Higgs Boson mass around 125 GeV leads to top squark masses ${\cal O}(10)$ TeV, far beyond the reach of colliders. Here, we pointed out that this conclusion is subject to several theoretical uncertainties. We find that electroweak symmetry breaking and evaluation of Higgs mass at a scale far away from the true electroweak symmetry breaking scale introduce a large uncertainty in Higgs mass calculation. We show that the electroweak symmetry breaking at the scale near the true vacuum expectation value of Higgs field can increase the Higgs Boson mass about 4-5 GeV and can lower the bounds on squarks and slepton masses to 1 TeV. Here we pointed out that the Higgs mass even with inclusion of radiative corrections can vary with electroweak symmetry breaking scale. We calculate it at two loop level and show that it varies substantially. We argue that Higgs mass like other coupling parameters can vary with energy scale and the Higgs potential with all orders loop corrections is scale invariant. This uncertainty to the Higgs mass calculation due to electroweak symmetry breaking around the supersymmetry breaking scale, normally taken as $\sqrt{m_{\tilde t_L} m_{\tilde t_R}}$, to minimize the 1-loop radiative corrections can be removed if one considers all significant radiative contributions to make Higgs potential renormalization group evolution scale invariant and evaluates electroweak symmetry breaking at the scale near the electroweak symmetry breaking scale. A large parameter space becomes allowed when one considers electroweak symmetry breaking at its true scale not only for producing correct values of the Higgs masses, but also for providing successful breaking of this symmetry in more parameter spaces.


I. INTRODUCTION
The mechanism of generation of masses for the stan- it has SM like coupling [3]. In minimal supergravity * The correspondence email address: abhijit.samanta@gmail.com (mSUGRA) model [4] bound on A 0 < 0 for m 0 > ∼ 1 TeV [5] (implying slepton masses > ∼ 1 TeV) are found in earlier studies due to the requirement of CP even Higgs mass (m h ) around 125 GeV. But, m h < 135 GeV implies that sparticle masses in MSSM should not exceed 1 TeV and m h > M Z implies the loop corrections from particles of new physics (sparticles) are very significant. There is no strong direct limit on the slepton masses from LHC and low mass sleptons below 1 TeV may give clean signals at International linear collider (ILC) as they may remain suppressed due to huge strong interaction background at LHC. As the hierarchical pattern is seen in the mass spectrum of SM and squarks masses are > ∼ 1 TeV; m h < 135 GeV strongly indicates that sleptons masses might be much below from 1 TeV. The bounds in earlier studies are obtained evaluating EWSB minima at the renormalization group evolution (RGE) scale Q 0 = √ mt L mt R and also generating spectra at this scale [6][7][8][9][10].
In this paper, we discuss the EWSB in mSUGRA model and its radiative corrections. Then we justify that one should evaluate EWSB minima at the true EWSB scale. Finally, we obtain the allowed parameter space (APS) using this EWSB scale in the framework of mSUGRA model and then compare the new APS with those obtained from considering the EWSB scale at √ mt L mt R (which is used in all mSUGRA spectrum generator packages available in literature [6][7][8][9] and also used in finding post-LHC constraints in mSUGRA model [5]).
We find a dramatically large allowed parameter space in mSUGRA model with almost no bounds on m 0 , m 1/2 and A 0 when EWSB minima is evaluated at Q 0 = v weak in contrary with the one where EWSB minima is evaluated

A. Radiative corrections
The tree level scalar potential keeping only the dependence on the neutral Higgs fields: Here, both the tree level potential V 0 and its parameters are strongly RGE scale dependent. However, if we include loop corrections at all orders; in principle, the effective potential V eff = V 0 + ∆V should be RGE scale independent. Otherwise, the perturbation theory will not work and the physics with V eff will no longer be valid.
From the minimization criteria one can find where, The value of ∆V can be different at different scale and it is not necessary to evaluate this at the scale where it is minimum. Only the necessary criteria is V eff should be scale invariant to make sure that the perturbation theory works at the scale where V eff is evaluated. The addition of 1-loop and 2-loop corrections stabilizes V eff with respect to RGE scale (from Q N P to Q EW ) and the the parameters obtained from this minimization criteria (µ and m 2 3 ) are also stabilized [17]. This implies that the perturbation theory works well and ignored amount of loop corrections higher than 2-loops does not become significant below Q N P to Q EW . Here, one should also note that Σ u,d can be large at any scale and may be even The one loop corrections ∆V 1 in Landau gauge is given by [11]: The contribution from stop quarks is given by: The loop corrections are very significant, without which the evaluation of parameters from minimization of the tree level potential may give even wrong results [12].
These radiative corrections depend strongly on renormalization scale Q and the contributions normally becomes

B. EWSB scale
The weak scale Q EW = ( 2 √ 2G F ) −1 = 175 GeV first entered physics, when Enrico Fermi constructed the current-current interaction description of β-decay and introduced the constant, G F , into modern physics [13].
The Standard Model [14][15][16]   and m 2 H d ) and the approximation of using Q N P as Q EW does not work. The value of m h is increased significantly when one evaluates EWSB at Q EW ≈ v weak (see Fig. 2).
On the otherhand, if one considers EWSB scale Q 0 ∼ TeV, EWSB also may not occur due to less running of In our calculation, we consider program SuSeFLAV-1.2 [7]. It considers full one loop corrections together with two loop leading contributions O(α t α s + α 2 t ) to the Higgs mass squared parameters following [18]. We have is a significant change in m h with change in Q 0 (see Fig.2 (right)).
The accurate spectra through EWSB can be found by generating them only at the true EWSB scale Q EW and the accurate supersymmetric spectra through supersymmetry breaking can be found by generating them only at the supersymmetry breaking scale Q N P . In generation of spectra through EWSB (masses of the Higgs particles), one should run all MSSM parameters up to Q EW , and in generation of the masses of sparticles one should use all MSSM parameters evaluated at Q N P . Since µ is generated at Q EW , one should take the RG running value of µ at Q N P from Q EW for calculating the masses of sparticles.

III. THE MSUGRA PARAMETER SPACE
We have compared the allowed mSUGRA parameter space for two cases of evaluation of EWSB minima: i) at Here, we consider the only parameter space where one can generate m h = 125.5 ± 0.5 GeV. No other constraints are considered (neutralino may not be the lightest supersymmetric particle (LSP)).
We find that a dramatically large allowed parameter space in mSUGRA model with almost no bounds on m 0 , m 1/2 and A 0 when EWSB minima is evaluated at Fig. 3). The parameter m 2 Hu goes to larger negative value as one decreases the RGE scale. This helps to have successful EWSB providing µ 2 positive and gives correct masses for Higgs particles by determining the exact shape of the Higgs potential at Q EW .