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Super No-Scale
SU(5)
F-
Arizona State University, December 1, 2010
Joel W. Walker
Sam Houston State University
Research done with: Dimitri Nanopoulos,
Tianjun Li and James A. Maxin
Based On:
• The Golden Point of No-Scale and No-Parameter F-SU(5)
(Li, Maxin, Nanopoulos, Walker) arXiv: 1007.5100
• The Golden Strip of Correlated Top Quark, Gaugino,
and Vectorlike Mass In No-Scale, No-Parameter F-SU(5)
(Li, Maxin, Nanopoulos, Walker) arXiv: 1010.2981
• Super No Scale F-SU(5) : Resolving the Gauge Hierarchy
Problem by Dynamic Determination of M1/2 and tan b
(Li, Maxin, Nanopoulos, Walker) arXiv: 1010.4550
• F- ast Proton Decay
(Li, Nanopoulos, Walker) to appear in NPB, arXiv: 0910.0860 ; 1003.2570
The Motivating Goals of
No-Scale
F-SU(5)
Maximum Efficiency in the correlation of
physical observations
 The Unification of apparently distinct
forces under a master symmetry group
 Reinterpretation of experimental
parameters and finely tuned scales as
dynamically evolved consequences of the
underlying equations of motion

The Tripodal Foundation of
No-Scale
F-SU(5)
1) The F-lipped SU(5) GUT
2) Extra TeV scale Vectorlike Multiplets
with F-theory origin
3) No-Scale Supergravity
Boundary Conditions
Pillar Number I
The F-lipped SU(5) GUT
Radiative Shielding & Charge Renormalization
Quantum Mechanics says that Short Distances correspond to High Energies. Also, truly empty space violates the Heisenberg
Uncertainty Principle. The quantum vacuum polarizes, and all measurements of charge vary with the interaction energy.
Grand Unification and Proton Decay
Slide Courtesy of Ed Kearns
Elementary Matter Particles of the Standard Model
http://CPEPweb.org
The Standard and Flipped SU(5) Particle Representations
Upper: Each generation of the Standard Model fits perfectly into a fundamental 5-bar and an antisymmetric 10 of SU(5). The
RH neutrino is “out”. Lower: The RH up/down quarks, and the electron/neutrino can “flip” places relative to standard SU(5).
Flipped Unification
A heuristic graphical representation of Flipped SU(5) in purple Vs. Standard SU(5) in red. Note that Flipped
SU(5) is not fully unified at M32. It “waits” for Super Unification at M51, which may be closer to MPlanck .
Motivations for Flipped SU(5)
The Missing Partner Mechanism
We achieve a Natural splitting between the double and triplet Higgs. We avoid
fine tuning and the overly rapid dimension 5 proton decay!
Consistency with Low Energy Phenomenology
Standard SU(5) unification predicts a value for the strong coupling at the Z-Boson mass which is much too large.
Attempts to fix this with heavy thresholds only speed dimension 5 proton decay. We can lower as by Flipping SU(5).
A Lesson from History
Nature repeats her favorite themes, in delicate reprise.
Pillar Number II
Extra TeV scale Vectorlike Multiplets
with F-theory origin
Grand Unification and String Phenomenology
These distinct points of view are natural symbiotic partners.
TeV Scale Vector Multiplets
Inclusion of TeV scale Vector Multiplets, as motivated by F-theory, creates a
dramatic early adjustment to the running of the gauge couplings.
Standard Unification with & without Vector Multiplets
Implicit Heavy thresholds are required to force the triple unification.
Flipped Unification with & without Vector Multiplets
Inclusion of TeV scale Vector Multiplets levels out the renormalization of the strong coupling, driving up the SU(5)
coupling, and speeding proton decay. The gap between the M32 scale couplings becomes extreme.
Pillar Number III
No-Scale Supergravity
Boundary Conditions
Motivations for Supersymmetry
Detection of Supersymmetric Particles is a key motivating goal of the Large Hadron Collider.
Minimal Supergravity (mSUGRA)
M0
Universal soft scalar mass
M1/2
Universal soft gaugino mass
μ
Higgsino Mixing Parameter
A
Universal Trilinear Coupling
B
Higgs Bilinear Coupling
tan β
Ratio of Higgs VEVs
|μ| and B can be determined by the requirement for REWSB,
so we are left with only five parameters:
M0, M1/2, A, tan β, and sgn(μ)
No Scale SUGRA: A Case Study in Reductionism
There is a function called the Kähler potential which must be specified by the
model builder in order to fix the metric of superspace, and determine the scalar
potential. It is not fixed by the symmetries of the theory. There is however a
particularly natural choice.
K = -3 ln (T + T* - Σφi*φi)
VSUGRA  0
CONSTRAINT:
m0 = 0,
A = 0,
B=0
The scalar potential is flat and
vanishing. Supersymmetry is exact,
and there is no cosmological
constant. This is all desirable at the
Tree Level.
m1/2 ≠ 0 for SUSY breaking
The gaugino mass m1/2 remains undetermined at the classical level.
All soft-terms though, are dynamically evolved in terms
of only the single parameter (m1/2), which may itself be
determined by radiative corrections to the potential !
Relation to String Theory
The no-scale structure emerges naturally as the
infrared limit of string theory.
In particular,
• Heterotic M-theory compactifications
• Type IIB flux compactifications – Flipped SU(5)
• F-theory compactifications (non-perturbative limit
of Type IIB)
But …. Implementation is Difficult

Simplest and most generic Universal Boundary
Conditions possible – But fails to give consistent
results applied at MGUT

The major problem is the non trivial
consequences of setting B=0 at the GUT scale.
The theory is so highly constrained that it fights
against attempts at fine tuning. This tension is
alleviated if the boundary conditions are instead
applied closer to the Planck scale. (Ellis et. al)
Three Ideas Fit Hand to Glove
The Flipped SU(5) GUT has a two stage
unification. The lower stage sets the
proton decay scale, but the upper scale
may be associated with the reduced
Planck Mass and gravitational physics.
 This association is possible only if the
RGEs are modified, as occurs naturally
with the F-theory vectorlike multiplets.
 With both these pieces in place, the NoScale boundary conditions come into their
own as a perfect fit to phenomenology.

Methodology A: Closed Form
Approximate Solutions
Advantages: All calculations are transparently visible, and
dependencies are explicit so that algebraic and differential
manipulation of key parameters is possible.
Disadvantages: Approximations may limit the predictive
power of the solution. The number of complex
interdependencies is so large that ensuring globally
consistent results is difficult or impossible.
Light Thresholds
As the renormalization scale passes the mass threshold of each Supersymmetric partner, they begin to
participate in quantum loops. This alters the slope of the coupling renormalization from that point onward.
Beta Function Coefficients of the MSSM
To correctly isolate the effects of the light thresholds, it is essential to know the individual
contributions to the CMSSM beta function coefficients from each superpartner.
Absorption of Light Thresholds into the RGE’s
The cumulative effect of a threshold presence may be absorbed into one constant for each coupling.
Improvement in Detail of the Threshold Analysis
In prior studies, the thresholds were applied to an effective shift in only the second coupling.
Presently, we account the shift individually to each of the three couplings.
The Second Loop
A fresh numerical evaluation of the Second Loop has been performed for each scenario under
consideration, including each distinct selection of Tan( b) and the MSSM mass spectrum.
Coefficients of the Second Loop
Improvement in Detail of the Two-Loop Analysis
As with the light thresholds, we expand the two-loop analysis to individually account for contributions to the
running of each of the three couplings, expanding the prior definition of our three effective parameters.
Closed Form Approximate Two-Loop Solution
We have developed a closed form approximation to the 2 nd loop contribution
which generally agrees with numerical evaluation to about 20%.
Renormalization Group Equations With 2nd Order Effects
Both Threshold and Second Loop Corrections are absorbed into an Effective Sine-Squared
Weinberg angle Plus a corresponding shift term for the Hypercharge and Strong Coupling.
The Standard SU(5) Limit
The “max” limit corresponds to a strict triple unification of the SM couplings. It is essential to recognize that the “max”
effective Weinberg angle is a dependent variable. Failure to match the expected value signals a failure of unification itself.
The Standard SU(5) Limit with MSSM Field Content
Note that the “predicted” value for the effective sine-squared Weinberg angle is a good match for the experimental number.
This implies that the actual 2nd order effects must finely cancel if the Standard SU(5) unification is to be consistent.
Flipped SU(5) Solutions
It is critically important to select a properly orthogonalized set of dependent functions. For Flipped SU(5) it is convenient
to choose the SU(5) and U(1)X couplings, and either the unification scale M32 OR the effective Weinberg angle.
Super Unification
The prospect exists of confining Grand Unification from both the Electroweak and Planck Scales. The restriction that
M51, and thus likewise M32, not creep too far forward may limit the potential “damage” from heavy threshold effects.
Super Unification with Vector Multiplets
Continuing the two-loop renormalization beyond the 3,2 partial unification can result in a super unification near the reduced
Planck scale. The wide coupling separation at M32 which was produced by the F-theory fields allows sufficient room to run.
Methodology B: High Precision
Numerical Integration
Advantages: Well tested public code exists which allows for a
highly accurate and simultaneously compatible determination of
the SUSY spectrum, the gauge, Yukawa and soft term running,
and the electroweak symmetry breaking, with leading and subleading corrections all accounted for.
Disadvantages: The procedure employed is opaque, obscured
behind thousands of lines of code. When considering novel
model constructions, it is difficult to ensure that customization
of the codebase is globally self consistent. Parameter
dependencies are hidden, revealed only by meticulous scanning.
Our Primary Tool of Analysis
Our primary numerical tools are the programs SUSPECT
(Djouadi, Kneur, Moultaka), and micrOMEGAs
(Belanger, Boudjema, Pukhov, Semenov), each customized for
flipped unification with vectorlike fields by James Maxin
• Minimization of the scalar Higgs potential with respect to both the up-type and
down-type Higgs fields yields two conditions on the parameter space.
• The scale of the Higgs VEVs is known however, from the Fermi coupling (or
alternatively the electroweak gauge couplings at MZ and the Z mass itself)
• We solve for the Higgs mixing term m, which is not fixed at the high scale.
• We solve for the bilinear soft term B, and enforce compatibility with the RGEevolved value of B from the high scale B=0 boundary. We allow a deviation
tolerance which is compatible with uncertainties in electroweak input data.
• This enforces a non-trivial constraint, providing for example a parametric curve
which specifies the dependency between tan b and M1/2 – Most often in practice,
these two parameters will be our inputs. More generally, we may expect to
interrelate any two “floating” parameters, including if desired, those more often
interpreted as fixed experimental input.
• We have cross referenced the gauge sector RGE results with our closed form
solution to ensure compatibility, making adjustments and corrections necessary.
Project Phase I
The Golden Point of No-Scale and No-Parameter F-SU(5)
(Li, Maxin, Nanopoulos, Walker) arXiv: 1007.5100
Key Experimental Constraints
7-Year WMAP Cold Dark Matter Relic
Density Measurement
 Experimental limits on the Flavor
Changing Neutral Current process b -> sg
 Anomalous magnetic moment of the muon
 Proton Lifetime greater than 8 x 1033 Y
 LEP limits on the light CP even Higgs mass
 Compliance with all precision electroweak
measurements (Mz, as, QW, aem, mt, mb)

* The Weinberg angle floats mildly according to original program design.
Project Phase II
The Golden Strip of Correlated Top Quark, Gaugino,
and Vectorlike Mass In No-Scale, No-Parameter F-SU(5)
(Li, Maxin, Nanopoulos, Walker) arXiv: 1010.2981
The Golden Point -> The Golden Strip
We relax the value of MV and scan the
parameter space
 We allow variation in the key electroweak
data to determine the appropriate level of
precision to ascribe to our results
 The strongest dependence is on mt, which
we thus allow to float as a free parameter

Constraining the Golden Strip
To enforce a decoupling limit, non SM processes
should contribute as 1/MN
 Lower bound on Anomalous Magnetic Moment
of the muon (g-2)m, which should enhance the
SM contribution puts an upper bound on M1/2
 Lower bound on b ->sg , which should cancel
the SM contribution puts a lower bound on M1/2
 The WMAP 7 year measurement depends on
both (M1/2,MV), cross-cutting the plane

We demonstrate how displacement of any single parameter (here seen strongly for
MV) will create motion away from the B=0 constraint. Also demonstrated however
is an example of the generic “flat direction” behavior, wherein here motion in M1/2
is compensated (primarily) by changes in the top quark mass.
Key Model Features
Dynamic Electroweak Symmetry Breaking
 Dual Unification scales set by RGEs
 In conjunction with experimental
constraints and running of the RGEs, the
free parameters (M1/2,MV) are also fixed
 With all freedom exhausted, mt is
correctly “postdicted”

Sample spectrum with a heavier top quark mass
Summary of Results
• mt = 173.0 – 174.4 GeV
• M1/2 = 455 – 481 GeV
• MV = 691 – 1020 GeV
• tanβ = 15
* This is very generic
• τp = 4.6 x 1034 yr
Proton lifetime testable at the next generation
DUSEL and Hyper-Kamiokande facilities.
Project Phase III
Super No Scale F-SU(5) : Resolving the Gauge Hierarchy
Problem by Dynamic Determination of M1/2 and tan b
(Li, Maxin, Nanopoulos, Walker) arXiv: 1010.4550
The Gauge Hierarchy Problem
• SUSY can Stabilize the Hierarchy MZ/Mplanck via
cancellation between Bosonic and Fermionic loops
• It softens quadratic scalar divergences and prevents
tree level mass terms via “chirality transmission”
• The question of why the Electroweak and
Supersymmetry breaking scales are proximal and
extremely light is the other side of the coin!
• “Dimensional Transmutation” via the
Renormalization group is part of the answer.
Dynamic secondary minimization of the Higgs
potential minimum may be the rest of the story.
Small Steps Backwards, Giant
Leaps Forward
For concreteness, we fix the vectorlike
particle mass at 1 TeV
 We revert to an experimentally fixed top
quark mass as well
 This is done to emphasize the new model
feature which is dynamic determination of
M1/2 from a much deeper perspective

d Vmin / d M1/2 = 0
Strategy and Goals
Minimization of the Minimum of the Higgs
potential – The Minimum Minimorum
 Dynamic apriori determination of M1/2
without reference to experiments on Dark
Matter, muon magnetic moment, or b->sg
 As we shift weight from a bottom-up to a
top-down perspective, prior constraints
become present “postdictions”

The Neutral Higgs Potential to Tree and First Loop Order
Summary of Results





With the vectorlike mass and low energy
precision measurements input, the B=0
condition isolates a curve of solutions in M1/2 –
tan b space.
Each point on this curve experiences consistent
radiative electroweak symmetry breaking, and
has a corresponding minimum of the Higgs
potential.
The smallest minimum is dynamically selected.
By choosing tan b we are also choosing M1/2.
The ratio MZ/MF is determined by the RGEs.
Three Key Experimental
Signatures of No-Scale FSU(5)
 F-ast Proton Decay around 4.6 x 1034 Y,
-Testable at next generation DUSEL
and Hyper-Kamiokande facilities
 TeV scale “Flippons”, i.e. Vectorlike
Multiplets which carry the quantum
numbers of Flipped SU(5)
– Testable at the LHC
 Tan(b) about 15 – Generically enforced by
experimental constraint AND Dynamics !
Grand Unification Predicts Proton Decay
Coupling Unification, Neutrino Masses, Supersymmetry, and the third Quark Generation are all either
directly confirmed, or have at least solid indirect experimental support. It is time for Proton Decay!
Bibliography
Proton Decay Channels
Dimension 5 decay can be dangerously fast. Dimension 6 decay can be so slow that you won’t see it!
Comparison of Relevant Time Scales
Having survived the overly rapid ‘ignoble’ dimension 5 decay channel, the question becomes whether dimension 6 decay is
too slow to be tested. It is grand comedy that our resources could expire ‘one zero short’, having come already so very far.
Suppression of Flipped Decay
This suppression seems at first sight detrimental, in that the dimension 6 decay has generally not been predicted as
problematically fast. However, the lowering of the M32 scale will more than compensate for this lifetime increase.
The Super-Kamiokande Experiment
Detection Prospects for the e+p0 Mode
Slide Courtesy of Ed Kearns
The M1/2 - M0 Plane with Vector Multiplets
Proton Lifetime in the Flipped SU(5) e+p0 channel, including TeV vector multiplets, is depicted
against phenomenological constraints on the MSSM. Background figure courtesy of Keith Olive.
Variation of Vector Multiplet Scale
Proton lifetime (solid blue) is measured in 1035 [Y] on the left numeric scale. The dimensionless SU(5) coupling (dash red) is
also measured on the left-hand scale. The unification mass (dot green) is measured in 10 16 [GeV] on the right-hand scale.
Variation of Tan(b)
Proton lifetime (solid blue) is measured in 1035 [Y] on the left numeric scale. The dimensionless SU(5) coupling (dash red) is
also measured on the left-hand scale. The unification mass (dot green) is measured in 10 16 [GeV] on the right-hand scale.
Heavy Thresholds with Vector Multiplets
Central values for proton lifetime at the MSSM Benchmark Points lie on the white boundary. The dark red / blue bands show
uncertainty of low energy measurements. The large light blue bars depict plausible variation of the heavy thresholds.
Comparison of Central Value Predictions
The 2009 central predictions for proton decay narrowly evades current detection bounds from Super-Kamiokande. Even
with the possibility of substantial heavy thresholds, the majority of the predicted range is testable in the next generation.
Reasons for the Decline in Proton Life Expectancy
Comparisons are relative to the 2002 report on Flipped SU(5) by Ellis, Nanopoulos, and Walker.
The increases and decreases are combined multiplicatively in sequence to develop the net change.
A Convergence of Large Experiments
Proton decay, hastened by the inclusion of TeV scale Vector Multiplets, represents an imminently
testable convergence of the most exciting particle physics experiments of the next decade.
Super No-Scale
SU(5)
F-
Arizona State University, December 1, 2010
Joel W. Walker
Sam Houston State University
Work done with: Dimitri Nanopoulos,
Tianjun Li and James A. Maxin