1. James Stirling (IPPP Durham)
LHC
James Stirling
(IPPP Durham)
Why are pdfs important for LHC phenomenology?
What do we know about pdfs?
What work still needs to be done?
What more can we learn about pdfs from LHC?
Workshop HP2, Zurich

2. pdfs at LHC
high precision (SM and BSM) cross section predictions require precision pdfs: th = pdf + …
improved signal and background predictions → easier to spot new physics deviations
‘standard candle’ processes (e.g. Z) to
check formalism (factorisation, DGLAP, …)
measure machine luminosity?
learning more about pdfs from LHC measurements. e.g.
high-ET jets → gluon?
W+/W– → quarks?
forward DY → small x? …
Workshop HP2, Zurich

3. x1P
proton
x2P M
momentum fractions x1 and x2 determined by mass and rapidity of X
x dependence of f(x,Q2) determined by fit to data, Q2 dependence determined by DGLAP equations:
DGLAP evolution
Q. is NLO (or NNLO) DGLAP sufficient at small x? Are higher-orders ~ αSn logm x important?
Workshop HP2, Zurich

4. how important is pdf precision?
Example 1: σ(MH=120 LHC
σpdf  ±3%, σptNNL0  ± 10%
σptNNLL  ± 8%
→ σtheory  ± 9%
Example 2: LHC
σpdf  ±3%, σptNNL0  ± 2%
→ σtheory  ± 4%
Example 3: quantitative limits
on New Physics depend
on pdfs
Catani et al,
hep-ph/

5. sensitivity of dijet cross section at LHC to large extra dimensions
LED accelerate the running of αS as the compactification scale Mc is approached
sensitivity attentuated by pdf uncertainties in SM prediction
Ferrag (ATLAS), hep-ph/
Workshop HP2, Zurich

6. typical data ingredients of a global pdf fit
Workshop HP2, Zurich

7. summary of DIS data + neutrino FT DIS data
Note: must impose cuts on DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically:
Q2 > GeV2
W2 = (1-x)/x Q2 > GeV2
Workshop HP2, Zurich

8. some current issues…
need a better understanding of differences between pdf sets (central values and error bands): not just ‘experimental errors’ (easier) but theoretical errors/assumptions too (harder)
are apparent ‘tensions’ between data sets caused by experiment or theory?
is fixed–order DGLAP adequate to describe small-x F2 , FL data from HERA? If not, what are implications for LHC phenomenology?
the impact of a full NNLO pdf fit? (needs NNLO jet )
Workshop HP2, Zurich

9. current issues contd.
impact (if any) on global fits of new Tevatron jet data, new HERA structure function data, and also HERA jet data? (via γ*g→jets)
flavour structure of sea: e.g. ubar  dbar and s  sbar (NuTeV)
relative behaviour of u and d at large x
QED/EW effects in pdfs (via O(α) corrections to DGLAP) …
Workshop HP2, Zurich

10. pdf uncertainties
MRST, CTEQ, Alekhin, GKK, … also produce ‘pdfs with errors’
typically, ‘error’ sets based on a ‘best fit’ set to reflect ±1 variation of all the parameters* {Ai,ai,…,αS} inherent in the fit
these reflect the uncertainties on the data used in the global fit (e.g. F2  ±3% → u  ±3%)
however, there are also systematic pdf uncertainties reflecting theoretical assumptions/prejudices in the way the global fit is set up and performed
* e.g.
Workshop HP2, Zurich

11. pdfs with errors….
CTEQ gluon distribution uncertainty using Hessian Method
output = best fit set + 2Np error sets
Hessian Matrix
“best fit” parameters
Workshop HP2, Zurich

12. high-x gluon from high ET jets data
both MRST and CTEQ use Tevatron jets data to determine the gluon pdf at large x
the errors on the gluon therefore reflect the measured cross section uncertainties
Workshop HP2, Zurich

13. Djouadi & Ferrag, hep-ph/0310209
Workshop HP2, Zurich

14. Higgs cross section: dependence on pdfs
Djouadi & Ferrag, hep-ph/
Workshop HP2, Zurich

15. Djouadi & Ferrag, hep-ph/0310209
Workshop HP2, Zurich

16. why do ‘best fit’ pdfs and errors differ?
different data sets in fit
different subselection of data
different treatment of exp. sys. errors
different choice of
tolerance to define   fi
(MRST: Δχ2=50, CTEQ: Δχ2=100, Alekhin: Δχ2=1)
factorisation/renormalisation scheme/scale
Q02
parametric form Axa(1-x)b[..] etc αS
treatment of heavy flavours
theoretical assumptions about x→0,1 behaviour
theoretical assumptions about sea flavour symmetry
evolution and cross section codes (removable differences!)
LHC
σNLO(W) (nb)
MRST2002
204 ± 4 (expt)
CTEQ6
205 ± 8 (expt)
Alekhin02
215 ± 6 (tot)
different Δχ2
similar partons
different partons
Workshop HP2, Zurich

17. tensions within the global fit
with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=?
‘tensions’ between data sets arise, for example,
between DIS data sets (e.g. H and N data, αS, …)
when jet and Drell-Yan data are combined with DIS data
Workshop HP2, Zurich

18. CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100
Workshop HP2, Zurich

19. Djouadi & Ferrag, hep-ph/0310209
Workshop HP2, Zurich

20. xg = Axa(1–x)becx(1+Cx)d
MRST: Q02 = 1 GeV2, Qcut2 = 2 GeV2
xg = Axa(1–x)b(1+Cx0.5+Dx)
– Exc(1-x)d
CTEQ6: Q02 = 1.69 GeV2, Qcut2 = 4 GeV2
xg = Axa(1–x)becx(1+Cx)d
Workshop HP2, Zurich

21. Note: CTEQ gluon ‘more or less’ consistent with MRST gluon
easy online comparison at HEPDATA repository: durpdg.dur.ac.uk/hepdata/pfd.html

22. parton luminosity functions
a quick and easy way to assess the mass and collider energy dependence of production cross sections
s M a b
i.e. all the mass and energy dependence is contained in the X-independent parton luminosity function in [ ]
useful combinations are
and also useful for assessing the uncertainty on cross sections due to uncertainties in the pdfs
Workshop HP2, Zurich

23. LHC / Tevatron
LHC
Tevatron
Campbell, Huston, S
Workshop HP2, Zurich

24. Workshop HP2, Zurich

25. Standard Candle cross sections as calibration?
exptl. pdf uncertainties on W, WH cross sections at LHC (MRST2001E)
could (W) or (Z) be used to calibrate other cross-sections, e.g. (WH), (ZH)?
(WH) more precisely predicted because it samples quark pdfs at higher x and Q2 than (W)
however, ratio shows no improvement in uncertainty, and can be worse
partons in different regions of x are often anti-correlated rather than correlated, partially due to sum rules.
Workshop HP2, Zurich

26. why NNLO?
The higher we calculate in fixed-order perturbation theory, the weaker the (renormalisation and factorisation) scale dependence and the smaller the theoretical error σth on the cross section
 = A αS(R)N [ 1 + C1 (R) αS(R) + C2 (R) αS(R)2 + …. ]
Other advantages of NNLO:
better matching of partons  hadrons
reduced power corrections
better description of final state kinematics (e.g. transverse momentum)
The calculation of the complete set of P(2) DGLAP splitting functions by Moch, Vermaseren and Vogt (hep-ph/ , ) provides the essential tool for a consistent NNLO pQCD global pdf fit. Only significant missing ingredient is NNLO correction to high-ET jet cross section.
Workshop HP2, Zurich

27. Anastasiou, Dixon, Melnikov, Petriello (hep-ph/0306192)
problem: NNLO fit
 smaller high-x sea quarks
 smaller high-x gluon
 tension with high-ET jet fit
Anastasiou, Dixon, Melnikov, Petriello (hep-ph/ )
Workshop HP2, Zurich

28. NNLO features quality of global fit slightly improved
αS slightly reduced
sizeable change in partons in some regions of (x,Q2)
new 2006 MRST NNLO pdfs (w/errors) in preparation
Workshop HP2, Zurich

29. small x convergence of fixed-order DGLAP at small x?
saturation (i.e. non-linear 1/Q2) contributions?
global fit slightly improved by inclusion of HO ln(1/x) terms (Thorne, White)
longer Q2 lever arm requires small-x pdf measurement at LHC
DGLAP evolution?
Workshop HP2, Zurich

30. HERA measurement of FL now likely
theories with extensions at small x, both resummations and higher twist, produce quite different predictions for FL(x,Q2) from that at NLO and NNLO
similar variation expected for other gluon-sensitive quantities, e.g. at LHC
HERA measurement of FL now likely
Thorne

31. forward Z0 production in LHCb …
Workshop HP2, Zurich

32. Workshop HP2, Zurich

33. low-mass Drell-Yan production in ATLAS…!
Workshop HP2, Zurich

34. very low-mass Drell-Yan production in ALICE
(pp running at 1031 cm-2 s-1)
Workshop HP2, Zurich

35. other pdf-related quantities…
Workshop HP2, Zurich

36. bbZ contribution to Z production @ LHC
Careful! This is in a VFNS. In a FFNS this contribution is generated by the NNLO contribution: gg→Zbb
Workshop HP2, Zurich

37. LHC: ratio of W– and W+ rapidity distributions
x1=0.52
x2=
x1=0.006
x2=0.006
ratio close to 1 because u  u etc.
(note: MRST error = ±1½%) –
sensitive to large-x d/u
and small x u/d ratios
Q. What is the experimental precision? –
Workshop HP2, Zurich

38. ! flavour decomposition of W cross sections at hadron colliders
recall that the only constraint on very small x quarks from inclusive DIS (F2ep) data is on the combination
4/9 [u+c+ubar+cbar]
+ 1/9 [d+s+dbar+sbar]
Workshop HP2, Zurich

39. summary and outlook
origin of differences between pdf sets (central values and error bands) is largely understood, and overall MRST vs. CTEQ differences are relatively small
is fixed–order DGLAP adequate to describe small-x F2 , FL data from HERA? If not, what are implications for LHC phenomenology? Can LHC measure small x pdfs?
needed for LHC start-up: full NLO and NNLO pdfs with errors (needs NNLO jet ) incorporating all available HERA and Tevatron data
pdf’ers still interested in flavour structure of sea: e.g. ubar  dbar and s  sbar (NuTeV). Can LHC provide information? (e.g. s g → W c )
Workshop HP2, Zurich

40. extra slides

41. QCD factorization theorem for short-distance inclusive processes
where X=W, Z, H, high-ET jets, … and  known
to some fixed order in pQCD and EW
in some leading logarithm approximation (LL, NLL, …) to all orders via resummation ^
full NNLO pQCD, supplemented by NNLL and electroweak corrections where appropriate, is the goal for LHC

42. extrapolation uncertainties
theoretical insight/guess: f ~ A x as x → 0
theoretical insight/guess: f ~ ± A x–0.5 as x → 0
Workshop HP2, Zurich

43. pdfs from global fits fi (x,Q2)   fi (x,Q2) Formalism NLO DGLAP
MSbar factorisation
Q02
functional Q02
sea quark (a)symmetry
etc.
fi (x,Q2)   fi (x,Q2)
αS(MZ )
Data
DIS (SLAC, BCDMS, NMC, E665,
CCFR, H1, ZEUS, … )
Drell-Yan (E605, E772, E866, …)
High ET jets (CDF, D0)
W rapidity asymmetry (CDF)
N dimuon (CCFR, NuTeV)
etc.
Who?
Alekhin, CTEQ, MRST,
GGK, Botje, H1, ZEUS,
GRV, BFP, …
Workshop HP2, Zurich

44. uncertainty in gluon distribution (CTEQ)
CTEQ6.1E: error sets
MRST2001E: error sets
Workshop HP2, Zurich

45. future hadron colliders: energy vs luminosity?
recall parton-parton luminosity:
so that
with  = MX2/s
for MX > O(1 TeV), energy  3 is better than luminosity  10 (everything else assumed equal!)
Workshop HP2, Zurich

46. what limits the precision of the predictions?
the order of the perturbative expansion
the uncertainty in the input parton distribution functions
example: LHC
σpdf  ±3%, σpt  ± 2%
→ σtheory  ± 4%
whereas for gg→H :
σpdf << σpt
2% total error
(MRST 2002)
4% total error
(MRST 2002)
Workshop HP2, Zurich

47. longer Q2 extrapolation smaller x
Workshop HP2, Zurich

48. differences between the MRST and Alekhin u and d sea quarks near the starting scale
ubar=dbar
Workshop HP2, Zurich

49. Workshop HP2, Zurich

50. σ(W) and σ(Z) : precision predictions and measurements at the LHC
σNLO(W) (nb)
MRST2002
204 ± 4 (expt)
CTEQ6
205 ± 8 (expt)
Alekhin02
215 ± 6 (tot)
different Δχ2
similar partons
different partons
4% total error
(MRST 2002)
Workshop HP2, Zurich

51. ±2%
±3%
contours correspond to ‘ experimental’ pdf errors only; shift of prediction using CTEQ6 pdfs shows effect of ‘theoretical’ pdf errors
Workshop HP2, Zurich

52. Workshop HP2, Zurich

53. Workshop HP2, Zurich

54. Workshop HP2, Zurich

55. (LO) W cross sections at the Tevatron and LHC using (NLO) partons from MRST, CTEQ and Alekhin
B.σ(W) (nb)
MRST2002
2.14
CTEQ6
2.10
Alekhin02
2.22
LHC
B.σ(W+) (nb)
B.σ(W) (nb)
W+/W–
MRST2002
10.1
7.6
1.33
CTEQ6
10.2
1.34
Alekhin02
10.7
7.9
1.35
Workshop HP2, Zurich

56. differences between the MRST, CTEQ and Alekhin strange quarks near the starting scale
Workshop HP2, Zurich

57. effect of NNLO correction on Higgs production at LHC
Workshop HP2, Zurich