# Presentation: 530021

## Squarks & Gluinos + Jets:from ttbar to SUSY at the LHC

- Peter Skands (Fermilab)
- with
-  T. Plehn (MPI Munich), D. Rainwater (U Rochester),
- & T. Sjöstrand (CERN & Lund U),

- SUSY EuroGDR, Barcelona, November 2005

## Overview

- QCD @ high energy: 								scales, logs & hands
- LHC: ttbar production
- LHC: SUSY pair production
- Outlook ...

## QCD

- Known Gauge Group and Lagrangian
- Rich variety of dynamical phenomena, not least _confinement_.

- Large coupling constant also means _perturbative_ expansion tricky.

- To calculate higher _perturbative_ orders, 2 approaches:
- Feynman Diagrams
- Complete matrix elements order by order ****
- Complexity rapidly increases ****
- Resummation
- In certain limits, we are able to sum the entire perturbative series to infinite order **** parton showers are examples of such approaches.
- Exact only in the relevant limits ****

## Approximations to QCD

- _Fixed order matrix elements: Truncated expansion in ____S__ ___
- Full intereference and helicity structure to given order.
- Singularities appear as low-pT log divergences.
- Difficulty (computation time) increases rapidly with final state multiplicity  limited to 2  5/6.

- _Parton Showers: infinite series in ____S__ (but only singular terms = collinear approximation)._
- Resums logs to all orders  excellent at low pT.
- Factorisation  Exponentiation  Arbitrary multiplicity
- Easy match to hadronisation models
- Interference terms neglected + simplified helicity structure + ambiguous phase space  large uncertainties away from singular regions.

## What’s what?

- Matrix Elements correct for ‘hard’ jets
- Parton Showers correct for ‘soft’ ones.

- So what *is* ‘hard’ and what is ‘soft’?

- And to what extent can showers be constructed and/or tuned to describe hard radiation?           (PS: I’m not talking about matching here)

## Collider Energy Scales

- HARD SCALES:
-  s : collider energy
-  pT,jet : extra activity
-  QX : signal scale (ttbar)
-  mX : large rest masses

- SOFT SCALES:
-   : decay widths
-  mp : beam mass
-  QCD : hadronisation
-  mi : small rest masses

- + “ARBITRARY” SCALES:
-  QF , QR : Factorisation & Renormalisation

## A handwaving argument

- _Handwavingly_, leading logs are:
- So, very roughly, logs become large for jet pT around 1/6 of the hard scale.

- A handwaving argument

- Quantify: what is a soft jet?

## Stability of PT at Tevatron & LHC

**Slide from Lynne Orre**
**Top Mass Workshop**

**ttbar**

## To Quantify:

- Compare MadGraph (for ttbar, and SMadGraph for SUSY), with 0, 1, and 2 explicit additional jets to:
- 5 different shower approximations (Pythia):

**NB: Renormalisation scale in p****T****-ordred showers also varied, between p****T****/2 and 3p****T**** **

- Last Week: D. Rainwater, T. Plehn & PS - hep-ph/0510144

- pT-ordered showers: T. Sjöstrand & PS - Eur.Phys.J.C39:129,2005

- ‘Wimpy Q2-ordered’ **(PHASE SPACE LIMIT < Q****F****) **
- ‘Power Q2-ordered’ **(PHASE SPACE LIMIT = s)**
- ‘Tune A’ (Q2-ordered) **(PHASE SPACE LIMIT ~ Q****F****)**

- ‘Wimpy pT-ordered’ **(PHASE SPACE LIMIT = Q****F****)**
- ‘Power pT-ordered’ **(PHASE SPACE LIMIT = s)**

## (S)MadGraph Numbers

- T = 600 GeV top

- sps1a

- 1) Extra 100 GeV jets are there ~ 25%-50% of the time!
- 2) Extra 50 GeV jets - ??? No control  We only know ~ a lot!

## ttbar + jets @ LHC

**SCALES [GeV]**
- s = (14000)2
- Q2Hard ~ (175+...)2
- 50 < pT,jet < 450

**RATIOS:**
- Q2H/s = (0.02)2
- 1/5 < pT / QH < 2.5

- _Process characterized by:_
-  _Mass scale is small_* *compared to s
-  _A 50-GeV jet is hard_, in comparison with hard scale ~ top mass, but is soft compared with s.

## ttbar + jets @ LHC

- _Hard tails_: More phase space (+ gluons)  more radiation.
-  Power Showers still reasonable (but large uncertainty!)
-  Wimpy Showers (dashed) drop catastrophically around top mass.

-  _Soft peak_: logs slightly larger (scale larger than mtop, since not threshold dominated here)  but fixed order still reasonable for 50 GeV jets.

**SCALES [GeV]**
- s = (14000)2
- Q2Hard ~ (175+...)2
- 50 < pT,jet < 450

**RATIOS**
- Q2H/s = (0.02)2
- 1/5 < pT / QH < 2.5

- NLO K-factor

- NLO K-factor

## SUSY + jets @ LHC

**SCALES [GeV]**
- s = (14000)2
- Q2Hard ~ (600)2
- 50 < pT,jet < 450

**RATIOS**
- Q2H/s = (0.05)2
- 1/10 < pT / QH < 1

- _Process characterized by:_
-  _Mass scale is large_ compared to s
-  _But a 50-GeV jet is now soft_, in comparison with hard scale ~ SUSY mass.

- (SPS1a  mgluino=600GeV)

## SUSY + jets @ LHC

- NLO K-factor

- NLO K-factor

- _Hard tails_: Still _a lot_ of radiation (pT spectra have moderate slope)
-  _Parton showers less uncertain_, due to _higher_ signal mass scale.

-  _Soft peak_: fixed order breaks down for ~ 100 GeV jets.  Reconfirmed by parton showers  universal limit below 100 GeV.

**SCALES [GeV]**
- s = (14000)2
- Q2Hard ~ (600)2
- 50 < pT,jet < 450

**RATIOS**
- Q2H/s = (0.05)2
- 1/10 < pT / QH < 1

**No description is perfect everywhere! **
****** ****To improve, go to ME/PS ****matching ****(CKKW / MC@NLO / ...) **

## Conclusions

- SUSY-MadGraph soon to be public.
- Comparisons to PYTHIA Q2- and pT2- ordered showers  New illustrations of old wisdom:
- _Hard jets_ (= hard in comparison with signal scale)  collinear approximation misses relevant terms  use matrix elements with explicit jets                 interference & helicity structure included.
- _Soft jets_ (= soft in comparison with signal process, but still e.g. 100 GeV for SPS1a)                            singularities give large logarithms                                                  use resummation / parton showers to resum          	   logs to all orders.

## Conclusions

- SUSY at LHC is more similar to top at Tevatron than to top at LHC, owing to similar *ratios* of scales involved
- (but don’t forget that ttbar is still mainly qq-initiated at the Tevatron).

- Parton Showers *can* produce realistic rates  for hard jets, though not perfectly 
- Ambiguities in hard region  between different approximations (e.g. wimpy vs power, Q2 vs pT)  gives possibility for systematic variation 
- Better showers = good  Matched approaches better! ☼

## Conclusions

## More SUSY: ~uL~uL

- ME Divergence much milder than for ~g~g !

- Possible cause: qq-initiated valence-dominated initial state  less radiation.

## More SUSY: ~uL~uL*

- Other sea-dominated initial states exhibit same behaviour as ~g~g