0000000000113848
AUTHOR
Claudia Vacca
Study ofB−→DK−π+π−andB−→Dπ−π+π−decays and determination of the CKM angleγ
We report a study of the suppressed B- -> DK-pi(+)pi(-) and favored B- -> D pi(-)pi(+)pi(-) decays, where the neutral D meson is detected through its decays to the K--/+pi(+/-) and CP -even K+K- and pi(+)pi(-) final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb(-1). We observe the first significant signals in the CP - even final states of the D meson for both the suppressed B- -> DK-pi(+)pi(-) and favored B- -> D pi(-)pi(+)pi(-) modes, as well as in the doubly Cabibbo suppressed D -> K+pi(-) final state of the B- -> D pi(-)pi(+)pi(-) decay. Evidence for the suppressed d…
Amplitude analysis ofB0→D¯0K+π−decays
The Dalitz plot distribution of B-0 -> (D) over bar K-0(+)pi(-) decays is studied using a data sample corresponding to 3.0 fb(-1) of pp collision data recorded by the LHCb experiment during 2011 and 2012. The data are described by an amplitude model that contains contributions from intermediate K* (892)(0), K*(1410)(0), K-2*(1430)(0) and D-2(*)(2460)(-) resonances. The model also contains components to describe broad structures, including the K-0(*)(1430)(0) and D-0(*)(2400)(-) resonances, in the K pi S-wave and the D pi S-and P-waves. The masses and widths of the D-0*(2400)(-) and D-2(*)(2460)(-) resonances are measured, as are the complex amplitudes and fit fractions for all components in…
Model-Independent Evidence forJ/ψpContributions toΛb0→J/ψpK−Decays
The data sample of Lambda(0)(b) -> J/psi pK(-) decays acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 fb(-1), is inspected for the presence of J/psi p or J/psi K- contributions with minimal assumptions about K(-)p contributions. It is demonstrated at more than nine standard deviations that Lambda(0)(b) -> J/psi pK(-) decays cannot be described with K- p contributions alone, and that J/psi K- contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for P-c(+)-> J/psi p charmonium-pentaquark states in the same data sample.
First Observation ofD0−D¯0Oscillations inD0→K+π−π+π−Decays and Measurement of the Associated Coherence Parameters
Charm meson oscillations are observed in a time-dependent analysis of the ratio of D0→K+π−π+π− to D0→K−π+π−π+ decay rates, using data corresponding to an integrated luminosity of 3.0fb−1 recorded by the LHCb experiment. The measurements presented are sensitive to the phase-space averaged ratio of doubly Cabibbo-suppressed to Cabibbo-favoured amplitudes rK3πD and the product of the coherence factor RK3πD and a charm mixing parameter y′K3π. The constraints measured are rK3πD=(5.67±0.12)×10−2, which is the most precise determination to date, and RK3πD⋅y′K3π=(0.3±1.8)×10−3, which provides useful input for determinations of the CP-violating phase γ in B±→DK±,D→K∓π±π∓π± decays. The analysis also …
Search for Hidden-Sector Bosons inB0→K*0μ+μ−Decays
A search is presented for hidden-sector bosons, $\chi$, produced in the decay ${B^0\!\to K^*(892)^0\chi}$, with $K^*(892)^0\!\to K^{+}\pi^{-}$ and $\chi\!\to\mu^+\mu^-$. The search is performed using $pp$-collision data corresponding to 3.0 fb$^{-1}$ collected with the LHCb detector. No significant signal is observed in the accessible mass range $214 \leq m({\chi}) \leq 4350$ MeV, and upper limits are placed on the branching fraction product $\mathcal{B}(B^0\!\to K^*(892)^0\chi)\times\mathcal{B}(\chi\!\to\mu^+\mu^-)$ as a function of the mass and lifetime of the $\chi$ boson. These limits are of the order of $10^{-9}$ for $\chi$ lifetimes less than 100 ps over most of the $m(\chi)$ range, a…
Measurement ofBc+Production in Proton-Proton Collisions ats=8 TeV
Production of B+c mesons in proton-proton collisions at a center-of-mass energy of 8~TeV is studied with data corresponding to an integrated luminosity of 2.0 fb−1 recorded by the LHCb experiment. The ratio of production cross-sections times branching fractions between the B+c→J/ψπ+ and B+→J/ψK+ decays is measured as a function of transverse momentum and rapidity in the regions 0<pT<20 GeV/c and 2.0<y<4.5. The ratio integrated within this kinematic range is measured to be (0.683±0.018±0.009)%, where the first uncertainty is statistical and the second systematic.
Updated determination of D0–D¯0 mixing and CP violation parameters with D0→K+π− decays
We report measurements of charm-mixing parameters based on the decay-time-dependent ratio of D0→K+π- to D0→K-π+ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of 5.0 fb-1 recorded by the LHCb experiment from 2011 through 2016. Assuming charge-parity (CP) symmetry, the mixing parameters are determined to be x′2=(3.9±2.7)×10-5, y′=(5.28±0.52)×10-3, and RD=(3.454±0.031)×10-3. Without this assumption, the measurement is performed separately for D0 and D¯0 mesons, yielding a direct CP-violating asymmetry AD=(-0.1±9.1)×10-3, and magnitude of the ratio of mixing parameters 1.00<|q/p|<1.35 at the 68.3% confidence level. All results incl…
First observation of the rareB+→D+K+π−decay
The B+→D+K+π- decay is observed in a data sample corresponding to 3.0 fb-1 of pp collision data recorded by the LHCb experiment during 2011 and 2012. The signal significance is 8σ and the branching fraction is measured to be B(B+→D+K+π-)=(5.31±0.90±0.48±0.35)×10-6, where the uncertainties are statistical, systematic and due to the normalization mode B+→D-K+π+, respectively. The Dalitz plot appears to be dominated by broad structures. Angular distributions are exploited to search for quasi-two-body contributions from B+→D2∗(2460)0K+ and B+→D+K∗(892)0 decays. No significant signals are observed and upper limits are set on their branching fractions.
First observation and amplitude analysis of theB−→D+K−π−decay
The B- -> D+K-pi(-) decay is observed in a data sample corresponding to 3.0 fb(-1) of pp collision data recorded by the LHCb experiment during 2011 and 2012. Its branching fraction is measured to be B(B- -> D+K-pi(-)) = (7.31 +/- 0.19 +/- 0.22 +/- 0.39) x 10(-5) where the uncertainties are statistical, systematic and from the branching fraction of the normalization channel B- -> D+pi(-)pi(-), respectively. An amplitude analysis of the resonant structure of the B- -> D+K-pi(-) decay is used to measure the contributions from quasi-two-body B- -> D-0* (2400)K-0(-), B- -> D-2* (2460)K-0(-), and B- -> D-J* (2760)K-0(-) decays, as well as from nonresonant sources. The D-J* (2760)(0) resonance is …
Measurement of the lifetime of theBc+meson using theBc+→J/ψπ+decay mode
The difference in total widths between the B+c and B+ mesons is measured using 3.0fb−1 of data collected by the LHCb experiment in 7 and 8 TeV centre-of-mass energy proton-proton collisions at the LHC. Through the study of the time evolution of B+c→J/ψπ+ and B+→J/ψK+ decays, the width difference is measured to beΔΓ≡ΓB+c−ΓB+=4.46±0.14±0.07mm−1c,where the first uncertainty is statistical and the second systematic. The known lifetime of the B+ meson is used to convert this to a precise measurement of the B+c lifetime,τB+c=513.4±11.0±5.7fs,where the first uncertainty is statistical and the second systematic.
Measurement of the SemileptonicCPAsymmetry inB0-B¯0Mixing
The semileptonic $CP$ asymmetry in $B^0-\overline{B}{}^0$ mixing, $a_{\rm sl}^d$, is measured in proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$, recorded by the LHCb experiment. Semileptonic $B^0$ decays are reconstructed in the inclusive final states $D^-\mu^+$ and $D^{*-}\mu^+$, where the $D^-$ meson decays into the $K^+\pi^-\pi^-$ final state, and the $D^{*-}$ meson into the $\overline{D}{}^0(\rightarrow K^+\pi^-)\pi^-$ final state. The asymmetry between the numbers of $D^{(*)-}\mu^+$ and $D^{(*)+}\mu^-$ decays is measured as a function of the decay time of the $B^0$ mesons. The $CP$ asymmetry is measured to be $a_{\rm sl}^d = (-0.02 \pm 0.19 \pm…
First experimental study of photon polarization in radiative B0s decays.
The polarization of photons produced in radiative $B^{0}_{s}$ decays is studied for the first time. The data are recorded by the LHCb experiment in $pp$ collisions corresponding to an integrated luminosity of 3fb$^{-1}$ at center-of-mass energies of $7$ and $8$TeV. A time-dependent analysis of the $B^{0}_{s} \to \phi \gamma$ decay rate is conducted to determine the parameter ${\mathcal{A}}^\Delta$, which is related to the ratio of right- over left-handed photon polarization amplitudes in $b \to s \gamma$ transitions. A value of ${\mathcal{A}}^\Delta=-0.98^{\,+0.46\,+0.23}_{\,-0.52\,-0.20}$ is measured. This result is consistent with the Standard Model prediction within two standard deviatio…
Search for CP violation inD0→π−π+π0decays with the energy test
A search for time-integrated CP violation in the Cabibbo-suppressed decay D-0 -> pi(-)pi(+)pi(0) ir is performed using for the first time an unbinned model-independent technique known as the energy test. Using proton-proton collision data, corresponding to an integrated luminosity of 2.0 fb(-1) collected by the LHCb detector at a centre-of-mass energy of root s = 8 TeV, the world's best sensitivity to CP violation in this decay is obtained. The data are found to be consistent with the hypothesis of CP symmetry with a p-value of (2.6 +/- 0.5)%. (C) 2014 The Authors. Published by Elsevier B.V.
Study of the rare Bs0 and B0 decays into the π+π−μ+μ− final state
A search for the rare decays B0s→π+π−μ+μ− and B0→π+π−μ+μ− is performed in a data set corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5-1.3 GeV/c2 and with muon pairs that do not originate from a resonance are considered. The first observation of the decay B0s→π+π−μ+μ− and the first evidence of the decay B0→π+π−μ+μ− are obtained and the branching fractions are measured to be B(B0s→π+π−μ+μ−)=(8.6±1.5(stat)±0.7(syst)±0.7(norm))×10−8 and B(B0→π+π−μ+μ−)=(2.11±0.51(stat)±0.15(syst)±0.16(norm))×10−8, where the third unc…
Observation ofJ/ψpResonances Consistent with Pentaquark States inΛb0→J/ψK−pDecays
Observations of exotic structures in the J/ψp channel, that we refer to as pentaquark-charmonium states, in Λ0b→J/ψK−p decays are presented. The data sample corresponds to an integrated luminosity of 3/fb acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude analysis is performed on the three-body final-state that reproduces the two-body mass and angular distributions. To obtain a satisfactory fit of the structures seen in the J/ψp mass spectrum, it is necessary to include two Breit-Wigner amplitudes that each describe a resonant state. The significance of each of these resonances is more than 9 standard deviations. One has a mass of 4380±8±29 MeV and a width of 205±1…
Precision Measurement ofCPViolation inBS0→J/ΨK+K−Decays
The time-dependent CP asymmetry in B-S(0) -> J/Psi K+K- decays is measured using pp collision data, corresponding to an integrated luminosity of 3.0 fb(-1), collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96 000 B-S(0) -> J/Psi K+K- decays, the CP-violating phase phi(s) is measured, as well as the decay widths GL and GH of the light and heavy mass eigenstates of the B-s(0)-(B) over bar (0)(s) system. The values obtained are phi(s) = -0.058 +/- 0.049 +/- 0.006 rad, Gamma(s) equivalent to (Gamma(L) + Gamma(H))/2 = 0.6603 +/- 0.0027 +/- 0.0015 ps(-1), and Delta Gamma(s) equivalent to Gamma(L)-Gamma(H) = 0.0805 +/- 0.0091 +/- 0.0032 ps(-1), where the f…
Measurement of the Ratio of Branching FractionsB(B¯0→D*+τ−ν¯τ)/B(B¯0→D*+μ−ν¯μ)
The branching fraction ratio R(D-*) = B((B) over bar (0) -> D-*(+)tau(-)(nu) over bar (tau))/B((B) over bar (0) -> D-*(+)mu(-)(nu) over bar (mu)) is measured using a sample of proton-proton collision data corresponding to 3.0 fb(-1) of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode tau(-) -> mu(-)(nu) over bar (mu)nu(tau). The semitauonic decay is sensitive to contributions from non-standard-model particles that preferentially couple to the third generation of fermions, in particular, Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate (B) over bar (0) decays gives R(D-*) =…
Search for weakly decaying b -flavored pentaquarks
Investigations of the existence of pentaquark states containing a single $b$ (anti)quark decaying weakly into four specific final states J/$\psi K^+\pi^- p$, J/$\psi K^- \pi^- p$, J/$\psi K^- \pi^+ p$, and $J/\psi \phi (1020) p$ are reported. The data sample corresponds to an integrated luminosity of 3.0/fb in 7 and 8 TeV pp collisions acquired with the LHCb detector. Signals are not observed and upper limits are set on the product of the production cross section times branching fraction with respect to that of the $\Lambda_b$.
Dalitz plot analysis ofB0→D¯0π+π−decays
The resonant substructures of $B^0 \to \overline{D}^0 \pi^+\pi^-$ decays are studied with the Dalitz plot technique. In this study a data sample corresponding to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collisions collected by the LHCb detector is used. The branching fraction of the $B^0 \to \overline{D}^0 \pi^+\pi^-$ decay in the region $m(\overline{D}^0\pi^{\pm})>2.1$ GeV$/c^2$ is measured to be $(8.46 \pm 0.14 \pm 0.29 \pm 0.40) \times 10^{-4}$, where the first uncertainty is statistical, the second is systematic and the last arises from the normalisation channel $B^0 \to D^*(2010)^-\pi^+$. The $\pi^+\pi^-$ S-wave components are modelled with the Isobar and K-matrix formalisms. …
Determination of γ and−2βsfrom charmless two-body decays of beauty mesons
Using the latest LHCb measurements of time-dependent CP violation in the B-s(0) -> K+K- decay, a U-spin relation between the decay amplitudes of B-s(0) -> K+K- and B-0 -> p(+)p(-) decay processes allows constraints to be placed on the angle gamma of the unitarity triangle and on the B-s(0) mixing phase -2 beta(s). Results from an extended approach, which uses additional inputs on B-0 -> pi(0)pi(0) and B+ -> pi(+)pi(0) decays from other experiments and exploits isospin symmetry, are also presented. The dependence of the results on the maximum allowed amount of U-spin breaking is studied. At 68% probability, the value gamma =( 63.5(-6.7)(+7.2))degrees modulo 180 degrees is determined. In an a…
Measurement of CP asymmetries in two-body B(s)0 -meson decays to charged pions and kaons
The time-dependent CP asymmetries in B0→π+π− and B0s→K+K− decays are measured using a data sample of p p collisions corresponding to an integrated luminosity of 3.0 fb−1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The same data sample is used to measure the time-integrated CP asymmetries in B0→K+π− and B0s→π+K− decays. The results are Cπ+π−=−0.34±0.06±0.01, Sπ+π−=−0.63±0.05±0.01, CK+K−=0.20±0.06±0.02, SK+K−=0.18±0.06±0.02, AΔΓK+K−=−0.79±0.07±0.10, AB0CP=−0.084±0.004±0.003, and AB0sCP=0.213±0.015±0.007, where the first uncertainties are statistical and the second systematic. Evidence for CP violation is found in the B0s→K+K− decay for the first time.
Quantum numbers of theX(3872)state and orbital angular momentum in itsρ0J/ψdecay
Angular correlations in B+→X(3872)K+ decays, with X(3872)→ρ0J/ψ, ρ0→π+π− and J/ψ→μ+μ−, are used to measure orbital angular momentum contributions and to determine the JPC value of the X(3872) meson. The data correspond to an integrated luminosity of 3.0 fb−1 of proton-proton collisions collected with the LHCb detector. This determination, for the first time performed without assuming a value for the orbital angular momentum, confirms the quantum numbers to be JPC=1++. The X(3872) is found to decay predominantly through S wave and an upper limit of 4% at 95% C.L. is set on the fraction of D wave.
Study ofCPviolation inB∓→Dh∓(h=K,π) with the modesD→K∓π±π0,D→π+π−π0andD→K+K−π0
An analysis of the decays of B--/+ -> DK -/+ and B--/+ -> D pi(-/+) is presented in which the D meson is reconstructed in the three-body final states K--/+pi(+/-)pi(0), pi(+)pi(-)pi(0) and K+K-pi(0). Using data from LHCb corresponding to an integrated luminosity of 3.0 fb(-1) of pp collisions, measurements of several CP observables are performed. First observations are obtained of the suppressed Atwood-Dunietz-Soni decay B--/+ -> [pi K-+(+/-)pi(0)](D)pi(-/+) and the quasi-Gronau-London-Wyler decay B--/+ -> [K+K-pi(0)](D)pi(-/+). The results are interpreted in the context of the unitarity triangle angle gamma and related parameters.
Observation of the rare B(s)(0) + decay from the combined analysis of CMS and LHCb data.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported licence.-- et al.
Amplitude analysis ofB+→J/ψϕK+decays
The first full amplitude analysis of B+→J/ψϕK+ with J/ψ→μ+μ−, ϕ→K+K− decays is performed with a data sample of 3 fb−1 of pp collision data collected at s√=7 and 8 TeV with the LHCb detector. The data cannot be described by a model that contains only excited kaon states decaying into ϕK+, and four J/ψϕ structures are observed, each with significance over 5 standard deviations. The quantum numbers of these structures are determined with significance of at least 4 standard deviations. The lightest is best described as a D±sD∗∓s cusp, but a resonant interpretation is also possible with mass consistent with, but width much larger than, previous measurements of the claimed X(4140) state. The mode…
Constraints on the unitarity triangle angleγfrom Dalitz plot analysis ofB0→DK+π−decays
The first study is presented of CP violation with an amplitude analysis of the Dalitz plot of B0→DK+π- decays, with D→K+π-, K+K-, and π+π-. The analysis is based on a data sample corresponding to 3.0 fb-1 of pp collisions collected with the LHCb detector. No significant CP violation effect is seen, and constraints are placed on the angle γ of the unitarity triangle formed from elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated with the B0→DK∗(892)0 decay are determined for the first time. These measurements can be used to improve the sensitivity to γ of existing and future studies of the B0→DK∗(892)0 decay.
Measurement of the Difference of Time-IntegratedCPAsymmetries inD0→K−K+andD0→π−π+Decays
A search for CP violation in $D^0 \rightarrow K^{-} K^{+} $ and $D^0 \rightarrow \pi^{-} \pi^{+} $ decays is performed using $pp$ collision data, corresponding to an integrated luminosity of $3~fb^{-1}$, collected using the LHCb detector at centre-of-mass energies of 7 and $8~$TeV. The flavour of the charm meson is inferred from the charge of the pion in $D^{*+}\rightarrow D^0\pi^+$ and $D^{*-}\rightarrow \bar{D^0}\pi^{-}$ decays. The difference between the CP asymmetries in $D^0 \rightarrow K^{-} K^{+} $ and $D^0 \rightarrow \pi^{-} \pi^{+} $ decays, $\Delta A_{CP} \equiv A_{CP}(K^{-} K^{+}) - A_{CP}(\pi^{-} \pi^{+})$, is measured to be $\left( -0.10 \pm 0.08(stat) \pm 0.03(syst) \right) \…
Amplitude analysis ofB−→D+π−π−decays
The Dalitz plot analysis technique is used to study the resonant substructures of $B^{-} \to D^{+} \pi^{-} \pi^{-}$ decays in a data sample corresponding to 3.0 ${\rm fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. A model-independent analysis of the angular moments demonstrates the presence of resonances with spins 1, 2 and 3 at high $D^{+}\pi^{-}$ mass. The data are fitted with an amplitude model composed of a quasi-model-independent function to describe the $D^{+}\pi^{-}$ S-wave together with virtual contributions from the $D^{*}(2007)^{0}$ and $B^{*0}$ states, and components corresponding to the $D^{*}_{2}(2460)^{0}$, $D^{*}_{1}(2680)^{0}$, $D^{*}_…
Observation of Bc+→J/ψD(*)K(*) decays
A search for the decays B + c → J / ψ D ( * ) 0 K + and B + c → J / ψ D ( * ) + K * 0 is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of 3 fb − 1 . The decays B + c → J / ψ D 0 K + and B + c → J / ψ D * 0 K + are observed for the first time, while first evidence is reported for the B + c → J / ψ D * + K * 0 and B + c → J / ψ D + K * 0 decays. The branching fractions of these decays are determined relative to the B + c → J / ψ π + decay. The B + c mass is measured, using the J / ψ D 0 K + final state, to be 6274.28 ± 1.40 ( stat ) ± 0.32 ( syst ) MeV / c 2 . This is the most precise single measurement of the B + c mass to date.
Study of J/ψ Production in Jets
The production of $J/\psi$ mesons in jets is studied in the forward region of proton-proton collisions using data collected with the LHCb detector at a center-of-mass energy of 13 TeV. The fraction of the jet transverse momentum carried by the $J/\psi$ meson, $z \equiv p_{\rm T}(J/\psi)/p_{\rm T}({\rm jet})$, is measured using jets with $p_{\rm T}({\rm jet}) > 20$ GeV in the pseudorapidity range $2.5 < \eta({\rm jet}) < 4.0$. The observed $z$ distribution for $J/\psi$ mesons produced in $b$-hadron decays is consistent with expectations. However, the results for prompt $J/\psi$ production do not agree with predictions based on fixed-order non-relativistic QCD. This is the first measurement o…
Observation of Two NewΞb−Baryon Resonances
Two structures are observed close to the kinematic threshold in the Ξb0π- mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0fb-1, recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content bds are expected in this mass region: the spin-parity JP=(1/2)+ and JP=(3/2)+ states, denoted Ξb′- and Ξb∗-. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be m(Ξb′-)-m(Ξb0)-m(π-)=3.653±0.018±0.006MeV/c2, m(Ξb∗-)-m(Ξb0)-m(π-)=23.96±0.12±0.06MeV/c2, Γ(Ξb∗-)=1.65±0.31±0.10MeV, where the first and second uncertainties are statistical and systema…
Measurements of charm mixing and CP violation using D0→K±π∓ decays
Measurements of charm mixing and CP violation parameters from the decay-time-dependent ratio of D0→K+π− to D0→K−π+ decay rates and the charge-conjugate ratio are reported. The analysis uses B¯¯¯¯→D∗+μ−X, and charge-conjugate decays, where D∗+→D0π+, and D0→K∓π±. The pp collision data are recorded by the LHCb experiment at center-of-mass energies s√ = 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb−1. The data are analyzed under three hypotheses: (i) mixing assuming CP symmetry, (ii) mixing assuming no direct CP violation in the Cabibbo-favored or doubly Cabibbo-suppressed decay amplitudes, and (iii) mixing allowing either direct CP violation and/or CP violation in the superpos…