# Presentation: 361596

## Radiation in high-^s final states

- Peter Skands (FNAL)
- with T. Plehn (MPI Munich) & D. Rainwater (U Rochester)

- ILC Workshop, Snowmass CO, Aug 2005

## Overview

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

## Collider Energy Scales

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

## 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

## Approximations to QCD

- _Fixed order matrix elements: Truncated expansion in ____S__ ___
- Full intereference and helicity structure included to given order.
- Divergences 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  large uncertainties away from singular regions.

## A handwaving argument

- A handwaving argument

- Quantify: what is a soft jet?

## A handwaving argument

- A handwaving argument

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

## ttbar + jets @ Tevatron

**SCALES [GeV]**
- s = (2000)2
- Q2Hard ~ (175)2
- 50 < pT,jet < 250

****** ****RATIOS**
- Q2H/s = (0.1)2
- 1/4 < pT / QH < 2

- _Process characterized by:_
-  Threshold production (mass large compared to s)
-  A 50-GeV jet is reasonably hard, in comparison with hard scale ~ top mass

## ttbar + jets @ Tevatron

**SCALES [GeV]**
- s = (2000)2
- Q2Hard ~ (175)2
- 50 < pT,jet < 250

**RATIOS**
- Q2H/s = (0.1)2
- 1/4 < pT / QH < 2

## ttbar + jets @ Tevatron

- _Hard tails_:
-  Power Showers (solid green & blue) surprisingly good (naively expect *collinear* approximation to be worse!)
-  Wimpy Showers (dashed) drop rapidly around top mass.

- _Soft peak_: logs large @ ~ mtop/6 ~ 30 GeV  fixed order _still good_ for 50 GeV jets (did not look explicitly below 50 GeV yet)

**SCALES [GeV]**
- s = (2000)2
- Q2Hard ~ (175)2
- 50 < pT,jet < 250

**RATIOS**
- Q2H/s = (0.1)2
- 1/4 < pT / QH < 2

## 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 still hard, in comparison with hard scale ~ top mass, but is now soft compared with s.

## ttbar + jets @ LHC

- _Hard tails_: More phase space  more radiation.
-  Power Showers still reasonable (but caution advised!)
-  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

## 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 again large compared to s
-  But a 50-GeV jet is now soft, in comparison with hard scale ~ SUSY mass.

- (SPS1a)

## SUSY + jets @ LHC

- _Hard tails_: Still _a lot_ of radiation (pT spectra have moderate slope)
-  Parton showers _less _uncertain, due to _higher_ signal mass scale. Drop of wimpy showers happens later ~ 600 GeV.

-  _Soft peak_: logs _BIG:_ 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

-  (2 jet sample: matrix element blowing up  artificially large norm. difference?)

## pT of hard system(Equivalent to pT,Z for Drell-Yan)

****** ****Resummation necessary**
**Bulk of cross section sits in peak sensitive to multiple emissions.**

- ~uL~g + 1 jet @ LHC
- pT of (~uL~g) system

- ttbar + 1 jet @ LHC
- pT of (ttbar) system

- ~g~g + 1 jet @ LHC
- pT of (~g~g) system

## 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)  large logarithms  use resummation / parton showers to resum logs to all orders.

## 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)  large logarithms  use resummation / parton showers to resum logs to all orders.