Decays of metastable vacua in SQCD

The decay rates of metastable SQCD vacua in ISS-type models, both towards supersymmetric vacua as well as towards other nonsupersymmetric configurations arising in theories with elementary spectators, are estimated numerically in the semiclassical approximation by computing the corresponding multifield bounce configurations. The scaling of the bounce action with respect to the most relevant dimensionless couplings and ratios of scales is analyzed. In the case of the decays towards the susy vacua generated by nonperturbative effects, the results confirm previous analytical estimations of this scaling, obtained by assuming a triangular potential barrier. The decay rates towards susy vacua generated by R-symmetry breaking interactions turn out to be more than sufficiently suppressed for the phenomenologically relevant parameter range, and their behavior in this regime differs from analytic estimations valid for parametrically small scale ratios. It is also shown that in models with spectator fields, even though the decays towards vacua involving nonzero spectator VEVs don't have a strong parametric dependence on the scale ratios, the ISS vacuum can still be made long-lived in the presence of R-symmetry breaking interactions.Comment: 22 pages, 7 figure

M-Branes and Metastable States

We study a supersymmetry breaking deformation of the M-theory background found in arXiv:hep-th/0012011. The supersymmetric solution is a warped product of R^{2,1} and the 8-dimensional Stenzel space, which is a higher dimensional generalization of the deformed conifold. At the bottom of the warped throat there is a 4-sphere threaded by \tilde{M} units of 4-form flux. The dual (2+1)-dimensional theory has a discrete spectrum of bound states. We add p anti-M2 branes at a point on the 4-sphere, and show that they blow up into an M5-brane wrapping a 3-sphere at a fixed azimuthal angle on the 4-sphere. This supersymmetry breaking state turns out to be metastable for p / \tilde{M} < 0.054. We find a smooth O(3)-symmetric Euclidean bounce solution in the M5-brane world volume theory that describes the decay of the false vacuum. Calculation of the Euclidean action shows that the metastable state is extremely long-lived. We also describe the corresponding metastable states and their decay in the type IIA background obtained by reduction along one of the spatial directions of R^{2,1}.Comment: 33 pages, 5 figures; v2 note adde

Higher-order scalar interactions and SM vacuum stability

Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales).Comment: plain Latex, 9 figure

The aa-theorem and the Asymptotics of 4D Quantum Field Theory

We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\ln\mu|)^{1/2}$ as $\mu \to 0$ ($\mu \to \infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theory. In particular, it rules out perturbative theories with scale but not conformal invariance, which are equivalent to theories with renormalization group pseudocycles. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.Comment: 41 pages, 2 figures. v2: Arguments clarified, some side comments corrected, connection to previous work by Jack and Osborn described, conclusions unaffecte

Two-Point Functions and S-Parameter in QCD-like Theories

We calculated the vector, axial-vector, scalar and pseudo-scalar two-point functions up to two-loop level in the low-energy effective field theory for three different QCD-like theories. In addition we also calculated the pseudo-scalar decay constant $G_M$. The QCD-like theories we used are those with fermions in a complex, real or pseudo-real representation with in general n flavours. These case correspond to global symmetry breaking pattern of $SU(n)_L\times SU(n)_R\to SU(n)_V$, $SU(2n)\to SO(2n)$ or $SU(2n)\to Sp(2n)$. We also estimated the S parameter for those different theories.Comment: 29 page

Effective String Theory Revisited

We revisit the effective field theory of long relativistic strings such as confining flux tubes in QCD. We derive the Polchinski-Strominger interaction by a calculation in static gauge. This interaction implies that a non-critical string which initially oscillates in one direction gets excited in orthogonal directions as well. In static gauge no additional term in the effective action is needed to obtain this effect. It results from a one-loop calculation using the Nambu-Goto action. Non-linearly realized Lorentz symmetry is manifest at all stages in dimensional regularization. We also explain that independent of the number of dimensions non-covariant counterterms have to be added to the action in the commonly used zeta-function regularization.Comment: 21 pages, 4 figures, v2: typo corrected, references added, published versio

Composite Leptoquarks at the LHC

If electroweak symmetry breaking arises via strongly-coupled physics, the observed suppression of flavour-changing processes suggests that fermion masses should arise via mixing of elementary fermions with composite fermions of the strong sector. The strong sector then carries colour charge, and may contain composite leptoquark states, arising either as TeV scale resonances, or even as light, pseudo-Nambu-Goldstone bosons. The latter, since they are coupled to colour, get a mass of the order of several hundred GeV, beyond the reach of current searches at the Tevatron. The same generic mechanism that suppresses flavour-changing processes suppresses leptoquark-mediated rare processes, making it conceivable that the many stringent constraints may be evaded. The leptoquarks couple predominantly to third-generation quarks and leptons, and the prospects for discovery at LHC appear to be good. As an illustration, a model based on the Pati-Salam symmetry is described, and its embedding in models with a larger symmetry incorporating unification of gauge couplings, which provide additional motivation for leptoquark states at or below the TeV scale, is discussed.Comment: 10 pp, version to appear in JHE

Theoretical Constraints on the Higgs Effective Couplings

We derive constraints on the sign of couplings in an effective Higgs Lagrangian using prime principles such as the naturalness principle, global symmetries, and unitarity. Specifically, we study four dimension-six operators, O_H, O_y, O_g, and O_gamma, which contribute to the production and decay of the Higgs boson at the Large Hadron Collider (LHC), among other things. Assuming the Higgs is a fundamental scalar, we find: 1) the coefficient of O_H is positive except when there are triplet scalars, resulting in a reduction in the Higgs on-shell coupling from their standard model (SM) expectations if no other operators contribute, 2) the linear combination of O_H and O_y controlling the overall Higgs coupling to fermion is always reduced, 3) the sign of O_g induced by a new colored fermion is such that it interferes destructively with the SM top contribution in the gluon fusion production of the Higgs, if the new fermion cancels the top quadratic divergence in the Higgs mass, and 4) the correlation between naturalness and the sign of O_gamma is similar to that of O_g, when there is a new set of heavy electroweak gauge bosons. Next considering a composite scalar for the Higgs, we find the reduction in the on-shell Higgs couplings persists. If further assuming a collective breaking mechanism as in little Higgs theories, the coefficient of O_H remains positive even in the presence of triplet scalars. In the end, we conclude that the gluon fusion production of the Higgs boson is reduced from the SM rate in all composite Higgs models. Our study suggests a wealth of information could be revealed by precise measurements of the Higgs couplings, providing strong motivations for both improving on measurements at the LHC and building a precision machine such as the linear collider.Comment: 37 pages, one figure; v2: improved discussion on dispersion relation and other minor modifications; version accepted for publication