Flow of entropy in the evolution of the B^0 anti B^0 system: Upper bound on CP violation from unidirectionality

We have previously studied the time-dependence of a B anti B meson mixture in terms of its density matrix. The requirement that the absolute value of the Stokes vector zeta(t) should evolve monotonically from its initial value zeta(0)=0 to its final value zeta(infinity)=1 was shown to lead to an upper bound on the CP violating overlap . In the present note we consider an entropy variable S as an alternative measure of mixing. We show that exactly the same upper bound emerges from the requirement that the flow of entropy is unidirectional (dS/dt<0). We compare the entropic current dS/dt with and without CP violation and identify certain physical features that appear when the bound on is violated.Comment: 8 pages, 4 figures. Typos corrected, comment on entropy added. To be published in Physical Review

An upper limit on CP violation in the Bs0−Bˉs0B^0_s-\bar{B}^0_s system

In a previous publication we noted that the time dependence of an incoherent $B^0-\bar{B}^0$ mixture undergoes a qualitative change when the magnitude of CP violation $\delta$ exceeds a critical value. Requiring, on physical grounds, that the system evolve from an initial incoherent state to a final pure state in a monotonic way, yields a new upper limit for $\delta$. The recent measurement of the wrong charge semileptonic asymmetry of $B_s^0$ mesons presented by the D0 collaboration is outside this bound by one standard deviation. If this result is confirmed it implies the existence of a new quantum mechanical oscillation phenomenon.Comment: 7 pages, 2 figures, version submitted for publication (Physical Review

Lepton Mass Effects in Single Pion Production by Neutrinos

We reconsider the Feynman-Kislinger-Ravndal model applied to neutrino-excitation of baryon resonances. The effects of lepton mass are included, using the formalism of Kuzmin, Lyubushkin and Naumov. In addition we take account of the pion-pole contribution to the hadronic axial vector current. Application of this new formalism to the reaction nu(mu) + p --> mu + Delta at E(nu) approx 1 GeV gives a suppressed cross section at small angles, in agreement with the screening correction in Adler's forward scattering theorem. Application to the process nu(tau) + p --> tau + Delta at E(nu) approx 7 GeV leads to the prediction of right-handed tau polarization for forward-going leptons, in line with a calculation based on an isobar model. Our formalism represents an improved version of the Rein-Sehgal model, incorporating lepton mass effects in a manner consistent with PCAC.Comment: 14 pages, 5 figures. Typos in eq. 9 and 27 corrected. Numbers in table I for coherent cross sections (RSA and RSC) corrected (normalization error). Figs 3 and 4 changed accordingly. These corrections also apply to the published version PRD 76, 113004 (2007

CP Violation and Arrows of Time Evolution of a Neutral KK or BB Meson from an Incoherent to a Coherent State

We study the evolution of a neutral $K$ meson prepared as an incoherent equal mixture of $K^0$ and $\bar{K^0}$. Denoting the density matrix by \rho(t) = {1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state $N(t)$ is found to decrease monotonically from one to zero, while the magnitude of the Stokes vector $|\vec{\zeta}(t)|$ increases monotonically from zero to one. This property qualifies these observables as arrows of time. Requiring monotonic behaviour of $N(t)$ for arbitrary values of $\gamma_L, \gamma_S$ and $\Delta m$ yields a bound on the CP-violating overlap $\delta = \braket{K_L}{K_S}$, which is similar to, but weaker than, the known unitarity bound. A similar requirement on $|\vec{\zeta}(t)|$ yields a new bound, $\delta^2 < {1/2} (\frac{\Delta \gamma}{\Delta m}) \sinh (\frac{3\pi}{4} \frac{\Delta \gamma}{\Delta m})$ which is particularly effective in limiting the CP-violating overlap in the $B^0$-$\bar{B^0}$ system. We obtain the Stokes parameter $\zeta_3(t)$ which shows how the average strangeness of the beam evolves from zero to $\delta$. The evolution of the Stokes vector from $|\vec{\zeta}| = 0$ to $|\vec{\zeta}| = 1$ has a resemblance to an order parameter of a system undergoing spontaneous symmetry breaking.Comment: 13 pages, 6 figures. Inserted conon "." in title; minor change in text. To appear in Physical review

Baryon Magnetic Moments and Proton Spin: A Model with Collective Quark Rotation

We analyse the baryon magnetic moments in a model that relates them to the parton spins $\Delta u$, $\Delta d$, $\Delta s$, and includes a contribution from orbital angular momentum. The specific assumption is the existence of a 3-quark correlation (such as a flux string) that rotates with angular momentum $\langle L_z \rangle$ around the proton spin axis. A fit to the baryon magnetic moments, constrained by the measured values of the axial vector coupling constants $a^{(3)}=F+D$, $a^{(8)}=3F-D$, yields $\langle S_z \rangle = 0.08 \pm 0.13$, $\langle L_z \rangle = 0.39 \pm 0.09$, where the error is a theoretical estimate. A second fit, under slightly different assumptions, gives $\langle L_z \rangle = 0.37 \pm 0.09$, with no constraint on $\langle S_z \rangle$. The model provides a consistent description of axial vector couplings, magnetic moments and the quark polarization $\langle S_z \rangle$ measured in deep inelastic scattering. The fits suggest that a significant part of the angular momentum of the proton may reside in a collective rotation of the constituent quarks.Comment: 16 pages, 3 ps-figures, uses RevTeX. Abstract, Sec. II, III and IV have been expande

Pair production and correlated decay of heavy Majorana neutrinos in e+e- collisions

We consider the process e^+e^-\to N_1N_2, where N_1 and N_2 are heavy Majorana particles, with relative CP given by \eta_{CP}=+1 or -1 decaying subsequently via N_1,N_2\to W^{\pm}e^{\mp}. We derive the energy and angle correlation of the dilepton final state, both for like-sign (e^{\mp}e^{\mp}) and unlike-sign (e^-e^+) configurations. Interesting differences are found between the cases \eta_{CP}=+1 and -1. The characteristics of unlike-sign e^+e^- dileptons originating from a Majorana pair N_1N_2 are contrasted with those arising from the reaction e^+e^-\to N\bar{N}\to W^+e^-W^-e^+, where N\bar{N} is a Dirac particle-antiparticle pair

Magnetic and axial vector form factors as probes of orbital angular momentum in the proton

We have recently examined the static properties of the baryon octet (magnetic moments and axial vector coupling constants) in a generalized quark model in which the angular momentum of a polarized nucleon is partly spin $\langle S_z \rangle$ and partly orbital $\langle L_z \rangle$. The orbital momentum was represented by the rotation of a flux-tube connecting the three constituent quarks. The best fit is obtained with $\langle S_z \rangle = 0.08\pm 0.15$, $\langle L_z \rangle = 0.42\pm 0.14$. We now consider the consequences of this idea for the $q^2$-dependence of the magnetic and axial vector form factors. It is found that the isovector magnetic form factor $G_M^{\mathrm{isovec}}(q^2)$ differs in shape from the axial form factor $F_A(q^2)$ by an amount that depends on the spatial distribution of orbital angular momentum. The model of a rigidly rotating flux-tube leads to a relation between the magnetic, axial vector and matter radii, $\langle r^2 \rangle_{\mathrm{mag}} = f_{\mathrm{spin}} \langle r^2 \rangle_{\mathrm{axial}} + \frac{5}{2} f_{\mathrm{orb}} \langle r^2 \rangle_{\mathrm{matt}}$, where $f_{\mathrm{orb}}/ f_{\mathrm{spin}} = \frac{1}{3}\langle L_z \rangle / G_A$, $f_{\mathrm{spin}} + f_{\mathrm{orb}} = 1$. The shape of $F_A(q^2)$ is found to be close to a dipole with $M_A = 0.92\pm 0.06$ GeV.Comment: 18 pages, 5 ps-figures, uses RevTe

Energy Spectrum of Leptons from e+e−→W+W−e^+e^- \to W^+W^- in the Presence of Strong W^+_LW^-_L Interaction

The energy spectrum of leptons, produced by the decay of one or both W's in the reaction $e^+e^- \to W^+W^-$, is a significant probe of the helicity structure of this process. We calculate the energy spectrum $d \sigma /d E$ of a single decay lepton, as well as the two-dimensional energy distribution $d \sigma/d E_+dE_-$. We then consider a possible strong final state interaction in the longitudinally polarized state of the W^+W^- system, parametrized by a \rho -like resonance in the region of 1.8 TeV. We show that such a resonance produces measurable effects in the lepton spectrum at $\sqrt{s}=500$ GeV. The results are compared with those obtained from a non-resonant interaction approximated by a phase factor $e^{i \delta}$ in the l=1 part of the W^+_LW^-_L amplitude.Comment: LaTeX, 12 pages including 3 eps figures, uses amssym and eps