# Posts Tagged upper bound

## Recent Postings from upper bound

### Upper Bound on the Gluino Mass in Supersymmetric Models with Extra Matters

We discuss the upper bound on the gluino mass in supersymmetric models with vector-like extra matters. In order to realize the observed Higgs mass of 125 GeV, the gluino mass is bounded from above in supersymmetric models. With the existence of the vector-like extra matters at around TeV, we show that such an upper bound on the gluino mass is significantly reduced compared to the case of minimal supersymmetric standard model. This is due to the fact that radiatively generated stop masses as well the stop trilinear coupling are enhanced in the presence of the vector-like multiplets. In a wide range of parameter space of the model with extra matters, the gluino is required to be lighter than $\sim 3$ TeV, which is likely to be within the reach of forthcoming LHC experiment.

### Upper Bound on the Gluino Mass in Supersymmetric Models with Extra Matters [Replacement]

We discuss the upper bound on the gluino mass in supersymmetric models with vector-like extra matters. In order to realize the observed Higgs mass of 125 GeV, the gluino mass is bounded from above in supersymmetric models. With the existence of the vector-like extra matters at around TeV, we show that such an upper bound on the gluino mass is significantly reduced compared to the case of minimal supersymmetric standard model. This is due to the fact that radiatively generated stop masses as well the stop trilinear coupling are enhanced in the presence of the vector-like multiplets. In a wide range of parameter space of the model with extra matters, the gluino is required to be lighter than $\sim 3$ TeV, which is likely to be within the reach of forthcoming LHC experiment.

### Upper Bound on the Gluino Mass in Supersymmetric Models with Extra Matters [Replacement]

We discuss the upper bound on the gluino mass in supersymmetric models with vector-like extra matters. In order to realize the observed Higgs mass of 125 GeV, the gluino mass is bounded from above in supersymmetric models. With the existence of the vector-like extra matters at around TeV, we show that such an upper bound on the gluino mass is significantly reduced compared to the case of minimal supersymmetric standard model. This is due to the fact that radiatively generated stop masses as well the stop trilinear coupling are enhanced in the presence of the vector-like multiplets. In a wide range of parameter space of the model with extra matters, the gluino is required to be lighter than $\sim 3$ TeV, which is likely to be within the reach of forthcoming LHC experiment.

### Bootstrap bound for conformal multi-flavor QCD on lattice [Cross-Listing]

The recent work by Iha et al shows an upper bound on mass anomalous dimension $\gamma_m$ of multi-flavor massless QCD at the renormalization group fixed point from the conformal bootstrap in $SU(N_F)_V$ symmetric conformal field theories under the assumption that the fixed point is realizable with the lattice regularization based on staggered fermions. We show that the almost identical but slightly stronger bound applies to the regularization based on Wilson fermions (or domain wall fermions) by studying the conformal bootstrap in $SU(N_f)_L \times SU(N_f)_R$ symmetric conformal field theories. For $N_f=8$, our bound implies $\gamma_m < 1.31$ to avoid dangerously irrelevant operators that are not compatible with the lattice symmetry.

### Bootstrap bound for conformal multi-flavor QCD on lattice

The recent work by Iha et al shows an upper bound on mass anomalous dimension $\gamma_m$ of multi-flavor massless QCD at the renormalization group fixed point from the conformal bootstrap in $SU(N_F)_V$ symmetric conformal field theories under the assumption that the fixed point is realizable with the lattice regularization based on staggered fermions. We show that the almost identical but slightly stronger bound applies to the regularization based on Wilson fermions (or domain wall fermions) by studying the conformal bootstrap in $SU(N_f)_L \times SU(N_f)_R$ symmetric conformal field theories. For $N_f=8$, our bound implies $\gamma_m < 1.31$ to avoid dangerously irrelevant operators that are not compatible with the lattice symmetry.

### Memory Effect in Upper Bound of Heat Flux Induced by Quantum Fluctuations [Replacement]

Thermodynamic behaviors in a quantum Brownian motion coupled to a classical heat bath is studied. We then define a heat operator by generalizing the stochastic energetics and show the energy balance (first law) and the upper bound of the expectation value of the heat operator (second law). We further find that this upper bound depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics.

### Memory Effect in Upper Bound of Heat Flux Induced by Quantum Fluctuations [Cross-Listing]

We develop a model of quantum open systems as a quantum Brownian motion coupled to a classical heat bath by introducing a mathematical definition of operator differentials. We then define a heat operator by extending the stochastic energetics and show that this operator satisfies properties corresponding to the first and second laws in thermodynamics. We further find that the upper bound of the heat flux depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics.

### Memory Effect in Upper Bound of Heat Flux Induced by Quantum Fluctuations [Replacement]

We develop a model of quantum open systems as a quantum Brownian motion coupled to a classical heat bath by introducing a mathematical definition of operator differentials. We then define a heat operator by extending the stochastic energetics and show that this operator satisfies properties corresponding to the first and second laws in thermodynamics. We further find that the upper bound of the heat flux depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics.

### Generalized upper bound for inelastic diffraction [Replacement]

For the inelastic diffraction, we obtain an upper bound valid in the whole range of the elastic scattering amplitude variation allowed by unitarity. We discuss the energy dependence of the inelastic diffractive cross-section on the base of this bound and recent LHC data.

### A generalized upper bound for inelastic diffraction

For the inelastic diffraction, we obtain an upper bound valid in the whole range of the elastic scattering amplitude variation allowed by unitarity. We discuss the energy dependence of the inelastic diffractive cross-section on the base of this bound and recent LHC data.

### Limits on CPT violation from solar neutrinos

Violations of CPT invariance can induce neutrino-to-antineutrino transitions. We study this effect for solar neutrinos and use the upper bound on the solar neutrino-to-antineutrino transition probability from the KamLAND experiment to constrain CPT-symmetry-violating coefficients of the general Standard-Model Extension. The long propagation distance from the Sun to the Earth allows us to improve existing limits by factors ranging from about a thousand to $10^{11}$.

### Limits on CPT violation from solar neutrinos [Replacement]

Violations of CPT invariance can induce neutrino-to-antineutrino transitions. We study this effect for solar neutrinos and use the upper bound on the solar neutrino-to-antineutrino transition probability from the KamLAND experiment to constrain CPT-symmetry-violating coefficients of the general Standard-Model Extension. The long propagation distance from the Sun to the Earth allows us to improve existing limits by factors ranging from about a thousand to $10^{11}$.

### The Upper Bound of Radiation Energy in the Myers-Perry Black Hole Collision [Replacement]

We have investigated the upper bound of the radiation energy in the head-on collision of two Myers-Perry black holes. Initially, the two black holes are far away from each other, and they become one black hole after the collision. We have obtained the upper bound of the radiation energy thermodynamically allowed in the process. The upper bound of the radiation energy is obtained in general dimensions. The radiation bound depends on the alignments of rotating axes for a given initial condition due to spin-spin interaction. We have found that the collision may not be occurred for a initially ultra-spinning black hole.

### The Upper Bound of Radiation Energy in the Myers-Perry Black Hole Collision [Replacement]

We have investigated the upper bound of the radiation energy in the head-on collision of two Myers-Perry black holes. Initially, the two black holes are far away from each other, and they become one black hole after the collision. We have obtained the upper bound of the radiation energy thermodynamically allowed in the process. The upper bound of the radiation energy is obtained in general dimensions. The radiation bound depends on the alignments of rotating axes for a given initial condition due to spin-spin interaction. We have found that the collision may not be occurred for a initially ultra-spinning black hole.

### The Upper Bound of Radiation Energy in the Myers-Perry Black Hole Collision

We have investigated the upper bound of the radiation energy in the head-on collision of two Myers-Perry black holes. Initially, the two black holes are far away from each other, and they become one black hole after the collision. We have obtained the upper bound of the radiation energy thermodynamically allowed in the process. The upper bound of the radiation energy is obtained in general dimensions. The radiation bound depends on the alignments of rotating axes for a given initial condition due to spin-spin interaction. We have found that the collision may not be occurred for a initially ultra-spinning black hole.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories -- a conformal bootstrap approach [Cross-Listing]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of~$SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator if the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.63$. Considering the lattice simulation of the many-flavor QCD with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor breaking effect of the staggered fermion and would prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.37$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories -- a conformal bootstrap approach [Replacement]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of the $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of the many-flavor QCD with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also found a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories -- a conformal bootstrap approach [Replacement]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of the $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of the many-flavor QCD with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also found a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories -- a conformal bootstrap approach [Replacement]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of the $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of the many-flavor QCD with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also found a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach [Replacement]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of many-flavor quantum chromodynamics with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach [Replacement]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of many-flavor quantum chromodynamics with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories -- a conformal bootstrap approach [Cross-Listing]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of~$SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator if the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.63$. Considering the lattice simulation of the many-flavor QCD with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor breaking effect of the staggered fermion and would prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.37$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy.

### Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach [Replacement]

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$\phi_i^{\Bar{k}}$ which belongs to the adjoint representation of $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$\phi_i^{\Bar{k}}$, $\Delta_{\phi_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of many-flavor quantum chromodynamics with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$\gamma_m^*\leq1.29$ from the relation~$\gamma_m^*=3-\Delta_{\phi_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

### An upper bound on the reheat temperature for short duration inflation

We calculate the upper bound on the reheating temperature given the non-observation of gravitational waves if the number of efolds during inflation are the minimum number required to address the horizon problem as formulated in terms of entropy. This bound is valid for canonical single field slow roll inflation with a generic potential. Our bound numerically is $T_{\text{reh}}\lesssim1.7\times10^{13}$ GeV, which is a factor of 428 less the usual bound one obtains from the non-observation of gravitational waves alone. If inflation lasted much longer than the minimum number of required efolds, our bound relaxes to coincide with the usual bound. We discuss the relevance for studies of primordial black holes.

### An upper bound on the reheat temperature for short duration inflation [Replacement]

We calculate the upper bound on the reheating temperature given the non-observation of gravitational waves if the number of efolds during inflation are the minimum number required to address the horizon problem as formulated in terms of entropy. This bound is valid for canonical single field slow roll inflation with a generic potential. Our bound numerically is $T_{\text{reh}}\lesssim1.7\times10^{13}$ GeV, which is a factor of 428 less the usual bound one obtains from the non-observation of gravitational waves alone. If inflation lasted much longer than the minimum number of required efolds, our bound relaxes to coincide with the usual bound. We discuss the relevance for studies of primordial black holes.

### Upper bound of the $N(1440) \rightarrow N(939) + \pi$ decay width obtained from a three-flavor parity doublet model

We study masses and decay widths of positive and negative parity nucleons using a three-flavor parity doublet model, in which we introduce three representations, $\left[({\bf 3} , \bar{{\bf 3}})\oplus (\bar{{\bf 3}} , {\bf 3})\right]$, $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$, and $\left[({\bf 8} , {\bf 1}) \oplus ({\bf 1} , {\bf 8})\right]$ of the chiral U$(3)_{\rm L}\times$ U$(3)_{\rm R}$ symmetry. We find an extended version of the Goldberger-Treiman relation among the mass differences and the coupling constants for pionic transitions. This relation leads to an upper bound for the decay width of $N(1440) \rightarrow N(939) + \pi$ independently of the model parameters. We perform the numerical fitting of the model parameters and derive several predictions, which can be tested in future experiments or lattice QCD analysis. Furthermore, when we use the axial coupling of the excited nucleons obtained from lattice QCD analyses, we also find that the ground state nucleon $N(939)$ consists of about 80% of $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$ component and about 20% of $\left[({\bf 8} , {\bf 1}) \oplus ({\bf 1} , {\bf 8})\right]$ component, and that the chiral invariant mass of $N(939)$ is about $250$ MeV.

### Constraints on just enough inflation preceded by a thermal era [Replacement]

If the inflationary era is preceded by a radiation dominated era in which the inflaton too was in thermal equilibrium at some very early time then the CMB data places an upper bound on the comoving temperature of the (decoupled) inflaton quanta. In addition, if one considers models of "just enough" inflation, where the number of e-foldings of inflation is just enough to solve the horizon and flatness problems, then we get a lower bound on the Hubble parameter during inflation, $H_{\rm inf}$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\rm inf}$ implies that such scenarios are compatible with the data only if the number of relativistic degrees of freedom in the thermal bath in the pre-inflationary Universe is extremely large (greater than $10^9$ or $10^{11})$. We are not aware of scenarios in which this can be satisfied.

### Constraints on just enough inflation preceded by a thermal era [Replacement]

If the inflationary era is preceded by a radiation dominated era in which the inflaton too was in thermal equilibrium at some very early time then the CMB data places an upper bound on the comoving temperature of the (decoupled) inflaton quanta. In addition, if one considers models of "just enough" inflation, where the number of e-foldings of inflation is just enough to solve the horizon and flatness problems, then we get a lower bound on the Hubble parameter during inflation, $H_{\rm inf}$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\rm inf}$ implies that such scenarios are compatible with the data only if the number of relativistic degrees of freedom in the thermal bath in the pre-inflationary Universe is extremely large (greater than $10^9$ or $10^{11})$. We are not aware of scenarios in which this can be satisfied.

### Constraints on just enough inflation preceded by a thermal era [Replacement]

If the inflationary era is preceded by a radiation dominated era in which the inflaton too was in thermal equilibrium at some very early time then the CMB data places an upper bound on the comoving temperature of the (decoupled) inflaton quanta. In addition, if one considers models of "just enough" inflation, where the number of e-foldings of inflation is just enough to solve the horizon and flatness problems, then we get a lower bound on the Hubble parameter during inflation, $H_{\rm inf}$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\rm inf}$ implies that such scenarios are compatible with the data only if the number of relativistic degrees of freedom in the thermal bath in the pre-inflationary Universe is extremely large (greater than $10^9$ or $10^{11})$. We are not aware of scenarios in which this can be satisfied.

### Constraints on just enough inflation preceded by a thermal era [Replacement]

If the inflationary era is preceded by a radiation dominated era in which the inflaton too was in thermal equilibrium at some very early time then the CMB data places an upper bound on the comoving temperature of the (decoupled) inflaton quanta. In addition, if one considers models of "just enough" inflation, where the number of e-foldings of inflation is just enough to solve the horizon and flatness problems, then we get a lower bound on the Hubble parameter during inflation, $H_{\rm inf}$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\rm inf}$ implies that such scenarios are compatible with the data only if the number of relativistic degrees of freedom in the thermal bath in the pre-inflationary Universe is extremely large (greater than $10^9$ or $10^{11})$. We are not aware of scenarios in which this can be satisfied.

### An Upper Bound on Neutron Star Masses from Models of Short Gamma-ray Bursts [Replacement]

The discovery of two neutron stars with gravitational masses $\approx 2~M_\odot$ has placed a strong lower limit on the maximum mass of nonrotating neutron stars, and with it a strong constraint on the properties of cold matter beyond nuclear density. Current upper mass limits are much looser. Here we note that, if most short gamma-ray bursts are produced by the coalescence of two neutron stars, and if the merger remnant collapses quickly, then the upper mass limit is constrained tightly. If the rotation of the merger remnant is limited only by mass-shedding (which seems probable based on numerical studies), then the maximum gravitational mass of a nonrotating neutron star is $\approx 2-2.2~M_\odot$ if the masses of neutron stars that coalesce to produce gamma-ray bursts are in the range seen in Galactic double neutron star systems. These limits would be increased by $\sim 4$% in the probably unrealistic case that the remnants rotate at $\sim 30$% below mass-shedding, and by $\sim 15$% in the extreme case that the remnants do not rotate at all. Future coincident detection of short gamma-ray bursts with gravitational waves will strengthen these arguments because they will produce tight bounds on the masses of the components for individual events. If these limits are accurate then a reasonable fraction of double neutron star mergers might not produce gamma-ray bursts. In that case, or in the case that many short bursts are produced instead by the mergers of neutron stars with black holes, the implied rate of gravitational wave detections will be increased.

### An Upper Bound on Neutron Star Masses from Models of Short Gamma-ray Bursts

The discovery of two neutron stars with gravitational masses $\approx 2~M_\odot$ has placed a strong lower limit on the maximum mass of a slowly rotating neutron star, and with it a strong constraint on the properties of cold matter beyond nuclear density. Current upper mass limits are much looser. Here we note that, if most short gamma-ray bursts are produced by the coalescence of two neutron stars, and if the merger remnant collapses quickly, then the upper mass limit is constrained tightly. We find that if the rotation of the merger remnant is limited only by mass-shedding (which seems plausible based on current numerical studies), then the maximum gravitational mass of a slowly rotating neutron star is between $\approx 2~M_\odot$ and $\approx 2.2~M_\odot$ if the masses of neutron stars that coalesce to produce gamma-ray bursts are in the range seen in Galactic double neutron star systems. These limits are increased by $\sim 4$% if the rotation is slowed by $\sim 30$%, and by $\sim 15$% if the merger remnants do not rotate at all. Future coincident detection of short gamma-ray bursts with gravitational waves will strengthen these arguments because they will produce tight bounds on the masses of the components for individual events. If these limits are accurate then a reasonable fraction of double neutron star mergers might not produce gamma-ray bursts. In that case, or in the case that many short bursts are produced instead by the mergers of neutron stars with black holes, the implied rate of gravitational wave detections will be increased.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Replacement]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Cross-Listing]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Lyth bound revisited [Cross-Listing]

Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.

### Maximum mass of a barotropic spherical star [Cross-Listing]

The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl's bound to a lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease the Barraco-Hamity's bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.

### Maximum mass of a barotropic spherical star

The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl's bound to a lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease the Barraco-Hamity's bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.

### Froissart Bound on Inelastic Cross Section Without Unknown Constants

Assuming that axiomatic local field theory results hold for hadron scattering, Andr\'e Martin and S. M. Roy recently obtained absolute bounds on the D-wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ which is one-fourth of the corresponding upper bound on $\sigma_{tot}$, and Wu, Martin,Roy and Singh improved the bound by adding the constraint of a given $\sigma_{tot}$. Here we use unitarity and analyticity to determine, without any high energy approximation, upper bounds on energy averaged inelastic cross sections in terms of low energy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms,together with the Martin-Roy absolute bounds on pion-pion D-waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. E.g. for $\pi^0 \pi^0$ scattering, defining $\sigma_{inel}=\sigma_{tot} -\big (\sigma^{\pi^0 \pi^0 \rightarrow \pi^0 \pi^0} + \sigma^{\pi^0 \pi^0 \rightarrow \pi^+ \pi^-} \big )$,we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\bar{\sigma}_{inel }(s,\infty)\equiv s\int_{s} ^{\infty } ds'\sigma_{inel }(s')/s'^2 \leq (\pi /4) (m_{\pi })^{-2} [\ln (s/s_1)+(1/2)\ln \ln (s/s_1) +1]^2$ where $1/s_1= 34\pi \sqrt{2\pi }\>m_{\pi }^{-2}$ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor $s_1$ is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic $\pi^0 \pi^0$cross section has a bound of the same form with $1/s_1$ replaced by $1/s_2=2/s_1$.

### Froissart Bound on Inelastic Cross Section Without Unknown Constants [Replacement]

Assuming that axiomatic local field theory results hold for hadron scattering, Andr\'e Martin and S. M. Roy recently obtained absolute bounds on the D-wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ which is one-fourth of the corresponding upper bound on $\sigma_{tot}$, and Wu, Martin,Roy and Singh improved the bound by adding the constraint of a given $\sigma_{tot}$. Here we use unitarity and analyticity to determine, without any high energy approximation, upper bounds on energy averaged inelastic cross sections in terms of low energy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms,together with the Martin-Roy absolute bounds on pion-pion D-waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. E.g. for $\pi^0 \pi^0$ scattering, defining $\sigma_{inel}=\sigma_{tot} -\big (\sigma^{\pi^0 \pi^0 \rightarrow \pi^0 \pi^0} + \sigma^{\pi^0 \pi^0 \rightarrow \pi^+ \pi^-} \big )$,we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\bar{\sigma}_{inel }(s,\infty)\equiv s\int_{s} ^{\infty } ds'\sigma_{inel }(s')/s'^2 \leq (\pi /4) (m_{\pi })^{-2} [\ln (s/s_1)+(1/2)\ln \ln (s/s_1) +1]^2$ where $1/s_1= 34\pi \sqrt{2\pi }\>m_{\pi }^{-2}$ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor $s_1$ is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic $\pi^0 \pi^0$cross section has a bound of the same form with $1/s_1$ replaced by $1/s_2=2/s_1$.

### Perturbative Unitarity Constraints on Charged/Colored Portals

Dark matter that was once in thermal equilibrium with the Standard Model is generally prohibited from obtaining all of its mass from the electroweak or QCD phase transitions. This implies a new scale of physics and mediator particles needed to facilitate dark matter annihilations. In this work, we consider scenarios where thermal dark matter annihilates via scalar mediators that are colored and/or electrically charged. We show how partial wave unitarity places upper bounds on the masses and couplings on both the dark matter and mediators. To do this, we employ effective field theories with dark matter as well as three flavors of sleptons or squarks with minimum flavor violation. For Dirac (Majorana) dark matter that annihilates via mediators charged as left-handed sleptons, we find an upper bound around 45 TeV (7 TeV) for both the mediator and dark matter masses, respectively. These bounds vary as the square root of the number of colors times the number of flavors involved. Therefore the bounds diminish by root two for right handed selectrons. The bounds increase by root three and root six for right and left handed squarks, respectively. Finally, because of the interest in natural models, we also focus on an effective field theory with only stops. We find an upper bound around 32 TeV (5 TeV) for both the Dirac (Majorana) dark matter and stop masses. In comparison to traditional naturalness arguments, the stop bound gives a firmer, alternative expectation on when new physics will appear. Similar to naturalness, all of the bounds quoted above are valid outside of a defined fine-tuned regions where the dark matter can co-annihilate. The bounds in this region of parameter space can exceed the well-known bounds from Griest and Kamionkowski. We briefly describe the impact on planned and existing direct detection experiments and colliders.

### Boundaries on Neutrino Mass from Supernovae Neutronization Burst by Liquid Argon Experiments

This work presents an upper bound on the neutrino mass using the emission of $\nu_e$ from the neutronization burst of a core collapsing supernova at 10~kpc of distance and a progenitor star of 15~M$_\odot$. The calculations were done considering a 34 kton Liquid Argon Time Projection Chamber similar to the Far Detector proposal of the Long Baseline Neutrino Experiment (LBNE). We have performed a Monte Carlo simulation for the number of events integrated in 5~ms bins. Our results are $m_\nu<2.71$~eV and $0.18~\mbox{eV}<m_\nu<1.70$~eV, at 95\% C.L, assuming normal hierarchy and inverted hierarchy, respectively. We have analysed different configurations for the detector performance resulting in neutrino mass bound of $\mathcal{O}(1)$~eV.

### Anisotropic flow in pp-collisions at the LHC [Replacement]

We discuss collective effects in $pp$--collisions at the LHC energies and derive an upper bound for the anisotropic flow coefficients $v_n$. A possibility of its verification via comparison with the measurements of $v_2$ is considered. We use an assumption on the relation of the two--particle correlations with the rotation of the transient state of matter.

### Upper bounds on sparticle masses from muon g-2 and the Higgs mass and the complementarity of future colliders

Supersymmetric (SUSY) explanation of the discrepancy between the measurement of $(g-2)_\mu$ and its SM prediction puts strong upper bounds on the chargino and smuon masses. At the same time, lower experimental limits on the chargino and smuon masses, combined with the Higgs mass measurement, lead to an upper bound on the stop masses. The current LHC limits on the chargino and smuon masses (for not too compressed spectrum) set the upper bound on the stop masses of about 10 TeV. The discovery potential of the future lepton and hadron colliders should lead to the discovery of SUSY if it is responsible for the explanation of the $(g-2)_\mu$ anomaly. This conclusion follows from the fact that the upper bound on the stop masses decreases with the increase of the lower experimental limit on the chargino and smuon masses.

### Upper bounds on sparticle masses from muon g-2 and the Higgs mass and the complementarity of future colliders [Replacement]

Supersymmetric (SUSY) explanation of the discrepancy between the measurement of $(g-2)_\mu$ and its SM prediction puts strong upper bounds on the chargino and smuon masses. At the same time, lower experimental limits on the chargino and smuon masses, combined with the Higgs mass measurement, lead to an upper bound on the stop masses. The current LHC limits on the chargino and smuon masses (for not too compressed spectrum) set the upper bound on the stop masses of about 10 TeV. The discovery potential of the future lepton and hadron colliders should lead to the discovery of SUSY if it is responsible for the explanation of the $(g-2)_\mu$ anomaly. This conclusion follows from the fact that the upper bound on the stop masses decreases with the increase of the lower experimental limit on the chargino and smuon masses.

### Quantum Noise Limits in White-Light-Cavity-Enhanced Gravitational Wave Detectors [Replacement]

Previously, we had proposed a gravitational wave detector that incorporates the white light cavity (WLC) effect using a compound cavity for signal recycling (CC-SR). Here, we first use an idealized model for the negative dispersion medium (NDM), and use the Caves model for phase-insensitive linear amplifier to account for the quantum noise (QN) from the NDM, to determine the upper bound of the enhancement in the sensitivity-bandwidth product. We calculate the quantum noise limited sensitivity curves for the CC-SR design, and find that the broadening of sensitivity predicted by the classical analysis is also present in these curves, but is somewhat reduced. Furthermore, we find that the curves always stay above the standard quantum limit (SQL). To circumvent this limitation, we modify the dispersion to compensate the non-linear phase variation produced by the opto-mechanical (OM) resonance effects. We find that the upper bound of the factor by which the sensitivity-bandwidth product is increased, compared to the highest sensitivity result predicted by Bunanno and Chen [Phys. Rev. D 64, 042006 (2001)], is ~14. We also present a simpler scheme (WLC-SR) where a dispersion medium is inserted in the SR cavity. For this scheme, we found the upper bound of the enhancement factor to be ~18. We then consider an explicit system for realizing the NDM, which makes use of five energy levels in M-configuration to produce Gain, accompanied by Electromagnetically Induced Transparency (the GEIT system). For this explicit system, we employ the rigorous approach based on Master Equation (ME) to compute the QN contributed by the NDM, thus enabling us to determine the enhancement in the sensitivity-bandwidth product definitively rather than the upper bound thereof. Specifically, we identify a set of parameters for which the sensitivity-bandwidth product is enhanced by a factor of 17.66.

### Viscosity bound for anisotropic superfluids in higher derivative gravity [Replacement]

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy ratio corresponding to the superfluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature. This proves the non universality of shear viscosity to entropy ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the shear viscosity to entropy ratio seems to get modified due to the finite temperature effects.