The analog of the Cachazo-Svrvcek-Witten rules for scattering amplitudes with massive quarks is derived following an approach previously employed for amplitudes with massive scalars. A prescription for the external wave-functions is given that leads to a one-to one relation between fields in the action and spin-states of massive quarks. Several examples for the application of the rules are given and the structure of some all-multiplicity amplitudes with a pair of massive quarks is discussed. The rules make supersymmetric relations to amplitudes with massive scalars manifest at the level of the action. The formalism is extended to several quark flavors with different masses.
We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrvcek and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and n gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for Z,W,γ^* --> qbar q + n gluons (analytically up to n=3, beyond via the Berends--Giele recursion r…
We illustrate the use of new on-shell methods, 4-dimensional unitarity cuts combined with on-shell recursions relations, by computing the A_4^{(1)}(phi,1^-,2^-,3^+,4^+) amplitude in the large top mass limit where the Higgs boson couples to gluons through an effective interaction.
I review recent progress in using twistor-inspired methods to compute perturbative scattering amplitudes in gauge theory, for application to collider physics.
We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dun…
Witten's twistor string theory has led to new representations of S-matrix in massless QFT as a single object, including Cachazo-He-Yuan formulas in general and connected formulas in four dimensions. As a first step towards more realistic processes of the standard model, we extend the construction to QCD tree amplitudes with massless quarks and those with a Higgs boson. For both cases, we find connected formulas in four dimensions for all multiplicities which are very similar to the one for Yang-Mills amplitudes. The formula for quark-gluon color-ordered amplitudes differs from the pure-gluon c…
We consider massive deformation of $U(2)$ gauge bosons in a recently developed holonomy formalism and propose a novel electroweak model. The massive gauge bosons arise from massive deformation of spinor momenta, which implies that the mass generation is implemented by Lorentz symmetry breaking rather than the spontaneous gauge symmetry breaking. Following the notation of the holonomy formalism, we interpret the weak hypercharge of a left-handed fermion doublet as the reciprocal of the Knizhnik-Zamolodchikov (KZ) parameter $κ= k + h^{\vee}$ where $k$ is the level number, fixed at $k = 1$, and $…
We propose a simple but realistic pattern of quark mass matrices at the string scale, which can be derived from orbifold models of superstring theory with no use of gauge symmetries. This pattern is left-right symmetric and preserves the structural parallelism between up and down quark sectors. Its phenomenological consequences on flavor mixing and $CP$ violation are confronted with current experiments at the weak scale by use of the renormalization-group equations in the framework of the minimal supersymmetric standard model. We find that good agreement is achievable without fine-tuning.
Remarkable progress inspired by twistors has lead to very simple analytic expressions and to new recursive relations for multi-parton color-ordered amplitudes. We show how such relations can be extended to include color and present the corresponding color-dressed formulation for the Berends-Giele, BCF and a new kind of CSW recursive relations. A detailed comparison of the numerical efficiency of the different approaches to the calculation of multi-parton cross sections is performed.
We use twistor inspired rules to compute the one-loop amplitude for a Higgs boson coupling to any number of negative helicity gluons in the large top mass limit.
The spectrum of doubly heavy baryons, hadrons made up of two heavy quarks and one light quark, is computed through a potential model with relativistic kinematics. The expression for the $Q\bar Q$ potential comes from the AdS/QCD correspondence.
A procedure inspired by the Tamm-Dancoff method is applied to the chiral quark model which has been extended to include additional degrees of freedom: a pseudoscalar isoscalar field as well as a triplet of scalar isovector fields. The simpler, generic $σ$ -- model has been used before as a test for the Tamm-Dancoff inspired approximation (TDIA). The extended chirial quark model is employed here to investigate possible novel effects of the additional degrees of freedom as well as to point out the necessesity to introduce a SU(3) flavour. Model predictions for the axial-vector coupling constant …
We derive a nonperturbative transverse momentum distribution for partons using a potential model to describe the quark-quark interaction inside the proton. We use this distribution to calculate the diferential cross-section of $π^0$-production for intermediate values of transverse momentum in $p-p$ collisions at high energies. Assuming a variable string tension constant for the quark-quark potential we obtain a very good description of the experimental data at different energies. The corresponding values of the mean transverse momentum of the partons are essentially lower than those obtained u…
The relativistic interacting quark-diquark model, constructed in the framework of point form dynamics, is extended to strange baryons. The strange and nonstrange baryon spectra are calculated and compared with the experimental data.
In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F-L (x, Q2) within this approach. We make predictions using the QCD based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible wi…
The QCD inspired potential model persued by us earlier has been recently modified to incorporate an additional factor 'c' in the linear cum Coulomb potential. While it felicitates the inclusion of standard confinement parameter b = 0.183GeV 2, unlike in previous work, it still falls short of explaining the Isgur-Wise function for the B mesons without adhoc adjustment of the strong coupling constant. In this work, we determine the factor 'c' from the experimental values of decay constants and masses and show that the reality constraint on 'c' yeilds bounds on the strong coupling constant as wel…
The spectrum of baryons with two heavy quarks is predicted, assuming a configuration of a light quark and a heavy diquark. The masses are computed within a semirelativistic quark model, using a potential obtained in the framework of the AdS/QCD correspondence. All the parameters defining the model are determined fitting the meson spectrum. The obtained mass of Ξ_{cc} is in agreement with the measurements.
We explain how a $SU(N_c)$ gauge theory, decoupled from the standard model and with a high-lying strong coupling scale, can incorporate apparently unrelated cosmological features, such as Inflation and dark matter, using well-understood dynamics from Quark-Gluon Plasma Physics. In our scenario, the evolution of the universe is throughoutly hot: Inflation occurs due to the bulk viscosity peak during the mixed phase to deconfinement, while dark matter is composed of weakly interacting glueballs formed in the same phase. We parametrize the temperature dependence of the EoS and the viscosity expec…
QCD amplitudes display a universal behaviour when one or more partons are soft and/or collinear. This can expressed in terms of antenna functions which are much simpler than the full amplitudes and yet correctly embody their infrared behaviour. We show how antenna functions can be naturally obtained via a twistor-inspired MHV approach. As an application, we present compact results for MHV and NMHV antennas functions valid for any number of gluons. These are sufficient to calculate the complete set of tree-level gluon antenna functions up to NNNLO. As an interesting corollary, we prove that spl…
AdS/QCD correspondence allows to compute the quark-antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schroedinger equation with relativistic kinematics) and a short range hyperfine splitting potential to describe the bound states of quark-antiquark. Comparison with experiment permits to fit the parameters of the model, namely the quark masses and the quark potential parameters. A discussion of heavy tetraquark masses, prompted by the hypothesis of a diquark-antidiquark structure for the puzzling state X(3872), is also presented.
We compare two QCD-inspired quark models with four-fermion interaction, without and with the remnant coupling to low-energy gluons, in the regime of dynamical chiral symmetry breaking (DCSB). The first one, the Nambu-Jona-Lasinio (NJL) model ensures the factorization of scalar and pseudoscalar meson poles in correlators, the well-known Nambu relation between the scalar meson mass and the dynamical quark mass, $m_σ = 2 m_{dyn}$, and the residual chiral symmetry in coupling constants characteristic for the linear $σ$-model. The second one, the Gauged NJL model, happens to be qualitatively differ…
We sketch here an approach to the computation of generalised parton distributions (GPDs), based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, $H_π^{\rm v}(x,ξ,t)$. Our analysis focuses on the case of zero skewness, $ξ=0$, and underlines that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to t…
We study the Dyson-Schwinger equation for the quark propagator in Minkowski space. In order to have analytical behaviour at the timelike axis of momenta under control, we use the Stieltjes and the Hilbert transformation for the interaction kernels and discuss the solution from the perspective of these transformations. In addition, a lattice fit for the gluon propagator and approximation for quark-gluon vertex are employed, and within the model the quark propagator is obtained through the solution of Dyson-Schwinger equation in Minkowski space. The resulting propagators in all studied cases do …
Horava-Witten M-Theory offers new ways in achieving the quark and lepton mass hierarchies not naturally available in supergravity unified models. In previous work, based on a torus fibered Calabi-Yau manifold with a del Pezzo base dP_7,a three generation SU(5)model with Wilson line breaking to the Standard Model was constructed. It was seen that if the additional 5- branes clustered near the distant orbifold plane, it was possible that such models could generate the observed hierarchies of quark masses without undue fine tuning. We update these results here and extend them to include the charg…
We discuss formulation of QCD in Minkowski-spacetime and effect of an operator product expansion by means of normal ordering of fields in the QCD Lagrangian. The formulation of QCD in the Minkowski-spacetime allows us to solve a constraint equation and decompose the gauge field propagator in the sum of an instantaneous part, which forms a bound state, and a retarded part, which contains the relativistic corrections. In Quantum Field Theory, for a Lagrangian with unordered operator fields, one can make normal ordering by means of the operator product expansion, then the gluon condensate appear.…
The renormalization of the effective QCD-Hamiltonian theory for the quark-antiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed point-Hamiltonian brings the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of the renormalized effective QCD-Hamiltonian comes from the pion mass and radius, for a given constituent quark mass. The 1s and excited 2s states of $\bar u q$ are calculated as a function of the mass of …
We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approac…
The effective interaction between a quark and an anti-quark as obtained previously with by the method of iterated resolvents is replaced by the so called up-down-model and applied to flavor off-diagonal mesons including the pion. The only free parameters are those of canonical quantum chromo-dynamics (QCD), particularly the coupling constant and the masses of the quarks. The so obtained light-cone wave function can be used to calculate the pion's form factor, particularly its mean-square radius can be computed analytically. The results allow for the exciting conclusion that the pion is built b…
We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/ψ$ and $ψ^{\prime}$ are alleviated …
The breakdown of E_6 gauge symmetry at high energies may lead to supersymmetric (SUSY) models based on the Standard Model (SM) gauge group together with extra U(1)_ψ and U(1)_χ gauge symmetries. To ensure anomaly cancellation the particle content of these E_6 inspired models involves extra exotic states that generically give rise to non-diagonal flavour transitions and rapid proton decay. We argue that a single discrete \tilde{Z}^{H}_2 symmetry can be used to forbid tree-level flavor-changing transitions, as well as the most dangerous baryon and lepton number violating operators. We present 5D…
Explicit chiral symmetry breaking is a natural feature of many QCD inspired models with multi-quark interactions. To carry out the 1/N expansion of these theories, one integrates over the quark fields. In the process of calculating the one-loop fermion determinant which is not chiral invariant due to quark masses, special care must be taken in order not to alter the original symmetry breaking pattern of the Lagrangian. We show how to do this consistently.
The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. The formalism is applied to physical mesons with a different flavor of quark and anti-quark. The excitation spectrum of the $ρ$-meson with its excellent agreement between theory and exper…
In the standard model (SM), the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the only origin of flavor violations (FVs). On the other hand, in general, there are a lot of sources of the FVs in a physics beyond the SM, through the diagonalizing matrices which make Yukawa matrices diagonal. Although most of the diagonalizing matrices are unknown ones, grand unified theories (GUTs) can fix these matrices. In particular, if we consider a GUT model based on the $SO(10)$ group, these diagonalizing matrices are strongly related to each other because of the matter unification. However, this unification c…
A resonance in the diphoton channel with invariant mass $m_{γγ} = 750$ GeV was claimed by the ATLAS and CMS collaborations at the run-2 LHC with $\sqrt{s}=13$ TeV. In this paper, we explain this diphoton excess as a pseudo-scalar singlet, which is produced at the LHC through gluon fusion with exotic scalar quarks running in the loop. We point out the scalar singlet might trigger a two-step electroweak phase transition, which can be strongly first oder. By assuming there are CP violations associated with interactions of the scalar quarks, the model is found to be able to generate adequate baryo…
The fully-charm and -bottom pentaquarks, \emph{i.e.} $cccc\bar{c}$ and $bbbb\bar{b}$, with spin-parity quantum numbers $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$, are investigated within a Lattice-QCD inspired quark model, which has already successfully described the recently announced fully-charm tetraquark candidate $X(6900)$, and has also predicted several other fully-heavy tetraquarks. A powerful computational technique, based on the Gaussian expansion method combined with a complex-scaling range approach, is employed to predict, and distinguish, bound, resonance and scatteri…
We perform a semi-perturbative calculation of the quark-gluon vertex inspired from the three-loop expanded 3PI effective action and investigate the relative strengths of the chirally symmetric/broken tensor structures below and above the crossover.
I present a new model for the quark mass matrices, which uses four scalar doublets together with a horizontal symmetry S3 x Z3. The model is inspired on a suggestion made a few years ago by Ma, but it is different. The predictions |Vts| \approx ms/mb and |Vub/Vcb| > 0.085 are obtained. Flavour-changing neutral Yukawa interactions do not exist in the down-type-quark sector.
The pion structure in Minkowski space is explored using the Nakanishi integral representation. A general framework is developed for the pion Bethe-Salpeter amplitude based on the Kallen-Lehmann representation of the dressed quarks with an ansatz for the pseudo-scalar $π-q\bar q$ vertex fulfilling the axial Ward-Takahashi identity. The Nakanishi weight functions are derived for the scalar amplitudes associated with the decomposition of the pion Bethe-Salpeter amplitude in different operator bases in the Dirac spinor space in terms of the involved spectral densities. The approach is applied to a…
The kaon electromagnetic (e.m.) form factor is reviewed considering a light-front constituent quark model. In this approach, it is discussed the relevance of the quark-antiquark pair terms for the full covariance of the e.m. current. It is also verified, by considering a QCD dynamical model, that a good agreement with experimental data can be obtained for the kaon weak decay constant once a probability of about 80% of the valence component is taken into account.
We present detailed numerical results for the pion space-like electromagnetic form factor obtained within a recently proposed model of the pion electromagnetic current in a confining light-front QCD-inspired model. The model incorporates the vector meson dominance mechanism at the quark level, where the dressed photon with $q^+>0$ decay in an interacting quark-antiquark pair,wich absorbs the initial pion and produces the pion in the final state.
In the context of Calabi-Yau string models we explore the origin of characteristic pattern of quark-lepton masses and the CKM matrix. The discrete $R$-symmetry $Z_K \times Z_2$ is introduced and the $Z_2$ is assigned to the $R$-parity. The gauge symmetry at the string scale, $SU(6) \times SU(2)_R$, is broken into the standard model gauge group at a very large intermediate energy scale. At energies below the intermediate scale down-type quarks and also leptons are mixed with unobserved heavy states, respectively. On the other hand, there are no such mixings for up-type quarks. Due to the large …
We address the old difficulty in accommodating the scalar quark-antiquark confining potential together with chiral symmetry breaking. We develop a quark confining potential inspired in the QCD scalar flux tube. The coupling to quarks consists in a double vector vertex. We study the Dirac and spin structure of this potential. In the limit of massless quarks the quark vertex is vector. Nevertheless symmetry breaking generates a new scalar quark vertex. In the heavy quark limit the coupling is mostly scalar. We solve the mass gap equation and find that this potential produces spontaneous chiral s…
We present compact analytic formulae for the one-loop amplitudes for Higgs + 4 parton scattering, $0 \to g g g g h$, $0 \to \bar{q} q gg h$ and $0\to \bar{q} q \bar{q}^\prime q^\prime h$, mediated by a loop of massive coloured quarks. We exploit the correspondence with a theory in which a massive coloured scalar circulates in the loop to avoid a proliferation in the number of terms in the result. In addition, we use momentum twistors and high precision numerical evaluations to simplify the expressions. The analytic results in this paper, in terms of spinor products, allow construction of an ef…
In the extra U(1) superstring inspired model, we examine the electroweak and U(1)-prime symmetry breaking with the singlet and exotic quark D, D+{\c}along with the study of heavy Z-prime boson in accordance with the top quark mass region. For this, we have done the analysis of complete renormalization group equations (RGEs)pertaining to the anomaly free E-{\6}-Eta model of rank 5. The Z-prime is found to the order of TeV or above with allowed small Z-Zprime mixing angle, for which the large singlet VEV is required. This is done by considering the only non-universality of Yukawa couplings at GU…
We present a fast hadronization model for the constituent quark plasma (CQP) produced in relativistic heavy ion collisions at SPS. The model is based on rate equations and on an equation of state inspired by the string phenomenology. This equation of state has a confining character. We display the time evolution of the relevant physical quantities during the hadronization process and the final hadron multiplicities. The results indicate that the hadronization of CQP is fast.
Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice d…
Inspired by the observed $X(2900)$, we study systematically the mass spectra of the ground pentaquark states with the $qqqq\bar{Q}$ ($Q=c,b$; $q=n,s$; $n=u,d$) configuration in the framework of the Chromomagnetic Interaction model. We present a detailed analysis of their stabilities and decay behaviors. Our results indicate that there may exist narrow states or even stable states. We hope that the present study may inspire experimentalist's interest in searching for such a type of the exotic pentaquark state.
A brief review of the problem of the determination of light-quark masses from QCD sum rules for the correlators of scalar and pseudoscalar currents is given. Special attention is paid to the description of the large-$N_f$ results, obtained in collaboration with Broadhurst and Maxwell, for the scalar correlator, and estimates of its higher-order perturbative uncertainties within the renormalon-inspired large-$β_0$ expansion in the $\overline{\rm MS}$ scheme are given. Brief discussion is presented of the results of calculations of higher-order perturbative QCD corrections to the relation betwee…
Master equations of the Lindblad type have recently been derived to describe the dynamics of quarkonium states in the quark-gluon plasma. Because their full resolution in three dimensions is very challenging, the equations are often reduced to one dimension. The main ingredient of these equations is the complex potential that describes the binding of the heavy quark-antiquark pairs and their interactions with the medium. In this work, we propose a one-dimensional complex potential parameterized to reproduce at best two key properties -- the temperature-dependent masses of the eigenstates and t…
We consider string phenomenological models based on 11D Horava-Witten M-theory with 5 branes in the bulk. If the 5-branes cluster close to the distant orbifold plane (d_n\equiv 1-z_n\simeq 0.1) and if the topological charges of the physical plane vanish (β^{(0)}_i=0), then the Witten εterms (to first order) are correctly small and a qualitative picture of the quark and lepton mass hierarchy arises without significant fine tuning. If right handed neutrinos exist, a possible gravitationally induced cubic holomorphic contribution to the Kahler potential can exist scaled by the 11D Planck mass. Th…
We discuss the 750 GeV diphoton excess at the LHC@13TeV in the framework of leptophobic U(1)$^\prime$ model inspired by $E_6$ grand unified theory (GUT). In this model, the Standard Model (SM) chiral fermions carry charges under extra U(1)$^\prime$ gauge symmetry which is spontaneously broken by a U(1)$^\prime$-charged singlet scalar ($Φ$). In addition, extra quarks and leptons are introduced to achieve the anomaly-free conditions, which is a natural consequence of the assumed $E_6$ GUT. These new fermions are vectorlike under the SM gauge group but chiral under new U(1)$^\prime$, and their ma…
