We calculate the leading electroweak (EW) corrections to the important process of Higgs production associated with two bottom quarks at the CERN Large Hadron Collider (LHC). Our study is restricted to the Standard Model (SM).
At tree-level Higgs production in association with a b-quark pair proceeds through the small Yukawa bottom coupling in the Standard Model. Even in the limit where this coupling vanishes, EW one-loop effects, through the top-Higgs Yukawa coupling in particular, can still trigger this reaction. This contribution is small for Higgs masses around 120GeV but it quickly picks up for higher Higgs masses especially because the one-loop amplitude develops a leading Landau singularity and new thresholds open up. These effects can be viewed as the production of a pair of top quarks which rescatter to give rise to Higgs production through WW fusion. An important part of the thesis is devoted to the topic of Landau singularities in one-loop Feynman diagrams and application to the specific process of bbH production at the LHC.
Since the 4-point leading Landau singularity is not integrable when the one-loop amplitude is squared, we regulate the cross section by taking into account the width of the internal top and W particles. This requires that we extend the usual box one-loop function to the case of complex masses. We show how this can be implemented analytically in our case.
We study in some detail the cross section at the LHC as a function of the Higgs mass and show how some distributions can be drastically affected compared to the tree-level result.
At tree-level Higgs production in association with a b-quark pair proceeds through the small Yukawa bottom coupling in the Standard Model. Even in the limit where this coupling vanishes, electroweak one-loop effects, through the top-Higgs Yukawa coupling in particular, can still trigger this reaction. This contribution is small for Higgs masses around 120GeV but it quickly picks up for higher Higgs masses especially because the one-loop amplitude develops a leading Landau singularity and new thresholds open up. These effects can be viewed as the production of a pair of top quarks which rescatt…
The effective string action of the color-electric flux tube in the dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. A modified Yukawa interaction appears as a boundary contribution and is reduced into the ordinary Yukawa interaction in the London Limit.
The candidate of minimal dark matter (MDM) is limited if one demands perturbativity up to a very high scale, and it was believed that the MDM model with a real scalar septuplet could keep perturbative up to the Planck or GUT scale. In this work we point out that it is not true after taking into account the running of the quartic self-couplings of the scalar septuplet. For the septuplet mass around $10$ TeV, which is suggested by the observed dark matter relic abundance, these couplings would hit the Landau pole at a scale $\sim 10^8-10^9$ GeV, much lower than the Planck scale. We attempt to pu…
We confront the perturbativity problem in the real scalar quintuplet minimal dark matter model. In the original model, the quintuplet quartic self-coupling inevitably hits a Landau pole at a scale $\sim 10^{14}$ GeV, far below the Planck scale. In order to push up this Landau pole scale, we extend the model with a fermionic quintuplet and three fermionic singlets which couple to the scalar quintuplet via Yukawa interactions. Involving such Yukawa interactions at a scale $\sim 10^{10}$ GeV can not only keep all couplings perturbative up to the Planck scale, but can also explain the smallness of…
We analysis the constraints of the general two Higgs doublet models via evolving the Yukawa coupling constants to high energy under renormalization group. We consider the appearance of a Landau pole or large off-diagonal Yukawa couplings which cause tree level flavour changing neutral currents. Our study shows the latter condition can be used to answer that how much $Z_2$ symmetry breaking can be allowed in a given 2HDM model.
We investigate one-loop renormalization group evolutions of extended sectors of Yukawa type couplings. It is shown that Landau Poles which usually provide necessary low energy upper bounds that saturate quickly with increasing initial value conditions, lead in some cases to the opposite behaviour: some of the low energy couplings decrease and become vanishingly small for increasingly large initial conditions. We write down the general criteria for this to happen in typical situations, highlighting a concept of {\sl repulsive} quasi-fixed points, and illustrate the case both within a two-Yukawa…
We study how general two Higgs doublet models can be constrained by considering their properties under renormalization group evolution of the Yukawa couplings. We take into account both the appearance of a Landau pole as well as off-diagonal Yukawa couplings leading to flavour changing neutral currents in violation with experimental constraints at the electroweak scale. We find that the latter condition can be used to limit the amount of Z2 symmetry breaking allowed in a given model.
The non-equilibrium dynamics of a Yukawa theory with N fermions coupled to a scalar field is studied in the large N limit with the goal of comparing the dynamics predicted from the renormalization group improved effective potential to that obtained including the fermionic backreaction. The effective potential is of the Coleman-Weinberg type. Its renormalization group improvement is unbounded from below and features a Landau pole. When viewed self-consistently, the initial time singularity does not arise. The different regimes of the dynamics of the fully renormalized theory are studied both an…
We investigate the leading one-loop Yukawa corrections to the process pp-> b anti-b H in the Standard Model. We find that the next-to-leading order correction to the cross section is small about -4% if the Higgs mass is 120GeV. However, the appearance of leading Landau singularity when $M_H > 2M_W$ can lead to a large correction at the next-to-next-to-leading order level for a Higgs mass around 160GeV.
A system of Schwinger-Dyson equations for pseudoscalar four-dimensional Yukawa model in the two-particle approximation is investigated. The simplest iterative solution of the system corresponds to the mean-field approximation (or, equivalently, to the leading order of 1/N-expansion) and includes a non-physical Landau pole in deep-Euclidean region for the pseudoscalar propagator $Δ$. It is argued, however, that a full solution may be free from non-physical singularities and has the self-consistent asymptotic behavior $p^2_eΔ\simeq C\,\log^{-4/5}\frac{p^2_e}{M^2}$. An approximate solution confir…
Effects of Final State Interactions on Landau Singularities
Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学亥姆霍兹射线与核物理研究所（理论）和贝特理论物理中心）；Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern（伯尔尼大学爱因斯坦基础物理中心理论物理研究所）；Institute for Nuclear Studies and Department of Physics, The George Washington University（乔治华盛顿大学核物理研究所和物理系）；Tbilisi State University（第比利斯国立大学）；Theory Center, Thomas Jefferson National Accelerator Facility（托马斯·杰斐逊国家加速器设施理论中心）
The Landau equations give a physically useful criterion for how singularities arise in Feynman amplitudes. Furthermore, they are fundamental to the uses of perturbative QCD, by determining the important regions of momentum space in asymptotic problems. Generalizations are also useful. We will show that in existing treatments there are significant gaps in derivations, and in some cases implicit assumptions that will be shown here to be false in important cases like the massless Feynman graphs ubiquitous in QCD applications. In this paper is given a new proof that the Landau condition is both ne…
The pinched/non-pinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities e.g. due to linear denominator…
Integrated forms of the one-loop evolution equations are given for the Yukawa couplings in the MSSM, valid for any value of $\tan β$, generalizable to virtually any number of Yukawa fermions, and including all gauge couplings. These forms turn out to have nice mathematical convergence properties which we prove, and we determine the ensuing convergence criteria. Furthermore, they allow to write down general sufficient and necessary conditions to avoid singularities in the evolution of the Yukawa couplings over physically relevant energy ranges. We also comment briefly on the possible use of the…
A constellation of quarkonium-mass peaks has been reported in the last decade, opening what could be an entire new spectroscopy of nuclear-physics like complexity. Salient among these structures are the $Z_c$, much analyzed at BESIII as nicely summarised by J.~Zhao at this conference. Their stature as new hadron states has often been challenged by proposals that the peaks arise from triangle singularities instead, because they appear in three-body reactions and often satisfy the special kinematic conditions of the Coleman-Norton theorem. To experimentally decide, we should like to resort to di…
The infrared behaviour of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dr…
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）；Center for Theoretical Physics, Department of Physics, Columbia University（哥伦比亚大学物理系理论物理中心）；Institute for Advanced Study（普林斯顿高等研究院）
We introduce a novel approach for solving the problem of identifying regions in the framework of Method of Regions by considering singularities and the associated Landau equations given a multi-scale Feynman diagram. These equations are then analyzed by an expansion in a small threshold parameter via the Power Geometry technique. This effectively leads to the analysis of Newton Polytopes which are evaluated using a Mathematica based convex hull program. Furthermore, the elements of the Gröbner Basis of the Landau Equations give a family of transformations, which when applied, reveal regions li…
We propose matter wavefunctions on resolutions of $T^2/\mathbb{Z}_N$ singularities with constant magnetic fluxes. In the blow-down limit, the obtained wavefunctions of chiral zero-modes result in those on the magnetized $T^2/\mathbb{Z}_N$ orbifold models, but the wavefunctions of $\mathbb{Z}_N$-invariant zero-modes receive the blow-up effects around fixed points of $T^2/\mathbb{Z}_N$ orbifolds. Such blow-up effects change the selection rules and Yukawa couplings among the chiral zero-modes as well as the modular symmetry, in contrast to those on the magnetized $T^2/\mathbb{Z}_N$ orbifold model…
We present a more detailed picture of the infrared regime of Landau gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered…
The severe constraints imposed on the parameter space of the minimal split supersymmetry model by the infrared fixed point solution of the top Yukawa coupling $Y_t$ are studied in detail in terms of the value of the top quark mass measured at the Tevatron together with the lower bound on the lightest Higgs mass established by LEP. The sensitive dependence of the higgsino mass parameter $μ$ and of the gaugino coupling strengths ${\tilde g}_{u,d}$, ${\tilde g}^\prime_{u,d}$ on the value of $Y_t$ in the vicinity of the Landau pole is a remarkable consequence. A few other interesting features emer…
A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions below N_f^* is suggested. Assuming an infrared fixed point is present in the perturbative part of the QCD coupling even in some range below N_f^* leads to the condition gamma(N_f^*)=1, where gamma is the critical exponent. This result is incompatible with the existence of an analogue of Seiberg free dual magnetic phase in QCD. Using the Banks-Zak…
In recent studies, the production rate of photons or lepton pairs by a quark gluon plasma has been found to be enhanced due to collinear singularities. This enhancement pattern is very dependent on rather strict collinearity conditions between the photon and the quark momenta. It was estimated by neglecting the collisional width of quasi-particles. In this paper, we study the modifications of this collinear enhancement when we take into account the possibility for the quarks to have a finite mean free path. Assuming a mean free path of order $(g^2T\ln(1/g))^{-1}$, we find that only low invaria…
We investigate the constraints on the leptoquark Yukawa couplings and Higgs-leptoquark quartic couplings for scalar doublet leptoquark $\tilde{R}_2$, scalar triplet leptoquark $\vec S_3$ and their combination with both three generations and one generation from perturbative unitarity and vacuum stability. Perturbative unitarity of all the dimensionless couplings have been studied via one- and two-loop beta-functions. Introduction of new $SU(2)$ multiplets in terms of these leptoquarks fabricate Landau poles at two-loop level in the gauge coupling $g_2$ at $10^{19.7}$ GeV and $10^{14.4}$ GeV, re…
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively…
Consistency of trans-unification RG evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10) GUT (NMSGUT). We compute the 1-loop RGE $β$ functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $β$ functions involving large irreps. Use of the RGEs identif…
We study the gluon propagator in the Landau gauge in SU(3) lattice QCD at $β$=5.7, 5.8 and 6.0 at the quenched level. The Euclidean Landau-gauge gluon propagator $D(r)\equiv D_{μμ}^{aa}(x)/24$ is found to be well described by four-dimensional Yukawa-type function $e^{-mr}/r$ in the infrared and intermediate region of $r \equiv (x_μx_μ)^{1/2}$ = 0.1 $\sim$ 1.0fm. The infrared effective gluon mass is obtained as $m \simeq$ 600MeV. Associated with the 4D Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff…
Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhib…
In order to relax the Landau pole constraint on "λ", which is a coupling constant between a singlet S and the MSSM Higgs, λSh_uh_d in the next-to-MSSM (NMSSM), and also maintain the gauge coupling unification, we consider U(1) gauge extensions of the NMSSM. For relatively strong U(1) gauge interactions down to low energies, we assign U(1) charges only to the Higgs and the third family of the chiral matter among the MSSM superfields. In the U(1)_Z [U(1)_Z\times U(1)_X] extension, the low energy value of λcan be lifted up to 0.85-0.95 [0.9-1.0], depending on the employed charge normalizations, w…
Padé approximants are employed in order to study the analytic structure of the four-dimensional SU(2) Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, are used as fitting functions to lattice data for the propagators, carefully propagating uncertainties due to the fit procedure and taking into account all possible correlations. Applying this procedure systematically to the gluon-propagator data, we observe the presence of a pair of complex poles at $p^2_{\mathrm{pole}} = (-0.37 \pm 0.05_{\mathrm{stat}} \pm 0.08_{\mathrm{sys}}) \pm …
We employ Padé approximants in the study of the analytic structure of the four-dimensional $SU(2)$ Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluon-propagator data, we confirm the presence of a pair of complex poles at $p_{\rm pole}^2 = \left[(-0.37 \,\pm\, 0.05_{\rm stat}\,\pm\, 0.08_{\rm sys}) \pm i\,(0.66\, \pm\, 0.03_{\rm stat}\, \pm\, 0.02_{\rm sys}…
The associated production of a Higgs boson and a top-quark pair is important for probing the Yukawa coupling of the top quark, and calls for better theoretical modeling. In this paper, we calculate the two-loop infrared divergences in $t\bar{t}H$ production at hadron colliders. To do that we compute the one-loop amplitudes to higher orders in the dimensional regulator $ε$. Numeric results for the infrared poles are given as a reference at several representative phase-space points. The result in this work servers as a part of the ongoing efforts towards the $t\bar{t}H$ cross sections at the nex…
We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions $β(a)$ are meromorphic functions of the running coupling and give finite positive value of the coupling $a(Q^2)$ in the infrared regime ("freezing"), $a(Q^2) \to a_0$ for $Q^2 \to 0$. Such couplings automatically have no singularities on the positive axis of the squared momenta $Q^2$ ($ \equiv -q^2$). Explicit integration of the renormalization group equation (RGE) leads to the implicit (inverted) solution for the coupling, of the form $\ln (Q^2/Q^2_{\rm in}) = {\cal H}(a)$. An analysis of this…
We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.
Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-abelian group naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead we propose an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings com…
I analyze the IR fixed point structure of Landau gauge QCD. Precisely the fixed point with a strong kinematic singularity of the quark-gluon vertex that proved crucial for the recently proposed confinement mechanism in the quenched approximation is absent in dynamical QCD. Therefore, the IR singularities do not induce asymptotic quark confinement but the long-range interaction is screened by unquenching loops at scales of the order of the quark mass. This provides the prerequisite for a microscopic description of deconfinement and string breaking. The fixed points determine the qualitative for…
F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of right-handed neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N_gen = 3 or the number of singularity points of certain types. If there i…
We consider multi-Higgs-doublet models which, for symmetry reasons, have a universal Higgs-Yukawa (HY) coupling, $g$. This is identified with the top quark $g=g_t\approx 1$. The models are concordant with the quasi-infrared fixed point, and the top quark mass is correctly predicted with a compositeness scale (Landau pole) at $M_{planck}$, with sensitivity to heavier Higgs states. The observed Higgs boson is a $\bar{t}t$ composite, and a first sequential Higgs doublet, $H_b$, with $g\approx g_t\approx 1$ coupled to $\bar{b}_R(t,b)_L$ is predicted at a mass $3.0 \lesssim M_b \lesssim 5.5$ TeV an…
A sequence of $n$-particle approximations for the system of Schwinger-Dyson equations is investigated in the model of a complex scalar field $ϕ$ and a real scalar field $χ$ with the interaction $gϕ^*ϕχ$. In the first non-trivial two-particle approximation, the system is reduced to a system of two nonlinear integral equations for propagators. The study of this system shows that for equal masses a critical coupling constant $g^2_c$ exists, which separates the weak- and strong-coupling regions with the different asymptotic behavior for deep Euclidean momenta. In the weak-coupling region ($g^2<g^2…
