We present evidence of $D^0$-$\bar{D^0}$ mixing using a time-dependent amplitude analysis of the decay D0->K+pi-pi0 in a data sample of 384 fb^-1 collected with the BaBar detector at the PEP-II e+e- collider at SLAC. Assuming CP conservation, we measure the mixing parameters x'_{Kpipi0} = [2.61^{+0.57}_{-0.68} (stat.) +- 0.39 (syst.)]%, y'_{Kpipi0} = [-0.06 ^{+0.55}_{-0.64} (stat.) +- 0.34 (syst.)]%. The confidence level for the data to be consistent with the no-mixing hypothesis is 0.1%, including systematic uncertainties. This result is inconsistent with the no-mixing hypothesis with a significance of 3.2 standard deviations. We find no evidence of CP violation in mixing.
The D0 meson can decay to the wrong sign K+pi- state either through a doubly Cabibbo suppressed decay or via mixing to the D0bar state followed by the Cabibbo favoured decay D0bar -> K+ pi-. We measure the rate of wrong sign decays relative to the Cabibbo favoured decay to (0.383 +- 0.044 +- 0.022)% and give our sensitivity to a mixing signal.
Recent results on Bs mixing, lifetime difference and rare decays obtained by the CDF and DO collaborations using the data samples collected at the Tevatron Collider in the period 2002 - 2005 are presented.
Current status of charm mixing search, lifetime difference measurement and rare decay search are reported. The best upper limit at 95% CL for mixing is reported from the CLEO collaboration. E791 has reported lifetime difference measurement and results of rare decay searches. Rare decay searches of the FOCUS collaboration are in progress and their sensitivities to branching ratios are at the level of a few x 10^{-6}.
We review basic phenomenology on $D^0$ mixing/CP violation and recent experimental results on them. $D^0$ mixing is established by combining results from multiple experiments but no CP violation in the charm sector has been seen. $D^0$ mixing from a single experiment will clarify the size of the mixing, and observation of CP violation in charm decays at the present level of experimental sensitivity would be clear signal of new physics beyond the standard model.
We present a brief review of CPV and mixing measurements in the charm sector, with emphasys in results published or presented since the previous edition of the Physics in Collision Symposia.
I discuss the results on $D^{0}$-$\bar{D}^{0}$ mixing through hadronic as well as semi-leptonic charm decays, rare flavor-changing neutral currents in the charm sector and the lepton flavor violating $τ$ decaying to charged lighter leptons. The results from both BABAR and Belle are presented in this review.
Using the CLEO II.V detector observing e+e- collisions at around 10.6 GeV we search for neutral D mixing in semileptonic D0 decays tagged in charged D* decays. Combining the results from the Kenu and K*enu channels we find that the rate for D mixing is less than 0.0078 at 90% C.L.
Standard model mixing and CP violation are expected to be small in the charm sector. Some argue that only in the presence of new physics do we currently expect to observe these effects. Fermilab experiment E791 has the largest sample of reconstructed charm decays recorded to date. We have made an exhaustive search for D0 D0-bar mixing and CP violation in this data. We present the charm mixing limits on the mixing parameter r_mix using hadronic and semileptonic decays, and also present preliminary limits on the CP asymmetry parameter, A_CP, for Cabibbo suppressed decays.
We present results of a search for $D^0$-$\kern 0.2em\bar{\kern -0.2em D}{}^0$~mixing and a measurement of $R_{\rm D}$, the ratio of doubly Cabibbo-suppressed decays to Cabibbo-favored decays, based on an analysis of $D^0 \to K^{+}π^{-}$ decays in 57.1~${fb}^{-1}$ of data collected at or just below the $Υ{(4S)}$ resonance with the {\slshape BABAR} detector at the PEP-II collider. Our results are compatible with no mixing and no $CP$ violation. At the 95% C.L., allowing for CP violation, we find the mixing parameters ${x^{\prime}}^2<0.0022$ and $-0.056<y^{\prime}<0.039$, and the mixing rate $R_…
The SuperB experiment at the Cabibbo Laboratory will provide new possibilities to study the physics of charm. The potential physics reach of the experiment when performing studies of rare decays, mixing and CP violation in charm decays is presented here and the implications of such measurements for new physics scenarios is discussed.
Recent measurements of mixing and $CP$ violation in charm decays at LHCb are presented. These include searches for direct $CP$ violation in $D^{0}\rightarrow K_{S}^{0}K_{S}^{0}$, $D_{(s)}^{+}\rightarrow h^{+} π^{0} $ and $D_{(s)}^{+}\rightarrow h^{+}η$ decays, and a search for time-dependent $CP$ violation in $D^{0}\rightarrow h^{+}h^{-}$ decays, where $h^{+}$ is either a $π^{+}$ or $K^{+}$ meson.
We have searched for mixing in the D0-D0bar system by measuring the decay-time distribution of D0->K+pi- decays. The analysis uses 90 fb^{-1} of data collected by the Belle detector at the KEKB e+e- collider. We fit the decay-time distribution for the mixing parameters x' and y' and also for the parameter R_D, which is the ratio of the rate for the doubly-Cabibbo-suppressed decay D0->K+pi- to that for the Cabibbo-favored decay D0->K-pi+. We do these fits both assuming CP conservation and allowing for CP violation. We use a frequentist method to obtain a 95% C.L. region in the x'^2 - y' plane. …
We present an analysis of the decay $D^0 \to K^+π^-$ from FOCUS. From a sample of 234 events we find a branching ratio of $\frac{Γ(D^0 \to K^+π^-)}{Γ(D^0 \to K^-π^+)} = (0.430^{+0.062}_{-0.061}\pm 0.031)%$ under the assumption of no mixing and no CP violation. We also present limits on charm mixing.
We measure the $D^0 - {\bar{D}}^0$ mixing parameters using a time-dependent amplitude analysis of the decay $D^0\toπ^+π^-π^0$. The data were recorded with the BABAR detector at center-of-mass energies at and near the $Υ(4S)$ resonance, and correspond to an integrated luminosity of approximately 468.1 ${\rm fb}^{-1}$. The neutral $D$ meson candidates are selected from $D^{*}(2010)^+\to D^0 π_s^+$ decays where the flavor at the production is identified by the charge of the low momentum pion, $π_s^+$. The measured mixing parameters are $x = (1.5\pm1.2\pm0.6) \%$ and $y = (0.2\pm0.9\pm0.5) \%$, wh…
Based on a dataset acquired by the BaBar experiment running on and near the $Υ(4S)$ resonance from 1999-2002, limits are set on the rate of $D^0$-- $\kern 0.2em\bar{\kern -0.2em D}{}^0$ mixing using the decay mode $D^{*+} \to D^0 π^{+}$, followed by a semi-leptonic decay of the $D^0$. Results are compared to previous BaBar analysis using hadronic decays. We also report on a search for the flavor-changing neutral current decays $D^0 \to e^{+} e^{-}$ ($μ^{+} μ^{-}$) and the lepton-flavor violation decays $D^0 \to e^{\pm} μ^{\mp}$.
The phenomenon of mixing in neutral meson systems has now been observed in all flavours, but only in the past year in the D0 system. The standard model anticipated that, for the charm sector, the mixing rate would be small, and also that CP violation, either in mixing or in direct decay, would be below the present levels of observability. It is hoped that further study of these phenomena might reveal signs of new physics. A review of recently available, experimental results is given.
Measurements by various international groups of researchers determine the strength of the weak interaction of the neutron, which gives us unique information on the question of the quark mixing. Neutron decay experiments now challenge the Standard Model of elementary particle physics with a deviation, 2.7 times the stated error.
During run I, the LHCb experiment at the LHC, CERN, collected 1.0 fb$^{-1}$ of pp collisions at $\sqrt{s} = 7$ TeV and 2.0 fb$^{-1}$ at $\sqrt{s} = 8$ TeV, yielding the world's largest sample of decays of charmed hadrons. This sample is used to search for direct and indirect CP violation in charm and to measure $D^{0}$ mixing parameters. Recent measurements from several complementary decay modes are presented.
We report the results of a search for D0-D0bar mixing in D0 -> K+ pi- decays based on 400 fb^{-1} of data accumulated by the Belle detector at KEKB. Both assuming CP conservation and allowing for CP violation, we fit the decay-time distribution for the mixing parameters x' and y', as well as for the parameter R_D, the ratio of doubly-Cabibbo-suppressed decays to Cabibbo-favored decays. The 95% confidence level region in the (x'^2,y') plane is obtained using a frequentist method. Assuming CP conservation, we find x'^2<0.72 x 10^{-3} and -9.9 x 10^{-3}<y'<6.8 x 10^{-3} at the 95% confidence leve…
A search for mixing in the neutral D meson system was performed using semileptonic D^0 -> K- e+ nu decays. The flavor of neutral D mesons at production was tagged by the charge of the slow pion from the decay D*+ -> D^0 π+. The measurement was performed using 140 fb^-1 of data recorded by the Belle detector. The yield of right and wrong sign decays arising from un-mixed and mixed events, respectively, was determined by a fit to kinematic observables. From the number of signal events we derive an upper limit for the time-integrated mixing rate r_D < 1.4 x 10^-3 at 90% C.L.
Studies of charm physics with the 2010 LHCb data sample are presented. Time-integrated searches for CP violation in D+ -> K- K+ pi+ and D0 -> K- K+, pi- pi+ are discussed.
Hadronic Z0 decays with identified electrons or muons have been used to measure the forward-backward asymmetries of e^+e^- --> Z0 --> bbbar and e^+e^- --> Z0 --> ccbar events. The asymmetries at three centre-of-mass energies, and the average B mixing parameter, chi, are determined in a simultaneous fit to events with one or two lepton candidates.
B mesons provide an ideal laboratory for measurements of CP violation and searches for CP violation beyond the Standard Model. Recent measurements of the mixing phases of the $B_s^0$ and $B^0$ mesons, $ϕ_s$ and $\sin2β$, using decays to $J/ψX$ final states are presented. In view of future improved measurements, a good understanding of pollution from sub-leading penguin topologies in these decays is needed. Those can be probed using suppressed decays like $B_s^0 \to J/ψK_S^0$ and $B_s^0 \to J/ψ\overline{K}^{*0}$. Recent results using these decay modes are presented.
Measurements of meson mixing and CP violation parameters obtained by the CDF and D0 experiments at the Fermilab Tevatron are presented. These include results on $B_s$ and $D$ meson mixing, and searches for CP violation in the decay $B^+ \to J/ψK^+$, in mixing through semileptonic $B_s$ meson decays, and in the interference between mixing and decay in the process $B_s \to J/ψϕ$.
Neutrons study a number of hot topics from the field of particle physics and cosmology: Recent measurements of various mixed American-British-French-German-Hungarian-Japan-Russian groups of researchers determine the strength of the weak interaction of the neutron, which gives us unique information on quark-mixing and the question of unitarity. Much to our surprise, with neutron-decay we find a deviation Delta = 0.0083(28) from the unitarity condition, an effect that cannot be explained by the current Standard Model of particle physics.
The LHCb experiment has collected the world's largest sample of charmed hadrons. This sample is used to measure observables related to $D^0 -\overline{D}^0$ mixing, direct $C\!P$ violation and $C\!P$ violation in mixing and interference in the charm sector. In this document, the most recent results from LHCb on the search of direct $C\!P$ violation in $D^0$ and $D_{(s)}^+$ decays are summarised, as well as the first observation of mass difference between neutral charm-meson eigenstates and the most precise measurement of time-dependent $C\!P$ asymmetry in $D^0 \to K^+ K^-$ and $D^0 \to π^+ π^-…
A search for D0-D0bar mixing and doubly-Cabibbo-suppressed decays of the D0 in hadronic final states
本文介绍了在费米实验室E791（一个固定靶粲强子产生实验）中寻找D 0-D 0巴混合和D 0的双重Cabibbo抑制衰变的结果。我们在衰变链D* -> pi D 0->（K pi或K pi pi pi）中寻找混合的证据。如果D* 衰变产生的π介子的电荷与D衰变产生的K介子的电荷相同（一个"错误符号“事件），混合可能已经发生。通过分析衰变时间的分布，可以将混合与其他来源的错误符号事件（如双重Cabibbo抑制衰变）区分开来。我们没有看到混合的证据。考虑到可能的CP破坏，我们对r_{mix}（混合衰变与非混合衰变之比）的结果是r_{mix}（D 0 bar-> D 0）=（0.18_{-0.39}^{+0.43} +-0.17）%和r_{mix}（D 0-> D 0 bar）=（0.70_{-0.53}^{+0.58} +-0.18）%。这些结果的敏感性与以前的测量结果相当，但在拟合数据时所作的假设明显更一般。我们提出的结果，从许多适合我们的数据在各种假设下。如果我们假设r_{mix} = 0，我们发现双Cabibbo抑制衰变与Cabibbo有利衰变的比值分别为r_{dcs}（K pi）=（0.68_{-0.33}^{+0.34} +-0.07）%和r_{dcs}（K pi pi pi）=（0.25_{-0.34}^{+0.36} +-0.03）%.
Recent results on mixing, CP violation and rare decays in charm physics from the LHCb experiment are presented. Study of ''wrong-sign'' $D^{0} \rightarrow K^+ π^-$ decays provides the highest precision measurements to date of the mixing parameters $x^{\prime 2}$ and $y^{\prime}$, and of CP violation in this decay mode. Direct and indirect CP violation in the $D^0$ system are probed to a sensitivity of around $10^{-3}$ using $D^0 \rightarrow K^+K^-$ and $D^0 \rightarrow π^+π^-$ decays and found to be consistent with zero. Searches for the rare decays $D^+_{(s)} \rightarrow π^+μ^+μ^-$, $D^+_{(s)…
Using the eight time dependences for the decays Upsilon(4S)-> B0 B0bar -> fj fk with the dacay into a flavor-specific state fj = ell+- X before or after the decay into a CP eigenstate fk = c cbar KS,KL, as measured by the BABAR experiment, we determine the three CPT-sensitive parameters Re(z) and Im(z) in B0-B0bar mixing and |Abar/A| in B0 -> c cbar K0 decays. We find Im(z) = 0.010 +- 0.030 +- 0.013, Re(z) = -0.065 +- 0.028 +- 0.014, and |Abar/A| = 0.999 +- 0.023 +- 0.017, in agreement with CPT symmetry.
We discuss the physics goals and rationale for a detector to study Beauty and Charm decays in the forward direction at the Fermilab Tevatron Collider. We then describe the BTeV detector which has been designed to achieve these goals and present its physics reach based on extensive simulation. We conclude by comparing BTeV to other experiments designed to explore similar topics.
Recent CLEO results on neutral charm meson decays presented at the XXXVIth Rencontres de Moriond are discussed. We find no evidence of CP asymmetry in five different two-body decay modes of the D0 to pairs of light pseudo-scalar mesons. We present a measurement of the mixing parameter y_CP = -0.011 +- 0.025 +- 0.014 by searching for a lifetime difference between the CP neutral K+ pi- final state and the CP even K+ K- and pi+ pi- final states. Finally, we describe the first measurement of the rate of wrong-sign D0 to K+ pi- pi0 decay: R_WS = (0.43 +0.11 -0.10 +- 0.07)%.
We report an improved measurement of D0-D0bar mixing and a search for CP violation in D0 decays to CP-even final states K+K- and pi+pi-. The measurement is based on the final Belle data sample of 976/fb. The results are y_CP=(1.11 +- 0.22 +- 0.09)% and A_Gamma=(-0.03 +- 0.20 +- 0.07)%, where the first uncertainty is statistical and the second is systematic.
Two measurements of mixing and $CP$ violation in charm decays performed at the LHCb experiment are presented. The former is a measurement of the mixing observable $y_{CP}-y_{CP}^{Kπ}$ in two-body $D^0$ decays, while the latter is a search for direct $CP$ violation in $D^+_{(s)}\rightarrowη^{(')}π^+$ decays.
The oscillation frequency of B0-B0bar mixing (Delta-m_d) has been measured using 29.1 fb^{-1} of datacollected with the Belle detector at KEKB. This measurement is made through the distributions of the proper decay time difference of B pairs in events tagged as same- and opposite-flavor decays. In each event, one $B$ is fully reconstructed in a flavor-specific hadronic decay mode, while the flavor of the other is extracted through a likelihood calculated from the b-flavor information carried in its final decay products. We obtain Delta-m_d = (0.528 +- 0.017 +- 0.011) ps^{-1}, where the first e…
A search for mixing in the neutral D meson system has been performed using semileptonic D^0 \to K^(*)- e^+ nu decays. Neutral D mesons from D^*+ \to D^0 pi+ decays are used; the flavor at production is tagged by the charge of the slow pion. The measurement is performed using 253 fb^-1 of data recorded by the Belle detector. From the yield of right-sign and wrong-sign decays arising from non-mixed and mixed events, respectively, we estimate the upper limit of the time-integrated mixing rate to be r_D < 1.0 x 10^-3 at 90 % C.L.
Based on the branching fractions of J/psi(psi(2S))-> VP from different collaborations, the pseudoscalar mixing is extensively discussed with a well established phenomenological model. The mixing angle is determined to be -14 degree by fitting to the new world average if only quark content is considered. After taking into account the gluonic content in eta and eta prime simultaneously, the investigation shows that eta favors only consisting of light quarks, while the gluonic content of eta prime is Z_{eta prime}^2=0.30\pm0.24.
The CP violating phase $ϕ_s$ can be measured in the interference between mixing and decay of $B_s^0$ mesons decaying to CP eigenstates. The phase $ϕ_s$ the decay width difference $ΔΓ_s$ and the average decay width $Γ_s$ have been measured at LHCb, using the full 1 fb$^{-1}$ of $pp$ collisions data at a centre-of-mass energy $\sqrt{s} $ = 7 TeV collected during the 2011 LHC run.
There has been significant recent experimental activity on the related topics of charm mixing and rare (flavor changing neutral current) decay. For mixing, several new results from direct (wrong sign) searches and first results from lifetime difference (Delta Gamma) searches have been reported. Limits for r_mix of approximately 5 x 10^{-4} (or better) are possible from work in progress. For rare decays, sensitivities to branching ratios are now at the level of a few x 10^{-6}.
In this report, we present a preliminary measurement of the Bs0 mixing parameter using samples of four partially reconstructed semileptonic Bs0 decays and one fully reconstructed hadronic decay mode, corresponding to approximately 2.4 fb^{-1} of integrated luminosity. We perform an unbinned likelihood fit to the proper decay length and obtain Dms = 18.53 +- 0.93 (stat.) +- 0.30 (syst) ps^{-1}$.
We discuss the impact of recent progress in semileptonic D decays on light flavour spectroscopy and estimate mixing parameters in the eta-eta^prime system.
Mixing and CP violation in charm meson decays provide a unique probe of possible physics beyond the standard model. In this paper, we give a brief review of the current measurements from the BABAR experiment.
The two body decays of $B_d$ and $B_s$ decays into $J/ψM$, where $M$ is a light meson, is studied under the very simple assumptions that the spectator quark does not play a role in the decay of the weak heavy quark or antiquark. This hypothesis leads to interesting relations between decay amplitudes. The assumption of SU(3) symmetry leads to additional relations between the decay amplitudes and in particular, the eight CP eigenstates $J/ψK_S$, $J/ψη$, $J/ψη^{\prime}$ and $J/ψπ^o$ are all given in terms of 0. If agreement with experiment validates these assumptions the parameters over determine…
Three different strategies to extract the weak mixing phase phi_s of the Bs system using B--> VV decays (Bs--> K* anti-K*, Bs--> phi anti-K* and Bs--> phi phi) are discussed. Those penguin-mediated decays are computed in the framework of a new combined QCD-Factorisation/Flavour Symmetry Method. Also some comments on the recent interesting results found by Babar concerning the decay B--> K* l+l- are included.
We investigate the impact of charm mixing on the model-independent gamma measurement using Dalitz plot analysis of the three-body D decay from B+->DK+ process, and show that ignoring the mixing at all stages of the analysis is safe up to a sub-degree level of precision. We also find that in the coherent production of D0-D0* system in e+e- collisions, the effect of charm mixing is enhanced, and propose a model-independent method to measure charm mixing parameters in the time-integrated Dalitz analysis at charm factories.
The parameter $y_{CP}$ is used to characterize mixing in the $D^0$-$\bar{D}{}^0$ meson system. To determine $y_{CP}$, one measures the effective decay width of a $D^0$ or $\bar{D}{}^0$ decaying to a $CP$ eigenstate, relative to the effective width for a decay to a Cabibbo-favored, flavor-specific final state. When using $y_{CP}$ to extract information about $D^0$-$\bar{D}{}^0$ mixing and $CP$ violation, the decay width of the Cabibbo-favored decay is usually assumed to equal $1/τ$, the reciprocal of the $D^0$ lifetime. However, there is a small correction to this that should be taken into acco…
$\Dz-\Dzb$ mixing and significant CP violation in the charm system may indicate the signature of new physics. In this study, we suggest that the coherent $\DzDzb$ events from the decay of $Υ(1S) \to \Dz \Dzb$ can be used to measure both mixing parameters and CP violation in charm decays. The neutral $D$ mesons from $Υ(1S)$ decay are strongly boosted, so that it will offer the possibility to measure the proper-time interval, $Δt$, between the fully-reconstructed $\Dz$ and $\Dzb$. Both coherent and time-dependent information can be used to extract $\Dz-\Dzb$ mixing parameters. The sensitivity of…
The status of possible new-physics signals in B_s,d-meson mixing and decay is reviewed. In particular, it is emphasized that the recent LHCb results, that find no evidence for a non-standard phase in B_s-barB_s mixing, make a consistent explanation of the D0 data on the like-sign dimuon charge asymmetry notoriously difficult. In order to clarify the inconclusive experimental situation, independent measurements of the semileptonic asymmetries are needed.
We perform a systematic study of sneutrino production and decays in the Minimal Supersymmetric Standard Model (MSSM) with slepton generation mixing. We study bosonic decays like sneutrino \to slepton^- + W^+/H^+ as well as fermionic ones. We show that the effect of slepton generation mixing on the sneutrino production and decays can be quite large in a significant part of the MSSM parameter space despite the very strong experimental limits on lepton flavour violating processes. This could have an important impact on the search for sneutrinos and the determination of the MSSM parameters at futu…
We consider the production of $B^* \bar B^*$ meson pairs in $e^+e^-$ annihilation near the threshold. The rescattering due to pion exchange between the mesons results in a mixing between three partial wave amplitudes: two $P$-wave with the total spin of the meson pair S=0 and S=2 and an F-wave amplitude. The mixing due to pion exchange with a low momentum transfer is calculable up to c.m. energy $E \approx 15 ÷20$\,MeV above the threshold. We find that the $P-F$ mixing is numerically quite small in this energy range, while the mixing of the two P-wave amplitudes is rapidly changing with energy…
We examine the impact of D-Dbar mixing in the extraction of the angle gamma of the unitarity triangle with B- ->D(*)K(*)- and B- ->D(*)pi- decays. We point out that the leading corrections, linear in the small mixing parameters x=Delta m/Gamma and y=Delta Gamma/2Gamma, depend on how the signal selection efficiency varies as a function of the D proper time, and we estimate the scale factor in a simplified case. We note that the charm mixing effect is suppressed in the GLW method. We discuss the case where the leading corrections become quadratic in x and y, and we point out some limitations of …
The $η$-$η^\prime$ mixing angle is deduced from an updated phenomenological analysis of $J/ψ$ decays into a vector and a pseudoscalar meson. Corrections due to non-ideal $ω$-$ϕ$ mixing are confirmed to be crucial to find $θ_P=(-16.9\pm 1.7)^\circ$, in agreement with most recent analyses. The newly reported values of $B(J/ψ\toρπ)$ by the BABAR and BES Collaborations make more difficult a reasonable description of data.
An analysis of various radiative $VPγ$ decays is performed using the two mixing angle description of the $η$-$η^\prime$ system. The agreement is excellent. Our results are expressed both in the ``octet-singlet'' and in the ``quark-flavour'' basis. It turns out that at the present experimental accuracy, the two angles are significantly different in the former, but not in the latter basis.
The semileptonic decays of the lowest-lying double-heavy baryons is treated in a quark model. For the $Ξ_{bb}$, hyperfine mixing in the spin wave function leaves the total rate for decay into the lowest lying daughter baryons essentially unchanged, but changes the relative rates into the $Ξ_{bc}$ and $Ξ_{bc}^\prime$. The same pattern is obtained in the decays of the $Ω_{bb}$. For the $Ξ_{bc}$, this mixing leads to factor of about 17 suppression in the decay rate to the $Ξ_{cc}^*$, and a factor of two suppression in the total decay rate. For the $Ω_{bc}$, the decay to the $Ω_{cc}^*$ is suppress…
It is well known, although sometimes ignored, that not only the d=5 but also d=6 proton decay depends on fermion mixings. In general we study carefully the dependence of d=6 decay on fermion mixings using the effective operator approach. We find that without specifying a theory it is impossible to make clear predictions. Even in a given model, it is often not possible to determine all the physical parameters. We point out that it is possible to make a clear test of any grand unified theory with symmetric Yukawa couplings. We discuss in some detail realistic theories based on SU(5) and SO(10) g…
