Spin Parity Research Articles

Systematical study of Ωc -like molecular states from interactions Ξc(′,*)K¯(*) and Ξ(*)D(*)

In this work, the $\Omega_c$-like molecular states are systematically investigated in a quasipotential Bethe-Salpeter equation approach. The relevant interactions $\Xi_c^{(*,')}\bar{K}^{(*)}$, $\Xi^{(*)}D^{(*)}$, and $\Omega^{(*)}_c(\pi/\eta/\rho/\omega)$ are described by light meson exchanges with the help of the effective Lagrangians with SU(3), chiral, and heavy quark symmetries. The obtained potential kernels of considered interactions are inserted into the quasipotential Bethe-Salpeter equation, and coupled-channel calculations are performed to find possible molecular states and its couplings to the channels considered. The results suggest that an isoscalar state can be produced from the $\Xi^*_c\bar{K}$ interaction with spin parity $3/2^-$, which can be related to state $\Omega_c(3120)$. And its isoscalar partner is predicted with a dominant decay in the $\Omega_c^*\pi$ channel. The isoscalar and isovector states with $1/2^-$ can be produced from the $\Xi'_c\bar{K}$ interaction with a threshold close to the mass of the $\Omega_c(3050)$ and $\Omega_c(3065)$. Their couplings to the $\Xi_c \bar{K}$ channel are very weak, and the isovector one has strong coupling to $\Omega_c\pi$. High precision measurement is helpful to confirm or search such molecular states. Experimental search of states with higher masses generated from interactions $\Xi^{(*,')}_c \bar{K}^*$ and $\Xi^* D^{(*)}$ are also suggested by the current results.

Resonances in heavy meson–heavy baryon coupled-channel interactions

The interactions of {bar{D}}^{(*)} Lambda _c - {bar{D}}^{(*)}Sigma _c^{(*)} are studied within the framework of a dynamical coupled-channel approach. A series of bound states and resonances with different spin and parity are dynamically generated in the hidden charm sector. Four S-wave bound states are found in the mass range of 4.3–4.5 GeV, close to the pentaquark states observed by LHCb. Two of the states have a spin parity of J^P= 1/2^- and the other two have J^P=3/2^-. In addition, several resonances with different spin and parity in higher partial waves are predicted.

Canonical interpretation of the Ds0(2590)+ resonance

The ${D}_{s0}(2590{)}^{+}$ resonance observed by LHCb Collaboration is a strong candidate of the ${D}_{s}({2}^{1}{S}_{0})$ state according to its spin parity and strong decay mode. However, the measured mass seems relatively lower than the previous theoretical predictions, which interests the coupled channel interpretations in the literature. In this work, we adopt an alternate approach, taking into account the screening effects in the potential model, to describe the ${D}_{s0}(2590{)}^{+}$ resonance. The mass spectrum and strong decays of the excited charmed-strange mesons are investigated within the modified relativized quark model and $^{3}{P}_{0}$ model. The calculated mass and width of the ${D}_{s0}(2590{)}^{+}$ are consistent with the experimental observations, which indicate that it can be reasonably interpreted as the ${D}_{s}({2}^{1}{S}_{0})$ state.

Spin and polarization analysis of the Zcs state

A polarization analysis is performed for the recent observation of $Z_{cs}$ exotic state in the $e^+e^-$ annihilation experiment with motivation for measuring its spin quantum number in the future. Starting with the unpolarized electron and positron beam, the polarization transfer to the $Z_{cs}$ state and its decay angular distribution patterns are investigated. Some observables are suggested for determination of the spin parity quantum numbers. An ensemble of Monte-Carlo events are used to show some moment distributions special for manifestation of the different $Z_{cs}$ spin scenarios.

Towards a classification of connected components of the strata of $k$-differentials

A k -differential on a Riemann surface is a section of the k -th power of the canonical bundle. Loci of k -differentials with prescribed number and multiplicities of zeros and poles form a natural stratification for the moduli space of k -differentials. The classification of connected components of the strata of k -differentials was known for holomorphic differentials, meromorphic differentials and quadratic differentials with at worst simple poles by Kontsevich-Zorich, Boissy and Lanneau, respectively. Built on their work we develop new techniques to study connected components of the strata of k -differentials for general k . As an application, we give a complete classification of connected components of the strata of quadratic differentials with arbitrary poles. Moreover, we distinguish certain components of the strata of k -differentials by generalizing the hyperelliptic structure and spin parity for higher k . We also describe an approach to determine explicitly parities of k -differentials in genus zero and one, which inspires an amusing conjecture in number theory. A key viewpoint we use is the notion of multi-scale k -differentials introduced by Bainbridge-Chen-Gendron-Grushevsky-Möller for k = 1 and extended by Costantini-Möller-Zachhuber for all k .

Mixing angles between the tetraquark states with two heavy quarks within QCD sum rules

LHCb Collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated, hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a linear combination of the flavor eigenstates, which is characterized by the mixing angle $\theta$. In the present work, the possible mixing angles between the $T_{cc}$ states are calculated. Moreover, the analysis are extended for all the possible tetraquarks scenarios with two heavy and two light quarks within the molecular picture although those states have not been observed yet. Our prediction on mixing angle between doubly charmed tetraquark states shows that $SU(3)$ symmetry breaking is around $7\%$ maximally.

Evidence supporting the existence of Pc(4380)± from the recent measurements of Bs→J/ψpp¯

Very recently, the LHCb collaboration released the newest measurements of $B_s \to J/\psi p\bar{p}$, where an enhancement structure near 4.34 GeV was observed in the invariant mass spectrum of $J/\psi p$ with the statistical significance of $3.1-3.7$ $\sigma$. In this work, by performing a combined analysis for the three invariant mass spectra of $B_s \to J/\psi p\bar{p}$, we find that this $J/\psi p$ structure near 4.34 GeV can correspond to the contributions from the $P_c(4380)^+$ state with the assumption of $J^{P}=3/2^{-}$ together with the reflections of $B_s \to (f_2^{*} \to p\bar{p})J/\psi$. Here, $P_c(4380)$ was first observed in $\Lambda_b \to J/\psi p K$ but not confirmed in the updated LHCb data in 2019, and $f_2^{*}$ means the exciting light isoscalar tensor meson around 2.0 GeV. Thus, this provides a possible evidence to support the existence of the pentaquark $P_c(4380)$. Specifically, the assumed spin parity $J^{P}=3/2^{-}$ of $P_c(4380)$ is consistent with a prediction of the theoretical explanation of an $S$-wave $\bar{D}\Sigma_c^*$ molecular bound state.

Decay processes of a pseudoscalar D(2900)

We study the decay properties of a $D(2900)$ state, with spin parity ${0}^{\ensuremath{-}}$, whose existence was proposed in an earlier study of the $DK\overline{K}$ and coupled-channel system. It was found in the former work that a $D$ meson appears with a mass of about 2900 MeV from the three-body dynamics while the charmless subsystem of the pseudoscalar mesons forms the ${f}_{0}(980)$ resonance. Motivated by the recent experimental investigations of $D$ mesons around 3000 MeV, we now study the two-body decays of $D(2900)$. We find that the nature of the said state sets the main decay channels to be ${D}^{*}\ensuremath{\pi}$, ${D}_{s}^{*}\overline{K}$ and ${D}_{s0}^{*}(2317)\overline{K}$. It turns out that decay width to the last one is the largest, making the ${D}_{s0}^{*}(2317)\overline{K}$ system to be the most favorable one to look for a signal of $D(2900)$. We compare the decay properties of our state with those of the $D$-meson states, proposed within quark models, near 3000 MeV. We hope that our findings and discussions can be useful for the future experimental investigations of charm mesons around 3000 MeV.

Coupled-channel effects of the Σc(*)D¯(*)−Λc(2595)D¯ system and molecular nature of the Pc pentaquark states from one-boson exchange model

The effects of the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, $P_c(4440)$ and $P_c(4457)$, are reinvestigated. Both the pion and $\rho$-meson exchanges are considered for the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics. It is found that the role of the $\Lambda_{c}(2595)\bar{D}$ channel in the descriptions of the $P_c(4440)$ and $P_c(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $\delta(\vec{r})$ term of the one-pion exchange (OPE) keep failing to reproduce the $P_c(4440)$ and $P_c(4457)$ states simultaneously. The OPE potential with the full $\delta(\vec{r})$ term results in a too large mass splitting for the $J^P=1/2^-$ and $3/2^-$ $\Sigma_c\bar{D}^*$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $\delta(\vec{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $\delta(\vec r)$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $\delta(\vec r)$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $\delta(\vec r)$ term in the OBE model reduced by about 80\%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the $P_c(4440)$ and $P_c(4457)$ are $3/2^-$ and $1/2^-$, respectively.

Spin squeezing from bilinear spin-spin interactions: Two simple theorems

We demonstrate two simple theorems about squeezing induced by bilinear spin-spin interactions that conserve spin parity -- including a vast majority of quantum spin models implemented by state-of-the-art quantum simulators. In particular we show that squeezing captures the first form of quantum correlations which are produced: 1) at equilibrium, by adiabatically turning on the spin-spin interactions starting from a factorized state aligned with an external, arbitrary field; 2) away from equilibrium, by evolving unitarily the same state with the interacting Hamiltonian.

α -decay properties of Pa220

The isotope $^{220}\mathrm{Pa}$ produced in the reaction $^{40}\mathrm{Ar}+^{187}\mathrm{Re}$ at a beam energy of 198.7 MeV was reinvestigated via the $\ensuremath{\alpha}$-spectroscopic method. A new $\ensuremath{\alpha}$-decaying state in $^{220}\mathrm{Pa}$ has been observed with an energy ${E}_{\ensuremath{\alpha}}=9664(40)\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$ and with a half-life ${T}_{1/2}={233}_{\ensuremath{-}56}^{+108}\phantom{\rule{0.28em}{0ex}}\mathrm{ns}$. The spin parity of the state is tentatively suggested to be (${3}^{\ensuremath{-}}$). The $\ensuremath{\alpha}$ energy and half-life of the (${1}^{\ensuremath{-}}$) ground state are measured to be ${E}_{\ensuremath{\alpha}}=9548(30)\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$ and ${T}_{1/2}=0.75(8)\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$, respectively. The reduced $\ensuremath{\alpha}$ width, inferred from the present data, fits well into the systematics for $N=129$ isotones.

Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder

The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (${J}_{2}=1$) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (${J}_{1}$) along the rungs. As a function of ${J}_{1}$, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of various gs properties such as spin gap, spin-spin correlations, spin density, and bond order reveal that the system has four distinct phases, namely, the AF phase at small ${J}_{1}$; the ferrimagnetic phase with gs spin ${S}_{G}=n$ for $1.44<{J}_{1}<4.74$ and with ${S}_{G}=2n$ for ${J}_{1}>5.63$, where $n$ is the number of unit cells; and a reentrant nonmagnetic phase at $4.74<{J}_{1}<5.44$. The system also shows the presence of spin current at specific ${J}_{1}$ values due to simultaneous breaking of both reflection and spin parity symmetries.

Time-dependent dynamics of nuclear spin symmetry and parity violation in dichlorodisulfane (ClSSCl) during and after coherent radiative excitation

Parity and nuclear spin symmetry are approximate symmetries, which for many primary processes in molecular spectroscopy and kinetics lead to almost exact constants of the motion. The symmetric isotopomer dichlorodisulfane (disulfur dichloride) is chiral with two enantiomers, each of which has also two nuclear spin isomers (ortho and para isomers). Electroweak quantum chemistry predicts a small ‘parity violating’ energy difference between the ground states of the enantiomers (M being more stable than P by about ). Furthermore recent microwave spectroscopy has indicated ‘forbidden’ transitions between ortho and para isomers. These phenomena allow for a comparative study of the time-dependent quantum dynamics of parity and nuclear spin symmetry violation in a chiral molecule for the first time. We report quantum dynamical calculations of coherent radiative excitation of the complex manifold of polyads with hyperfine structure in ClSSCl. We demonstrate almost complete (near 100%) transfer of population from an almost pure para-ground state to an almost pure excited ortho state. Short-pulse excitation from the para-ground state to an excited time-dependent para chromophore state shows intramolecular interconversion between para and ortho nuclear spin isomers under isolation after the pulse on a time scale of a few nanoseconds to a few microsecond depending on the excited polyad. We also demonstrate the preparation of exotic ‘chameleon states’, which are superpositions of energy eigenstates corresponding to ortho- and para- nuclear spin symmetry isomers at the same time. The results are discussed in relation to the strong separation of time scales between the primary processes of nuclear spin symmetry isomerisation (nanoseconds to microseconds) and parity change (seconds) and in relation to possible experiments to measure in this molecule. We also compare with the rate processes of nuclear spin symmetry isomerisation induced by thermal black body radiation, depending on temperature, occurring on time scales from less than seconds to more than 100 years.

Hidden and doubly heavy molecular states from interactions D^{(*)}_{(s)}{{bar{D}}}^{(*)}_{s}/B^{(*)}_{(s)}{{bar{B}}}^{(*)}_{s} and {D}^{(*)}_{(s)}D_{s}^{(*)}/{B}^{(*)}_{(s)}B_{s}^{(*)}

In this work, we perform a systematical investigation about the possible hidden and doubly heavy molecular states with open and hidden strangeness from interactions of D^{(*)}{{bar{D}}}^{(*)}_{s}/B^{(*)}{{bar{B}}}^{(*)}_{s}, {D}^{(*)}_{s}{{bar{D}}}^{(*)}_{s}/{{B}}^{(*)}_{s}{{bar{B}}}^{(*)}_{s}, {D}^{(*)}D_{s}^{(*)}/{B}^{(*)}B_{s}^{(*)}, and D_{s}^{(*)}D_{s}^{(*)}/B_{s}^{(*)}B_{s}^{(*)} in a quasipotential Bethe-Salpeter equation approach. The interactions of the systems considered are described within the one-boson-exchange model, which includes exchanges of light mesons and J/psi /varUpsilon meson. Possible molecular states are searched for as poles of scattering amplitudes of the interactions considered. The results suggest that recently observed Z_{cs}(3985) can be assigned as a molecular state of D^*{bar{D}}_s+D{bar{D}}^*_s, which is a partner of Z_c(3900) state as a D{bar{D}}^* molecular state. The calculation also favors the existence of hidden heavy states D_s{bar{D}}_s/B_s{bar{B}}_s with spin parity J^P=0^+, D_s{bar{D}}^*_s/B_s{bar{B}}^*_s with 1^{+}, and D^*_s{bar{D}}^*_s/B^*_s{bar{B}}^*_s with 0^+, 1^+, and 2^+. In the doubly heavy sector, the bound states can be found from the interactions (D^*D_s+DD^*_s)/(B^*B_s+BB^*_s) with 1^+, D_s{bar{D}}_s^*/B_s{bar{B}}_s^* with 1^+, D^*D^*_s/B^*B^*_s with 1^+ and 2^+, and D^*_sD^*_s/B^*_sB^*_s with 1^+ and 2^+. Some other interactions are also found attractive, but may be not strong enough to produce a bound state. The results in this work are helpful for understanding the Z_{cs}(3985), and future experimental search for the new molecular states.

Ground and excited state masses of Ωc0 , Ωcc+ and Ωccc++ baryons

The masses of ground and excited states of ${\mathrm{\ensuremath{\Omega}}}_{c}^{0}$, ${\mathrm{\ensuremath{\Omega}}}_{cc}^{+}$, and ${\mathrm{\ensuremath{\Omega}}}_{ccc}^{*++}$ baryons are calculated within the framework of Regge phenomenology. Here our attempt is to assign a possible spin parity to these obtained masses. Our calculated masses in the $(J,{M}^{2})$ plane with both natural (${J}^{P}=1/{2}^{+},3/{2}^{\ensuremath{-}},5/{2}^{+},\dots{}$) and unnatural (${J}^{P}=3/{2}^{+},5/{2}^{\ensuremath{-}},7/{2}^{+},\dots{}$) spin parities are in agreement with the experimental observations where available and reasonably close to other theoretical predictions. Further, we fix the slope and intercept of each Regge line in the $(n,{M}^{2})$ plane and estimate the masses of higher excited states of these baryons. The obtained mass relations and the mass value predictions could provide useful information in future experimental searches and the spin-parity assignment of these states.

Bell-state tomography in a silicon many-electron artificial molecule

An error-corrected quantum processor will require millions of qubits, accentuating the advantage of nanoscale devices with small footprints, such as silicon quantum dots. However, as for every device with nanoscale dimensions, disorder at the atomic level is detrimental to quantum dot uniformity. Here we investigate two spin qubits confined in a silicon double quantum dot artificial molecule. Each quantum dot has a robust shell structure and, when operated at an occupancy of 5 or 13 electrons, has single spin-frac{1}{2} valence electron in its p- or d-orbital, respectively. These higher electron occupancies screen static electric fields arising from atomic-level disorder. The larger multielectron wavefunctions also enable significant overlap between neighbouring qubit electrons, while making space for an interstitial exchange-gate electrode. We implement a universal gate set using the magnetic field gradient of a micromagnet for electrically driven single qubit gates, and a gate-voltage-controlled inter-dot barrier to perform two-qubit gates by pulsed exchange coupling. We use this gate set to demonstrate a Bell state preparation between multielectron qubits with fidelity 90.3%, confirmed by two-qubit state tomography using spin parity measurements.

Pcs(4459) and other possible molecular states from Ξc(*)D¯(*) and Ξc′D¯(*) interactions

Recently, the LHCb Collaboration reported a new structure ${P}_{cs}(4459)$ with a mass of 19 MeV below the ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ threshold. It may be a candidate of molecular state from the ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ interaction. In the current work, we perform a coupled-channel study of the ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}{\overline{D}}^{*}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}{\overline{D}}^{*}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}\overline{D}$, ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}\overline{D}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}$ interactions in the quasipotential Bethe-Salpeter equation approach. With the help of the heavy quark chiral effective Lagrangian, the potential is constructed by light meson exchanges. Two ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ molecular states are produced with spin parities ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$. The lower state with $3/{2}^{\ensuremath{-}}$ can be related to the observed ${P}_{cs}(4450)$ while two-peak structure cannot be excluded. Within the same model, other strange hidden-charm pentaquarks are also predicted. Two states with spin parities $1/{2}^{\ensuremath{-}}$ and a state with $3/{2}^{\ensuremath{-}}$ are predicted near the ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}\overline{D}$, ${\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}\overline{D}$ thresholds, respectively. As two states near ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ threshold, two states are produced with $1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$ near the ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}{\overline{D}}^{*}$ threshold. The couplings of the molecular states to the considered channels are also discussed. The experimental research of those states are helpful to understand the origin and internal structure of the ${P}_{cs}$ and ${P}_{c}$ states.

Observation of a New Excited D_{s}^{+} Meson in B^{0}→D^{-}D^{+}K^{+}π^{-} Decays.

Using pp collision data corresponding to an integrated luminosity of 5.4 fb^{-1} collected with the LHCb detector at a center-of-mass energy of 13TeV, the B^{0}→D^{-}D^{+}K^{+}π^{-} decay is studied. A new excited D_{s}^{+} meson is observed decaying into the D^{+}K^{+}π^{-} final state with large statistical significance. The pole mass and width, and the spin parity of the new state are measured with an amplitude analysis to be m_{R}=2591±6±7 MeV, Γ_{R}=89±16±12 MeV, and J^{P}=0^{-}, where the first uncertainty is statistical and the second systematic. Fit fractions for all components in the amplitude analysis are also reported. The new resonance, denoted as D_{s0}(2590)^{+}, is a strong candidate to be the D_{s}(2^{1}S_{0})^{+} state, the radial excitation of the pseudoscalar ground-state D_{s}^{+} meson.

Atomic Line Defects and Topological Superconductivity in Unconventional Superconductors

Topological superconductors (TSCs) are correlated quantum states with simultaneous off-diagonal long-range order and nontrivial topological invariants. They produce gapless or zero energy boundary excitations, including Majorana zero modes and chiral Majorana edge states with topologically protected phase coherence essential for fault-tolerant quantum computing. Candidate TSCs are very rare in nature. Here, we propose a novel route toward emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum structures such as atomic line defects in unconventional spin-singlet $s$-wave and $d$-wave superconductors. We show that inversion symmetry breaking and charge transfer due to the missing atoms lead to the occupation of incipient impurity bands and mixed parity spin singlet and triplet Cooper pairing of neighboring electrons traversing the line defect. Nontrivial topological invariants arise and occupy a large part of the parameter space, including the time reversal symmetry breaking Zeeman coupling due to applied magnetic field or defect-induced magnetism, creating TSCs in different topological classes with robust Majorana zero modes at both ends of the line defect. Beyond providing a novel mechanism for the recent discovery of zero-energy bound states at both ends of an atomic line defect in monolayer Fe(Te,Se) superconductors, the findings pave the way for new material realizations of the simplest and most robust 1D TSCs using embedded quantum structures in unconventional superconductors with large pairing energy gaps and high transition temperatures.

Spin Parity of Spiral Galaxies. III. Dipole Analysis of the Distribution of SDSS Spirals with 3D Random Walk Simulations

Abstract Observation has not yet determined whether the distribution of spin vectors of galaxies is truly random. It is unclear whether is there any large-scale symmetry-breaking in the distribution of the vorticity field in the universe. Here, we present a formulation to evaluate the dipole component D max of the observed spin distribution, whose statistical significance σ D can be calibrated by the expected amplitude for 3D random walk (random flight) simulations. We apply this formulation to evaluate the dipole component in the distribution of Sloan Digital Sky Survey (SDSS) spirals. Shamir published a catalog of spiral galaxies from the SDSS DR8, classifying them with his pattern recognition tool into clockwise and counterclockwise (Z-spiral and S-spiral, respectively). He found significant photometric asymmetry in their distribution. We have confirmed that this sample provides dipole asymmetry up to a level of σ D = 4.00. However, we also found that the catalog contains a significant number of multiple entries of the same galaxies. After removing the duplicated entries, the number of samples shrunk considerably to 45%. The actual dipole asymmetry observed for the “cleaned” catalog is quite modest, σ D = 0.29. We conclude that SDSS data alone do not support the presence of a large-scale symmetry-breaking in the spin vector distribution of galaxies in the local universe. The data are compatible with a random distribution.