![Page 1: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/1.jpg)
Dark Matter, the Higgs Mass, and String Phenomenology
Based on 1202.1546 and 1203.5796 (with K. Givens)
![Page 2: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/2.jpg)
Necessary conditions for string pheno
• The model must have enough freedom to have a tunable CC – by choice of fluxes for example – currently the only available mechanism for getting a sufficiently dense ‘discretuum”.
• All the moduli should be stabilized at a SUSY breaking minimum with the latter scale being low enough to allow a meaningful phenomenology. Even if the exact mechanism for finding a minimum with CC at 10^-3 eV scale is not known the theoretical predictions should be insensitive to the tuning of the CC.
• Phenomenological and Cosmological constraints should be satisfied.
• The output should not depend strongly on the details of the SM construction – the only meaningful predictions are generic ones. Such details can easily be swamped by the tuning of the CC.
• LVS phenomenology satisfies all these criteria – though a concrete construction of the MSSM (without chiral exotics) is not yet available
• In the heterotic case MSSM like models exist – Moduli stabilization and tuning of CC not so clear.
![Page 3: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/3.jpg)
The CC and ‘predictivity’
![Page 4: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/4.jpg)
![Page 5: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/5.jpg)
![Page 6: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/6.jpg)
![Page 7: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/7.jpg)
1. Begin with the low energy limit of IIB string theory compactified on a Calabi-Yau Orientifold chosen to be of the “Swiss Cheese” type BBCQ
2. Leads to LVS – only known moduli stabilization scenario with SUSY breaking minimum
3. Assume MSSM located on D3 branes at a singularity. Alternatively on a stack of magnetized D7 branes wrapping a 4-cycle
![Page 8: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/8.jpg)
General SUGRA framework
At the two derivative level the form of the action is determined by these.
![Page 9: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/9.jpg)
SUGRA Inputs
![Page 10: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/10.jpg)
Potential
![Page 11: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/11.jpg)
Requirements for SUSY Breaking
Need a Minimum with
The second condition is CC=0. Involves fine tuning (after quantum corrections).
Even if not satisfied exactly the phenomenological conclusions must NOT be sensitive to this constraint!
i.e. This SUSY breaking must result in non-zero scalar and gaugino masses whose values are not very sensitive to the value of the CC.
The second condition is CC=0. Involves fine tuning (after quantum corrections).
Even if not satisfied exactly the phenomenological conclusions must NOT be sensitive to this constraint!
i.e. This SUSY breaking must result in non-zero scalar and gaugino masses whose values are not very sensitive to the value of the CC.
![Page 12: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/12.jpg)
Validity of SUGRA approximationIn String theory 4D SUGRA comes after integrating out massive states. Derivative expansion is actually a superderivative expansion in SUSY
Total # fixed is
For validity of expansion generically:
M lowest integrated out scale
String example:
![Page 13: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/13.jpg)
GMSB: SUSY Breaking Field X. Messenger scale
Generically SUSY breaking scale small/two derivative expansion valid i.e. If M is highest scale integrated out
However in LVS models where couplings are suppressed this restriction may be too strong – currently being investigated with FQ
€
F X
X02 <<1
![Page 14: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/14.jpg)
Expansion in MSSM Fields
NOTE: Above formulae valid at quantum level with appropriate change in K. Eg: NOTE: Above formulae valid at quantum level with appropriate change in K. Eg:
−>
Soni-WeldonIbanez-LuestKap-LouisBrignole et al.
![Page 15: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/15.jpg)
Weyl Transformations
![Page 16: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/16.jpg)
Weyl Anomaly Effects
KLKonishiNSVZA-H,M
![Page 17: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/17.jpg)
Different versions of LVS
• mSUGRA like – assumes moduli mixing. Depends on pushing Field Theoretic arguments beyond string scale• LARGE VS. Really Really want to see strings at LHC! Need internal volume ~ 10^30 in string units. Need to introduce explicit SUSY breaking in 4D such as a Dbar brane.• MSSM on magnetized D7 branes wrapping a 4-cycle – realizes a partially sequestered phenomenology CAQS, CMV• MSSM on D3 branes at a singularity – leads to sequestered phenomenology BCKMQ, deA
![Page 18: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/18.jpg)
• Status of first two scenarios is theoretically unclear
• Will only consider the third and fourth
• The third has cosmological problems like mSUGRA
• Only version of LVS which may survive both theoretical and phenomenological constraints is the last one.
• Unfortunately this leads in large part to an unobservable (at the LHC) SUSY partners!
![Page 19: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/19.jpg)
Classical Results
To obtain LVS need to choose “Swss Cheese’ type manifold and include alpha’ corrections
![Page 20: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/20.jpg)
Classical Results
Minimize and find F-terms:
![Page 21: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/21.jpg)
FCNC issues D7 case
First investigate constraints for MSSM on D7 brane wrapping a magnetized 4-cycle. Matter from Wilson line modulimoduli
Jockers-Louis
![Page 22: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/22.jpg)
FCNC suppression requires
>
Even with relatively high values of gravitino and soft masses
We need extremely large values of the volume
This actually leads to < TeV scale soft masses if we can take W of O(1) (√F/M?). No cosmological gravitino problem but serious modulus problem.
![Page 23: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/23.jpg)
The brane field fluctuations may also be identified as matter JL
Metric from holomorphic dilaton
In original LVS minimum
Uplift needs to give a CC =0
![Page 24: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/24.jpg)
The gaugino mass controlled by small cycle wrapped by D7 branes
Get mSUGRA scenario in the second case!
Cosmological gravitino/moduli problems require m_3/2> 10 TeVTo avoid cosmological modulus problem sinceneed gravitinos at 100TeV scale
Largest is 2π so this gives gaugino masses > 5 TeV
Gives a viable phenomenology but little hierarchy fine tuning at 1/10^6 level!
![Page 25: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/25.jpg)
FCNC in D3 case
However the harmonic form of small cycle from blowing up a singularity expected to fall off as R^-6 so we then end up with
BCKMQ deA
However the situation is changed completely by Weyl anomaly generated gaugino masses in this case.
![Page 26: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/26.jpg)
inoAMSB = Weyl anomaly+ Gaugino Mediation
Leads to one loop order gaugino masses:Leads to one loop order gaugino masses:
Scalar masses generated by RGScalar masses generated by RG
Integrates to (with high scale soft mass suppressed)Integrates to (with high scale soft mass suppressed)
![Page 27: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/27.jpg)
In this case the quantum generated soft mass from inoAMSB is
In contrast to the classical soft mass
The FCNC constraint is cosiderably softened to
Hence we get
![Page 28: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/28.jpg)
Non Perturbative FCNC effectsBerg et al
![Page 29: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/29.jpg)
![Page 30: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/30.jpg)
![Page 31: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/31.jpg)
![Page 32: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/32.jpg)
Phenomenology of inoAMSB
Collaborators : H. Baer, K. Givens, S. Rajagopalan and S. Summy
Boundary conditions at High (GUT?) scale: Boundary conditions at High (GUT?) scale:
Also to a good approximation in these modelsAlso to a good approximation in these models
μ and Bμ terms depend on uplift. Take phenomenological approach: values determined by E-W symmetry breaking. B parameter traded for μ fixed by Z - mass
Initial values for RG evolution.Initial values for RG evolution.
Parameter space Parameter space
![Page 33: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/33.jpg)
![Page 34: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/34.jpg)
![Page 35: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/35.jpg)
![Page 36: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/36.jpg)
Output
• A two parameter (+ sign of μ) phenomenology
• All SUSY breaking soft terms essentially determined by gravitino mass and tanβ
•Avoiding FCNC leads to CYO Vol >10^4 in string units hence avoiding modulus problem implies 500TeV <m_3/2
•This gives a Higgs mass in 122-126 GeV range – m_3/2=500TeV tanβ=40 gives M_Higgs =124GeV.
•For m_3/2=500TeV LSP is around 1.4TeV! No SUSY partners will be seen at LHC even with 100fb^-1 of data.
![Page 37: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/37.jpg)
Main Prediction
If this line of reasoning is correct then the LHC will not see superpartners!
Certainly consistent with current data!!
Obviously an argument for resurrecting the SSC!!!
![Page 38: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/38.jpg)
Summary
• LVS gives either mSUGRA like or inoAMSB like phenomenology
• mSUGRA like seems to be ruled out by Cosmology
• inoAMSB may survive (assuming modulus problem is OK – thermal inflation?
• In this case correlation between dark matter density and Higgs mass but if former saturated Higgs mass in right range but no SUSY will be seen at LHC!
![Page 39: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/39.jpg)
Is there a Way out?
• Assume that the string construction gives the NMSSM rather than the MSSM. Don’t expect much change besides additional scalar state to stabilize.
• So if TeV scale SUSY particles are found the whole construction will be vitiated.
• We would need different types of SUSY breaking and moduli stabilization mechanisms within string theory –perhaps heterotic strings.
![Page 40: Dark Matter, the Higgs Mass, and String Phenomenology](https://reader036.vdocument.in/reader036/viewer/2022062305/568148b5550346895db5cc5e/html5/thumbnails/40.jpg)
Acknowledgements
• Fernado Quevedo and Joe Conlon for discussions on LVS etc.
• Howie Baer, Kevin Givens, Summy Heaya, Shibi Rajagopalan for collaboration on phenomenology of inoAMSB
• DOE grant DE-FG02-91-ER-40672 for support