Up-down Quark Mass Difference Research Articles

Charge-symmetry-breaking effects on neutron β decay in nonrelativistic quark models

A formalism for the study of charge-symmetry-breaking (CSB) effects is discussed and used to analyze the effects of charge-symmetry breaking on neutron $\ensuremath{\beta}$ decay. The effect of including CSB reduces the $\ensuremath{\beta}$-decay matrix element by an amount on the order of ${10}^{\ensuremath{-}4}$, a value much larger than the previous estimate. The earlier calculation used the neutron-proton mass difference as the CSB operator instead of the matrix element of the sum of the individual terms between the ground and excited states. The electromagnetic and dynamic effects of the up-down quark mass difference oppose the up-down quark mass difference leading to a small $n\ensuremath{-}p$ mass difference, but add coherently in computing the excitation matrix elements causing large enhancements. The current uncertainty in the value of ${V}_{ud}$ is also on the order of ${10}^{\ensuremath{-}4}$. An improvement of that uncertainty by an order of magnitude would require that charge-symmetry-breaking effects should be included in future analyses.

Isospin Splittings in the Light-Baryon Octet from Lattice QCD and QED

While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a prominent example. Here, we include these effects by adding them to valence quarks in a lattice QCD calculation based on Nf=2+1 simulations with five lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment.

1+1+1flavorQCD+QEDsimulation at the physical point

We present the results of $1+1+1$ flavor $\mathrm{QCD}+\mathrm{QED}$ simulation at the physical point, in which the dynamical quark effects in QED and the up-down quark mass difference are incorporated by the reweighting technique. The physical quark masses together with the lattice spacing are determined with ${m}_{{\ensuremath{\pi}}^{+}}$, ${m}_{{K}^{+}}$, ${m}_{{K}^{0}}$ and ${m}_{{\ensuremath{\Omega}}^{\ensuremath{-}}}$ as physical inputs. Calculations are carried out using a set of $2+1$ flavor QCD configurations near the physical point generated by the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\ensuremath{\beta}=1.9$ on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice. We evaluate the values of the up, down and strange quark masses individually with nonperturbative QCD renormalization.

Isospin mass splittings of heavy baryons in heavy quark symmetry

In this paper, the electromagnetic mass differences of heavy hadrons are discussed, while the relevant hyperfine interactions are ignored. The effects of one-photon exchange interaction and up-down quark mass difference are parametrized. Two mass difference equations $2{\ensuremath{\Sigma}}_{c}^{+}\ensuremath{-}({\ensuremath{\Sigma}}_{c}^{++}+{\ensuremath{\Sigma}}_{c}^{0})=2{\ensuremath{\Sigma}}_{b}^{0}\ensuremath{-}({\ensuremath{\Sigma}}_{b}^{+}+{\ensuremath{\Sigma}}_{b}^{\ensuremath{-}})$ and $({\ensuremath{\Xi}}_{cc}^{+}\ensuremath{-}{\ensuremath{\Xi}}_{cc}^{++})+({\ensuremath{\Xi}}_{bb}^{\ensuremath{-}}\ensuremath{-}{\ensuremath{\Xi}}_{bb}^{0})=2({\ensuremath{\Xi}}_{bc}^{0}\ensuremath{-}{\ensuremath{\Xi}}_{bc}^{+})$ for the heavy baryons are obtained. In addition, the masses of ${\ensuremath{\Sigma}}_{b}^{0}$, ${\ensuremath{\Xi}}_{b}^{0}$, and ${\ensuremath{\Xi}}_{cc}^{++}$ are predicted based on the known experimental data.

Charge symmetry breaking inNNscattering with an interaction from effective field theory

The effect of isospin breaking pion s-wave rescattering is included in elastic $\mathrm{NN}$ scattering at low energies using an interaction obtained from effective field theory. Although this mechanism gave a large contribution to charge symmetry breaking in $n\stackrel{\ensuremath{\rightarrow}}{p}d{\ensuremath{\pi}}^{0},$ the effect is rather small in $\mathrm{pp}$ vs $\mathrm{nn}$ scattering parameters and in the ${}^{3}\mathrm{H}{\ensuremath{-}}^{3}\mathrm{He}$ binding energy difference. This smallness is caused by large cancellation of the up-down quark mass difference contribution and electromagnetic effects to the $\mathrm{np}$ mass difference.

Density dependence of charge symmetry breaking

We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of mirror nuclei at high density by adding a single neutron or proton to a quark gluon plasma. In this high-density limit we find an anomaly equal to two-thirds of the Coulomb exchange energy of a proton. This effect is dominated by quark electromagnetic interactions---rather than by the up-down quark mass difference. At normal density we calculate the Coulomb energy of neutron matter using a string-flip quark model. We find a nonzero Coulomb energy because of the neutron's charged constituents. This effect could make a significant contribution to the ONS anomaly.

Axial baryon number nonconserving antisymmetric tensor four-quark effective interaction

We discuss the phenomenological consequences of the ${U}_{A}(1)$ symmetry-breaking two-flavor four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the ``duality'' symmetry of this interaction. Starting from the Fierz transform of the two-flavor 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by a Nambu--Jona-Lasinio- type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (1) Four antisymmetric tensor and four antisymmetric pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (2) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (3) The mixing of massive antisymmetric tensor fields with vector fields leads to two sets of spin-one states. The second set of spin-one mesons is heavy and has not been observed. Moreover at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the antisymmetric tensor interaction. The tachyonic state also shows up as a pole in the spacelike region of the EM form factors. (4) The axial-vector fields' mixing with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift of axial vector mesons is negligible. (5) The antisymmetric tensor version of the Veneziano-Witten ${U}_{A}(1)$ symmetry-breaking interaction does not lead to tachyons, or any antisymmetric tensor field propagation to leading order in ${N}_{C}.$

Compositeantisymmetric tensor bosons in a four-fermion interactionmodel

We discuss the phenomenological consequences of the UA(1) symmetry-breaking two-flavour four-fermionantisymmetric (AS) Lorentz tensor interaction Lagrangians. Weuse the recently developed methods that respect the `duality'symmetry of this interaction. Starting from the Fierztransform of the two-flavour 't Hooft interaction (afour-fermion Lagrangian with AS tensor interaction termsaugmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalarinteraction responsible for dynamical symmetry breaking andquark mass generation), we find the following.(a) Four antisymmetrictensor and four AS pseudotensor bosons exist which satisfy amass relation previously derived for scalar and pseudoscalarmesons from the 't Hooft interaction. (b) Antisymmetrictensor bosons mix with vector bosons via one-fermion-loopeffective couplings so that both kinds of bosons have theirmasses shifted and the fermions (quarks) acquire anomalousmagnetic moment form factors that explicitly violate chiralsymmetry. (c) The mixing of massive AS tensor fields withvector fields leads to two sets of spin-1 states. Thesecond set of spin-1 mesons is heavy and has not beenobserved. Moreover, at least one member of this second setis tachyonic, under standard assumptions about the source andstrength of the AS tensor interaction. The tachyonic statealso shows up as a pole in the space-like region of the electromagneticform factors. (d) The mixingof axial-vector fields withantisymmetric tensor bosons is proportional to the (small)isospin-breaking up-down quark mass difference, so themixing-induced mass shift is negligible. (e) The AS tensor versionof the Veneziano-Witten UA(1) symmetry-breakinginteraction does not lead to tachyons, or any AS tensor fieldpropagation to leading order in NC.

Single-particle spin–orbit strengths of the nucleon and hyperons by [formula omitted] quark-model

The quark-model hyperon–nucleon interaction suggests an important antisymmetric spin–orbit component. It is generated from a color analogue of the Fermi–Breit interaction dominating in the one-gluon exchange process between quarks. We discuss the strength S B of the single-particle spin–orbit potential, following the Scheerbaum's prescription. Using the SU 6 quark-model baryon–baryon interaction which was recently developed by the Kyoto–Niigata group, we calculate NN, ΛN and ΣN G-matrices in symmetric nuclear matter and apply them to estimate the strength S B . The ratio of S B to the nucleon strength S N∼−40 MeV fm 5 is S Λ/S N∼1/5 and S Σ/S N∼1/2 in the Born approximation. The G-matrix calculation of the model FSS modifies S Λ to S Λ/S N∼1/12 . For S N and S Σ , the effect of the short-range correlation is comparatively weak against meson-exchange potentials with a short-range repulsive core. The significant reduction of the Λ single-particle potential arises from the combined effect of the antisymmetric LS force, the flavor-symmetry breaking originating from the strange to up-down quark-mass difference, as well as the effect of the short-range correlation. The density dependence of S B is also examined.

QED-QCD mixing effect and isospin violation in 1S0NN scattering

The charge dependence of the nucleon-nucleon scattering length due to the quark effects are examined in a quark cluster model. In addition to the effects induced by the up-down quark mass difference and quark-exchange Coulomb interaction, we consider the interference effects of QCD and QED suggested by Maltman, Stephenson, and Goldman. We find that the total contribution of the quark effects to a pp − a nn is large and in the direction indicated by the experiments. The effect is, however, small for a pp − a np .

Up-down quark mass difference effect in nuclear many-body systems.

A charge-symmetry-breaking nucleon-nucleon force due to the up-down quark mass difference is evaluated in the quark cluster model. It is applied to the shell-model calculation for the isovector mass shifts of isospin multiplets and the isospin-mixing matrix elements in 1s0d-shell nuclei. We find that the contribution of the quark mass difference effect is large and agrees with experiment. This contribution may explain the Okamoto-Nolen-Schiffer anomaly, alternatively to the meson-mixing contribution, which is recently predicted to be reduced by the large off-shell correction.

The A = 3 Nolen-Schiffer anomaly and the up-down quark mass difference

A recently proposed nonrelativistic many-body quark model is used to generate class III nucleon-nucleon potentials in a Born-Oppenheimer approach. These potentials, when treated in first-order perturbation theory with a simple ansatz for the three-nucleon wave function, allow us to make an estimate of the 3He 3He mass difference. For accepted values of the constituent up-down quark mass difference we find that approximately sixty percent of the A = 3 Nolen-Schiffer anomaly can be accounted for solely from the up-down quark kinetic energy difference.

Charge-symmetry-breaking corrections to pseudoscalar meson-nucleon coupling constants due to up-down current quark mass difference and their effects on NN scattering lengths.

The charge-symmetry-breaking corrections due to the isospin breaking part of the quantum chromodynamic Hamiltonian, determined by the up-down current quark mass difference, ${H}_{\mathrm{QCD}=\mathrm{half}({m}_{u}\mathrm{\ensuremath{-}}{m}_{d})(\mathrm{\ifmmode \bar{u}\else \={u}\fi{}}\mathrm{u}\mathrm{\ensuremath{-}}\mathrm{d}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}\mathrm{d}}$), on \ensuremath{\pi}NN and \ensuremath{\eta}NN coupling constants and their effect on (\ensuremath{\delta}a${)}_{\mathrm{CSB}={a}_{\mathrm{pp}}\mathrm{\ensuremath{-}}{a}_{\mathrm{nn}}}$ are estimated. The effects of ${H}_{\mathrm{QCD}}$ on the pseudoscalar meson-nucleon coupling constants are calculated via ${\ensuremath{\pi}}^{0}$-\ensuremath{\eta},\ensuremath{\eta}' mixing, giving rise to charge-symmetry-breaking one-boson-exchange [one-pion-exchange and one-\ensuremath{\eta}-exchange] and two-boson-exchange [two-pion-exchange, \ensuremath{\pi}\ensuremath{\eta}-exchange etc.] potentials. The importance of charge-symmetry-breaking two-boson exchange is emphasized.

Nucleon-nucleon interactions and quarks I: General considerations with numerical results in the 1S0 channel

In this paper, we discuss a general development of a quark-model description of nucleon-nucleon (NN) interactions, assuming that quarks are Dirac particles and nucleons are specified approximately by flavor SU(6) wave functions. The down (d) quark is differentiated from the up (u) quark allowing isospin symmetry violating effects. As a simple model calculation, we include effects due to one-gluon exchange (which dictates the short-range behavior of NN forces), one-pion exchange (which gives rise to the Yukawa tail in NN forces), single sigma-exchange (which mocks up to the intermediate attraction in an economical manner), and one-photon exchange (which contributes to isospin symmetry violations). To avoid introduction of additional shape parameters, we adopt a double-sphere geometry with an adjustable isolated nucleon radius. All quark-interchange effects are explicitly evaluated and Pauli blocking is incorporated. Numerical results in the 1 S 0 p− p, n− p, and n− n channels are described and discussed. In particular, it is found that the simple one-boson exchange model (at the quark level) provides a reasonable description of the 1 S 0 phase shifts for 10 MeV ≤ T CM ≤ 150 MeV with T CM the center-of-mass [CM] kinetic energy. It is also found that, with the nonzero up-down quark mass difference as determined by an overall fit to the observed baryon mass splittings, isospin-symmetry violating effects arising from quark interchange are of marginal numerical importance for a nucleon radius R of 0.8 fm and become fairly sizable for R = 1.0 fm. It turns out that, for R = 0.8 fm, the predicted a nn with a nn the low-energy scattering lengths in the 1 S 0 n- n channel is in good agreement with a recent experimental result of Gabioud et al. and the observed large charge dependent effect as given by | a np | − | a nn | can also be understood.

Up-down quark mass difference: Couplings of pions to nucleons or isobars and low-energy nucleon-nucleon scattering

We investigate effects of the up-down quark mass difference on the couplings of pions to nucleons or isobars. The calculated $\ensuremath{\pi}\mathrm{NN}$ and $\ensuremath{\pi}\mathrm{N}\ensuremath{\Delta}$ couplings are used to derive the long-range one-pion-exchange potential and the intermediate-range attraction for the three different cases: p-p, n-p, and n-n. The resultant potentials are then used to determine numerically the low-energy scattering parameters, including both the scattering length $a$ and the effective range $r$. Our results indicate that a reasonable up-down quark mass difference such as 10 MeV yields a value for $|{a}_{\mathrm{pp}}|\ensuremath{-}|{a}_{\mathrm{nn}}|$ of about + 0.6 fm, which is sizable from the experimental point of view. Our results also suggest that the large observed value for $|{a}_{\mathrm{np}}|\ensuremath{-}|{a}_{\mathrm{nn}}|$ can be understood primarily as a manifestation of the pion mass difference.[NUCLEAR REACTIONS Application of quark models to nuclear physics; effects of the up-down quark mass difference on couplings of pions to nucleons or isobars; charge dependence and charge symmetry breaking in low energy nucleon-nucleon scattering.]

Up-down quark mass differences in the MIT bag model

The contribution of quark masses to the splittings of hadron isospin multiplets is calculated in a phenomenological way within the framework of the MIT bag model. A value for the up-down quark mass difference is extracted.