We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the Minimal Supersymmetric Standard Model. We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the Standard Model.
I discuss the effects of QCD radiative corrections in Supersymmetric theories. After summarizing the SUSY--QCD lagrangian in the Minimal Supersymmetric extension of the Standard Model, I will discuss the new features introduced by SUSY, and the main complications compared to standard QCD corrections. I will then discuss a few examples of QCD calculations in SUSY theories, for standard processes and for processes involving SUSY particles including the extended Higgs sector. [Talk given at "QCD 97", Montpellier 3-9 July 1997.]
We present the calculations of the supersymmetric QCD corrections to the total cross sections for single top production at the Fermilab Tevatron and the CERN Large Hadron Collider in the minimal supersymmetric standard model. Our results show that for the s-channel and t-channel, the supersymmetric QCD corrections are at most about 1%, but for the associated production process, the supersymmetric QCD corrections increase the total cross sections significantly, which can reach about 6% for most values of the parameters, and the supersymmetric QCD corrections should be taken into consideration i…
In this paper we evaluate the renormalization constants and anomalous dimensions for the squark wave function and mass within supersymmetric QCD. These results complement the ones obtained in Ref. \cite{Harlander:2009mn} and thus provide further confirmation on the applicability of dimensional reduction to supersymmetric QCD at three-loop order. The three-loop anomalous dimension constitute important input to precision predictions of the supersymmetric mass spectrum as obtained from the evolution from the GUT to the TeV energy scale.
We evaluate the supersymmetric QCD corrections to single top quark production via $q \bar q'\to t \bar b$ at the Fermilab Tevatron in the minimal supersymmetric model. We find that within the allowed range of squark and gluino masses the supersymmetric QCD corrections can enhance the cross section by a few percent. The combined effects of SUSY QCD, SUSY EW, and the Yukawa couplings can exceed 10% for the smallest allowed $\tanβ~ (\simeq 0.25)$ but are only a few percent for $\tanβ>1$.
We compute the total cross section and the transverse momentum distribution for single charged slepton and sneutrino production at hadronic colliders including NLO supersymmetric and non-supersymmetric QCD corrections. The supersymmetric QCD corrections can be substantial. We also resum the gluon transverse momentum distribution and compare our results with two Monte Carlo generators. We compute branching ratios of the supersymmetric decays of the slepton and determine event rates for the like-sign dimuon final state at the Tevatron and at the LHC.
We investigate the virtual photon structure function in the supersymmetric QCD (SQCD), where we have squarks and gluinos in addition to the quarks and gluons. Taking into account the heavy particle mass effects to the leading order in QCD and SQCD we evaluate the photon structure function and numerically study its behavior for the QCD and SQCD cases.
We calculate the supersymmetric ${\cal O}(α_s)$ QCD corrections to the width of the decay $H^+ \rightarrow \st\bar{\sb}$ within the Minimal Supersymmetric Standard Model. We find that the QCD corrections are significant, but that they do not invalidate our previous conclusionat tree-level on the dominance of the $\st\bar{\sb}$ mode in a wide parameter region.
The colour connection structure of QCD ($2\to2$) processes is discussed, with emphasis on its application to the supersymmetric 2 parton $\to$ 2 sparton processes, which are currently being implemented in the HERWIG Monte Carlo event generator. The procedure described by Marchesini and Webber is found to be inadequate, and a new method is proposed. However, this alteration is unlikely to significantly affect the theoretical predictions for soft gluon radiation. A complete list of supersymmetric QCD $2\to2$ matrix elements and their colour decompositions is presented.
We calculate the supersymmetric QCD corrections in order $α_s$ to the the widths of the Higgs boson decays $H^+ \to \st \bar\sb$ and $H^0, A^0 \to \st \bar\st, \sb \bar\sb$ in the on--shell scheme within the Minimal Supersymmetric Standard Model. We find that the QCD corrections are significant, but that the squark pair decay modes are still dominant in a wide parameter region.
We compute the leading QCD corrections to K-Kbar mixing in the supersymmetric standard model with general soft supersymmetry-breaking parameters. We construct the ΔS=2 effective Lagrangian for three hierarchies of supersymmetric particle masses, namely, when the gluino mass is comparable to, much greater than, or much less than the masses of the first two generation squarks. We find that the QCD corrections tighten the limits on squark mass splittings by more than a factor of two.
The one-loop supersymmetric QCD corrections to the top quark semileptonic decays $t\to b \bar{l} {ν_l}$ are considered. The corrections are found to reduce the decay width. In the still acceptable parameter space the corrections to the percentage change in top quark semileptonic decay width can reach the level of -0.7%.
Supersymmetric QCD corrections to top quark pair production by photon fusion are calculated in the minimal supersymmetric standard model taking into account of the effects of stops in the corrections to the total cross-section of t anti-t production at the future electron-positron linear collider. We find that the relative correction can be a few percent for reasonable values of the parameters.
A short presentation of the results of the analytical evaluation of the O(α_s^2) QCD contributions in the fermionic decay rates of the neutral CP-odd minimal supersymmetric Higgs particle is made. The corrections due to the nonvanishing quark masses are included. The results are presented both in terms of running and pole quark masses.
Supersymmetric (SUSY) QCD corrections to the lightest neutral Higgs boson associated production with top quark pair are studied in the minimal supersymmetric standard model (MSSM) at Linear colliders. Our calculations show that the SUSY QCD effects generally are very moderate (say 10%) and under control, except for some rescattering effects which lead to a breakdown of perturbation theory and require a more detailed study. In the vicinity of the production threshold for the favorable model parameters under the framework of the on-shell renormalization scheme, SUSY QCD can be as large as about …
QCD corrections to top quark pair production via fusion of both polarized and unpolarized photons are calculated in Supersymmetric Model. The corrections are found to be sizable. The dependence of the corrections on the masses of the supersymmetric particles is also investigated. Furthermore, we studied CP asymmetry effects arising from the complex couplings in the MSSM. The CP violating parameter can reach $10^{-2}$ for favorable parameter values.
We calculate the supersymmetric QCD correction to top-quark production at the Fermilab Tevatron, allowing for arbitrary left-right mixing of the squarks. We find that the correction is significant for several combinations of gluino and squark masses, e.g. +33% for m_{\tilde g}=200 GeV, m_{\tilde t} = m_{\tilde q} =75 GeV.
The leading-log QCD corrections to K-Kbar mixing in R-symmetric supersymmetric models are computed using effective field theory techniques. The spectrum topology where the gluino is significantly heavier than the squarks is motivated and focused on. It is found that, like in the MSSM, QCD corrections can tighten the kaon mass difference bound by roughly a factor of three. CP violation is also briefly considered, where QCD corrections can constrain phases to be as much as a factor of ten smaller than the uncorrected value.
The strength of the dynamically generated Yukawa coupling among composite fields is calculated. The system of N=1 supersymmetric SU(2) gauge theory with massive three flavors is considered as an example. We use the techniques of "integrating in" the gluino-gluino bound state in the low energy effective theory and the instanton calculation and Shifman-Vainshtein-Zakharov sum rule (QCD sum rule) in the fundamental theory. The obtained value of the Yukawa coupling is of the order of unity. The method which is developed in this paper can be applied to the other supersymmetric gauge theories.
We deduce the gluino contribution to the three-loop QCD βfunction within the minimal supersymmetric Standard Model (MSSM) from its standard QCD expression. The result is a first step in the computation of the full MSSM three-loop βfunction. In addition, in the case of a light gluino it provides the strong three-loop SUSY correction to the extrapolation of the strong coupling constant from the low energy regime to the Z region and up to the squark threshold.
Two-loop four-gluon N=4 susy amplitudes are evaluated via cutting techniques as a testing ground for QCD. A conjecture for four-point amplitudes to all loop orders is described. We also present a new conjecture for the leading-color part of the two-loop five-gluon amplitudes.
In this paper we review the hadroproduction mechanisms of double-charm baryons for the different experimental environments and reinterpret the SELEX and LHCb results.
We present a complete calculation of the QCD corrections (of the order $α_s$) to the width of the decay $H^+ \to t \bar{b}$ within the Minimal Supersymmetric Standard Model. We find that the QCD corrections are quite important, and that the supersymmetric QCD corrections (due to gluino, stop and sbottom exchange) can be comparable to or even larger than the standard QCD corrections in a large region of the supersymmetric parameter space. This is mainly due to the effect of large left-right mixings of stop and sbottom. This could significantly affect the phenomenology of the $H^+$ search.
Supersymmetric relations between dimensionless couplings receive finite correction at one-loop when supersymmetry is broken softly. We calculate the $O(α_s)$ correction to the squark decay width to a quark and an electroweak gaugino, which is found to be nonvanishing. Logarithmic correction appears when the gluino is heavy.
The supersymmetric QCD corrections to the hadronic width of a heavy charged Higgs boson, basically dominated by the top-quark decay mode $H^{+}\rightarrow t \bar{b}$, are evaluated at ${\cal O}(α_s)$ within the MSSM and compared with the standard QCD corrections. The study of such quantum effects, which turn out to be rather large, is essential to understand the hypothetical supersymmetric nature of a heavy charged Higgs boson potentially produced in the near future at the Tevatron and/or at the LHC.
We calculate the one-loop supersymmetric QCD corrections to the width of the $W$-boson. We find that these are of order $\sim {{ α_s} \over π} {1 \over 20} { {M^2_W} \over {M_S^2}} Γ_{u {\bar d}}$, where $M_S$ is the supersymmetry breaking scale and $ Γ_{u {\bar d}}$ the tree level hadronic width for $W^+ \rightarrow u {\bar d} $. Due to the appearance of the suppression factor $\sim {1 \over 20}$ these are at least two orders of magnitude smaller than the standard QCD corrections $\sim {{ α_s} \over π} Γ_{u {\bar d}}$ and hence of the order of the two-loop electroweak effects. Therefore super…
The QCD corrections to the top-quark pair production via both polarized and unpolarized gluon fusion in $pp$ collisions are calculated in the Minimal Supersymmetric Model(MSSM). We find the MSSM QCD corrections can reach 4% and may be observable in future precise experiments. Furthermore, we studied the CP violation in the MSSM, our results show that the CP violating parameter is sensitive to the masses of SUSY particles (It becomes zero, when the c.m. energy is less than twice the masses of both gluino and stop quarks.) and may reach $10^{-3}$.
We calculate QCD correction to the neutralino annihilation cross section into quark anti-quark final state and discuss its implications to the calculation of neutralino relic density. We see that the QCD correction enhances the pair-annihilation cross section by O(10 %) when final-state quarks are non-relativistic. Consequently, when the lightest neutralinos dominantly annihilate into a t\bar{t} pair, the relic density of the lightest neutralino is significantly affected by the QCD correction, in particular when the lightest-neutralino mass is close to the top-quark mass.
Within the minimal supersymmetric extension of the Standard Model (MSSM) the associated production of neutral Higgs bosons with top and bottom quarks belongs to the most important Higgs-boson production processes at the LHC. At large values of tan(beta), in particular, bottom--Higgs associated production constitutes the dominant production channel within the MSSM. We have calculated the next-to-leading-order supersymmetric QCD corrections to neutral Higgs production through the parton processes q qbar, gg -> t tbar / b bbar + h/H/A and present results for the total cross sections. The genuine …
We reinvestigate the leading QCD corrections to the radiative decay $b \to s γfor supersymmetric extensions of the Standard Model. Although the major contributions to the corrections originate from the running of the effective Lagrangian from the W scale down to the $b$ scale, additional corrections are expected from large mass splittings between the particles running in the loops, as well as from integrating out heavy particles at scales different from the W mass. The calculation is performed in the framework of effective field theories.
The identity of the quark-squark-gluino Yukawa coupling with the corresponding quark-quark-gluon QCD coupling in supersymmetric theories can be examined experimentally at the Large Hadron Collider (LHC). Extending earlier investigations of like-sign di-lepton final states, we include jets in the analysis of the minimal supersymmetric standard model, adding squark-gluino and gluino-pair production to squark-pair production. Moreover we expand the method towards model-independent analyses which cover more general scenarios. In all cases, squark decays to light charginos and neutralinos persist t…
The dominant production process for heavy charged Higgs bosons at the LHC is the associated production with heavy quarks. We have calculated the next-to-leading-order supersymmetric QCD corrections to charged-Higgs production through the parton processes $q\bar{q},gg \to tbH^{\pm}$ and present results for total cross sections and differential distributions. The QCD corrections reduce the renormalization and factorization scale dependence and thus stabilize the theoretical predictions. We present a comparison of the next-to-leading-order results for the inclusive cross section with a calculatio…
The discovery of charged Higgs bosons is of particular importance, since their existence is predicted by supersymmetry and they are absent in the Standard Model (SM). If the charged Higgs bosons are too heavy to be produced in pairs at future linear colliders, single production associated with a top and a bottom quark is enhanced in parts of the parameter space. We present the next-to-leading-order calculation in supersymmetric QCD within the minimal supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD corrections. In addition to the usual approach to perform the loop inte…
We calculate the two-loop QCD correction to the scalar quark contributions to the electroweak gauge-boson self-energies at zero momentum-transfer in the supersymmetric extension of the Standard Model. We then derive the $O(α_s)$ correction to the contribution of the scalar top and bottom quark loops to the rho parameter, which is the most sizable supersymmetric contribution to the electroweak mixing angle and the W-boson mass. The two-loop corrections modify the one-loop contribution by up to 30%; the gluino decouples for large masses. Contrary to the SM case where the QCD corrections are nega…
We calculate NLO QCD corrections to the lightest neutral Higgs boson production associated with top quark pair at hadron colliders in the minimal supersymmetric standard model(MSSM). Our calculation shows that the total QCD correction significantly reduces its dependence on the renormalization/factorization scale. The relative correction from the SUSY QCD part approaches to be a constant, if either $M_S$ or $m_{\tilde{g}}$ is heavy enough. The corrections are generally moderate(in the range of few percent to 20%) and under control in most of the SUSY parameter space. The relative correction is…
In the supersymmetry (SUSY) models, because of the mass difference between the left- and right-top squarks, the supersymmetric QCD interactions can generate parity violating effects in the production of $ t \bar t$ pairs. We show that SUSY QCD radiative corrections to the parity violating asymmetry in the production rates of the left- and right-handed top quarks via the $q \bar q \ra t \bar t$ process can reach about 3% at the Fermilab Tevatron with $\sqrt{s}=2$ TeV. This could be observable with an integrated luminosity larger than $2 fb^{-1}$. We also show that in these models the SUSY QCD r…
We compute the three-loop QCD corrections to the decoupling constant for $α_s$ which relates the Minimal Supersymmetric Standard Model to Quantum Chromodynamics with five or six active flavours. The new results can be used to study the stability of $α_s$ evaluated at a high scale from the knowledge of its value at $M_Z$. We furthermore derive a low-energy theorem which allows the calculation of the coefficient function of the effective Higgs boson-gluon operator from the decoupling constant. This constitutes the first independent check of the matching coefficient to three loops.
I present the results of the QCD corrections to the H+ --> t anti-b decay within the minimal supersymmetric standard model, if gluinos and scalar quarks are taken within the relevant loop diagram. I include the mixing of the scalar partners of the left- and right-handed top quark, which is proportional to the top quark mass. The standard corrections via gluons and quarks are about +8% for a charged Higgs mass of 300 GeV and about -11% for a Higgs mass of 800 GeV. I show that the standard corrections are diminished or enhanced by a non-negligible amount for certain values of the supersymmetric …
The one-loop supersymmetric QCD quantum effects on the width of the unconventional top quark decay mode $t\rightarrow H^{+}\, b$ are evaluated within the MSSM. The study of this process is useful to hint at the supersymmetric nature of the charged Higgs emerging from that decay. Remarkably enough, recent calculations of supersymmetric corrections to $Z$-boson observables have shown that the particular conditions by which the decay $t\rightarrow H^{+}\, b$ becomes competitive with the standard decay $t\rightarrow W^{+}\,b$ have a chance to be realized in nature. This further motivates us to foc…
We present the two-loop helicity amplitudes for the scattering of two gluons into two gluons in QCD, which are relevant for next-to-next-to-leading order corrections to jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity variants of dimensional regularization. Summing our expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Glover, Oleari and Tejeda-Yeomans. We also present the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-…
We present a complete next-to-leading-order calculation of the QCD corrections to $B^0-\bar{B}^0$ ($K^0-\bar{K}^0$) mixing in the framework of the minimal flavor violating (MFV) supersymmetry. We take into account the contributions from the gluino and find that the gluino-mediated corrections modify the LO result obviously even when the mass of gluino $m_{\tilde{g}} \gg m_{\rm w}$. In general, one cannot neglect gluino contributions.
We compute the full set of weak-scale gauge and Yukawa threshold corrections in the minimal supersymmetric standard model, and use them to study the effects of the supersymmetric particle spectrum on gauge and Yukawa coupling unification.
Small size QCD instantons may spoil the axion solution to the strong CP problem if QCD is not asymptotically free at high energy scales. We examine this issue in supersymmetric models using a manifestly supersymmetric scheme to compute the axion potential induced by small size instantons. Applying this scheme for a class of illustrative models, it is found that the resulting high energy axion potential is highly model-dependent, but suppressed by more powers of the soft supersymmetry breaking parameters and/or of the other small mass scales than what is expected based on a naive instanton grap…
A Fortran-program for the production cross-sections of squarks and gluinos at hadron colliders is described. It includes full next-to-leading order SUSY-QCD corrections to all possible final states ($\squark\squarkbar, \gluino\gluino, \squark\gluino, \squark\squark$). The program allows to calculate total cross-sections as well as differential distributions in the transverse momentum p_t and the rapidity y of one of the outgoing particles. In addition cuts in p_t and y can easily be implemented.
We calculate supersymmetric QCD corrections (squark/gluino loops) to quark pair production in e+ e- annihilation, allowing for mixing between left- and right-handed squarks and taking into account the effects of nonzero quark masses. Corrections to the Z boson partial widths are generally small and positive, except in the case of large b-squark mixing, where they become negative. At high-energy e+ e- colliders, larger corrections to the total cross sections are possible. Corrections to forward-backward asymmetries are negligible except possibly for top quarks, where they are sensitive to t-squ…
We consider the neutralino sector in the Minimal Non--minimal Supersymmetric Standard Model (MNSSM). We argue that there exists a theoretical upper bound on the lightest neutralino mass in the MNSSM. An approximate solution for the mass of the lightest neutralino is obtained.
We present the results of the contributions to the decay rate of the lightest Higgs particle into a charm-anticharm and bottom-antibottom pair within the minimal supersymmetric standard model when scalar quarks and a gluino are taken within the relevant loop diagrams. We show that in the case where the vacuum expectation values of the Higgs particles obey the condition $v_1\ll v_2$\ the scalar quarks and gluino change the decay rate by not more than a few per cent. These small contributions make it difficult to distinguish the Higgs particle of the standard model from the supersymmetric one.
We review very nice mechanism to generate masses to all the neutrinos in the Minimal Supersymmetric Standard Model (MSSM) without break $R$-parity. In consequence we get viable axion as Dark Matter candidate and at the same time solve the $μ$-problem in a similar way as done in the Next to Minimal Supersymmetric Model (NMSSM).
In this lectures, we give a review about the Minimal Supersymmetric Standard Model (MSSM) with $R$-Parity Violation because it provides an attractive way to generate neutrino masses, lepton mixing angles in acconcordance to present neutrino data.
The code NMSDECAY allows to compute widths and branching ratios of sparticle decays in the Next-to-Minimal Supersymmetric Standard Model. It is based on a generalization of SDECAY, to include the extended Higgs and neutralino sectors of the NMSSM. Slepton 3-body decays, possibly relevant in the case of a singlino-like lightest supersymmetric particle, have been added. NMSDECAY will be part of the NMSSMTools package, which computes Higgs, sparticle masses and Higgs decays in the NMSSM.
The renormalization of the Minimal Supersymmetric Standard Model is discussed. In particular we focus on the soft-supersymmetry breaking sector of the MSSM and comment on non-renormalization theorems.
We present the next-to-leading order QCD corrected total cross sections and the distributions of the transverse momenta of the final anti-bottom-quark, top-quark and charged Higgs-boson for the processes of $p\bar p/pp \to t\bar b H^-+X$ in the minimal supersymmetric standard model(MSSM) at the Tevatron and the LHC. We find that the NLO QCD corrections significantly modify the leading-order distributions of the transverse momenta of final particles($p_T^b$, $p_T^t$ and $p_T^{H^-}$), and the total NLO QCD corrections reduce the dependence of the cross section on the renormalization and factoriz…
We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FD…
The effective bottom Yukawa couplings are analyzed for the minimal supersymmetric extension of the Standard Model at two-loop accuracy within SUSY-QCD. They include the resummation of the dominant corrections for large values of tg(beta). In particular the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-induced SUSY-electroweak contributions are addressed. The residual theoretical uncertainties range at the per-cent level.
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) includes a Higgs iso-singlet superfield in addition to the two Higgs doublet superfields of the minimal supersymmetric extension. The Higgs sector and neutralino sectors of this model are examined within the context of a future linear collider.
The next-to-minimal supersymmetric extension of the Standard Model (NMSSM) is one of the most favored supersymmetric models. After an introduction to the model, the Higgs sector and the neutralino sector are discussed in detail. Theoretical, experimental, and cosmological constraints are studied. Eventually, the Higgs potential is investigated in the approach of bilinear functions. Emphasis is placed on aspects which are different from the minimal supersymmetric extension.
In the context of the Supersymmetric Standard Model with hierarchical sfermion masses, we re-analyze the QCD corrections to Delta F=2 effective Hamiltonian properly including effects which have been neglected so far. The point is that some Delta F=2 diagrams, involving both the heavy and the light sparticles, exhibit a logarithmic dependence on the ratio between the two masses, signalling a sensitivity to all the momenta between the two scales. In order to properly deal with these terms one has to take into account the mixing between Delta F=1 and Delta F=2 operators. In typical situations thi…
We calculate symmetry-restoring counterterms in supersymmetric QCD at the one-loop level. First we determine loop corrections to the supersymmetry and gauge transformations and find counterterms in such a way that the symmetry algebra holds at the one-loop level. Then these results are used to derive the symmetry-restoring counterterms to all trilinear interactions. In order to obtain unique results it is crucial to use the Slavnov-Taylor identity, which does not only contain supersymmetric and gauge Ward identities but also describes the symmetry algebra. In dimensional regularization this pr…
We study two phases of supersymmetric QCD associated to the singularities of the renormalization constant of the fermion mass operator. We find a behavior of the potential between two charges for the phases of interest that it is consistent with Seiberg results on these aspects based on a different method.
