Super No-Scale F - SU(5) Joel W. Walker Sam Houston State University Research done with: Dimitri Nanopoulos, Tianjun Li and James A. Maxin Arizona State University, December 1, 2010

Based On: The Golden Point of No-Scale and No-Parameter F -SU(5) (Li, Maxin, Nanopoulos, Walker) arXiv: The Golden Strip of Correlated Top Quark, Gaugino, and Vectorlike Mass In No-Scale, No-Parameter F -SU(5) (Li, Maxin, Nanopoulos, Walker) arXiv: Super No Scale F -SU(5) : Resolving the Gauge Hierarchy Problem by Dynamic Determination of M 1/2 and tan  (Li, Maxin, Nanopoulos, Walker) arXiv: F - ast Proton Decay (Li, Nanopoulos, Walker) to appear in NPB, arXiv: ;

The Motivating Goals of No-Scale F -SU(5) Maximum Efficiency in the correlation of physical observations Maximum Efficiency in the correlation of physical observations The Unification of apparently distinct forces under a master symmetry group 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 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

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 M 32. It “waits” for Super Unification at M 51, which may be closer to M Planck.

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  s 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 M 32 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) M 0 Universal soft scalar mass M 1/2 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: M 0, M 1/2, 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. The scalar potential is flat and vanishing. Supersymmetry is exact, and there is no cosmological constant. This is all desirable at the Tree Level. The gaugino mass m 1/2 remains undetermined at the classical level. CONSTRAINT: m 0 = 0, A = 0, B = 0 m 1/2 ≠ 0 for SUSY breaking All soft-terms though, are dynamically evolved in terms of only the single parameter (m 1/2 ), which may itself be determined by radiative corrections to the potential ! K = -3 ln (T + T* - Σφ i *φ i )

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) Relation to String Theory

But …. Implementation is Difficult Simplest and most generic Universal Boundary Conditions possible – But fails to give consistent results applied at M GUT Simplest and most generic Universal Boundary Conditions possible – But fails to give consistent results applied at M GUT 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) 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. 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. 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 No- Scale boundary conditions come into their own as a perfect fit to phenomenology. With both these pieces in place, the No- Scale 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(  ) 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 2 nd 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 2 nd 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 M 32 OR the effective Weinberg angle.

Super Unification The prospect exists of confining Grand Unification from both the Electroweak and Planck Scales. The restriction that M 51, and thus likewise M 32, 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 M 32 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 sub- leading 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 M Z and the Z mass itself) We solve for the Higgs mixing term , which is not fixed at the high scale. We solve for the bilinear soft term B, and enforce compatibility with the RGE- evolved 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  and M 1/2 – 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.

The Golden Point of No-Scale and No-Parameter F -SU(5) (Li, Maxin, Nanopoulos, Walker) arXiv: Project Phase I

Key Experimental Constraints 7-Year WMAP Cold Dark Matter Relic Density Measurement 7-Year WMAP Cold Dark Matter Relic Density Measurement Experimental limits on the Flavor Changing Neutral Current process b -> s  Experimental limits on the Flavor Changing Neutral Current process b -> s  Anomalous magnetic moment of the muon Anomalous magnetic moment of the muon Proton Lifetime greater than 8 x Y Proton Lifetime greater than 8 x Y LEP limits on the light CP even Higgs mass LEP limits on the light CP even Higgs mass Compliance with all precision electroweak measurements (M z,  s,  W,  em, m t, m b ) Compliance with all precision electroweak measurements (M z,  s,  W,  em, m t, m b ) * The Weinberg angle floats mildly according to original program design. * The Weinberg angle floats mildly according to original program design.

The Golden Strip of Correlated Top Quark, Gaugino, and Vectorlike Mass In No-Scale, No-Parameter F -SU(5) (Li, Maxin, Nanopoulos, Walker) arXiv: Project Phase II

The Golden Point -> The Golden Strip We relax the value of M V and scan the parameter space We relax the value of M V 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 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 m t, which we thus allow to float as a free parameter The strongest dependence is on m t, 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/M N To enforce a decoupling limit, non SM processes should contribute as 1/M N Lower bound on Anomalous Magnetic Moment of the muon (g-2) , which should enhance the SM contribution puts an upper bound on M 1/2 Lower bound on Anomalous Magnetic Moment of the muon (g-2) , which should enhance the SM contribution puts an upper bound on M 1/2 Lower bound on b ->s , which should cancel the SM contribution puts a lower bound on M 1/2 Lower bound on b ->s , which should cancel the SM contribution puts a lower bound on M 1/2 The WMAP 7 year measurement depends on both (M 1/2,M V ), cross-cutting the plane The WMAP 7 year measurement depends on both (M 1/2,M V ), cross-cutting the plane

We demonstrate how displacement of any single parameter (here seen strongly for M V ) 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 M 1/2 is compensated (primarily) by changes in the top quark mass.

Key Model Features Dynamic Electroweak Symmetry Breaking Dynamic Electroweak Symmetry Breaking Dual Unification scales set by RGEs Dual Unification scales set by RGEs In conjunction with experimental constraints and running of the RGEs, the free parameters (M 1/2,M V ) are also fixed In conjunction with experimental constraints and running of the RGEs, the free parameters (M 1/2,M V ) are also fixed With all freedom exhausted, m t is With all freedom exhausted, m t is correctly “postdicted”

Sample spectrum with a heavier top quark mass

Summary of Results m t = – GeV M 1/2 = 455 – 481 GeV M V = 691 – 1020 GeV tanβ = 15 * This is very generic τ p = 4.6 x yr Proton lifetime testable at the next generation DUSEL and Hyper-Kamiokande facilities.

Super No Scale F -SU(5) : Resolving the Gauge Hierarchy Problem by Dynamic Determination of M 1/2 and tan  (Li, Maxin, Nanopoulos, Walker) arXiv: Project Phase III

The Gauge Hierarchy Problem SUSY can Stabilize the Hierarchy M Z /M planck 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 For concreteness, we fix the vectorlike particle mass at 1 TeV We revert to an experimentally fixed top quark mass as well 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 M 1/2 from a much deeper perspective This is done to emphasize the new model feature which is dynamic determination of M 1/2 from a much deeper perspective d V min / d M 1/2 = 0 d V min / d M 1/2 = 0

Strategy and Goals Minimization of the Minimum of the Higgs potential – The Minimum Minimorum Minimization of the Minimum of the Higgs potential – The Minimum Minimorum Dynamic apriori determination of M 1/2 without reference to experiments on Dark Matter, muon magnetic moment, or b->s  Dynamic apriori determination of M 1/2 without reference to experiments on Dark Matter, muon magnetic moment, or b->s  As we shift weight from a bottom-up to a top-down perspective, prior constraints become present “postdictions” 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 M 1/2 – tan  space. With the vectorlike mass and low energy precision measurements input, the B=0 condition isolates a curve of solutions in M 1/2 – tan  space. Each point on this curve experiences consistent radiative electroweak symmetry breaking, and has a corresponding minimum of the Higgs potential. 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. The smallest minimum is dynamically selected. By choosing tan  we are also choosing M 1/2. By choosing tan  we are also choosing M 1/2. The ratio M Z /M F is determined by the RGEs. The ratio M Z /M F is determined by the RGEs.

Three Key Experimental Signatures of No-Scale F - SU(5) F -ast Proton Decay around 4.6 x Y, F -ast Proton Decay around 4.6 x Y, -Testable at next generation DUSEL and Hyper-Kamiokande facilities TeV scale “ F lippons”, i.e. Vectorlike TeV scale “ F lippons”, i.e. Vectorlike Multiplets which carry the quantum numbers of Flipped SU(5) – Testable at the LHC Tan(  ) about 15 – Generically enforced by experimental constraint AND Dynamics ! Tan(  ) 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 M 32 scale will more than compensate for this lifetime increase.

The Super-Kamiokande Experiment

Detection Prospects for the e +  0 Mode Slide Courtesy of Ed Kearns

The M 1/2 - M 0 Plane with Vector Multiplets Proton Lifetime in the Flipped SU(5) e +  0 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 [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 [GeV] on the right-hand scale.

Variation of Tan(  ) Proton lifetime (solid blue) is measured in [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 [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.

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. Comparison of Central Value Predictions

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 F - SU(5) Joel W. Walker Sam Houston State University Work done with: Dimitri Nanopoulos, Tianjun Li and James A. Maxin Arizona State University, December 1, 2010