# Presentation: 744681

## QCD Resummations for Hadronic Collisions

**Werner Vogelsang**
**RBRC and BNL Nuclear Theory**
**RHIC/AGS Users’ Meeting 2005  **

## Outline:

-     qT resummations and threshold resummations
- How is resummation done?
- Phenomenology
- Conclusions

**Outline:**

**Collab. with   ****G. Sterman, A. Kulesza; D. de Florian**

## I. Introduction

## Characterized by large scale  Q  ~  pT,  M,  MW, ...  

**Hard scattering in hadron collisions**

##   fa,b parton distributions :  non-perturbative, but universal

**  ****f****a,b**** parton distributions :  ****non-perturbative, but universal**

**  ****corrections to formula :   ****down by inverse powers of Q**

## Successes :

## at RHIC

**at ****RHIC**

## Slide 8

## •  when one reaches an “exclusive boundary”

** ****theory fails even in  the presence of a hard scale**

**•****  ****when one reaches an “exclusive boundary”**

## •  first-order correction :

**“****recoil logarithms”**

## qT  distribution is measurable : 

**q****T  ****distribution is measurable : **

## •  other example of this type : back-to-back correlatn.

**large scale is**
**jet p****T**

## •  perturbation theory appears in distress

**•  ****phenomenon (and solution) well understood **

**For q****T********0  real radiation is inhibited, **
** ****only soft emission is allowed:  affects IR cancellations**

## •  the cross sections just considered are in a way special:

**from parton k****T**

**large scale Q,  differential in (small) observed q****T **

## “threshold logarithms”

**“****threshold logarithms”**

## •  unlike qT, one doesn’t really measure partonic energy ...

## Perhaps involved in explanation of shortfall of NLO

**Apanasevich  et al.**
**(see also Aurenche et al.; **
** ****Bourrely, Soffer)**

**Perhaps involved in explanation of shortfall of NLO**
**for                         at lower energies ?**

##       = Resummation !

**• **** ****two-scale problems **

## II. How resummation is done

## If both occur  exponentiation of 1-gluon em. 

**Consider  emission of  ****n****  soft gluons :**

**If both occur ******** exponentiation of 1-gluon em.**** **

## Concerning (1) :

**Concerning (1) :**

## Concerning (2) :

**phase-space  ****delta-functions  ****connect gluons**

**For Drell-Yan cross section at small q****T**** :**

## Choice of transform depends on observable : 

**Choice of transform depends on observable : **

**for threshold logs**

## •  exponentiation gives :

****** ****for q****T**** resummation in DY, find LL**

## •  What is the general structure ?

**Fixed  order **

**Resummation**

## III. Phenomenology of Resummation

## Kulesza, Sterman, WV

**Kulesza, Sterman, WV**

## Why non-perturbative piece ?

## Contribution from very low k

**• **** ****suggests Gaussian non-pert. contribution with **
**    ****logarithmic Q dependence**

**•****  ****for Z production at CDF & D0, fit gives coefficient  ****0.8 GeV****2**

**•****  ****more “global”  fits see log(Q) dependence  ****Davies, Webber, Stirling;**
**                                                                                                   ****Landry et al., Ladinsky, Yuan; Qiu, Zhang**

## •  dashed line: including Sudakov effects

- •  dashed line: including Sudakov effects

## at lower  energies

**Apanasevich  et al.**
**(see also Aurenche et al.; Bourrely, Soffer)**

**at lower  energies**

## Why problems in fixed-target regime ?

**Why problems in fixed-target regime ?**

** ****Why “near perfect” at colliders ?**

##   soft-gluon effects  exponentiate :

## How dominant are they ?

******  ****subleading terms important at collider energies**

**How dominant are they ?**

## Slide 35

## E706

**de Florian, WV**

**E706**

## WA70

**de Florian, WV**

## Application to prompt photons:

**“****direct” contributions:**

**“****fragmentation” contributions:**

**relatively small resum. effects**

**a bit like ********0  ****production,**
**but less gg********gg because**
**D****g********   ****is smaller**

## de Florian, WV

**de Florian, WV**

## de Florian, WV

**de Florian, WV**

## Can one estimate non-pert.

**  ****power corrections here ?**** **

## •  ill-defined because of strong-coupling regime

**DY:**

**• **** ****regime of very  low         :  **

**• **** ****overall powers all**** even,  exponentiating ! **

**Sterman, WV**

## •  for single-inclusive cross sections                       :  

**• **** ****then,                      **

**•  ****connects         and         to  values from         resummation ?**

**• **** ****qualitatively,  for inclusive hadrons,  replace    **

**Sterman, WV**

**fairly small effect**

## IV. Conclusions

##   resummation can be crucial in hadronic cross sections