arXiv subjects

Carlos Schat

Publications and source records attributed to Carlos Schat.

At least 19 recordsLinked to original sources

arXiv2017

Towers of positive parity excited baryons and their mixing in the large $N_c$ limit

We consider configuration mixing for the nonstrange positive parity excited baryons in the $[\mathbf{56'},0^+],[\mathbf{56},2^+], [\mathbf{70},0^+] $ and $[\mathbf{70},2^+]$ quark model $SU(6) \times O(3)$ multiplets contained in the $N=2$ band. Starting from the effective mass operator for these states we show by an explicit calculation that in the large $N_c$ limit they fall into six towers of degenerate states labeled by $K=0,1,1',2,2',3$. We find that the mixing of the quark model states is much simpler than what is naively expected. To leading order in $N_c$ only states carrying the same $K$ label can mix, which implies that for the spin-flavor states we started with configuration mixing can be parameterized by just two constants, $μ_{K=1}$ and $μ_{K=2}$.

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arXiv2016

Time-reversal-invariance-violating nucleon-nucleon potential in the 1/N_c expansion

We apply the large-$N_c$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-$N_c$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which however are suppressed by 1/$N_c$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral EFT potential in the TV parity-violating case, leads to large-$N_c$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings.

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arXiv2015

Operator analysis of effective spin-flavor interactions for L=1 excited baryons

We match the non-relativistic quark model, with both flavor dependent and flavor independent effective quark-quark interactions, to the spin-flavor operator basis of the 1/Nc expansion for the L=1 non-strange baryons. We obtain analytic expressions for the coefficients of the 1/Nc operators in terms of radial integrals that depend on the shape and relative strength of the spin-spin, spin-orbit and tensor interactions of the model, which are left unspecified. We obtain several new, parameter-free relations between the seven masses and the two mixing angles that can discriminate between different spin-flavor structures of the effective quark-quark interaction. We discuss in detail how a general parametrization of the mass matrix depends on the mixing angles and is constrained by the assumptions on the effective quark-quark interaction. We find that, within the present experimental uncertainties, consistency with the best values of the mixing angles as determined by a recent global fit to masses and decays does not exclude any of the two most extreme possibilities of flavor dependent (independent) quark-quark interactions, as generated by meson (gluon) exchange interactions.

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arXiv2015

The parity-violating nucleon-nucleon force in the 1/N_c expansion

Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the $1/N_c$ expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon (NN) potential. We show there are two leading-order operators, both of which affect $\vec{p}p$ scattering at order $N_c$. We find an additional four operators at $O(N_c^0 \sin^2 θ_W)$ and six at $O(1/N_c)$. Pion exchange in the PV NN force is suppressed by $1/N_c$ and $\sin^2 θ_W$, providing a quantitative explanation for its non-observation up to this time. The large-$N_c$ hierarchy of other PV NN force mechanisms is consistent with estimates of the couplings in phenomenological models. The PV observed in $\vec{p}p$ scattering data is compatible with natural values for the strong and weak coupling constants: there is no evidence of fine tuning.

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arXiv2013

Three-nucleon forces in the 1/Nc expansion

The operator structures that can contribute to three-nucleon forces are classified in the 1/Nc expansion. At leading order in 1/Nc a spin-flavor independent term is present, as are the spin-flavor structures associated with the Fujita-Miyazawa three-nucleon force. Modern phenomenological three-nucleon forces are thus consistent with this O(Nc) leading force, corrections to which are suppressed by a power series in 1/Nc^2. A complete basis of operators for the three-nucleon force, including all independent momentum structures, is given explicitly up to next-to-leading order in the 1/Nc expansion.

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arXiv2011

Roy-Steiner equations for gamma gamma -> pi pi

Starting from hyperbolic dispersion relations, we derive a system of Roy--Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on high-energy input, we also consider once- and twice-subtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equations are valid. As an application, we consider the resolution of the $γγ\toππ$ partial waves by a Muskhelishvili--Omnès representation with finite matching point. We find a sum rule for the isospin-two $S$-wave, which, together with chiral constraints, produces an improved prediction for the charged-pion quadrupole polarizability $(α_2-β_2)^{π^\pm}=(15.3\pm 3.7)\cdot 10^{-4} {\rm fm}^5$. We investigate the prediction of our dispersion relations for the two-photon coupling of the $σ$-resonance $Γ_{σγγ}$. The twice-subtracted version predicts a correlation between this width and the isospin-zero pion polarizabilities, which is largely independent of the high-energy input used in the equations. Using this correlation, the chiral perturbation theory results for pion polarizabilities, and our new sum rule, we find $Γ_{σγγ}=(1.7\pm 0.4)\,{\rm keV}$.

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arXiv2011

Roy-Steiner equations for $γγ\toππ$

Starting from hyperbolic dispersion relations, we present a system of Roy--Steiner equations for pion Compton scattering that respects analyticity and unitarity requirements, gauge invariance, as well as crossing symmetry, and thus all symmetries of the underlying quantum field theory. To suppress the dependence on the high-energy region, we also consider once- and twice-subtracted versions of the equations, where the subtraction constants are identified with dipole and quadrupole pion polarizabilities. We consider the resolution of the $γγ\toππ$ partial waves by a Muskhelishvili-Omnès representation with finite matching point, and discuss the consequences for the two-photon coupling of the $σ$ resonance as well as its relation to pion polarizabilities.

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arXiv2010

Matching the quark model to the 1/Nc expansion

We compute the coefficients of the effective mass operator of the 1/Nc expansion for negative parity L=1 excited baryons using the Isgur-Karl model in order to compare the general approach, where the coefficients are obtained by fitting to data, with a specific constituent quark model calculation. We discuss the physics behind the fitted coefficients for the scalar part of the most general two-body quark-quark interaction. We find that both pion exchange and gluon exchange lead to the dominance of the same operator at the level of the effective mass operator, which is also observed from data.

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arXiv2010

Testing for three-body quark forces in L=1 excited baryons

We discuss the matching of the quark model to the effective mass operator of the 1/Nc expansion using the permutation group S_N. As an illustration of the general procedure we perform the matching of the Isgur-Karl model for the spectrum of the negative parity L=1 excited baryons. Assuming the most general two-body quark Hamiltonian, we derive two correlations among the masses and mixing angles of these states which should hold in any quark model. These correlations constrain the mixing angles and can be used to test for the presence of three-body quark forces.

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arXiv2010

1/Nc expansion and the spin-flavor structure of the quark interaction in the constituent quark model

We study the hierarchy of the coefficients in the 1/Nc expansion for the negative parity L=1 excited baryons from the perspective of the constituent quark model. This is related to the problem of determining the spin-flavor structure of the quark interaction. The most general two-body scalar interaction between quarks contains the spin-flavor structures $t_1^a t_2^a, \vec s_1\cdot \vec s_2$ and $ \vec s_1\cdot \vec s_2 t_1^a t_2^a$. We show that in the limit of a zero range interaction all these structures are matched onto the same hadronic mass operator $S_c^2$, which gives a possible explanation for the dominance of this operator in the 1/Nc expansion for the L=1 states and implies that in this limit it is impossible to distinguish between these different spin-flavor structures. Modeling a finite range interaction through the exchange of a vector and pseudoscalar meson, we propose a test for the spin-flavor dependence of the quark forces. For the scalar part of the quark interaction we find that both pion exchange and gluon exchange are compatible with data.

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arXiv2009

Vertex Displacements for Acausal Particles: Testing the Lee-Wick Standard Model at the LHC

We propose to search for wrong displaced vertices, where decay products of the secondary vertex move towards the primary vertex instead of away from it, as a signature for microscopic violation of causality. We analyze in detail the leptonic sector of the recently proposed Lee-Wick Standard Model, which provides a well motivated framework to study acausal effects. We find that, assuming Minimal Flavor Violation, the Lee-Wick partners of the electron, {\tilde l}^e and \tilde e, can produce measurable wrong vertices at the LHC, the most promising channel being q \bar{q} --> \bar{\tilde l}^e {\tilde l}^e --> e^+ e^- jjjj. A Monte-Carlo simulation using MadGraph/MadEvent suggests that for M_l < 450 GeV the measurement of these acausal vertex displacements should be accessible in the LHC era.

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arXiv2009

Permutation group S_N and hadron spectroscopy

We discuss the application of the permutation group S_N to a few problems in hadron physics. A method is proposed for matching a quark model Hamiltonian onto the effective Hamiltonian of the 1/Nc expansion, which makes use of the transformation properties of the states and operators under S_N. This method is used to obtain information about the spin-flavor structure of the quark interaction Hamiltonian from the spectrum of the negative parity L=1 excited baryons. Assuming the most general 2-body quark Hamiltonian, we derive two correlations among the masses and mixing angles of these states which should hold in any quark model. These correlations constrain the mixing angles, and can be used to test for the presence of 3-body quark interactions. We find that the pure gluon-exchange model is disfavored by data, independently of any assumptions about the hadronic wave functions.

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arXiv2009

The Isgur-Karl model revisited

We show how to match the Isgur-Karl model to the spin-flavor quark operator expansion used in the 1/Nc studies of the non-strange negative parity L=1 excited baryons. Using the transformation properties of states and interactions under the permutation group S_3 we are able to express the operator coefficients as overlap integrals, without making any assumption on the spatial dependence of the quark wave functions. The general mass operator leads to parameter free mass relations and constraints on the mixing angles that are valid beyond the usual harmonic oscillator approximation. The Isgur-Karl model with harmonic oscillator wave functions provides a simple counterexample that demonstrates explicitly that the alternative operator basis for the 1/Nc expansion for excited baryons recently proposed by Matagne and Stancu is incomplete.

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arXiv2009

Quark Forces from Hadron Spectroscopy

We consider the implications of the most general two-body quark-quark interaction Hamiltonian for the spin-flavor structure of the negative parity L=1 excited baryons. Assuming the most general two-body quark interaction Hamiltonian, we derive two correlations among the masses and mixing angles of these states, which constrain the mixing angles, and can be used to test for the presence of three-body quark interactions. We find that the pure gluon-exchange model is disfavored by data, independently of any assumptions about the hadronic wave functions.

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arXiv2008

Electroweak precision constraints on the Lee-Wick Standard Model

We present the constraints on the parameter space of the Lee-Wick Standard Model coming from electroweak precision observables. The model predicts a large positive S and a negative T. We show that it is possible to find some regions in parameter space with a fermionic state as light as 2.4-3.5 TeV. We also propose a simple extension of the model including a fourth generation. In this case it is possible to pass the electroweak constraints with Lee-Wick fermionic masses of order 0.4-1.5 TeV and Lee-Wick gauge masses of order 3 TeV.

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arXiv2008

The permutation group S_N and large Nc excited baryons

We study the excited baryon states for an arbitrary number of colors Nc from the perspective of the permutation group S_N of N objects. Classifying the transformation properties of states and quark-quark interaction operators under S_N allows a general analysis of the spin-flavor structure of the mass operator of these states, in terms of a few unknown constants parameterizing the unknown spatial structure. We explain how to perform the matching calculation of a general two-body quark-quark interaction onto the operators of the 1/Nc expansion. The inclusion of core and excited quark operators is shown to be necessary. Considering the case of the negative parity L=1 states transforming in the MS of S_N, we discuss the matching of the one-gluon and the Goldstone-boson exchange interactions.

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arXiv2008

Electroweak precision constraints on the Lee-Wick Standard Model

We perform an analysis of the electroweak precision observables in the Lee-Wick Standard Model. The most stringent restrictions come from the S and T parameters that receive important tree level and one loop contributions. In general the model predicts a large positive S and a negative T. To reproduce the electroweak data, if all the Lee-Wick masses are of the same order, the Lee-Wick scale is of order 5 TeV. We show that it is possible to find some regions in the parameter space with a fermionic state as light as 2.4-3.5 TeV, at the price of rising all the other masses to be larger than 5-8 TeV. To obtain a light Higgs with such heavy resonances a fine-tuning of order a few per cent, at least, is needed. We also propose a simple extension of the model including a fourth generation of Standard Model fermions with their Lee-Wick partners. We show that in this case it is possible to pass the electroweak constraints with Lee-Wick fermionic masses of order 0.4-1.5 TeV and Lee-Wick gauge masses of order 3 TeV.

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arXiv2007

Excited Baryons in Large Nc QCD: Matching the 1/Nc expansion to quark models using the permutation group S_N

We show how to match quark models to the 1/Nc expansion of QCD. As an example we discuss in detail the mass operator of orbitally excited baryons and match it to the one-gluon exchange and the one-boson exchange variants of the quark model. The matching procedure is very general and makes use of the transformation properties of states and operators under S_N^{orb} \times S_N^{sp-fl}, the permutation group acting on the orbital and spin-flavor degrees of freedom of N quarks.

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