# Presentation: 804901

## Gauge Coupling Unification, SUSY Scale and Strong Coupling Running

**Gauge Coupling Unification, SUSY Scale and Strong Coupling Running**

**Dimitri Bourilkov**
**University of Florida**
**PANIC05, Particles and Nuclei International Conference                          **** ****Santa Fe, NM, USA - October 24-28, 2005**

## Introduction

**Introduction**

**3 separate couplings at the Z peak ...**

**What happens at much higher scales?**

## Motivation I

**By 1991 the *****weak coupling was measured with much higher precision than the strong***** one at LEP**
**In a famous paper U.Amaldi et al. (****PL **B260** (1991) 447****) showed that in contrast to the SM the MSSM leads to a single unification scale**
**          ****M****SUSY ****= 10****3.0****±1.0**** GeV**
**          ****M****GUT****  = 10****16.0±0.3**** GeV**
**          ****1/********GUT**** = 25.7 ± 1.7**
**At the time the relative error in ********(M****Z****), sin****2******_**MS**_** and ********s****(M****Z****) was 0.24 %, 0.77 % and 4.6 %**

## Motivation II

**From RPP 2004 ****the relative error in ********(M****Z****), sin****2******_**MS**_** and ********s****(M****Z****) is  0.014%, 0.065% and 1.7%, so we have improved by *****more***** than an order of magnitude *****except for the strong coupling (less than 3 times)***
**So new analyses are in order (here we expand the analysis from       ****hep-ph/0410350 ****)**

**Other recent analyses:**
**W. de Boer, C.Sander,**
**      ****hep-ph/0307049**
**B.Allanach et al., hep-ph/0407067**
**N.Arkani-Hamed, S.Dimopoulos,**
**      ****hep-th/0405159**
**Example of a fit with ****M****SUSY**** = M****TOP**

## Side Remark

**It is amazing that we are trying to extrapolate from 10****2**** to 10****16**** GeV**
**From experiments we now that even *****interpolation*** **or modest extrapolations** **can be non-trivial**
**We measure the “offsets” around the Z peak and rely on theory to give us the “slopes” of the running couplings – *****without errors***** – up to the GUT scale**
**This may be an illusion e.g. extra dimensions could modify the running already at TeV scales, so the “unification” point could be imaginary**

## Experimental Inputs

**From Review of Particle Properties 2004**
**1/********(M****Z****) = 127.918 ± 0.018**
**sin****2********MS  ****= 0.23120 ± 0.00015**
******s****(M****Z****) is a different story (larger statistical errors and theory uncertainties); will use latest results (LEPEWWG 05) for both “high” and “low” values**
******s****(M****Z****) = 0.1223 ± 0.0038  from  ********h**** / ************ @ Z (LEPEWWG)**
******s****(M****Z****) = 0.1182 ± 0.0027 S.Bethke 2004 (DIS, ********, ********, Z)**
******s****(M****Z****) = 0.1179 ± 0.0030 ********o****l**** = ********0****h******** ****l****/********h**** (LEPEWWG)**
******s****(M****Z****) = 0.1170 ± 0.0026 ALEPH 4-jet rate @ Z**

## Analysis technique

******2**** minimization with 3 parameters: ****fit with MINUIT**
**M****SUSY ****, ****M****GUT**** , 1/********GUT**
**Strong correlation (> 0.999) between M****GUT**** and 1/********GUT ****: problem can be re-factored with 2 parameters, taking 1/********GUT  ****as the weighted average of the 3 couplings at any given scale (****results are numerically the same except the error on the GUT coupling****)**
**Even so the correlation ****M****SUSY ****– ****M****GUT ****is > 0.96**
**Threshold corrections around the GUT scale (– 4%) for 2-loop-RG running fits**

## Running Couplings

**1-loop Renormalization Group (RG) running**** – can solve analytically **
**1/********(********) = 1/********(********) - (b****i****/2********) . ln(********/********)**
**The coefficients for the 3 couplings are *****independent*** **and given by the SM or MSSM**
**2-loop-RG running****: additional terms so the 3 couplings *****depend on each other***** – solved numerically; the errors depend on the *****scale*** **(for typical GUT scales they grow by 4, 12 and 6 % for the 3 couplings)**

## Results - SM

## Example of SUSY Fit

## Fit Results

** **

|  |       MSUSY 
          [GeV] |       MGUT
          [GeV] |     1/GUT |
| --- | --- | --- | --- |
| Low s(MZ)  0.117-0.118 |  |  |  |
|   S. Bethke 2004 | 101.6±0.5 | 1016.6±0.15 | 22.4 ± 0.9 |
|   ol = 0h l/h | 101.6±0.55 | 1016.6±0.17 | 22.6 ± 1.0 |
|   ALEPH 4-jet rate | 101.8±0.5 | 1016.6±0.15 | 22.8 ± 0.9 |
| High s(MZ)  0.122 |  |  |  |
|   h /  @ Z | 101.0±0.6 | 1016.8±0.2 | 21.3 ± 1.1 |

## New Analysis - Add More Data

**LEP2 has measured the qq cross section above Z with combined precision ~ 1% and theoretical uncertainty < 0.3 %**
**Fit the data with SM or SUSY running couplings (SUSY scale as parameter)**
**1/********(1,2,3) change in SM by  -0.9, 1.3, 11.3% from Z -> 201 GeV**
**1/********(1,2,3) will change by       -1.2, 0.4, 7.5% e.g. for SUSY scale ~ 130 GeV**

**Slight excess ~ 2 ******** is “filled” nicely by SUSY running**
**     ****93 < M****SUSY**** < 183 GeV          @ 95 % CL ****(preliminary)**

## Measurements of s

**The measurements are difficult and dominated by systematic uncertainties both at LEP2 (****theory and hadronization****) and CDF (****energy scale and resolution;** **interplay with the gluon PDF uncertainty at high X values****).**

**The**** ****experimental precision starts to approach the size of expected SUSY effects****, and we need better control of the systematics (****e.g. with increased statistics in Run 2****).**

## Conclusions

**The MSSM still provides coupling unification at a GUT scale well below the Planck scale for the newest set of measurements**** **
**The strong coupling is a key for interpreting the results: ****the “high” values require uncomfortably low SUSY scales ~ 10 GeV – excluded**
**The “low” ********s****(M****Z****)**** values favor SUSY scales just around the corner: ****M****SUSY  ****< ****265**** (419) GeV for ****Bethke ‘04**** (ALEPH 4-jet) at one-sided 95 % CL ******** ****or reversing the argument an attractive “low” SUSY scale favors ********s****(M****Z****) ~ 0.117 – 0.119**
**The LEP2 qq data hint to SUSY scales ****93 < M****SUSY**** < 183 GeV ******** in the same range favored by the unification fits**
**The SUSY scales emerging from this analysis are well in the LHC (TEVATRON?) direct discovery range**
**The GUT scale is higher: ****M****GUT****  ******** 10****16.6±0.15**** GeV ****& ****pushing the proton lifetime (~ 10****36**** years) well beyond the experimental limits (~ 5 x 10****33**** years)**