Relation between heat kernel method and scattering spectral method

Taking into account the available accelerator and astrophysical constraints, the mass of the lightest neutral Higgs boson h in the minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses (CMSSM) has been estimated to lie between 114 and ??130?GeV. Recent data from ATLAS and CMS hint that m _h ??125?GeV, though m _h ??119?GeV may still be a possibility. Here we study the consequences for the parameters of the CMSSM and direct dark matter detection if the Higgs hint is confirmed, focusing on the strips in the (m _1/2,m ₀) planes for different tan?? and A ₀ where the relic density of the lightest neutralino ?? falls within the range of the cosmological cold dark matter density allowed by WMAP and other experiments. We find that if m _h ??125?GeV focus-point strips would be disfavoured, as would the low-tan?? ${\tilde{\tau}}$ ?C?? and ${\tilde{t}}_{1} $ ?C?? coannihilation strips, whereas the ${\tilde{\tau}}$ ?C?? coannihilation strip at large tan?? and A ₀>0 would be favoured, together with its extension to a funnel where rapid annihilation via direct-channel H/A poles dominates. On the other hand, if m _h ??119?GeV more options would be open. We give parameterisations of WMAP strips with large tan?? and fixed A ₀/m ₀>0 that include portions compatible with m _h =125?GeV, and present predictions for spin-independent elastic dark matter scattering along these strips. These are generally low for models compatible with m _h =125?GeV, whereas the XENON100 experiment already excludes some portions of strips where m _h is smaller.     

The CMSSM and NUHM1 in light of 7 TeV LHC, B s →μ + μ − and XENON100 data

We make a frequentist analysis of the parameter space of the CMSSM and NUHM1, using a Markov Chain Monte Carlo (MCMC) with 95 (221) million points to sample the CMSSM (NUHM1) parameter spaces. Our analysis includes the ATLAS search for supersymmetric jets?+? signals using ～5/fb of LHC data at 7 TeV, which we apply using PYTHIA and a Delphes implementation that we validate in the relevant parameter regions of the CMSSM and NUHM1. Our analysis also includes the constraint imposed by searches for BR(B _s →μ ⁺ μ ^?) by LHCb, CMS, ATLAS and CDF, and the limit on spin-independent dark matter scattering from 225 live days of XENON100 data. We assume M _h ～125 GeV, and use a full set of electroweak precision and other flavour-physics observables, as well as the cold dark matter density constraint. The ATLAS_5/fb constraint has relatively limited effects on the 68 and 95 % CL regions in the (m ₀,m _1/2) planes of the CMSSM and NUHM1. The new BR(B _s →μ ⁺ μ ^?) constraint has greater impacts on these CL regions, and also impacts significantly the 68 and 95 % CL regions in the (M _A ,tanβ) planes of both models, reducing the best-fit values of tanβ. The recent XENON100 data eliminate the focus-point region in the CMSSM and affect the 68 and 95 % CL regions in the NUHM1. In combination, these new constraints reduce the best-fit values of m ₀,m _1/2 in the CMSSM, and increase the global χ ² from 31.0 to 32.8, reducing the p-value from 12 % to 8.5 %. In the case of the NUHM1, they have little effect on the best-fit values of m ₀,m _1/2, but increase the global χ ² from 28.9 to 31.3, thereby reducing the p-value from 15 % to 9.1 %.     

The CMSSM and NUHM1 after LHC Run 1

We analyze the impact of data from the full Run 1 of the LHC at 7 and 8 TeV on the CMSSM with \(\mu > 0\) and \(<0\) and the NUHM1 with \(\mu > 0\) , incorporating the constraints imposed by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment. We use the following results from the LHC experiments: ATLAS searches for events with \({E\!\!/}_{T}\) accompanied by jets with the full 7 and 8 TeV data, the ATLAS and CMS measurements of the mass of the Higgs boson, the CMS searches for heavy neutral Higgs bosons and a combination of the LHCb and CMS measurements of \(\mathrm{BR}(B_s \rightarrow \mu ^+\mu ^-)\) and \(\mathrm{BR}(B_d \rightarrow \mu ^+\mu ^-)\) . Our results are based on samplings of the parameter spaces of the CMSSM for both \(\mu >0\) and \(\mu <0\) and of the NUHM1 for \(\mu > 0\) with 6.8 \(\times 10^6\) , 6.2 \(\times 10^6\) and 1.6 \(\times 10^7\) points, respectively, obtained using the MultiNest tool. The impact of the Higgs-mass constraint is assessed using FeynHiggs 2.10.0, which provides an improved prediction for the masses of the MSSM Higgs bosons in the region of heavy squark masses. It yields in general larger values of \(M_h\) than previous versions of FeynHiggs, reducing the pressure on the CMSSM and NUHM1. We find that the global \(\chi ^2\) functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs-mass and the \({E\!\!/}_{T}\) searches, with best-fit values that are comparable to the \(\chi ^2/\mathrm{dof}\) for the best Standard Model fit. We provide 95 % CL lower limits on the masses of various sparticles and assess the prospects for observing them during Run 2 of the LHC.     

t\bar{t}H\to t\bar{t}\tau^{+}\tau^{-} —toward the measurement of the top-Yukawa coupling

One of the main goals of the ATLAS experiment is to measure various Higgs boson couplings as accurately as possible. Such a measurement is mandatory for a full understanding of the Higgs sector. One of the most challenging measurements of the Higgs boson properties is the determination of the Yukawa coupling to the top quark. To complement the $t\bar {t}H\rightarrow t\bar {t}\ensuremath {\mathit {b}\bar {\mathit {b}}}$ channel, which is the most significant in the low Higgs mass region (m _H ～120 GeV), we introduce a feasibility study of the $t\bar {t}H$ channel with the Higgs decaying to a pair of τ leptons. The signal events were reconstructed using the full and the fast simulation of the ATLAS detector. It is shown that both the distributions and the number of expected events after the same cuts agree, and that we can use the fast simulation to complete the analysis. We obtain a significance of 1.6σ for the low luminosity condition (30 fb^?1) and m _H =120 GeV, and 2.0σ for the high luminosity condition (300 fb^?1) and m _H =120 GeV. The observability of Higgs boson in this channel is demonstrated to be very marginal, even in the absence of taking into account $t\bar {t}+\mathrm{jets}$ .     

Demonstration of the origins of cooperativity within SU2×L 6 mapping over\left\{ {I\tilde H_\upsilon } \right\} Liouvillian carrier subspaces characterising the MQ-NMR cluster [A]6(L 6) and its\{ |kq\upsilon :[\tilde \lambda ] > > \} tensorial bases

The fundamental mappings over carrier subspace and substructures associated with \(\{ |kq\upsilon > > \} \) augmented spin algebras of Liouville space, and their mapping onto a subduced symmetry, are derived for [A]₆(L ₆) spin clusters within the combinatorial context of Rota-Cayley algebra over a field. Use of suitable lexical sets of combinatorialp-tuples (number partitions) over {|IM(M ₁?M _n )>}M, followed by the subsequent use ofL _n inner tensor product (ITP) algebra, allows the substructure of Liouville space to be derived. For SU2×L ₆ mapping over the simply-reducible \(\left\{ {I\tilde H_\upsilon } \right\}\) carrier subspaces, the \(D^k \left( {\tilde U} \right) \times \tilde \Gamma ^{\left[ {\tilde \lambda } \right]} \left( \upsilon \right)\) (L ₆) dual irreps, also arise as a consequence of the Liouville space recoupling termsv≡{k ₁?k _n } being distinct labels for \(\left\{ {I\tilde H_\upsilon } \right\}\) which are themselves amenible to combinatorial analysis within the concept of Rota-Cayley algebra. Hence, theL _n -induced symmetry aspects of multiquantum NMR density matrix formalisms and their dual \(\{ |kq\upsilon :[\tilde \lambda ] > > \} \) tensorial bases of spin cluster problems are derived and the nature of the cooperative, aspect between the individual symmetries comprising the duality is demonstrated, i.e. in the context of the operator bases of Liouville space. These practical arguments correlate, well with those based on an augmented boson pattern algebra derived from a Heisenburg algebra for superoperators, ?_±,?₀. An earlier, treatment of conventional Hilbert space SU2×L ₆ dualitycould only be realised in terms of standard SU2 boson algebra. Since the recoupling Rota-‘field’v for Liouville space is an explicit aspect of the dual mapping, a direct demonstration of cooperativity exists.     

Confronting the MSSM and the NMSSM with the discovery of a signal in the two photon channel at the LHC

We confront the discovery of a boson decaying into two photons, as reported recently by ATLAS and CMS, with the corresponding predictions in the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM). We perform a scan over the relevant regions of parameter space in both models and evaluate the MSSM and NMSSM predictions for the dominant Higgs production channel and the photon–photon decay channel. Taking into account the experimental constraints from previous direct searches, flavor physics, electroweak measurements as well as theoretical considerations, we find that a Higgs signal in the two photon channel with a rate equal to, or above, the SM prediction is viable over the full mass range 123?M _H ?127 GeV, both in the MSSM and the NMSSM. We find that besides the interpretation of a possible signal at about 125 GeV in terms of the lightest $\mathcal {CP}$ -even Higgs boson, both the MSSM and the NMSSM permit also a viable interpretation where an observed state at about 125 GeV would correspond to the second-lightest $\mathcal {CP}$ -even Higgs boson in the spectrum, which would be accompanied by another light Higgs with suppressed couplings to W and Z bosons. We find that a significant enhancement of the γγ rate, compatible with the signal strengths observed by ATLAS and CMS, is possible in both the MSSM and the NMSSM, and we analyse in detail different mechanisms in the two models that can give rise to such an enhancement. We briefly discuss also our predictions in the two models for the production and subsequent decay into two photons of a $\mathcal {CP}$ -odd Higgs boson.     

Supersymmetry and dark matter in light of LHC 2010 and XENON100 data

We make frequentist analyses of the CMSSM, NUHM1, VCMSSM and mSUGRA parameter spaces taking into account all the public results of searches for supersymmetry using data from the 2010 LHC run and the XENON100 direct search for dark matter scattering. The LHC data set includes ATLAS and CMS searches for $\mathrm{jets} + {\not}E_{T}$ events (with or without leptons) and for the heavier MSSM Higgs bosons, and the upper limit on BR(B _s →μ ⁺ μ ^?) including data from LHCb as well as CDF and DØ. The absence of signals in the LHC data favours somewhat heavier mass spectra than in our previous analyses of the CMSSM, NUHM1 and VCMSSM, and somewhat smaller dark matter scattering cross sections, all close to or within the pre-LHC 68% CL ranges, but does not impact significantly the favoured regions of the mSUGRA parameter space. We also discuss the impact of the XENON100 constraint on spin-independent dark matter scattering, stressing the importance of taking into account the uncertainty in the π-nucleon σ term Σ _πN , which affects the spin-independent scattering matrix element, and we make predictions for spin-dependent dark matter scattering. Finally, we discuss briefly the potential impact of the updated predictions for sparticle masses in the CMSSM, NUHM1, VCMSSM and mSUGRA on future e ⁺ e ^? colliders.     

HiggsSignals: Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC

HiggsSignals is a Fortran90 computer code that allows to test the compatibility of Higgs sector predictions against Higgs rates and masses measured at the LHC or the Tevatron. Arbitrary models with any number of Higgs bosons can be investigated using a model-independent input scheme based on HiggsBounds. The test is based on the calculation of a $\chi ^2$ measure from the predictions and the measured Higgs rates and masses, with the ability of fully taking into account systematics and correlations for the signal rate predictions, luminosity and Higgs mass predictions. It features two complementary methods for the test. First, the peak-centered method, in which each observable is defined by a Higgs signal rate measured at a specific hypothetical Higgs mass, corresponding to a tentative Higgs signal. Second, the mass-centered method, where the test is evaluated by comparing the signal rate measurement to the theory prediction at the Higgs mass predicted by the model. The program allows for the simultaneous use of both methods, which is useful in testing models with multiple Higgs bosons. The code automatically combines the signal rates of multiple Higgs bosons if their signals cannot be resolved by the experimental analysis. We compare results obtained with HiggsSignals to official ATLAS and CMS results for various examples of Higgs property determinations and find very good agreement. A few examples of HiggsSignals applications are provided, going beyond the scenarios investigated by the LHC collaborations. For models with more than one Higgs boson we recommend to use HiggsSignals and HiggsBounds in parallel to exploit the full constraining power of Higgs search exclusion limits and the measurements of the signal seen at $m_H\approx 125.5$  GeV.     

Constraints on supersymmetry from LHC data on SUSY searches and Higgs bosons combined with cosmology and direct dark matter searches

The ATLAS and CMS experiments did not find evidence for Supersymmetry using close to 5/fb of published LHC data at a center-of-mass energy of 7 TeV. We combine these LHC data with data on $B^{0}_{s}\to \mu^{+}\mu^{-}$ (LHCb experiment), the relic density (WMAP and other cosmological data) and upper limits on the dark matter scattering cross sections on nuclei (XENON100 data). The excluded regions in the constrained Minimal Supersymmetric SM (CMSSM) lead to gluinos excluded below 1270 GeV and dark matter candidates below 220 GeV for values of the scalar masses (m ₀) below 1500 GeV. For large m ₀ values the limits of the gluinos and the dark matter candidate are reduced to 970 GeV and 130 GeV, respectively. If a Higgs mass of 125 GeV is imposed in the fit, the preferred SUSY region is above this excluded region, but the size of the preferred region is strongly dependent on the assumed theoretical error.     

Flavoured co-annihilation

In minimal supergravity (mSUGRA) or CMSSM, one of the main co-annihilating partners of the neutralino is the lightest stau, $\tilde{\tau}_1$ . In the presence of flavour violation in the right-handed sector, the co-annihilating partner would be a flavour mixed state. The flavour effect is two-fold: (a) It changes the mass of $\tilde{\tau}_{1}$ , thus modifying the parameter space of the co-annihilation and (b) flavour violating scatterings could now contribute to the cross-sections in the early Universe. In fact, it is shown that for large enough ??~0.2, these processes would constitute the dominant channels in co-annihilation regions. The amount of flavour mixing permissible is constrained by flavour violating ?????? or ????e processes. For ??_RR mass insertions, the constraints from flavour violation are not strong enough in some regions of the parameter space due to partial cancellations in the amplitudes. In mSUGRA, the regions with cancelations within LFV amplitudes do not overlap with the regions of co-annihilations. In non-universal Higgs model (NUHM), however, these regions do overlap leading to significant flavoured co-annihilations. At the LHC and other colliders, these regions can constitute for interesting signals.     

DKP oscillator in the presence of magnetic field in (1+2)-dimensions for spin-zero and spin-one particles in noncommutative phase space

In view of the discovery of a new boson by the ATLAS and CMS Collaborations at the LHC, we present an update of the global Standard Model (SM) fit to electroweak precision data. Assuming the new particle to be the SM Higgs boson, all fundamental parameters of the SM are known allowing, for the first time, to overconstrain the SM at the electroweak scale and assert its validity. Including the effects of radiative corrections and the experimental and theoretical uncertainties, the global fit exhibits a p-value of 0.07. The mass measurements by ATLAS and CMS agree within 1.3σ with the indirect determination $M_{H}=94^{\,+25}_{\,-22}~\mathrm{GeV}$ . Within the SM the W boson mass and the effective weak mixing angle can be accurately predicted to be M _W =80.359±0.011 GeV and $\sin ^{2}\theta ^{\ell }_{{\rm eff}}= 0.23150\pm 0.00010$ from the global fit. These results are compatible with, and exceed in precision, the direct measurements. For the indirect determination of the top quark mass we find $m_{t}= 175.8^{\:+2.7}_{\:-2.4}~ \mathrm {GeV}$ , in agreement with the kinematic and cross-section-based measurements.     

The higgs boson mass from precision electroweak data

We present a new global fit to precision electroweak data, including new low- and high-energy data and analyzing the radiative corrections arising from the minimal symmetry breaking sectors of the Standard Model (SM) and its supersymmetric extension (MSSM). It is shown that present data favor a Higgs mass ofO(M _z):M _H=76 _?50 ⁺¹⁵² GeV. We confront our analysis with (meta) stability and perturbative bounds on the SM Higgs mass, and the theoretical upper bound on the MSSM Higgs mass. Present data do not discriminate significantly between the SM and MSSM Higgs mass ranges. We comment in passing on the sensitivity of the Higgs mass determination to the values ofα(M _z) andα _s(M _z).     

Another calculation of the Higgs mass and the top mass from the principles of H. B. Nielsen: m H ≅ 163GeV for M t ≅ 190GeV

We calculate the Higgs mass and the top mass starting from the principle that there are two, essentially degenerate minima in the Higgs effective potential; the second is at about the Planck energy scale M _P = 1.2 × 10¹⁹ GeV. Thus the parameter of the quartic self-coupling λ _h vanishes, as does β _λH at M _P. The new element is the addition of a quantum interaction term which couples the square of the Higgs field to the square of a pseudoscalar field, in the domain of the energy scale between about 10¹⁴ GeV and M _P. We modify β _λH at one loop. The pseudoscalar field which is introduced may be the field which is responsible for a spontaneous breakdown of discrete symmetry — for CP noninvariance at an energy scale of (10¹⁵–10¹⁶) GeV. The result is then a closer value for m _H ? 163 GeV for the top pole-mass M _t ? 190 GeV; both values are now close to the electroweak scale parameter $\langle {\phi _H}\rangle /\sqrt 2 = 175{\text{ GeV}}$ . In terms of dimensionless running coupling parameters, which determine the masses near to the electroweak scale, we get $\sqrt {{\lambda _H}} \cong 0.06$ and $gt/\sqrt 2 \cong 0.72$ , values that are close to each other and close to unity.     

Higgs bosons and neutrinos in the left-right model

The left-right asymmetric model featuring the bidoublet and two triplets of Higgs fields is investigated. It was established that, from an analysis of the reaction l ^?γ → W ^?ν_l, it is possible to deduce not only information about the properties of the singly charged Higgs bosons $\tilde \delta ^{( - )} $ and h ^(?) but also an answer to the question of whether the neutrino is a Majorana or a Dirac particle. The processes $f_i \bar f_j \to \Delta _1^{( - - )} \tilde \delta ^{( + )} $ and e^?μ^? → Δ _1,2 ^(—) γ leading to the production of doubly charged Higgs bosons are investigated. It is shown that information about the properties of singly charged Higgs bosons can also be obtained by studying the ultrahighenergy cosmic neutrinos from the reaction e ^?ν _e →μ^?ν_μ.     

Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid ³He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ～ 325 GeV. They together satisfy the Nambu sum rule M ₁ ² + M ₂ ² = 4M _t ² , where M _t ～ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ～210 GeV. In this case the Nambu sum rule is 2M ₁ ² + 2M ₂ ² = 4M _t ² . In addition, the properties of the Higgs modes in superfluid ³He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M ₊ ² + M _? ² = 4M _t ² .     

Likelihood analysis of the sub-GUT MSSM in light of LHC 13-TeV data

We describe a likelihood analysis using MasterCode of variants of the MSSM in which the soft supersymmetry-breaking parameters are assumed to have universal values at some scale \(M_\mathrm{in}\) below the supersymmetric grand unification scale \(M_\mathrm{GUT}\), as can occur in mirage mediation and other models. In addition to \(M_\mathrm{in}\), such ‘sub-GUT’ models have the 4 parameters of the CMSSM, namely a common gaugino mass \(m_{1/2}\), a common soft supersymmetry-breaking scalar mass \(m_0\), a common trilinear mixing parameter A and the ratio of MSSM Higgs vevs \(\tan \beta \), assuming that the Higgs mixing parameter \(\mu > 0\). We take into account constraints on strongly- and electroweakly-interacting sparticles from \(\sim 36\)/fb of LHC data at 13 TeV and the LUX and 2017 PICO, XENON1T and PandaX-II searches for dark matter scattering, in addition to the previous LHC and dark matter constraints as well as full sets of flavour and electroweak constraints. We find a preference for \(M_\mathrm{in}\sim 10^5\) to \(10^9 \,\, \mathrm {GeV}\), with \(M_\mathrm{in}\sim M_\mathrm{GUT}\) disfavoured by \(\Delta \chi ^2 \sim 3\) due to the \(\mathrm{BR}(B_{s, d} \rightarrow \mu ^+\mu ^-)\) constraint. The lower limits on strongly-interacting sparticles are largely determined by LHC searches, and similar to those in the CMSSM. We find a preference for the LSP to be a Bino or Higgsino with \(m_{\tilde{\chi }^0_{1}} \sim 1 \,\, \mathrm {TeV}\), with annihilation via heavy Higgs bosons H / A and stop coannihilation, or chargino coannihilation, bringing the cold dark matter density into the cosmological range. We find that spin-independent dark matter scattering is likely to be within reach of the planned LUX-Zeplin and XENONnT experiments. We probe the impact of the \((g-2)_\mu \) constraint, finding similar results whether or not it is included.     

Heavy gluino and squark decays atp \bar p collider

The recent limits, \(m_{\tilde g} , m_{\tilde q} \gtrsim 40\) , GeV for gluino and squark masses obtained from experiments at the collider are based on jet +p _T analysis, in the hypothesis that the gluino or the squark decays into photino+quarks with a branching ratio near to one. We show that this hypothesis is generally not justified for higher masses of the gluino and the squarks, 50 GeV \( \lesssim m_{\tilde g,\tilde q} \lesssim \) 150 GeV, relevant to present and future \(\bar p\) colliders. In an interesting range of the parameters we study the different decay modes and the related signatures, among which isolated leptons or photons in the final states.     

Charged Higgs boson discovery potential at a 500 GeV e+e− linear collider

The discovery potential for charged Higgs bosons has been studied with full-statistics background simulations for $\sqrt s$ =500 GeV and ?=10fb^?1. For the hadronic decay channels $H^ + H^ - \to \operatorname{c} \bar s\bar cs$ , a microvertex detector is crucial for establishing a signal over the $e^ + e^ - \to t\bar t$ background. A combination with a search in the channels $H^ + H^ - \to c\bar s\tau ^ - \nu ,\tau ^ + \nu \tau ^ - \bar \nu$ allows detection sensitivity for charged Higgs bosons up to a mass of about 210GeV, independent of the charged Higgs decay modes. Sensitivity regions in them _A-tanβ parameter space of the Minimal Supersymmetric extention of the Standard Model (MSSM) are given.