Pole mass of the W boson at two-loop order in the pure MS-bar scheme

I provide a calculation at full two-loop order of the complex pole squared mass of the W boson in the Standard Model in the pure MS-bar renormalization scheme, with Goldstone boson mass effects resummed. This approach is an alternative to earlier ones that use on-shell or hybrid renormalization schemes. The renormalization scale dependence of the real and imaginary parts of the resulting pole mass are studied. Both deviate by about $\pm 4$ MeV from their median values as the renormalization scale is varied from 50 GeV to 200 GeV, but the theory error is likely larger. A surprising feature of this scheme is that the 2-loop QCD correction has a larger scale-dependence, but a smaller magnitude, than the 2-loop non-QCD correction, unless the renormalization scale is chosen very far from the top-quark mass.Comment: 17 pages. v2: benchmark input parameters changed, reference adde

Two-loop effective potential for the minimal supersymmetric standard model

I compute the complete two-loop effective potential for the minimal supersymmetric standard model in the Landau gauge. This enables an accurate determination of the minimization conditions for the vacuum expectation values of the Higgs fields. Checks on the result follow from supersymmetric limits and from renormalization-scale invariance. The renormalization group equations for the field-independent vacuum energy and the vacuum expectation values are also presented. I provide numerical examples showing the improved accuracy and scale dependence obtained with the full two-loop effective potential.Comment: 30 page

Automatic Gauged R-Parity

In the minimal supersymmetric standard model, the existence of R-parity is not required for the internal consistency of the theory and might therefore be regarded as ad hoc. I catalog some simple conditions which are sufficient to guarantee that R-parity survives as an unbroken gauged discrete subgroup of the continuous gauge symmetry in certain extensions of the minimal supersymmetric standard model. If these criteria are met, R-parity is automatic. [Based on a talk given at the International Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY93) at Northeastern University, Boston, March 29-April 1 1993.]Comment: 9 pages, NUB-3063-93T

Z boson pole mass at two-loop order in the pure MS-bar scheme

I obtain the complex pole squared mass of the Z boson at full two-loop order in the Standard Model in the pure MS-bar renormalization scheme. The input parameters are the running gauge couplings, the top-quark Yukawa coupling, the Higgs self-coupling, and the vacuum expectation value that minimizes the Landau gauge effective potential. The effects of non-zero Goldstone boson mass are resummed. Within a reasonable range of renormalization scale choices, the scale dependence of the computed pole mass is found to be comparable to the current experimental uncertainty, but the true theoretical error is likely somewhat larger.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1503.0378

Taming the Goldstone contributions to the effective potential

The standard perturbative effective potential suffers from two related problems of principle involving the field-dependent Goldstone boson squared mass, G. First, in general G can be negative, and it actually is negative in the Standard Model; this leads to imaginary contributions to the effective potential that are not associated with a physical instability, and therefore spurious. Second, in the limit that G approaches zero, the effective potential minimization condition is logarithmically divergent already at two-loop order, and has increasingly severe power-law singularities at higher loop orders. I resolve both issues by resumming the Goldstone boson contributions to the effective potential. For the resulting resummed effective potential, the minimum value and the minimization condition that gives the vacuum expectation value are obtained in forms that do not involve G at all.Comment: 25 pages. v2: typo in 21st line of eq. (4.20) fixed. Reference adde

Signal-background interference for a singlet spin-0 digluon resonance at the LHC

Dijet mass distributions can be used to search for spin-0 resonances that couple to two gluons. I show that there is a substantial impact on such searches from the interference between the resonant signal and the continuum QCD background amplitudes. The signal dijet mass distribution is qualitatively modified by this interference, compared to the naive expectation from considering only the pure resonant contribution, even if the total width of the resonance is minimal and very small compared to the experimental dijet mass resolution. The impact becomes more drastic as the total width of the resonance increases. These considerations are illustrated using examples relevant to the 750 GeV diphoton excess recently observed at the LHC.Comment: 14 pages. v5 fixes errors in equations (2.10)-(2.15

Non-standard supersymmetry breaking and Dirac gaugino masses without supersoftness

I consider models in which non-standard supersymmetry breaking terms, including Dirac gaugino masses, arise from F-term breaking mediated by operators with a $1/M^3$ suppression. In these models, the supersoft properties found in the case of D-term breaking are absent in general, but can be obtained as a special case that is a fixed point of the renormalization group equations. The $\mu$ term is replaced by three distinct supersymmetry-breaking parameters, decoupling the Higgs scalar potential from the Higgsino masses. Both holomorphic and non-holomorphic scalar cubic interactions with minimal flavor violation are induced in the supersymmetric Standard Model Lagrangian.Comment: 22 pages. v2: references adde

Three-loop Standard Model effective potential at leading order in strong and top Yukawa couplings

I find the three-loop contribution to the effective potential for the Standard Model Higgs field, in the approximation that the strong and top Yukawa couplings are large compared to all other couplings, using dimensional regularization with modified minimal subtraction. Checks follow from gauge invariance and renormalization group invariance. I also briefly comment on the special problems posed by Goldstone boson contributions to the effective potential, and on the numerical impact of the result on the relations between the Higgs vacuum expectation value, mass, and self-interaction coupling.Comment: 25 pages. v2: references adde

Quasi-fixed points from scalar sequestering and the little hierarchy problem in supersymmetry

In supersymmetric models with scalar sequestering, superconformal strong dynamics in the hidden sector suppresses the low-energy couplings of mass dimension two, compared to the squares of the dimension one parameters. Taking into account restrictions on the anomalous dimensions in superconformal theories, I point out that the interplay between the hidden and visible sector renormalizations gives rise to quasi-fixed point running for the supersymmetric Standard Model squared mass parameters, rather than driving them to 0. The extent to which this dynamics can ameliorate the little hierarchy problem in supersymmetry is studied. Models of this type in which the gaugino masses do not unify are arguably more natural, and are certainly more likely to be accessible, eventually, to the Large Hadron Collider.Comment: 23 page

Top-quark pole mass in the tadpole-free MS-bar scheme

The complex pole mass of the top quark is presented at full two-loop order in the Standard Model, augmenting the known four-loop QCD contributions. The input parameters are the MS-bar Yukawa and gauge couplings, the Higgs self-coupling, and the Higgs vacuum expectation value (VEV). Here, the VEV is defined as the minimum of the full effective potential in Landau gauge, so that tadpoles vanish. This is an alternative to earlier results that instead minimize the tree-level potential, resulting in a VEV that is gauge-fixing independent but accompanied by negative powers of the Higgs self-coupling in perturbative expansions. The effects of non-zero Goldstone boson mass are eliminated by resummation. I also study the renormalization scale dependence of the calculated pole mass.Comment: 24 pages. v2: references added, no other change