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Register a new userConsistency of Higgsplosion in Localizable QFT
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We show that large n-particle production rates derived in the semiclassical Higgsplosion limit of scalar field theoretical models with spontaneous symmetry breaking, are consistent with general principles of localizable quantum field theory. The strict localizability criterium of Jaffe defines quantum fields as operator-valued distributions acting on test functions that are localized in finite regions of space-time. The requirement of finite support of test functions in space-time ensures the causality property of QFT. The corresponding localizable fields need not be tempered distributions, and they fit well into the framework of local quantum field theory.
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In a scalar theory which we use as a simplified model for the Higgs sector, we adopt the semiclassical formalism of Son for computations of $n$-particle production cross-sections in the high-multiplicity $nto infty$ weak-coupling $lambda to 0$ regime with the value of $lambda n$ held fixed and large. The approach relies on the use of singular classical solutions to a certain boundary value problem. In the past this formalism has been successfully used and verified in computations of perturbative multi-particle processes at tree-level, and also at the next-to-leading order level in the small $lambda n$ expansion near the multi-particle mass threshold. We apply this singular solutions formalism in the regime of ultra-high multiplicities where $lambda n gg 1$, and compute the leading positive $sim n,sqrt{lambda n}$ contribution to the exponent of the multi-particle rate in this large $lambda n$ limit. The computation is carried out near the multi-particle mass threshold where the multiplicity $n$ approaches its maximal value allowed by kinematics. This calculation relies on the idea of Gorsky and Voloshin to use a thin wall approximation for the singular solutions that resemble critical bubbles. This approximation is justified in precisely the high-multiplicity $sqrt{lambda n} to infty$ regime of interest. Based on our results we show that the scalar theory with a spontaneous symmetry breaking used here as a simplified model for the Higgs sector, is very likely to realise the high-energy Higgsplosion phenomenon.
A quantum field theoretical model for the dynamics of the disoriented chiral condensate is presented. A unified approach to relate the quantum field theory directly to the formation, decay and signals of the DCC and its evolution is taken. We use a background field analysis of the O(4) sigma model keeping one-loop quantum corrections (quadratic order in the fluctuations). An evolution of the quantum fluctuations in an external, expanding metric which simulates the expansion of the plasma, is carried out. We examine, in detail, the amplification of the low momentum pion modes with two competing effects, the expansion rate of the plasma and the transition rate of the vacuum configuration from a metastable state into a stable state.We show the effect of DCC formation on the multiplicity distributions and the Bose-Einstein correlations.
We investigate how to include bound states in a thermal gas in the context of quantum field theory (QFT). To this end, we use for definiteness a scalar QFT with a $varphi^{4}$ interaction, where the field $varphi$ represents a particle with mass $m$. A bound state of the $varphi$-$varphi$ type is created when the coupling constant is negative and its modulus is larger than a certain critical value. We investigate the contribution of this bound state to the pressure of the thermal gas of the system by using the $S$-matrix formalism involving the derivative of the phase-shift scattering. Our analysis, which is based on an unitarized one-loop resumed approach which renders the theory finite and well-defined for each value of the coupling constant, leads to following main results: (i) We generalize the phase-shift formula in order to take into account within a unique formal approach the two-particle interaction as well as the bound state (if existent). (ii) textit{On the one hand}, the number density of the bound state in the system at a certain temperature $T$ is obtained by the standard thermal integral; this is the case for any binding energy, even if it is much smaller than the temperature of the thermal gas. (iii) textit{On the other hand}, the contribution of the bound state to the total pressure is partly -- but not completely -- canceled by the two-particle interaction contribution to the pressure. (iv) The pressure as function of the coupling constant is textit{continuous} also at the critical coupling for the bound state formation: the jump in pressure due to the sudden appearance of the bound state is exactly canceled by an analogous jump (but with opposite sign) of the interaction contribution to the pressure.
We introduce and discuss two inter-related mechanisms operative in the electroweak sector of the Standard Model at high energies. Higgsplosion, the first mechanism, occurs at some critical energy in the 25 to 10^3 TeV range, and leads to an exponentially growing decay rate of highly energetic particles into multiple Higgs bosons. We argue that this a well-controlled non-perturbative phenomenon in the Higgs-sector which involves the final state Higgs multiplicities n in the regime n lambda >> 1 where lambda is the Higgs self-coupling. If this mechanism is realised in nature, the cross-sections for producing ultra-high multiplicities of Higgs bosons are likely to become observable and even dominant in this energy range. At the same time, however, the apparent exponential growth of these cross-sections at even higher energies will be tamed and automatically cut-off by a related Higgspersion mechanism. As a result, and in contrast to previous studies, multi-Higgs production does not violate perturbative unitarity. Building on this approach, we then argue that the effects of Higgsplosion alter quantum corrections from very heavy states to the Higgs boson mass. Above a certain energy, which is much smaller than their masses, these states would rapidly decay into multiple Higgs bosons. The heavy states become unrealised as they decay much faster than they are formed. The loop integrals contributing to the Higgs mass will be cut off not by the masses of the heavy states, but by the characteristic loop momenta where their decay widths become comparable to their masses. Hence, the cut-off scale would be many orders of magnitude lower than the heavy mass scales themselves, thus suppressing their quantum corrections to the Higgs boson mass.
Time operator is studied on the basis of field quantization, where the difficulty stemming from Paulis theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative energy states by imposing Virasoro constraints. Applying the index theorem, one can show that in a different subspace of a Fock space, there is a different self-adjoint time operator. However, the self-adjoint time operator in the maximal subspace of the Fock space can also represent the self-adjoint time operator in the other subspaces, such that it can be taken as the single, universal time operator. Furthermore, a new insight on Paulis theorem is presented.
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