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On the Lie algebra structure of HH1(A) of a finite-dimensional algebra A
Let A be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of A is a simple directed graph, then HH1(A) is a solvable Lie algebra. The second main result shows that if the Ext-quiver of A has no loops and at most two parallel arrows in any direction, and if HH1(A) is a simple Lie algebra, then char(k)neq2 and HH1(A)2(k). The third result investigates symmetric algebras with a quiver which has a vertex with a single loop
The Nielsen Identities of the SM and the definition of mass
In a generic gauge theory the gauge parameter dependence of individual Green
functions is controlled by the Nielsen identities, which originate from an
enlarged BRST symmetry. We give a practical introduction to the Nielsen
identities of the Standard Model (SM) and to their renormalization and
illustrate the power of this elegant formalism in the case of the problem of
the definition of mass.We prove to all orders in perturbation theory the
gauge-independence of the complex pole of the propagator for all physical
fields of the SM, in the most general case with mixing and CP violation. At the
amplitude level, the formalism provides an intuitive and general understanding
of the gauge recombinations which makes it particularly useful at higher
orders. We also include in an appendix the explicit expressions for the
fermionic two-point functions in a generic R_\xi gauge.Comment: 28 pages, LaTeX2e, 4 Postscript Figures, final version to appear on
PRD, extensive revision
Muon anomalous magnetic dipole moment in supersymmetric theories
We study the muon anomalous magnetic dipole moment in supersymmetric
theories. The impact of the recent Brookhaven E821 experimental measurement on
both model-independent and model-dependent supersymmetric parameter spaces is
discussed in detail. We find that values of tan\beta as low as 3 can be
obtained while remaining within the E821 one-sigma bound. This requires a light
smuon; however, we show that, somewhat surprisingly, no model-independent bound
can be placed on the mass of the lightest chargino for any tan\beta greater
than or equal to 3. We also show that the maximum contributions to the
anomalous magnetic moment are insensitive to CP-violating phases. We provide
analyses of the supersymmetric contribution to the muon anomalous magnetic
moment in dilaton-dominated supergravity models and gauge-mediated
supersymmetry-breaking models. Finally, we discuss how other phenomena, such as
, relic abundance of the lightest superpartner, and the Higgs
mass may be correlated with the anomalous magnetic moment, but do not
significantly impact the viability of a supersymmetric explanation, or the mass
limits obtainable on smuons and charginos.Comment: 28 page
Light MSSM Higgs boson mass to three-loop accuracy
The light CP even Higgs boson mass, Mh, is calculated to three-loop accuracy
within the Minimal Supersymmetric Standard Model (MSSM). The result is
expressed in terms of DRbar parameters and implemented in the computer program
H3m. The calculation is based on the proper approximations and their
combination in various regions of the parameter space. The three-loop effects
to Mh are typically of the order of a few hundred MeV and opposite in sign to
the two-loop corrections. The remaining theory uncertainty due to higher order
perturbative corrections is estimated to be less than 1 GeV.Comment: 39 pages, 13 figures. v2: minor changes, typos fixe
A Non Standard Model Higgs at the LHC as a Sign of Naturalness
Light states associated with the hierarchy problem affect the Higgs LHC
production and decays. We illustrate this within the MSSM and two simple
extensions applying the latest bounds from LHC Higgs searches. Large deviations
in the Higgs properties are expected in a natural SUSY spectrum. The discovery
of a non-Standard-Model Higgs may signal the presence of light stops accessible
at the LHC. Conversely, the more the Higgs is Standard-Model-like, the more
tuned the theory becomes. Taking the ratio of different Higgs decay channels at
the LHC cancels the leading QCD uncertainties and potentially improves the
accuracy in Higgs coupling measurements to the percent level. This may lead to
the possibility of doing precision Higgs physics at the LHC. Finally, we
entertain the possibility that the ATLAS excess around 125 GeV persists with a
Higgs production cross-section that is enhanced compared to the SM. This
increase can only be accommodated in extensions of the MSSM and it may suggest
that stops lie below 400 GeV, likely within reach of next year's LHC run.Comment: 22 pages, 14 figures. v2: lambdaSUSY point changed, typos fixed,
references added, conclusions unchange
Direct Detection of Dark Matter in the MSSM with Non-Universal Higgs Masses
We calculate dark matter scattering rates in the minimal supersymmetric
extension of the Standard Model (MSSM), allowing the soft
supersymmetry-breaking masses of the Higgs multiplets, m_{1,2}, to be
non-universal (NUHM). Compared with the constrained MSSM (CMSSM) in which
m_{1,2} are required to be equal to the soft supersymmetry-breaking masses m_0
of the squark and slepton masses, we find that the elastic scattering cross
sections may be up to two orders of magnitude larger than values in the CMSSM
for similar LSP masses. We find the following preferred ranges for the
spin-independent cross section: 10^{-6} pb \ga \sigma_{SI} \ga 10^{-10} pb, and
for the spin-dependent cross section: 10^{-3} pb \ga \sigma_{SD}, with the
lower bound on \sigma_{SI} dependent on using the putative constraint from the
muon anomalous magnetic moment. We stress the importance of incorporating
accelerator and dark matter constraints in restricting the NUHM parameter
space, and also of requiring that no undesirable vacuum appear below the GUT
scale. In particular, values of the spin-independent cross section another
order of magnitude larger would appear to be allowed, for small \tan \beta, if
the GUT vacuum stability requirement were relaxed, and much lower cross-section
values would be permitted if the muon anomalous magnetic moment constraint were
dropped.Comment: 30 pages LaTeX, 40 eps figure
Search for Heavy Neutral MSSM Higgs Bosons with CMS: Reach and Higgs-Mass Precision
The search for MSSM Higgs bosons will be an important goal at the LHC. We
analyze the search reach of the CMS experiment for the heavy neutral MSSM Higgs
bosons with an integrated luminosity of 30 or 60 fb^-1. This is done by
combining the latest results for the CMS experimental sensitivities based on
full simulation studies with state-of-the-art theoretical predictions of MSSM
Higgs-boson properties. The results are interpreted in MSSM benchmark scenarios
in terms of the parameters tan_beta and the Higgs-boson mass scale, M_A. We
study the dependence of the 5 sigma discovery contours in the M_A-tan_beta
plane on variations of the other supersymmetric parameters. The largest effects
arise from a change in the higgsino mass parameter mu, which enters both via
higher-order radiative corrections and via the kinematics of Higgs decays into
supersymmetric particles. While the variation of can shift the
prospective discovery reach (and correspondingly the ``LHC wedge'' region) by
about Delta tan_beta = 10, we find that the discovery reach is rather stable
with respect to the impact of other supersymmetric parameters. Within the
discovery region we analyze the accuracy with which the masses of the heavy
neutral Higgs bosons can be determined. We find that an accuracy of 1-4% should
be achievable, which could make it possible in favourable regions of the MSSM
parameter space to experimentally resolve the signals of the two heavy MSSM
Higgs bosons at the LHC.Comment: 24 pages, 8 figure
CP Violation in Supersymmetry with Effective Minimal Flavour Violation
We analyze CP violation in supersymmetry with Effective Minimal Flavour
Violation, as recently proposed in arXiv:1011.0730. Unlike the case of standard
Minimal Flavour Violation, we show that all the phases allowed by the flavour
symmetry can be sizable without violating existing Electric Dipole Moment
constraints, thus solving the SUSY CP problem. The EDMs at one and two loops
are precisely analyzed as well as their correlations with the expected CP
asymmetries in B physics.Comment: 22 pages, 7 figures. v2: Discussion in section 2 extended,
conclusions unchanged. Matches published versio
Higgs boson mass limits in perturbative unification theories
Motivated in part by recent demonstrations that electroweak unification into
a simple group may occur at a low scale, we detail the requirements on the
Higgs mass if the unification is to be perturbative. We do this for the
Standard Model effective theory, minimal supersymmetry, and next-to-minimal
supersymmetry with an additional singlet field. Within the Standard Model
framework, we find that perturbative unification with sin2(thetaW)=1/4 occurs
at Lambda=3.8 TeV and requires mh<460 GeV, whereas perturbative unification
with sin2(thetaW)=3/8 requires mh<200 GeV. In supersymmetry, the presentation
of the Higgs mass predictions can be significantly simplified, yet remain
meaningful, by using a single supersymmetry breaking parameter Delta_S. We
present Higgs mass limits in terms of Delta_S for the minimal supersymmetric
model and the next-to-minimal supersymmetric model. We show that in
next-to-minimal supersymmetry, the Higgs mass upper limit can be as large as
500 GeV even for moderate supersymmetry masses if the perturbative unification
scale is low (e.g., Lambda=10 TeV).Comment: 20 pages, latex, 6 figures, references adde
On SUSY GUTs with a degenerate Higgs mass matrix
Certain supersymmetric grand unified models predict that the coefficients of
the quadratic terms in the MSSM Higgs potential should be degenerate at the GUT
scale. We discuss some examples for such models, and we analyse the
implications of this peculiar condition of a GUT-scale degenerate Higgs mass
matrix for low-scale MSSM phenomenology. To this end we explore the parameter
space which is consistent with existing experimental constraints by means of a
Markov Chain Monte Carlo analysis.Comment: 31 pages, 27 figures; v2: typos correcte
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