Posts Tagged confidence level

Recent Postings from confidence level

First observation of the decay $B_{s}^{0} \to K_{S}^{0} K^{*}(892)^{0}$

A search for $B_{(s)}^{0} \to K_{S}^{0} K^{*}(892)^{0}$ decays is performed using $pp$ collision data, corresponding to an integrated luminosity of $1.0~\text{fb}^{-1}$, collected with the LHCb detector at a centre-of-mass energy of $7~\text{TeV}$. The $B_{s}^{0} \to K_{S}^{0} K^{*}(892)^{0}$ decay is observed for the first time, with a significance of 7.1 standard deviations. The branching fraction is measured to be \begin{equation*} \mathcal{B}(B_{s}^{0} \to K_{S}^{0} K^{*}(892)^{0}) = (10.9 \pm 2.5 \pm 1.2) \times 10^{-6},\\ \end{equation*} where the first uncertainty is statistical and the second is systematic. No evidence is found for the decay $B^{0} \to K_{S}^{0} K^{*}(892)^{0}$ and an upper limit is set on the branching fraction, $\mathcal{B}(B^{0} \to K_{S}^{0} K^{*}(892)^{0}) < 0.64 \ \times 10^{-6}, $ at $90\,\% $ confidence level. All results are consistent with Standard Model predictions.

Cosmological test using strong gravitational lensing systems

As one of the probes of universe, strong gravitational lensing systems allow us to compare different cosmological models and constrain vital cosmological parameters. This purpose can be reached from the dynamic and geometry properties of strong gravitational lensing systems, for instance, time-delay $\Delta\tau$ of images, the velocity dispersion $\sigma$ of the lensing galaxies and the combination of these two effects, $\Delta\tau/\sigma^2$. In this paper, in order to carry out one-on-one comparisons between $\Lambda$CDM universe and $R_h=ct$ universe, we use a sample containing 36 strong lensing systems with the measurement of velocity dispersion from the SLACS and LSD survey. Concerning the time-delay effect, 12 two-image lensing systems with $\Delta\tau$ are also used. In addition, Monte Carlo (MC) simulations are used to compare the efficiency of the three methods as mentioned above. From simulations, we estimate the number of lenses required to rule out one model at the $99.7\%$ confidence level. Comparing with constraints from $\Delta\tau$ and the velocity dispersion $\sigma$, we find that using $\Delta\tau/\sigma^2$ can improve the discrimination between cosmological models. Despite the independence tests of these methods reveal a correlation between $\Delta\tau/\sigma^2$ and $\sigma$, $\Delta\tau/\sigma^2$ could be considered as an improved method of $\sigma$ if more data samples are available.

Result of the search for neutrinoless double-$\beta$ decay in $^{100}$Mo with the NEMO-3 experiment

The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double $\beta$ ($0\nu\beta\beta$) decay. We report final results of a search for $0\nu\beta\beta$ decays with $6.914$ kg of $^{100}$Mo using the entire NEMO-3 data set with a detector live time of $4.96$ yr, which corresponds to an exposure of 34.3 kg$\cdot$yr. We perform a detailed study of the expected background in the $0\nu\beta\beta$ signal region and find no evidence of $0\nu\beta\beta$ decays in the data. The level of observed background in the $0\nu\beta\beta$ signal region $[2.8-3.2]$ MeV is $0.44 \pm 0.13$ counts/yr/kg, and no events are observed in the interval $[3.2-10]$ MeV. We therefore derive a lower limit on the half-life of $0\nu\beta\beta$ decays in $^{100}$Mo of $T_{1/2}(0\nu\beta\beta)> 1.1 \times 10^{24}$ yr at the $90\%$ Confidence Level, under the hypothesis of light Majorana neutrino exchange. Depending on the model used for calculating nuclear matrix elements, the limit for the effective Majorana neutrino mass lies in the range $\langle m_{\nu} \rangle < 0.33$–$0.62$ eV. We also report constraints on other lepton-number violating mechanisms for $0\nu\beta\beta$ decays.

Neutrino mass matrices with one texture zero and a vanishing neutrino mass

Assuming Majorana nature of neutrinos, we investigate the singular one texture zero neutrino mass matrices in the flavor basis. We find that for the normal mass ordering with $m_1=0$, all the six one texture zero classes are now ruled out at 3$\sigma$ confidence level, whereas for inverted mass ordering with $m_3=0$ only four classes out of total six can accommodate the latest neutrino oscillation data at 3$\sigma$ confidence level. Moreover, only two classes can accommodate the present data at 1$\sigma$ confidence level. We examine the phenomenological implications of the allowed classes for the effective Majorana mass, Dirac and Majorana CP-violating phases. Working within the framework of type-I seesaw mechanism, we present simple discrete Abelian symmetry models leading to all the phenomenologically allowed classes.

Search for $D^0\to\gamma\gamma$ and improved measurement of the branching fraction for $D^0 \to \pi^0\pi^0$ [Replacement]

Using $2.92$ fb$^{-1}$ of electron-positron annihilation data collected at $\sqrt{s} = 3.773$~GeV with the BESIII detector, we report the results of a search for the flavor-changing neutral current process $D^0\to\gamma\gamma$ using a double-tag technique. We find no signal and set an upper limit at $90\%$ confidence level for the branching fraction of $B(D^0\to\gamma\gamma) < 3.8\times10^{-6}$. We also investigate $D^0$-meson decay into two neutral pions, obtaining a branching fraction of $B(D^0\to\pi^0\pi^0) = (8.24\pm0.21(\text{stat.})\pm0.30(\text{syst.}))\times10^{-4}$, the most precise measurement to date and consistent with the current world average

Fine-structure constant constraints on dark energy [Cross-Listing]

We use astrophysical and atomic clock tests of the stability of the fine-structure constant $\alpha$, together with Type Ia supernova and Hubble parameter data, to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, $\zeta$, to the electromagnetic sector) the $\alpha$ variation. We show how current data tightly constrains a combination of $\zeta$ and the dark energy equation of state $w_0$. At the $95\%$ confidence level and marginalizing over $w_0$ we find $|\zeta|<5\times10^{-6}$, with the atomic clock tests dominating the constraints. The forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.

Fine-structure constant constraints on dark energy

We use astrophysical and atomic clock tests of the stability of the fine-structure constant $\alpha$, together with Type Ia supernova and Hubble parameter data, to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, $\zeta$, to the electromagnetic sector) the $\alpha$ variation. We show how current data tightly constrains a combination of $\zeta$ and the dark energy equation of state $w_0$. At the $95\%$ confidence level and marginalizing over $w_0$ we find $|\zeta|<5\times10^{-6}$, with the atomic clock tests dominating the constraints. The forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.

Fine-structure constant constraints on dark energy [Cross-Listing]

We use astrophysical and atomic clock tests of the stability of the fine-structure constant $\alpha$, together with Type Ia supernova and Hubble parameter data, to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, $\zeta$, to the electromagnetic sector) the $\alpha$ variation. We show how current data tightly constrains a combination of $\zeta$ and the dark energy equation of state $w_0$. At the $95\%$ confidence level and marginalizing over $w_0$ we find $|\zeta|<5\times10^{-6}$, with the atomic clock tests dominating the constraints. The forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.

Fine-structure constant constraints on dark energy [Cross-Listing]

We use astrophysical and atomic clock tests of the stability of the fine-structure constant $\alpha$, together with Type Ia supernova and Hubble parameter data, to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, $\zeta$, to the electromagnetic sector) the $\alpha$ variation. We show how current data tightly constrains a combination of $\zeta$ and the dark energy equation of state $w_0$. At the $95\%$ confidence level and marginalizing over $w_0$ we find $|\zeta|<5\times10^{-6}$, with the atomic clock tests dominating the constraints. The forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.

Are long gamma-ray bursts standard candles?

Gamma-ray bursts (GRBs) are widely proposed as an effective probe to trace the Hubble diagram of the Universe in high redshift range. However, the calibration of GRBs is not as easy as that of type-Ia supernovae (SNe Ia). Most calibrating methods at present take use one or some of the empirical luminosity corrections, e.g., Amati relation. One of the underlying assumptions of these calibrating methods is that the empirical correlation is universal over all redshifts. In this paper, we check to what extent this assumption holds. Assuming that SNe Ia exactly trace the Hubble diagram of the Universe, we re-investigate the Amati relation for low redshift ($z<1.4$) and high redshift ($z>1.4$) GRBs, respectively. It is found that the Amati relation of low-$z$ GRBs differs from that of high-$z$ GRBs at more than $3\sigma$ confidence level. This result is insensitive to cosmological models.

An efficient probe of the cosmological CPT violation

We develop an efficient method based on the linear regression algorithm to probe the cosmological CPT violation using the CMB polarisation data. We validate this method using simulated CMB data and apply it to recent CMB observations. We find that a combined data sample of BICEP1 and BOOMERanG 2003 favours a nonzero isotropic rotation angle at $2.3\sigma$ confidence level, ie, $\Delta\alpha=-3.3 \pm1.4$ deg (68% CL) with systematics included.

Testing the isotropy of the Universe by using the JLA compilation of type-Ia supernovae

We probe the possible anisotropy in the accelerated expanding Universe by using the JLA compilation of type-Ia supernovae. We constrain the amplitude and direction of anisotropy in the anisotropic cosmological models. For the dipole-modulated $\Lambda$CDM model, the anisotropic amplitude has an upper bound $D<1.04\times10^{-3}$ at the $68\%$ confidence level. Similar results are found in the dipole-modulated $w$CDM and CPL models. Our studies show that there are no significant evidence for the anisotropic expansion of the Universe. Thus the Universe is still well compatible with the isotropy.

Testing the isotropy of the Universe by using the JLA compilation of type-Ia supernovae [Cross-Listing]

We probe the possible anisotropy in the accelerated expanding Universe by using the JLA compilation of type-Ia supernovae. We constrain the amplitude and direction of anisotropy in the anisotropic cosmological models. For the dipole-modulated $\Lambda$CDM model, the anisotropic amplitude has an upper bound $D<1.04\times10^{-3}$ at the $68\%$ confidence level. Similar results are found in the dipole-modulated $w$CDM and CPL models. Our studies show that there are no significant evidence for the anisotropic expansion of the Universe. Thus the Universe is still well compatible with the isotropy.

Probe Higgs boson pair production via the $3 \ell 2 j$ + missing $E_T$ mode

We perform a detailed hadron-level study on the sensitivity of Higgs boson pair production via the $WW^{*}WW^{*}$ channel with the final state $3 \ell 2 j$ + missing $E_T$ at the LHC with the collision energy $\sqrt{S} = 14$ TeV and a future 100 TeV collider. To avoid the huge background from $pp \to Z W + \textrm{jets}$ processes, we confine to consider the four lepton patterns: $e^\pm e^\pm \mu^\mp $ and $\mu^\pm \mu^\pm e^\mp$. We propose a partial reconstruction method to determine the most reliable combination. After that, we examine a few crucial observables which can discriminate efficiently signal and background events, especially we notice that the observable $m_{\rm T2}$ is very efficient. For the LHC 14 TeV collisions, with an accumulated 3000 fb$^{-1}$ dataset, we find that the sensitivity of this mode can reach up to 1.5 $\sigma$ for the Standard Model and the triple coupling of Higgs boson $\lambda_3$ in the simplest effective theory can be constrained into the range [-1, 8] at $95\%$ confidence level; at a 100 TeV collider with the integrated luminosity 3000 fb$^{-1}$, the sensitivity can reach up to 13 $\sigma$ for the Standard Model and we find that all values of $\lambda_3$ in the effective theory can be covered up to 3$\sigma$ even without optimising signals. To precisely measure the triple coupling of Higgs boson $\lambda_3=1$ of the Standard Model at a 100 TeV collider, by using the invariant mass of three leptons which is robust to against the contamination of underlying events and pileup effects and by performing a $\chi^2$ analysis, we find that it can be determined into a range [0.8, 1.5] at $95\%$ confidence level.

Probe Higgs boson pair production via the $3 \ell 2 j$ + missing $E_T$ mode [Replacement]

We perform a detailed hadron-level study on the sensitivity of Higgs boson pair production via the $WW^{*}WW^{*}$ channel with the final state $3 \ell 2 j$ + missing $E_T$ at the LHC with the collision energy $\sqrt{S} = 14$ TeV and a future 100 TeV collider. To avoid the huge background from $pp \to Z W + \textrm{jets}$ processes, we confine to consider the four lepton patterns: $e^\pm e^\pm \mu^\mp $ and $\mu^\pm \mu^\pm e^\mp$. We propose a partial reconstruction method to determine the most reliable combination. After that, we examine a few crucial observables which can discriminate efficiently signal and background events, especially we notice that the observable $m_{\rm T2}$ is very efficient. For the LHC 14 TeV collisions, with an accumulated 3000 fb$^{-1}$ dataset, we find that the sensitivity of this mode can reach up to 1.5 $\sigma$ for the Standard Model and the triple coupling of Higgs boson $\lambda_3$ in the simplest effective theory can be constrained into the range [-1, 8] at $95\%$ confidence level; at a 100 TeV collider with the integrated luminosity 3000 fb$^{-1}$, the sensitivity can reach up to 13 $\sigma$ for the Standard Model and we find that all values of $\lambda_3$ in the effective theory can be covered up to 3$\sigma$ even without optimising signals. To precisely measure the triple coupling of Higgs boson $\lambda_3=1$ of the Standard Model at a 100 TeV collider, by using the invariant mass of three leptons which is robust to against the contamination of underlying events and pileup effects and by performing a $\chi^2$ analysis, we find that it can be determined into a range [0.8, 1.5] at $95\%$ confidence level.

Testing Cosmological Models with Type Ic Super Luminous Supernovae

The use of type Ic Super Luminous Supernovae (SLSN Ic) to examine the cosmological expansion introduces a new standard ruler with which to test theoretical models. The sample suitable for this kind of work now includes 11 SLSNe Ic, which have thus far been used solely in tests involving $\Lambda$CDM. In this paper, we broaden the base of support for this new, important cosmic probe by using these observations to carry out a one-on-one comparison between the $R_{\rm h}=ct$ and $\Lambda$CDM cosmologies. We individually optimize the parameters in each cosmological model by minimizing the $\chi^{2}$ statistic. We also carry out Monte Carlo simulations based on these current SLSN Ic measurements to estimate how large the sample would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. The currently available sample indicates a likelihood of $\sim$$70-80\%$ that the $R_{\rm h}=ct$ Universe is the correct cosmology versus $\sim$$20-30\%$ for the standard model. These results are suggestive, though not yet compelling, given the current limited number of SLSNe Ic. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim$$240$ SLSNe Ic would be sufficient to rule out $R_{\rm h}=ct$ at this level of confidence, while $\sim$$480$ SLSNe Ic would be required to rule out $\Lambda$CDM if the real Universe is instead $R_{\rm h}=ct$. This difference in required sample size reflects the greater number of free parameters available to fit the data with $\Lambda$CDM. If such SLSNe Ic are commonly detected in the future, they could be a powerful tool for constraining the dark-energy equation of state in $\Lambda$CDM, and differentiating between this model and the $R_{\rm h}=ct$ Universe.

Probing Cosmological Isotropy With Type IA Supernovae [Cross-Listing]

We investigate the validity of the Cosmological Principle by mapping the cosmological parameters $H_0$ and $q_0$ through the celestial sphere. In our analysis, performed in a low-redshift regime to follow a model-independent approach, we use two compilations of type Ia Supernovae (SNe Ia), namely the Union2.1 and the JLA datasets. Firstly, we show that the angular distributions for both SNe Ia datasets are statistically anisotropic at high confidence level ($p$-value $<$ 0.0001), in particular the JLA sample. Then we find that the cosmic expansion and acceleration are mainly of dipolar type, with maximal anisotropic expansion [acceleration] pointing towards $(l,b) \simeq (326^{\circ},12^{\circ})$ [$(l,b) \simeq (174^{\circ},27^{\circ})$], and $(l,b) \simeq (58^{\circ},-60^{\circ})$ [$(l,b) \simeq (225^{\circ},51^{\circ})$] for the Union2.1 and JLA data, respectively. Secondly, we use a geometrical method to test the hypothesis that the non-uniformly distributed SNe Ia events could introduce anisotropic imprints on the cosmological expansion and acceleration. For the JLA compilation, we found significant correlations between the celestial distribution of data points and the directional studies of $H_0$ and $q_0$, suggesting that these results can be attributed to the intrinsic anisotropy of the sample. In the case of the Union2.1 data, nonetheless, these correlations are less pronounced, and we verify that the dipole asymmetry found in the $H_0$ analyses coincides with the well-known bulk-flow motion of our local group. From these analyses, we conclude that the directional asymmetry on the cosmological parameters maps are mainly either of local origin or due to celestial incompleteness of current SNe Ia samples.

Probing Cosmological Isotropy With Type IA Supernovae [Cross-Listing]

We investigate the validity of the Cosmological Principle by mapping the cosmological parameters $H_0$ and $q_0$ through the celestial sphere. In our analysis, performed in a low-redshift regime to follow a model-independent approach, we use two compilations of type Ia Supernovae (SNe Ia), namely the Union2.1 and the JLA datasets. Firstly, we show that the angular distributions for both SNe Ia datasets are statistically anisotropic at high confidence level ($p$-value $<$ 0.0001), in particular the JLA sample. Then we find that the cosmic expansion and acceleration are mainly of dipolar type, with maximal anisotropic expansion [acceleration] pointing towards $(l,b) \simeq (326^{\circ},12^{\circ})$ [$(l,b) \simeq (174^{\circ},27^{\circ})$], and $(l,b) \simeq (58^{\circ},-60^{\circ})$ [$(l,b) \simeq (225^{\circ},51^{\circ})$] for the Union2.1 and JLA data, respectively. Secondly, we use a geometrical method to test the hypothesis that the non-uniformly distributed SNe Ia events could introduce anisotropic imprints on the cosmological expansion and acceleration. For the JLA compilation, we found significant correlations between the celestial distribution of data points and the directional studies of $H_0$ and $q_0$, suggesting that these results can be attributed to the intrinsic anisotropy of the sample. In the case of the Union2.1 data, nonetheless, these correlations are less pronounced, and we verify that the dipole asymmetry found in the $H_0$ analyses coincides with the well-known bulk-flow motion of our local group. From these analyses, we conclude that the directional asymmetry on the cosmological parameters maps are mainly either of local origin or due to celestial incompleteness of current SNe Ia samples.

Probing Cosmological Isotropy With Type IA Supernovae

We investigate the validity of the Cosmological Principle by mapping the cosmological parameters $H_0$ and $q_0$ through the celestial sphere. In our analysis, performed in a low-redshift regime to follow a model-independent approach, we use two compilations of type Ia Supernovae (SNe Ia), namely the Union2.1 and the JLA datasets. Firstly, we show that the angular distributions for both SNe Ia datasets are statistically anisotropic at high confidence level ($p$-value $<$ 0.0001), in particular the JLA sample. Then we find that the cosmic expansion and acceleration are mainly of dipolar type, with maximal anisotropic expansion [acceleration] pointing towards $(l,b) \simeq (326^{\circ},12^{\circ})$ [$(l,b) \simeq (174^{\circ},27^{\circ})$], and $(l,b) \simeq (58^{\circ},-60^{\circ})$ [$(l,b) \simeq (225^{\circ},51^{\circ})$] for the Union2.1 and JLA data, respectively. Secondly, we use a geometrical method to test the hypothesis that the non-uniformly distributed SNe Ia events could introduce anisotropic imprints on the cosmological expansion and acceleration. For the JLA compilation, we found significant correlations between the celestial distribution of data points and the directional studies of $H_0$ and $q_0$, suggesting that these results can be attributed to the intrinsic anisotropy of the sample. In the case of the Union2.1 data, nonetheless, these correlations are less pronounced, and we verify that the dipole asymmetry found in the $H_0$ analyses coincides with the well-known bulk-flow motion of our local group. From these analyses, we conclude that the directional asymmetry on the cosmological parameters maps are mainly either of local origin or due to celestial incompleteness of current SNe Ia samples.

Hubble Space Telescope observations of the NUV transit of WASP-12b

We present new observations of four closely-spaced NUV transits of the hot Jupiter-like exoplanet WASP-12b using HST/COS, significantly increasing the phase resolution of the observed NUV light curve relative to previous observations, while minimising the temporal variation of the system. We observe significant excess NUV absorption during the transit, with mean normalised in-transit fluxes of $F_\mathrm{norm}\simeq0.97$, i.e. $\simeq$2-5 $\sigma$ deeper than the optical transit level of $\simeq0.986$ for a uniform stellar disk (the exact confidence level depending on the normalisation method used). We further observe an asymmetric transit shape, such that the post-conjunction fluxes are overall $\simeq$2-3 $\sigma$ higher than pre-conjunction values, and characterised by rapid variations in count rate between the pre-conjunction and out of transit levels. We do not find evidence for an early ingress to the NUV transit as suggested by earlier HST observations. However, we show that the NUV count rate observed prior to the optical transit is highly variable, but overall $\simeq$2.2-3.0 $\sigma$ below the post-transit values and comparable in depth to the optical transit, possibly forming a variable region of NUV absorption from at least phase $\phi\simeq$0.83, limited by the data coverage.

No evidence for the blue-tilted power spectrum of relic gravitational waves [Cross-Listing]

In this paper, we constrain the tilt of the power spectrum of relic gravitational waves by combining the data from BICEP2/Keck array and Planck (BKP) and the Laser Interferometer Gravitational-Waves Observatory (LIGO). From the data of BKP B-modes, the constraint on the tensor tilt is $n_t=0.66^{+1.83}_{-1.44}$ at the $68%$ confidence level. By further adding the LIGO upper limit on the energy density of gravitational waves, the constraint becomes $n_t=-0.76^{+1.37}_{-0.52}$ at the $68%$ confidence level. We conclude that there is no evidence for a blue-tilted power spectrum of relic gravitational waves and either sign of the index of tensor power spectrum is compatible with the data.

No evidence for the blue-tilted power spectrum of relic gravitational waves [Cross-Listing]

In this paper, we constrain the tilt of the power spectrum of relic gravitational waves by combining the data from BICEP2/Keck array and Planck (BKP) and the Laser Interferometer Gravitational-Waves Observatory (LIGO). From the data of BKP B-modes, the constraint on the tensor tilt is $n_t=0.66^{+1.83}_{-1.44}$ at the $68%$ confidence level. By further adding the LIGO upper limit on the energy density of gravitational waves, the constraint becomes $n_t=-0.76^{+1.37}_{-0.52}$ at the $68%$ confidence level. We conclude that there is no evidence for a blue-tilted power spectrum of relic gravitational waves and either sign of the index of tensor power spectrum is compatible with the data.

No evidence for the blue-tilted power spectrum of relic gravitational waves

In this paper, we constrain the tilt of the power spectrum of relic gravitational waves by combining the data from BICEP2/Keck array and Planck (BKP) and the Laser Interferometer Gravitational-Waves Observatory (LIGO). From the data of BKP B-modes, the constraint on the tensor tilt is $n_t=0.66^{+1.83}_{-1.44}$ at the $68%$ confidence level. By further adding the LIGO upper limit on the energy density of gravitational waves, the constraint becomes $n_t=-0.76^{+1.37}_{-0.52}$ at the $68%$ confidence level. We conclude that there is no evidence for a blue-tilted power spectrum of relic gravitational waves and either sign of the index of tensor power spectrum is compatible with the data.

No evidence for the blue-tilted power spectrum of relic gravitational waves [Cross-Listing]

In this paper, we constrain the tilt of the power spectrum of relic gravitational waves by combining the data from BICEP2/Keck array and Planck (BKP) and the Laser Interferometer Gravitational-Waves Observatory (LIGO). From the data of BKP B-modes, the constraint on the tensor tilt is $n_t=0.66^{+1.83}_{-1.44}$ at the $68%$ confidence level. By further adding the LIGO upper limit on the energy density of gravitational waves, the constraint becomes $n_t=-0.76^{+1.37}_{-0.52}$ at the $68%$ confidence level. We conclude that there is no evidence for a blue-tilted power spectrum of relic gravitational waves and either sign of the index of tensor power spectrum is compatible with the data.

Nonparametric test of consistency between cosmological models and multiband CMB measurements

We present a novel approach to test the consistency of the cosmological models with multiband CMB data using a nonparametric approach. In our analysis we calibrate the REACT (Risk Estimation and Adaptation after Coordinate Transformation) confidence levels associated with distances in function space (confidence distances) based on the Monte Carlo simulations in order to test the consistency of an assumed cosmological model with observation. To show the applicability of our algorithm, we confront Planck 2013 temperature data with concordance model of cosmology considering two different Planck spectra combination. In order to have an accurate quantitative statistical measure to compare between the data and the theoretical expectations, we calibrate REACT confidence distances and perform a bias control using many realizations of the data. Our results in this work using Planck 2013 temperature data put the best fit $\Lambda$CDM model at $95\% (\sim 2\sigma)$ confidence distance from the center of the nonparametric confidence set which hints towards considerable inconsistency. Repeating the analysis excluding the Planck $217 \times 217$ GHz spectrum data, the best fit $\Lambda$CDM model shifts to $70\% (\sim 1\sigma)$ confidence distance from the center of the nonparametric confidence set. The most prominent features in the data deviating from the best fit $\Lambda$CDM model seems to be at low multipoles $ 18 < \ell < 26$ at greater than $2\sigma$, $\ell \sim 750$ at $\sim1$ to $2\sigma$ and $\ell \sim 1800$ at greater than $2\sigma$ level. Excluding the $217\times217$ GHz spectrum the feature at $\ell \sim 1800$ becomes substantially less significance at $\sim1$ to $2 \sigma$ confidence level. Results of our analysis based on the new approach we propose in this work are in agreement with other analysis done using alternative methods.

Nonparametric test of consistency between cosmological models and multiband CMB measurements [Replacement]

We present a novel approach to test the consistency of the cosmological models with multiband CMB data using a nonparametric approach. In our analysis we calibrate the REACT (Risk Estimation and Adaptation after Coordinate Transformation) confidence levels associated with distances in function space (\textit{confidence distances}) based on the Monte Carlo simulations in order to test the consistency of an assumed cosmological model with observation. To show the applicability of our algorithm, we confront Planck 2013 temperature data with concordance model of cosmology considering two different Planck spectra combination. In order to have an accurate quantitative statistical measure to compare between the data and the theoretical expectations, we calibrate REACT confidence distances and perform a bias control using many realizations of the data. Our results in this work using Planck 2013 temperature data put the best fit $\Lambda$CDM model at $95\% (\sim 2\sigma)$ confidence distance from the center of the nonparametric confidence set while repeating the analysis excluding the Planck $217 \times 217$ GHz spectrum data, the best fit $\Lambda$CDM model shifts to $70\% (\sim 1\sigma)$ confidence distance. The most prominent features in the data deviating from the best fit $\Lambda$CDM model seems to be at low multipoles $ 18 < \ell < 26$ at greater than $2\sigma$, $\ell \sim 750$ at $\sim1$ to $2 \sigma$ and $\ell \sim 1800$ at greater than $2\sigma$ level. Excluding the $217\times217$ GHz spectrum the feature at $\ell \sim 1800$ becomes substantially less significance at $\sim1$ to $2 \sigma$ confidence level. Results of our analysis based on the new approach we propose in this work are in agreement with other analysis done using alternative methods.

Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity's rainbow scenario [Cross-Listing]

We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$ and energy scale $M$ in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\%$ confidence level.

Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity's rainbow scenario [Replacement]

We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$ and energy scale $M$ in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\%$ confidence level.

Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity's rainbow scenario [Replacement]

We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$ and energy scale $M$ in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\%$ confidence level.

Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity's rainbow scenario [Replacement]

We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$ and energy scale $M$ in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\%$ confidence level.

Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity's rainbow scenario [Cross-Listing]

We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$ and energy scale $M$ in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\%$ confidence level.

Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity's rainbow scenario

We propose the gravity’s rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$ and energy scale $M$ in the gravity’s rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at the $68\%$ confidence level.

Is there a population of unidentified gamma-ray sources distributed along the super-galactic plane?

The distribution on the sky of unidentified sources at the highest energies where such a population is evident is investigated. For this purpose, sources without identification in the first Fermi-LAT catalog >10 GeV (1FHL) that are good candidates for detection above the 50-100 GeV regime are selected. The distributions of these objects around the Galactic and super-galactic plane are explored. By using a Kolmogorov-Smirnov test it is examined if these sources are distributed homogeneously around these planes. Surprisingly, an indication for an inhomogeneous distribution is found for the case of the super-galactic plane where a homogeneous distribution can be excluded by a confidence level of 95%. On a 90% confidence level also a homogeneous distribution of sources around the Galactic plane can be excluded. For the hypothesis that this reflects the true distribution of sources rather than a statistical fluctuation, implications for the underlying source populations are discussed.

Dimension-six anomalous $tq\gamma$ couplings in $\gamma \gamma$ collision at the LHC

We have investigated the flavor changing top quark physics on the dimension-six anomalous $tq\gamma$ ($q=u,c$) couplings through the process $pp\to p\gamma \gamma p\to p t\bar{q}p$ at the LHC by considering different forward detector acceptances. In this paper, we have taken into account and examine the effects of top quark decay. The sensitivity bounds on the anomalous couplings and, $t\to q\gamma$ branching ratio have been obtained at the $95\%$ confidence level for the effective lagrangian approach. Besides, we have investigated the effect of the anomalous couplings on single top quark spin asymmetry.

Dimension-six anomalous $tq\gamma$ couplings in $\gamma \gamma$ collision at the LHC [Replacement]

We have investigated the flavor changing top quark physics on the dimension-six anomalous $tq\gamma$ ($q=u,c$) couplings through the process $pp\to p\gamma \gamma p\to p t\bar{q}p$ at the LHC by considering different forward detector acceptances. In this paper, we have taken into account and examine the effects of top quark decay. The sensitivity bounds on the anomalous couplings and, $t\to q\gamma$ branching ratio have been obtained at the $95\%$ confidence level for the effective lagrangian approach. Besides, we have investigated the effect of the anomalous couplings on single top quark spin asymmetry.

Very Weak Primordial Gravitational Waves Signal from BICEP2 and Planck HFI 353GHz Dust Polarization

The dust polarization is parameterized as a power law form of the multipole $l$: $D^{XX}_{l}=A^{XX}l(l+1)l^{\alpha_{XX}}/(2\pi)$ ($XX$ denotes $BB$ or $EE$), where $A^{XX}$ is its amplitude with the ratio $A^{BB}/A^{EE}=0.52\pm 0.02$ and $\alpha_{BB,EE}=-2.42\pm 0.02$. Extrapolating to $150$GHz from $353$GHz yields a value of $D^{BB}_{l=80}=(1.32\pm 0.29)\times 10^{-2}\mu K^2$ (and an additional uncertainty $(+0.28,-0.24)\times 10^{-2}\mu K^2$) over the range $40<l<120$. Based on these data, in this brief paper, we report the tensor-to-scalar ratio $r=A_{t}/A_{s}$ defined at $k_0=0.05 \text{Mpc} ^{-1}$ by joining the BICEP2+{\it Planck}2013+WMAP9+BAO+HST and {\it Planck} HFI $353$GHz dust polarization and its implication to the detection of the primordial gravitational waves. Considering the $\Lambda$CDM+$r$ model, we found $r<0.108$ at $95\%$ confidence level with $\sigma_{stat}=0.29$ and $r<0.129$ at $95\%$ confidence level with $\sigma_{stat+extr}=0.29+0.28$. The results imply no significant evidence for the primordial gravitational waves in $1\sigma$ regions. However the post probability distribution of $r$ peaks at a small positive value. And $r$ moves to larger positive values when the extrapolation error bars are included. This might imply a very weak signal of the primordial gravitational waves. It also implies the crucial fact in calibrating the amplitude of the dust polarizations in detecting the primordial gravitational waves in the future.

Detecting Primordial Gravitational Waves Signal from BICEP2 and {\it Planck} HFI $353$GHz Dust Polarization [Replacement]

The dust polarization is parameterized as a power law form of the multipole $l$: $D^{XX}_{l}=A^{XX}l(l+1)l^{\alpha_{XX}}/(2\pi)$ ($XX$ denotes $BB$ or $EE$), where $A^{XX}$ is its amplitude with the ratio $A^{BB}/A^{EE}=0.52\pm 0.02$ and $\alpha_{BB,EE}=-2.42\pm 0.02$. Extrapolating to $150$GHz from $353$GHz yields a value of $D^{BB}_{l=80}=(1.32\pm 0.29)\times 10^{-2}\mu K^2$ (and an additional uncertainty $(+0.28,-0.24)\times 10^{-2}\mu K^2$) over the range $40<l<120$. Based on these data, we report the tensor-to-scalar ratio $r=A_{t}/A_{s}$ defined at $k_0=0.05 \text{Mpc} ^{-1}$ by joining the BICEP2+{\it Planck}2013+WMAP9+BAO+HST and {\it Planck} HFI $353$GHz dust polarization and its implication to the detection of the primordial gravitational waves. Considering the $\Lambda$CDM+$r$ model, we found $r<0.108$ at $95\%$ confidence level with $\sigma_{stat}=0.29$ and $r<0.129$ at $95\%$ confidence level with $\sigma_{stat+extr}=0.29+0.28$. The results imply no significant evidence for the primordial gravitational waves in $1\sigma$ regions. However the post probability distribution of $r$ peaks at a small positive value. And $r$ moves to larger positive values when the extrapolation error bars are included. This might imply a very weak signal of the primordial gravitational waves. It also implies the crucial fact in calibrating the amplitude of the dust polarizations in detecting the primordial gravitational waves in the future. When the running of the scalar spectral tilt is included, we found $r<0.079$ at $95\%$ confidence level with $\sigma_{stat}=0.29$ and $r=0.091_{-0.069}^{+0.042}$ at $95\%$ confidence level with $\sigma_{stat+extr}=0.29+0.28$. The later one implies the detection of the primordial gravitational waves in $1\sigma$ regions at the cost of decreasing the value of $D^{BB}_{l=80}$ to $0.67_{-0.25}^{+0.25}$.

Evidence of $\Upsilon(1S) \to J/\psi+\chi_{c1}$ and search for double-charmonium production in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays [Replacement]

Using data samples of $102\times10^6$ $\Upsilon(1S)$ and $158\times10^6$ $\Upsilon(2S)$ events collected with the Belle detector, a first experimental search has been made for double-charmonium production in the exclusive decays $\Upsilon(1S,2S)\rightarrow J/\psi(\psi’)+X$, where $X=\eta_c$, $\chi_{cJ} (J=~0,~1,~2)$, $\eta_c(2S)$, $X(3940)$, and $X(4160)$. No significant signal is observed in the spectra of the mass recoiling against the reconstructed $J/\psi$ or $\psi’$ except for the evidence of $\chi_{c1}$ production with a significance of $4.6\sigma$ for $\Upsilon(1S)\rightarrow J/\psi+\chi_{c1}$. The measured branching fraction $\BR(\Upsilon(1S)\rightarrow J/\psi+\chi_{c1})$ is $(3.90\pm1.21(\rm stat.)\pm0.23 (\rm syst.))\times10^{-6}$. The $90\%$ confidence level upper limits on the branching fractions of the other modes having a significance of less than $3\sigma$ are determined. These results are consistent with theoretical calculations using the nonrelativistic QCD factorization approach.

Evidence of $\Upsilon(1S) \to J/\psi+\chi_{c1}$ and search for double-charmonium production in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays [Cross-Listing]

Using data samples of $102\times10^6$ $\Upsilon(1S)$ and $158\times10^6$ $\Upsilon(2S)$ events collected with the Belle detector, a first experimental search has been made for double-charmonium production in the exclusive decays $\Upsilon(1S,2S)\rightarrow J/\psi(\psi’)+X$, where $X=\eta_c$, $\chi_{cJ} (J=~0,~1,~2)$, $\eta_c(2S)$, and $X(3940)$. No significant signal is observed in the spectra of the mass recoiling against the reconstructed $J/\psi$ or $\psi’$ except for the evidence of $\chi_{c1}$ production with a significance of $4.6\sigma$ for $\Upsilon(1S)\rightarrow J/\psi+\chi_{c1}$. The measured branching fraction $\BR(\Upsilon(1S)\rightarrow J/\psi+\chi_{c1})$ is $(3.98\pm1.24(\rm stat.)\pm0.22 (\rm syst.))\times10^{-6}$. The $90\%$ confidence level upper limits on the branching fractions of the other modes having a significance of less than $3\sigma$ are determined. These results are consistent with theoretical calculations using the nonrelativistic QCD factorization approach.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Cross-Listing]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at 95% confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.117$ at 95% confidence level. Our results imply that the chaotic inflation model is marginally disfavored at 95% confidence level. Especially, the $\half m^2\phi^2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Cross-Listing]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at 95% confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.117$ at 95% confidence level. Our results imply that the chaotic inflation model is marginally disfavored at 95% confidence level. Especially, the $\half m^2\phi^2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Cross-Listing]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at 95% confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.117$ at 95% confidence level. Our results imply that the chaotic inflation model is marginally disfavored at 95% confidence level. Especially, the $\half m^2\phi^2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

 

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