# Presentation: 024039

## Proton structure, partons and DGLAP

- quark-parton model
- Evidence for gluons.  Need for colour.
- QCD as a gauge theory
- RGE, running coupling and the beta function
- QCD effects in DIS
- DGLAP equations,  universal partons
- Global parton analyses
- Diffractive DIS and diffractive partons

- CONTENTS

- School on QCD....Calabria,   July 2007   ---    Alan Martin (Durham)

## electron-proton scattering

**q**

- electron

- proton

- quark

- quark acts as if free,
- yet never seen ?
- big puzzle   ~1970
-               QCD

- virtual photon

- (real particle:                                    )

## H1 detector at HERA

- struck quark

- proton
- fragments

- outgoing electron

## Slide 4

## Slide 5

## Slide 6

## e-p scattering

- now
- M=mp
- R=Rp

## Slide 8

## Slide 9

## Slide 10

## QCD scaling

- violations

## F2

- x=0.002

- F2

- Q2

- x=0.65

- x=0.13

- Wilczek’s QCD
- log Q2 scaling
- violations

## e-quark

## (for moment assume

## We will assume  exchange only --- so F3=0 --- come back to this later

- We will assume  exchange only --- so F3=0 --- come back to this later

## 4

## Slide 18

## Slide 19

## Slide 20

## {       Y+     }

- {       Y+     }

- ignore Z exch

## Slide 22

## Slide 23

## Y+ = 1 + (1-y)2

- 2

- Y+ = 1 + (1-y)2

- Y- = 1 - (1-y)2

- c=0

## (e+p)~(1-y)2xd

- (e+p)~(1-y)2xd

## W

- 

- ,Z

## Slide 27

## Slide 28

## Slide 29

## Slide 30

## Puzzle “explained” by QCD 

- Puzzle “explained” by QCD
- non-abelian gauge theory

## Slide 32

## Slide 33

## Slide 34

## Slide 35

## Slide 36

## Running

- coupling

- QED

## QED

- QED coupling
- runs

- Vacuum is
- polarised

## Slide 39

## QCD

- like

## Nobel prize -- 2004

- QCD -- 1973

- Gross  Wilczek   Politzer

## Slide 42

## Slide 43

## Slide 44

## Slide 45

## Slide 46

## Slide 47

## Slide 48

## Slide 49

## Slide 50

## Slide 51

## Slide 52

## Slide 53

## 7 pages later...

- Moch, Vermaseren and Vogt,
- hep-ph/0403192, hep-ph/0404111

## Slide 55

## Slide 56

## Slide 57

## Slide 58

## Slide 59

## Slide 60

## Slide 61

## (1-x)

- (1-x)

- x

## Thus should use a Variable Flavour Number Scheme

- Thus should use a Variable Flavour Number Scheme
- in which a matching is performed at the heavy quark
- thresholds

## Slide 64

## MRST

## Slide 67

## DGLAP

## Q2

**DGLAP**

- Higgs

- Q2

- x

**HERA**

**LHC**

- 10-5

- 10-3

## Rates at LHC

- or, more exciting,
- something totally
- unexpected

## DIS

- Diffractive DIS

- If then assume, Regge factorization:

- gap

- same

## Q2

- Q2

- x

**HERA**

**LHC**

- 10-5

- 10-3

- HERA: a unique probe of small x

## Q2

- Q2

- x

**HERA**

**LHC**

- 10-5

- 10-3

- HERA: a unique probe of small x

## HERA

- Regge

- confinement

- BFKL

- DGLAP

- ln Q2

- ln 1/x

- saturation

- absorptive corr.

**HERA**

- pQCD

- soft

- Has HERA seen
-   BFKL?
-   Absorption?
-   Regge (soft
-                pQCD)

- small x domain
- unique to HERA

## “soft” – particles go forward – no large scale – no pQCD

- domain of Regge exchange:  at HE  Pomeron exchange

- DL:

- 1.08

- 0.25

- shrinks

## HERA data for

- DL

-     p   p
- less rescattering
- than  pp  pp

- smaller

- larger

## BFKL:

- LL+NLL+partial
- all-order resum

## Photoprod. of vector mesons

- soft

- hard

- (J/)~(gluon)2
- better theory
- gluon 10-4<x<10-2

## To identify BFKL need to “neutralize” DGLAP

- Ex.1:   forward jet with kT~Q
- choose xj as large as possible,
- xj~0.1,   lose small (x/xj) “reach”

- t

- Ex. 2:     p  Y  at large t
- measure W dependence in a
- bin at large t for MY<5 GeV, say

- Y

- W

## Evidence of absorptive/

- DIS leading neutron
- data reveal information
- on the parton distributions
- of  in the unexplored
- small x domain.

-  exch

-  with abs.

- (1/)d/dxL

- xL

- 1

- 0.4

- rescatt. effects at HERA

- 1.

## 2. Diffractive dijet production at HERA:

-     Interesting rescattering effects predicted,
-     but await the final experimental (H1, ZEUS) verdict.

- 4. Impact parameter dep. dipole description, with DGLAP
-     evolution, of vector meson production, DVCS, F2,....
-     gives evidence of a saturation scale Qs2 < 1 GeV2
-     in the HERA kinematical domain.

- 3. HERA data for  p  V p, with V =, J/.., gives an
-     effective Pomeron slope, ’, which decreases as
-     Q2+M2 increases --- i.e. rescatt./absorption decreases

## gap

- electron

- outgoing
- proton

- X

- diffractive DIS:  epeX+p  (*pX+p)

-  DIS:  epeX      (*pX)

- HERA finds that about 10% of these events are

## Diffractive deep inelastic scattering     (DDIS)

## Diffractive DIS occurs at about 10-20% the rate of DIS

- How should we analyse DDIS data?
- How do we treat DDIS events in global analyses of DIS data?

-   are they in the input distributions?
-   or, do we allow for them in the DGLAP evolution?

## DDIS data (,xP,Q2)

- DDIS data (,xP,Q2)
- ZEUS:  LPS + MX
- H1:       FPS + LRG

## DDIS scaling violations

- x=0.18

- x=0.67

## collinear factn proved for DDIS (Collins),  but

- collinear factn proved for DDIS (Collins),  but
- important modifications in the HERA regime

- Conventionally DDIS analyses use two levels of factorisation
-            - collinear factorization and Regge factorization

- Regge factn

## lots of gluons at high x,

- lots of gluons at high x,
- theoretically puzzling from
- a perturbative viewpoint

## Hint of problem with Regge factorisation assumption

- assumes Pomeron ~ hadron of size R
- Regge factn occurs in non-pert region <0, where ~1/R
- but  P(0)~1.2 from DDIS  >  P(0)~1.08  from soft data
-  small-size component from pQCD domain with larger P(0)

-  Replaces Regge factorization by pQCD

- Collinear factorization, which holds asymptotically, must be
-          modified in the HERA regime:
-            -- inhomogeneous term in DGLAP evolution
-            -- direct charm contribution
-            -- twist-4 FLD component

- New DDIS analysis---Watt, Martin, Ryskin

## rapidity gap

- rapidity gap

- pert. contrib.

## given by pQCD

## inclusion of the inhomogeneous term makes  gP  smaller

- xP=0.003
- Q2=15 GeV2

- gP

- inhomog. term

- inclusion of the inhomogeneous term makes  gP  smaller

## g:  valence-like

- S: Pomeron-like
- whereas expect
-   g ~ S ~ 0.1
- (xg ~ x –g
-  xS ~ x –S )
- Would have
- anticipated both
- driven by same
- vac. singularity

- global partons at

- but one of the
- HERA surprises....

## Pomeron made of

- two gluons

- need to introduce
- col. singlet qq pair

- Now Pomeron flux factors depend on  Sp  as well as  gp

- as well as

## diffractive partons  gD, qD  can be used to predict 

- diffractive processes with hard scale?  Yes, but...

- direct+resolved
- Pomeron
- (cf. photon)

## HERA

**HERA**

**CDF**

- soft
- rescatt.

- CDF diffr. dijet data

- gap

- gap

## Contribution of diffractive F2 to inclusive F2

- Apply the AGK cutting rules to              contrib.

- AGK in QCD: Bartels & Ryskin

- F2abs ~ - F2D

- negative    (~Glauber shadowing)

- Im Tel ~ tot

- Analysis of DDIS data can quantify absorptive corrections
-                                                            to global partons

- In practice, altho’ reduces the need for a negative gluon, it is still
- valence-like at low scales

## Q2

- Q2

- DGLAP evolution:
- parton creation

- Regge

- 0                 ~1 GeV2

- Absorption:
- parton
- recombination

- hadronparton
- transition

- Diffractive DIS data
- provide the link via
- the AGK cutting rules

## yW=0:   

- yW=0:
- x1=x2= MW/sqrt(s)
-          = 80/2000
-          = 0.04 (Tevatron)

- y:
- x1=MWey/sqrt(s)
- x2=MWe-y/sqrt(s)

- this gives the total W  ------  but given rapidities correspond to

## forward W, Z, dijet... production at LHC samples small and high x

- but no acceptance, no triggers?!

- yW=0:    x1=x2=MW/sqrt(s)  = 80/14000 = 0.006 (LHC)

## Slide 102

## Drell-Yan prod.

- Anastasiou, Dixon, Melnikov, Petriello

- pp
- LO:  qq
- NLO: gqq
-          qqg
-       +virt. interf.
- Unique determn
- of sea quark
- distribution at
- large x

## u(x,Q2=10 GeV2)

- u(x,Q2=10 GeV2)

- NNLO

- NLO

- % error

## s from DIS

- but  all include the crucial BCDMS  F2 data

******s**** from DIS**

- RPP2006

## 8 orders of magnitude!

- Highest *E**T* jets ever!

## examples of ‘precision’ phenomenology

**W, Z production**

**jet production**

**NNLO QCD**

**NLO QCD**

## NNLO phenomenology already under way...

-  the pQCD series appears to be under control
-  with sufficient theoretical precision, these ‘standard candle’ processes could be used to measure the ***machine luminosity***

## W prod. at the LHC

- Anastasiou, Dixon,
- Melnikov, Petriello

- LO:   udW+         duW--

## Other uncertainties include

**Other uncertainties include**
- selection of data fitted;  choice of x,Q2,W2 cuts
- Theoretical uncertainties
- higher-order DGLAP     NLO, **NNLO...**
- sln(1/x)  and sln(1-x)  effects
- absorptive corrections from parton recombination
- residual higher-twist effects
- QED effects
- Uncertainties due to input assumptions
- isospin-violating effects  MRST
- s not equal to s               CTEQ
- heavy-target corrections
- choice of input parametrization

- no NuTeV sin2W anomaly?

## Slide 111

## DIS and related data

- global partons

- predictions at
- hadron colliders

- Djouadi and Ferrag

- F2(x,Q2)

- Q2

- x

- MH

## how large is the DGLAP domain ?

are BFKL  (log 1/x)  effects evident ?

is there any evidence of absorptive corrections, or even parton saturation ?

HERA observes diffractive DIS (at ~10% of DIS).   What role does it play ?

- how large is the DGLAP domain ?
- are BFKL  (log 1/x)  effects evident ?
- is there any evidence of absorptive corrections, or even parton saturation ?
- HERA observes diffractive DIS (at ~10% of DIS).   What role does it play ?

## Slide 114

## xBFKL tamed

- xBFKL tamed

- Ciafaloni, Colferai
- and Salam

## zPgg(z)

- “BFKL” power growth in x
- does not start until here

- LO DGLAP

- zPgg(z)

- LL BFKL

- Resum BFKL

## Salam

- NLLO DGLAP ~ resum BFKL
- additional log 1/x effects
- small at HERA  (x>10-4)

- BFKL effects negligible in NNLO DGLAP analyses of HERA data

## g:  valence-like

- S: Pomeron-like
- whereas expect
- g ~ S ~ 0.1
- (xg ~ x –g
-  xS ~ x –S )

- global partons at

- but one of the
- HERA surprises....

## Slide 119

## Slide 120

## W~100 GeV      x~10-3

- W~100 GeV      x~10-3

## Slide 122