Quark Mass Splitting Research Articles

Isospin Symmetry Breaking in Atomic Nuclei

In this paper, the importance of isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for the nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon–nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the N = Z system in the density functional approach

Holographic Non-Abelian Flavour Symmetry Breaking

We investigate a holographic model for both spontaneous and explicit symmetry breaking of non-abelian flavour symmetries. This consists of a bottom-up model inspired by the top-down D3/probe D7-brane model. It incorporates the running anomalous dimensions of the fields. We ensure that in the holographic bulk, the full non-abelian flavour symmetries for massless quarks are present. The quark masses are spontaneously generated field values in the bulk and there is a resultant bulk Higgs mechanism. We provide a numerical technique to find the mass eigenvalues from a system of mixed holographic fields, testing it against an analytic model of N=2 supersymmetric matter fields. We apply these ideas to two-flavour QCD with both u−d quark mass splitting and multi-trace bulk action terms that are expected to break U(Nf)V to SU(Nf)V×U(1)V away from large N. We also discuss three-flavour QCD with strange quark mass splitting and applications to more exotic symmetry breaking patterns of potential relevance for composite Higgs models.

Baryonic form factors of the pion and kaon in a chiral quark model

The baryonic form factor of charged pions is studied in detail in the Nambu--Jona-Lasinio model with constituent quarks, where the spontaneously broken chiral symmetry is the key dynamical ingredient guaranteeing the would-be Goldstone boson nature of the pseudoscalar mesons octet. In general, this form factor arises when the isospin symmetry is broken, which is the case if the $u$ and $d$ quark masses are split, as in the real world, or if the electromagnetic effects were taken into account. We obtain estimates for this basic property of the pion resulting from the quark mass splitting for a range of model parameters, and importantly, for different pion masses, going up to the values used in lattice QCD. We find very stable model results, with the mean square radius of $\pi^+$ in the range $(0.05-0.07~{\rm fm})^2$. From charge conjugation, the baryonic form factor of $\pi^+$ and $\pi^-$ are equal and opposite. We also obtain the transverse-coordinate, relativistically invariant baryonic density of the charged pion. In $\pi^+$, the inner region carries a negative, and the outside -- a positive baryon number density, both cancelling to zero, as obviously the pion carries no net baryon charge. We also carry out an analogous analysis for the kaon, where the effect is much larger due to the sizable $s$ and $u/d$ quark mass splitting. We discuss the prospects of lattice QCD measurements of the baryonic form factors of charged pions and kaons.

Neutron-proton mass difference from gauge/gravity duality

Using gauge/gravity duality as a tool, we compute the strong sector, isospin breaking induced contribution to the neutron-proton mass difference in the Witten-Sakai-Sugimoto model of large $N$ QCD with two non-degenerate light flavors. The mass difference, for which we provide an analytic expression, turns out to be positive and proportional to the down-up quark mass splitting, consistently with expectations and previous estimates based on effective QCD models. Extrapolating the model parameters to fit QCD hadronic observables, we find that the strong sector contribution to the nucleon mass splitting overcomes the electromagnetic contribution and is about $0.25\%$ of the average nucleon mass in the model, a result which approaches recent lattice QCD estimates. Our formula is extended to resonances and $\Delta$ baryons. We thus use it to compute the strong sector contribution to $\Delta$ baryons mass differences. Finally, we also provide details of how isospin breaking affects the holographic instanton solution describing the baryons.

A DYNAMICAL MECHANISM TO EXPLAIN THE TOP-BOTTOM QUARK MASS HIERARCHY

We discuss the mass splitting between the the top and bottom quarks in a technicolor scenario. The model proposed here contains a left–right electroweak gauge group. An extended technicolor group and mirror fermions are introduced. The top-bottom quark mass splitting turns out to be intimately connected to the breaking of the left–right gauge symmetry. Weak isospin violation occurs within the experimental limits.

QCD atθ∼πreexamined: Domain walls and spontaneousCPviolation

We consider QCD at $\ensuremath{\theta}\ensuremath{\sim}\ensuremath{\pi}$ with two, one and zero light flavors ${N}_{f},$ using the Di Vecchia--Veneziano--Witten effective Lagrangian. For ${N}_{f}=2,$ we show that $\mathrm{CP}$ is spontaneously broken at $\ensuremath{\theta}=\ensuremath{\pi}$ for finite quark mass splittings, ${z=m}_{d}{/m}_{u}\ensuremath{\ne}1.$ In the $z\ensuremath{-}\ensuremath{\theta}$ plane, there is a line of first order transitions at $\ensuremath{\theta}=\ensuremath{\pi}$ with two critical end points, ${z}_{1}^{*}<z<{z}_{2}^{*}.$ We compute the tension of the domain walls that relate the two $\mathrm{CP}$ violating vacua. For ${m}_{u}{=m}_{d},$ the tension of the family of equivalent domain walls agrees with the expression derived by Smilga from chiral perturbation theory at next-to-leading order. For ${z}_{1}^{*}<z<{z}_{2}^{*},$ $z\ensuremath{\ne}1,$ there is only one domain wall and a wall-some sphaleron at $\ensuremath{\theta}=\ensuremath{\pi}.$ At the critical points, ${z=z}_{1,2}^{*},$ the domain wall fades away, $\mathrm{CP}$ is restored and the transition becomes of second order. For ${N}_{f}=1,$ $\mathrm{CP}$ is spontaneously broken only if the number of colors ${N}_{c}$ is large and/or if the quark is sufficiently heavy. Taking the heavy quark limit $(\ensuremath{\sim}{N}_{f}=0)$ provides a simple derivation of the multibranch $\ensuremath{\theta}$ dependence of the vacuum energy of large ${N}_{c}$ pure Yang-Mills theory. In the large ${N}_{c}$ limit, there are many quasistable vacua with a decay rate $\ensuremath{\Gamma}\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{N}_{c}^{4}).$

QCD at large θ-angle axion cosmology

We use the chiral Lagrangian to investigate the global properties of the N-flavor QCD vacuum as a function of the θ parameter. In the case of exact quark degeneracy we find evidence for first-order phase transitions at θ = π · (odd integer). The first-order transitions are smoothed by quark mass splittings, although interesting effects remain at realistic quark masses. We emphasize the role of the η′ condensate in our analysis. Finally, we discuss the implications of our results on the internal hadronic structure of axion domain walls and axion cosmology.

The αS3 corrections to the effective neutral current and to the Z decay rate in the heavy top quark limit

We find the effective neutral current in the heavy top quark limit up to and including the terms of order α S 3. The result is then employed to compute the correction of the same order to the axial part of the Z decay rate into hadrons ( Λ Z h ) induced by the top-bottom quark mass splitting. The calculations confirm the prediction made in a previous work of K.G. Ch. and J.H. Kühn (Phys. Lett. B 308 (1993) 127), namely, the effect of the singlet corrections of order α S 3 to the axial part of the Λ Z h should not exceed 25%–30% (depending on the values chosen for α s ( M Z ) and m t of the magnitude of the leading (singlet) α s 2 term.

High energy isospin breaking in technicolor theories

Within technicolor theories, we explore the impact of four-fermion interactions on the fermion mass splittings via explicit breaking of the custodial SU(2) R symmetry. Assuming they do not lead tounacceptably large flavor-changing neutral currents, the question is whether the large b-t quark mass splitting can be accommodated given the limits on ϱ−1, where ϱ ≡ M w 2 M z cos 2 θ w . We argue that this is possible, although further increases in the experimental bound on m t may be difficult to accommodate in the present framework.

Fourth-generation t'-quarkonium formation and decay signatures.

Conditions for t'-quarkonium formation are examined. Provided the weak quark decay is suppressed by a small quark mass splitting, ${M}_{t\mathcal{'}}$-${M}_{b\mathcal{'}}$\ensuremath{\lesssim}${M}_{W}$, the t'-quarkonium states may form. If ${M}_{t\mathcal{'}}$-${M}_{b\mathcal{'}}$\ensuremath{\lesssim}60 GeV, the pseudoscalar ${\ensuremath{\eta}}_{t\mathcal{'}}$ and vector ${\ensuremath{\psi}}_{t\mathcal{'}}$ quarkonium states preferentially decay through quark-antiquark annihilation. The decay mode ${\ensuremath{\eta}}_{t\mathcal{'}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma} is enhanced by a factor 16 relative to the ${\ensuremath{\eta}}_{b\mathcal{'}}$ decay and, for ${M}_{t\mathcal{'}}$\ensuremath{\lesssim}250 GeV, leads to a rate of ${\ensuremath{\eta}}_{t\mathcal{'}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma} events that is observable above the continuum qq\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma} background with a resolution of \ifmmode\pm\else\textpm\fi{}2% in high-luminosity pp collisions at \ensuremath{\surd}s =40 TeV. The decays ${\ensuremath{\eta}}_{t\mathcal{'}}$,${\ensuremath{\psi}}_{t\mathcal{'}}$\ensuremath{\rightarrow}Z\ensuremath{\gamma} are also enhanced relative to the b'-quarkonium decays and, if a \ifmmode\pm\else\textpm\fi{}1% resolution is attainable, lead to an observable rate of Z\ensuremath{\gamma} events for ${M}_{t\mathcal{'}}$\ensuremath{\lesssim}160 GeV.

THE γγ SIGNAL OF PSEUDOSCALAR t′-QUARKONIUM AT THE SSC

Decays of fourth generation t′-quarkonium states are examined. Although b′-quarkonium decays are hard to see, the ηt′→γγ decay is enhanced by a factor of 16 relative to the ηb′→γγ decay. Provided the fourth generation quark mass splitting is small, O(few GeV), the decay ηt′→γγ leads to a rate of two photon events that is observable above the continuum [Formula: see text] background in high luminosity pp collisions at [Formula: see text] for Mt′<O(250 GeV ).

Scalar quark mass splitting effects in lepton-proton interactions

The mass splitting of scalar quarks of the same flavour leads to parity violation in deep inelastic scattering, even at one photon exchange level. This effect modifies the asymmetries measured in the polarized lepton-proton scattering. We calculate them in leading order and give numerical estimates of their shapes.

Constraints on the colour dielectric model of the nucleus

We examine the consequences of an up-down quark mass splitting in the colour dielectric model of the nucleus. In particular it is seen that this introduces a binding energy difference for protons and neutrons in the nucleus. We show that if this binding energy difference is to be acceptably small then the colour dielectric model of the nucleus in its present form is insufficient to explain the EMC effect. However it does provide a possible explanation of the Nolen-Schiffer anomaly.

Finite proton-neutron mass difference

With the only assumption that the up-down quark mass splitting is a weak electromagnetic radiative effect, the proton-neutron mass difference is shown to be finite. This happens in a new representation where the mass difference can be completely calculated (no unknown terms) in very good agreement with experiment.

Mass generation by radiative corrections in minimal SO(10)

Starting with Higgs fields belonging to the 10, 16, 45 representations of SO(10) we see how by radiative corrections we induce effective mass terms transforming like the 5, 10 and 45 of SU(5) and e.g. generate a Majorana mass for the neutrino, and a small electron-d quark mass splitting.