# Presentation: 666893

## SUSY and Open Questions in HEP

**6.1 Generations**
**6.2 Parameters for Masses and Mixing**
**6.3 Mass Scales**
**6.4 Grand Unification**
**6.5 SUSY - p Stability and Coupling Constants**
**6.6 SUSY - Cross Sections at the LHC**
**6.7 SUSY Signatures and Spectroscopy**
**6.8 Cosmological Constants (and SUSY?)**
**6.9 SUSY and Gravity**

## 3 - Why are there 3 and only 3 light “generations”?

**The SM is widely felt to be incomplete.**
**There are many parameters, mostly masses and weak mixing decay angles which are unspecified in the SM.**
**There are regularities which are not explained in the SM. For example the quark and lepton doublets of the SM are replicated 3 times. Why?**

## Z Decay Widths

**The Z decays into quark and lepton pairs:**
**Z --> qq, ll, ******
**The ******** are not detected. Measuring the “invisible” Z decay rate we conclude that there are 3 and only 3 light species of neutrinos (below Z threshold).**
**This conclusion is consistent with the measurement of primordial deuterium abundance where the ******** effect the nucleosynthesis rates.**
**N******** = 3**

## Z Decay BR in Comphep

**Check the BR in Comphep for 2 body Z decays. Couplings at tree level specified by the gauge interaction. Note that neutrinos account for 30% of the BR. Therefore in measuring the B-W width directly by varying the C.M. energy and the individual rates, there is a mismatch due to “invisible” decay modes.**

## Three “Generations”

**There are 3 "generations" of quarks and leptons which have identical interactions and different masses. The pattern of those masses is not understood, as we lack the dynamics. “Who ordered that”. Note 5 orders of magnitude in mass from e to t.**

## 4 -  What explains the pattern of quark and lepton masses and mixing?

**There must be CP violation for the Universe to consist largely of matter without significant antimatter. **
**Within the context of the SM the smallest number of generations allowing for a complex weak mixing matrix (CKM Matrix) is 3. Thus, the most economical SM number of generations agrees with N******** **

## The Weak Decays of Quarks

**The quark flavors are conserved in strong interactions.  **
**The flavors change in weak decays, the most familiar being beta decay, which at the quark level is; u --> d W****+**** --> d e****+**** ********e****.**
**Experiments determine  the matrix V characterizing the strength of the couplings in the weak decays of quarks, with ********~ 0.2 and A ~ 1. The**** ****matrix is completely phenomenological.**
- 	**Why is V approximately diagonal ?**
- 	**Why is b --> c so slow with respect to u --> s ?**
- 	**Is V complex? Unitary? Does Im(p) "explain" CP violation?**
**What is the dynamics of weak decays between generations? How  can we compute the elements of V? Why is ********~ 0.2? There is clearly a pattern here, but the dynamics is not known.**

## Unitary Triangle – BaBar and Belle

**Check Comphep parameters and constraints:**
**All the data is consistent with a unitary CKM mixing matrix ******** 3 generations with no new Physics yet indicated**

## 5 - Why are the known mass scales so different? QCD ~ 0.2 GeV < <> ~ 174 GeV << MGUT ~ 1016 GeV < MPL ~ 1019 GeV 

**The QCD scale is that mass when strong forces become strong (asymptotic freedom). It is ~ meson (qq bound states) masses.**
**The Higgs (EW) vacuum expectation value is ~ the W and Z masses. ***** <************> ~ 174 GeV ***
**This exhausts the known forces. What explains the enormous “desert” - a factor 10****14****? How can the scales remain stable in the presence of quantum loop corrections? This is called the hierarchy problem.**

## Grand Unified Theories

**Perhaps the strong and electroweak forces are related. In that case leptons and quarks are related and would make transitions. The p would be unstable. The unification mass scale of a GUT must be large enough so that the decay rate for p is < the rate limit set by experiment. Note that there is no symmetry imposing a conservation law that we know of requiring proton stability. “Baryon conservation” is simply put in by hand.**
**The coupling constants "run" in quantum field theories due to vacuum fluctuations. For example, in EM the e charge is shielded by virtual ******** fluctuations into e****+****e****-**** pairs on a distance scale set by, ********e**** ~ 1/m****e****. Thus ********increases as M decreases,********(0) = 1/137, ********(M****Z****) = 1/128.**

**                                        ****e                           **
**                ********                                     ******** **
**e**
**                                        ****e**

## “Running” Coupling Constants

**x**

**X**

**q**

**q     q-k**

**k**

**A diverges - cutoff at scale ******** and (as q****2****->0) renormalize charge to observed value, ********R**

## Running of  in QED

**Diverges – need a cutoff. However, can still connect different scales, Q and m. Done to all orders in perturbation theory. The ln(Q****2****) behavior is typical.**

## Running of EW and QCD Coupling “Constants”

- In electromagnetism the *e**+**e**-* vacuum pairs shield the “bare” charge which means that electromagnetism gets stronger at shorter distances; *b* = - 2nf/12, where *n**f* is the number of fermions that can make virtual pairs at a scale *Q*. In SU(3) the strong interactions become weak at short distances. This is because the gluons themselves carry a color charge whereas the photon is uncharged. Likewise the *W* and *Z*, *SU*(2), self-couple having triplet vertices such as  - because they carry weak “charge”. Thus we expect that the *SU*(2) coupling strength also gets weaker with increasing mass scale due to an anti-screening of the weak charge

*b**3* = (33 – 2*n**f*)/12
*b**2* = (22 - 2*n**f** *– 1⁄2)/12
-  *b**1* = -2*n**f* /12

*1*/**(*Q*2) = *1*/**(*m*2) + *b*[*ln*(*Q*2/*m*2)].

**+ factors  ******** antiscreening by bosons, - factors ******** screening by fermions.**

## Running Couplings

**EM coupling at the Z pole is larger than at large distances (the familiar fine structure constant). The strong coupling is also observed to run (Chpt. 4)**

## Grand Unified Theories

**A particular theory, SU(3) - strong, SU(2) - weak, U(1) - EM defines the b parameters - which represent the quantum loops of bosons and fermions and their distance/mass dependence. In SU(3) we know (asymptotic freedom) that the strong interactions become weak at short distances. This is because the gluons themselves carry a color charge (non - Abelian) whereas the photon is uncharged. Likewise the W and Z, SU(2), couple - WWW,  ZWW  vertices - because they carry EW “charge”.**
**Use precision data at M****z**** to look for possible unification of strong, EM , and weak forces.**
******3****-1**** = 8.40**
******2 ****-1**** = 29.67**
******-1**** = 128.3**

## GUT and Evolution of 

**Note the rough convergence to a common GUT coupling at a mass ~ 10****15**** GeV. However, the convergence is not perfect.**

## 6 - Why is charge quantized?

**There appears to be approximate unification of the couplings at a mass scale M****GUT**** ~ 10****15**** GeV.**
**Then we combine quarks and leptons into GUT multiplets - the simplest possibility being SU(5).**
- [*d**R** d**B** d**G** e**+** ****e*] : 3(-1/3 ) + 1 + 0 = 0
**Since the sum of the projections of a group generator in a group multiplet is = 0 (e.g. the angular momentum sum of m), charge must be quantized in units of the electron charge.**
**In addition, we see that quarks must have 1/3 fractional charge because there are 3 colors of quarks - SU(3).**

## GUT Predicts W

**A GUT has a single gauge coupling constant for the single gauge group – SU(5) ?. Thus, ******** and ********W**** must be related. The SU(5) prediction is that sin(********W****) = e/g = ********3/8, sin****2**** ********W ****= 0.375.**
**This prediction applies only at M****GUT**
**Running ********1**** and ********2**** back down to the Z mass, the prediction becomes; **
**This prediction, 0.206, is in ~ agreement with the measurement of**** ********W ****from the W and Z masses, sin****2**** ********W ****= 0.231****. ****Recall that in the SM the Weinberg angle is a free parameter.**

*sin*2***W*(*M**Z*2) ~ (3/8)/[1 +* bln*(*M**Z*2/*M**GUT*2)], with *b* =

## GUT Mass Relations

**Since quarks and leptons are in the same GUT multiplets, each generation is related**
*     **m**d** = m**e*      (3-9) MeV = 0.5 MeV
- 	*m**s** = m***      (60 - 170) MeV = 105 MeV
- 	*m**b** = m***      (4.1 - 4.8) GeV = 1.78 GeV
**These relations are not well satisfied at the ~ 1 GeV mass scale. They simply validate what we mean by “generations” - a pair of quarks and charged leptons of similar mass scale. There is some progress in taking them to be valid at the GUT scale and then evolving them**** ****down to currently available energies.**
**Note that quarks are heavier than leptons because they have color and color runs strongly down from the GUT scale to the Z mass scale.**

## 7 - Why do neutrinos have such small masses?

**There is no known reason for the neutrino to be massless. In contrast, the gluon and photon are gauge bosons and are required to be massless to preserve gauge invariance.**
**There are 3 widely separated mass scales, the QCD, the EW and the GUT. Thus, SU(5) has a plausible mechanism (“seesaw”) to make the neutrino mass eigenstates of low mass.**
**              ***m**** ~ m**q*2/*M**GUT *~ 10-12 -10-6 -10-2 *eV ( 3 v generations?)*
**Recent neutrino oscillation results indicate a neutrino mass difference of ~ 0.1 eV. In the seesaw, one expects a 3 generational structure for neutrino masses also.**

## Neutrino Oscillations – Solar and Atmospheric

- *m**atm* ~ 0.05 eV

**Note that these are squared mass differences, not masses. Note also that the weak mixing of flavor eigenstates is large – unlike the case for quarks.**

- *m**sol*    ~ 0.007 eV

## Possible Neutrino Masses

**Assume solar is due to e to muon oscillation and atmospheric is due to muon to tau oscillation. Assume an approximate seesaw normal generational hierarchy. There are also cosmological limits on the masses themselves from the neutrino background  limits for HDM of ~ 0.5 eV.**

## 8 - Why is matter (protons) ~ stable?

**There is no gauge motivated conservation law making protons stable.**
**Indeed, SU(5) relates quarks and leptons and possesses “leptoquarks” with masses ~ the GUT mass scale.**
**Thus we expect protons (uud) to decay via                        ,               **
**                    ****.  Thus ***p**** e*+ + **o or *** + ****+*
**Looking at the GUT extrapolation, we find 1/******** ~ 40 at a GUT mass of ~ 10****15**** GeV.**
**One dimensional grounds, the proton lifetime should be**
- *p* = 1/***p* ~ ***GUT*2(*m**p*/*M**GUT*)4*m**p*  or ***p* ~ 4 x 1031 *yr*.
** ****Recall the m****5**** quark weak decay widths.**
**The current experimental limit is 10****32**** yr****. ****The limit is in disagreement with a careful estimate of the p decay lifetime in simple SU(5) GUT models. Thus we need to look a bit harder at the grand unification scheme.**

## 9 - Why is the Universe made of matter?

**The present state of the Universe is very matter-antimatter asymmetric.**
**The necessary conditions for such an asymmetry are that CP is violated, that Baryon number is not conserved, and that the Universe went through a phase out of thermal equilibrium.**
**The existence of 3 generations allows for CP violation. CP violation (1964, K****L**** decay to 2 pions ) fixed in the CKM matrix by BaBar and Belle.**
**The GUT has, of necessity, baryon non-conserving reactions due to lepto-quarks.**
**Thus the possibility to explain the asymmetry exists in GUTs, although agreement with the data, N****B****/N******** ****~ 10****-9****, and calculation may not be plausible. ( hope  “leptogenesis” – CP violation in the neutrino sector ? But not established yet - )**

## Supersymmetry

**There is a symmetry which relates fermions and bosons - “supersymmetry”.**
**The generators of this symmetry contain the Poincare generators and a spinor connecting J states to J-1/2 states. **
**Recall that in a quantum loop the fermions and bosons contribute with opposite signs (e.g. top and Higgs in the W boson mass loops). **
**Thus SUSY is very stable under radiative corrections – solves the “hierarchy problem”.**
**This is fine, but is there any “evidence” for a “SUSY - GUT”?**

## Tevatron SUSY – Run I

**Backgrounds are QCD jet mismeasures, and Z invisible decays. SUSY signals should dominate at large values of missing transverse momentum. No evidence yet.**

## Tevatron Run I SUSY Limits

**SUSY search uses jets and missing Pt (LSP) in setting limits on SUSY masses. The lightest supersymmetric particle (LSP) is neutral and stable (by assumption). No evidence yet at Tevatron.**

## SUSY and Unification

**All particles in the SM must have a SUSY partner. None have yet been observed. Therefore, SUSY must be a broken symmetry, with SUSY masses > 100 GeV.**
**The running of coupling constants is altered by these new particles in the loops. The evidence for unification is now stronger, with M****GUT**** = 2 x 10****16**** GeV and 1/********GUT**** ~ 24.**
**The unification requirement indicates that the SUSY particles are in the (100 - 1000) GeV mass range, which is accessible at the LHC.**
**The prediction for sin****2********W**** at the Z mass is also altered because the evolution down from 3/8 is changed. The prediction goes from 0.206 to 0.23, significantly improving the agreement with experiment, 0.2312.**

## GUT and Evolution of 

**SUSY particles intervene at masses ~ (100,1000) GeV. The modified loop running improves the convergence at the GUT mass.**

- MGUT = 2 x 1016 GeV and 1*/****GUT* ~ 24

## SUSY Predictions

**The decay of protons is slowed ( recall M****GUT****-4**** dependence) in SUSY-GUT removing the conflict with experimental upper limits. The proton is quasi-stable because M****GUT**** is very large.**
**The 2 mass scales, M****GUT ****and M****Z ****make SU(5) without SUSY difficult to keep stable under radiative (loop) corrections. If the Higgs mass is fixed at the GUT scale, then there is a quadratic divergence in running down to the Z mass scale. Thus 2 numbers of order M****GUT**** must subtract to a number of order M****Z****.**
**In unbroken SUSY the SUSY partners of the SM particles are mass degenerate, and thus the loop corrections vanish, solving the “hierarchy problem”.**
**With SUSY breaking, the Higgs mass gets radiative corrections due to the differences of masses of the SUSY and SM partners.                       **
**              **
**SUSY requires that the Higgs has a mass ~ the Z mass. Radiative corrections --> M****H**** < 130 GeV.**** ****Thus in SUSY a light Higgs is expected.**
**Therefore, SUSY solves the hierarchy problem, but only if M****SUSY**** is < 1 TeV, and hence also accessible at the LHC.**

## SUSY  MMSM Mass Spectrum

**Why SUSY?**
**GUT Mass scale, unification**
**Improved Weinberg angle prediction**
**p decay rate**
**Neutrino mass (seesaw)**
**Mass hierarchy – Planck/EW**
**Dark matter candidate**
**String connections**

**MMSM has ~ SM light h and ~ mass degenerate H,A. LSP is neutralino. Squarks and gluinos are heavy.**

## MMSM in Comphep

**Check MMSM model – variables, constraints and particles**

## WMAP and Other Constraints

**LEP2**
**g-2**
**WMAP (LSP is dark matter)**
**LSP is neutral**

**Taken at face value, the MMSM is excluded for all values of the  parameters**

## SUSY Cross Sections

**The SUSY cross sections for squarks and gluinos are large because they have strong couplings.**
**Dimensionally,**
****** ****~ ********s****2****/(2M)****2 **
**or ~ 1 pb  for M = 1 TeV.**

## SUSY Signatures

**The gluino pair production cascade decays to jets + leptons + missing Et.**
**The gaugino pairs cascade decay to missing Et + 3 leptons which is a very clean signature **

## Gluino Production

**SUSY – 4 TeV g+g as a function of gluino mass**

## Comphep – Gluino Pairs at LHC

## Gluino Decays

**In SUSY there are many decay modes. Typically there is a cascade down to the neutralino or chargino and ultimately to the LSP which is often the neutralino.**

## SUSY and SM Backgrounds

**The SUSY signals involving jets and missing E****T**** dominate for gluinos with missing Et > 150 GeV **
**Study for CMS squark and gluino search**

## Lower SUSY Masses

- MSUSY  

**Position of peak correlated to SUSY mass scale**

**Measurement of**** ****SUSY mass scale**** ******** 20%  **
**(mSUGRA) with 10 fb****-1**

**Low trigger thresholds necessary to measure mass scale in overlap region with Tevatron (400 GeV)**

## SUSY Cross Sections at LHC

**Squarks and gluinos are most copious (strong production). Cascade decay to LSP (         ) ******** study jets and missing energy. E.g. 600 GeV squark. Dramatic event signatures and large cross section mean we will discover SUSY quickly at the LHC, if it exists.**

## SUSY – Squark/Gluino Mass “Reach”

**SUSY – Squark/Gluino Mass “Reach”**

**WMAP**

**1 year at 1/10 design luminosity.**
**SUSY discovery would happen quickly.**

##  SUSY – Mass Scale

- 1 year at l/10th design luminosity

**Will immediately start to measure the fundamental SUSY parameters.**
**With 4 jets + missing energy the SUSY mass scale can be established to 20 %.**

**CMS can set limits on SUSY(SUGRA) particles such that < 2 TeV is excluded. Recall that SUSY masses must be < 1 TeV if the hierarchy problem is to be solved. CMS can also set limits on the LSP mass which span the cosmologically interesting range for dark matter.**

**Notes:**
And once we have data, we can immediately start to measure the SUSY parameters.  For example, the average value of this simple variable correlates well with the squark or gluino mass.  

## SUSY – Neutralinos in Run II

## SUSY – Neutralinos

**Can be created directly in D-Y pair production or by decays, e.g. squark 2 body cascade decays.**

## Sparticle Cascades

**Use SUSY cascades to the stable LSP to sort out the new spectroscopy.**
**Decay chain used is :**
**Then**
**And**
**Final state is**

## Sparticle Masses

**Sparticle Masses**

- Sequential
- 2-body decay:  edge in M*ll*

**10 fb****-1**

**An example of the kind of analysis done, from 1 year at 1/10****th**** design luminosity.**

**Notes:**
By a year, we’ll be doing sophisticated analyses to identify and measure the masses of the lighter sparticles.  Here is an example of an analysis that uses the mass distributions from di-lepton events to get a jacobian whose leading edge is related to the mass of the second lightest neutralino.  Events with two different types of leptons are used to estimate the background distribution, which is subtracted.  

##  Sparticle Reconstruction 

**Can measure mass differences to better than 10%. The LSP is inferred from missing Et which makes the overall mass scale less well determined.**

## SUSY Higgs -->bb

**In general the Higgs decay to bb is buried in an enormous QCD background from g --> bb. In the SUSY case the associated production h + W with enhanced decay of h --> bb makes discovery possible if very good b tagging can be achieved for favored values of the SUSY parameters (tan(********)). ttH associated production may also be favorable.**

**SUSY Higgs -->bb**

## 10 - What is “Dark Matter” Made Of?

**If one simply counts stars, there is only 0.01 of the closure density seen.Yet the Universe appears to be flat (supernovae). What is it made of?**
**If you try to measure the mass of a galaxy dynamically, you look at the orbital velocity (Doppler shift) v as a function of radius. This method measures all mass, not just visible mass.  Newton tells us that, GM(r)/r = v****2****. For uniform central density, M(r) ~ r****3****, and v ~ r. Beyond the central luminous region, M(r) ~ constant, and v ~ 1/********r is expected. This situation is familiar from our solar system – Keplers’ Laws.**
**In fact, one observes, v ~ constant which indicates M(r) ~ r for the “dark matter” contribution to galactic dynamics.**
**Is this the SUSY partners - the LSP relics of the Big Bang, or the******** mass? SUSY certainly provides a dark matter candidate. This is another argument for SUSY. In fact, for SUSY masses ~ 1 TeV, the cross section must be ~ electroweak scale for the proper neutralino relic density.**

## Galactic Rotation Curves

**The rise of v as r is observed, but no falloff is observed out to 60 kpc, well beyond the luminous region of typical galaxies.**

## 11 - Why is the cosmological constant small?

**The vacuum expectation value of the Higgs field is 174 GeV, corresponding to a mass density of ~ 174 p/(0.00115 fm)****3 ****– recall the Higgs potential quartic piece, **
**The closure density of the Universe is ~ 1 p/m****3****. The EW vev is  therefore ~ 10****56**** times larger. Note that recent observations support a non-zero cosmological constant ~ the closure density.**
**Recall that a vacuum loop will have different signed contributions to the vev for fermions and bosons as with other loops. If the couplings are SUSY related, the contribution to the cosmological constant might be reduced. Still the discrepancy is “astronomical”.**
**Local SUSY theories, “supergravity” have both positive and negative contributions to the vacuum energy ---> one can perhaps have a cosmological constant consistent with observations.**

## 12 - How does gravity fit in with the strong, electromagnetic and weak forces?

**A local SUSY theory (since SUSY has both spin and Poincare generators) contains gravity. "SUSY is what Einstein would have written if he knew about fermions as well as bosons". Local SUSY will be a theory of general coordinate transformations - General Relativity.**
**The Planck scale, V = GM****2****/r, occurs when the gravitational coupling constant becomes strong and ~ 1, ********G**** = GM****2****/hc ~ 1, or M****PL**** = ********hc/G = 1.2 x 10****19**** GeV.**
**A renormalizable theory of gravity appears to be impossible with point particles. Using extended particles (“strings”) as the fundamental entities, a well behaved theory of gravity is possible but only in a space of high dimensionality. Perhaps gravity appears to be weak because it can propagate in all dimensions while the other forces cannot.**
**These “theories of everything” are, so far, devoid of testable predictions and are perhaps in the province of philosophy and not physics. Time will tell.**

## Running of Classical Gravity

- G  =  ~ 1, at a mass scale MPL = = 1.2 x 1019 GeV

**Naively, using classical gravitational coupling the couping is = the GUT coupling of 1/24 at a mass of ~ 2.5 x 10****17**** GeV, not too far from the GUT mass. This may be indicating something fundamental.**

## Summary for Hadron Collider Physics

**The LHC will explore the full (100 - 1000 GeV) allowed region of Higgs masses. Precision data indicates that the Higgs is light. If the Higgs is, in fact, light then its’ couplings can probably be explored by observing decays into .**
**There appears to be a GUT scale that indicates new dynamics.  The GUT explains charge quantization, predicts the rough value of ********W,**** allows for the matter dominance of the Universe and explains the small values of the neutrino masses. However it fails in p decay, precise Weinberg angle prediction and quadratic radiative corrections to Higgs mass scales – the hierarchy problem.**
**Preserving the scales (hierarchy problem) can be accomplished in SUSY. SUSY raises the GUT scale, making the p quasi-stable. The Weinberg angle SUSY prediction is in accord with the precision data. The SUSY LSP provides a natural candidate to explain the observation of galactic “dark matter”. A local SUSY GUT can incorporate gravity. It can also reduce the cosmological constant problem. A common GUT coupling and preservation of loop cancellations requires SUSY mass < 1 TeV. The LHC will fully explore this SUSY mass range either definitively proving or disproving this attractive hypothesis.**
**If there are extra dimensions, then the LHC is well positioned to study the TeV mass scale where their effects should appear if they are part of the solution of the hierarchy problem.  **
**The generational regularities in mass and quark and neutrino mixing matrix elements will probably not be informed by data taken at the LHC. We still haven’t a clue “**who ordered that”.