Theory of Proton-Proton Collisions

James StirlingIPPP, Durham University

SSI 2006 2

references

“QCD and Collider Physics”

RK Ellis, WJ Stirling, BR WebberCambridge University Press (1996)

also

“Handbook of Perturbative QCD”

G Sterman et al (CTEQ Collaboration)www.phys.psu.edu/~cteq/

SSI 2006 3

… and

“Hard Interactions of Quarks and Gluons: a Primer for LHC Physics ”

JM Campbell, JW Huston, WJ Stirling (CSH)

www.pa.msu.edu/~huston/seminars/Main.pdf

to appear in Rep. Prog. Phys.

SSI 2006 4

past, present and future proton/antiproton colliders…

Tevatron (1987→)Fermilab

proton-antiproton collisions√S = 1.8, 1.96 TeV

LHC (2007 → )CERNproton-proton and heavy ion collisions√S = 14 TeV

SppS (1981 → 1990)CERNproton-antiproton collisions√S = 540, 630 GeV

-

discoveries

1970 1980 1990 2000 20202010

tc b W,Z H, SUSY?

Higgs discovery at LHC

SUSY discovery at LHC

SSI 2006 6

Scattering processes at high energy hadron colliders can be classified as either HARD or SOFT

Quantum Chromodynamics (QCD) is the underlying theory for all such processes, but the approach (and the level of understanding) is very different for the two cases

For HARD processes, e.g. W or high-ET jet production, the rates and event properties can be predicted with some precision using perturbation theory

For SOFT processes, e.g. the total cross section or diffractive processes, the rates and properties are dominated by non-perturbative QCD effects, which are much less well understood

What can we calculate?

Outline• Basics: QCD, partons, pdfs

– basic parton model ideas for DIS– scaling violation & DGLAP– parton distribution functions

• Application to hadron colliders– hard scattering & basic kinematics– the Drell Yan process in the parton model– order αS corrections to DY, singularities, factorisation– examples of other hard processes and their phenomenology – parton luminosity functions – uncertainties in the calculations

• Beyond fixed-order inclusive cross sections– Sudakov logs and resummation– parton showering models (basic concepts only!)– the role of non-perturbative contributions: intrinsic kT,– underlying event/minimum bias contributions– theoretical frontiers: exclusive production of Higgs

Basics of QCD

• renormalisation of the coupling

• colour matrix algebra

0

1

μ (GeV)

αS(μ)

perturbative

non-perturbative

quark quark

αS = gS2/4π

gluongluon

gluon

gS Taij

gluon

gS fabc

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Asymptotic Freedom

“What this year's Laureates discovered was something that, at first sight, seemed completely contradictory. The interpretation of their mathematical result was that the closer the quarks are to each other, the weaker is the 'colour charge'. When the quarks are really close to each other, the force is so weak that they behave almost as free particles. This phenomenon is called ‘asymptotic freedom’. The converse is true when the quarks move apart: the force becomes stronger when the distance increases.”

1/r

αS(r)

SSI 2006 10

deep inelastic scattering and the parton model

qμ

pμ

X

electron

proton

• variablesQ2 = –q2 (resolution)

x = Q2 /2p·q (inelasticity)

• structure functionsdσ/dxdQ2 ∝ α2 Q-4 F2(x,Q2)• (Bjorken) scalingF2(x,Q2) → F2(x) (SLAC, ~1970)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0

0.2

0.4

0.6

0.8

1.0

1.2

Q2 (GeV2) 1.5 3.0 5.0 8.0 11.0 8.75 24.5 230 80 800 8000

F 2(x,Q

2 )

Bjorken 1968

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• photon scatters incoherently off massless, pointlike, spin-1/2 quarks

• probability that a quark carries fraction ξ of parent proton’s momentum is q(ξ), (0< ξ < 1)

the parton model (Feynman 1969)

• the functions u(x), d(x), s(x), … are called parton distribution functions (pdfs) - they encode information about the proton’s deep structure

...)(91)(

91)(

94

)()()()( 2

,

21

0,

2

+++=

=−= ∑∫∑

xsxxdxxux

xqxexqedxF qqq

qqq

ξδξξξ

infinitemomentumframe

SSI 2006 12

extracting pdfs from experiment• different beams

(e,μ,ν,…) & targets (H,D,Fe,…) measure different combinations of quark pdfs

• thus the individual q(x)can be extracted from a set of structure function measurements• gluon not measured directly, but carries about 1/2 the proton’s momentum

[ ][ ]...2

...2

...)(91)(

94)(

91

...)(91)(

91)(

94

2

2

2

2

+++=

+++=

++++++=

++++++=

sduF

usdF

ssdduuF

ssdduuF

n

p

en

ep

ν

ν

( ) 55.0)()(1

0=+∫∑ xqxqxdx

q

eNN FFss 22 365

−== ν

SSI 2006 13

35 years of Deep Inelastic Scattering

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0

0.2

0.4

0.6

0.8

1.0

1.2

Q2 (GeV2) 1.5 3.0 5.0 8.0 11.0 8.75 24.5 230 80 800 8000

F 2(x,Q

2 )

SSI 2006 14

(MRST) parton distributions in the proton

10-3 10-2 10-1 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

MRST2001

Q2 = 10 GeV2

up down antiup antidown strange charm gluon

x

f(x,

Q2 )

x Martin, Roberts, S, Thorne

HERA

e+, e− (28 GeV) p (920 GeV)

electron proton

quark

a deep inelastic scattering event at HERA

SSI 2006 17

35 years of Deep Inelastic Scattering

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0

0.2

0.4

0.6

0.8

1.0

1.2

Q2 (GeV2) 1.5 3.0 5.0 8.0 11.0 8.75 24.5 230 80 800 8000

F 2(x,Q

2 )

SSI 2006 18

scaling violations and QCD

quarks emit gluons!0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

x

F2

Q1

Q2 > Q1

The structure function data exhibit systematic violations of Bjorken scaling:

++ + …+

where the logarithm comes from(‘collinear singularity’) and

then convolute with a ‘bare’ quark distribution in the proton:

p xp

q0(x)

next, factorise the collinear divergence into a ‘renormalised’quark distribution, by introducing the factorisation scale μ2 :

then finite, by construction

note arbitrariness of ‘factorisation scheme dependence’

q(x,μ2) is not calculable in perturbation theory,* but its scale (μ2)dependence is: Dokshitzer

GribovLipatovAltarelliParisi

*lattice QCD?

we can choose C such that Cq= 0, the DIS scheme, or use dimensional regularisation and remove the poles at N=4, the MS scheme, with Cq ≠ 0

___

note that we are free to choose μ2 = Q2 in which case

… and thus the scaling violations of the structure function follow those of q(x,Q2) predicted by the DGLAP equation:

coefficient function,see QCD book

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

x

F 2

Q1

Q2 > Q1

q

the rate of change of F2 is proportional to αS(DGLAP), hence structure function data can be used to measure the strong coupling!

however, we must also includethe gluon contribution

… and with additional terms in the DGLAP equations

splittingfunctions

note that at small (large) x, the gluon (quark) contribution dominates the evolution of the quark distributions, and therefore of F2

coefficient functions- see QCD book

DGLAP evolution: physical picture• a fast-moving quark loses momentum by emitting a gluon:

• … with phase space kT2 < O(Q2 ), hence

• similarly for other splittings

• the combination of all such probabilistic splittings correctly generates the leading-logarithm approximation to the all-orders in pQCD solution of the DGLAP equations

kTp ξp

Altarelli, Parisi (1977)

basis of parton shower Monte Carlos!

• the bulk of the information on pdfs comes from fitting DIS structure function data, although hadron-hadron collisions data also provide important constraints (see later)

• pdfs are useful in two ways:– they are essential for predicting hadron collider cross sections, e.g.

– they give us detailed information on the quark flavour content of the nucleon

• no need to solve the DGLAP equations each time a pdf is needed; high-precision approximations obtained from ‘global fits’ are available ‘off the shelf”, e.g.

parton distribution functions

Hp p

input | output

SSI 2006 25

how pdfs are obtained

• choose a factorisation scheme (e.g. MSbar), an order in perturbation theory (see below, e.g. LO, NLO, NNLO) and a ‘starting scale’ Q0 where pQCD applies (e.g. 1-2 GeV)

• parametrise the quark and gluon distributions at Q0,, e.g.

• solve DGLAP equations to obtain the pdfs at any x and scale Q > Q0 ; fit data for parameters {Ai,ai, …αS}

• approximate the exact solutions (e.g. interpolation grids, expansions in polynomials etc) for ease of use

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pdfs from global fits - summary

Who?CTEQ, MRST, Alekhin,H1, ZEUS, …

http://durpdg.dur.ac.uk/hepdata/pdf.html

DataDIS (SLAC, BCDMS, NMC, E665,CCFR, H1, ZEUS, … )Drell-Yan (E605, E772, E866, …)High ET jets (CDF, D0)W rapidity asymmetry (CDF,D0)νN dimuon (CCFR, NuTeV)etc.

fi (x,Q2) ± δ fi (x,Q2)

αS(MZ )

FormalismLO, NLO or NNLO DGLAPMSbar factorisationQ0

2

functional form @ Q02

sea quark (a)symmetryetc.

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(MRST) parton distributions in the proton

10-3 10-2 10-1 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

MRST2001

Q2 = 10 GeV2

up down antiup antidown strange charm gluon

x

f(x,

Q2 )

x Martin, Roberts, S, Thorne

SSI 2006 28

where to find parton distributions

HEPDATA pdf websitehttp://durpdg.dur.ac.uk/hepdata/pdf.html

• access to code for MRST, CTEQ etc

• online pdf plotting

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1972-77 1977-80 2004

going to higher orders in pQCD is straightforward in principle, since the above structure for F2 and for DGLAP generalises in a straightforward way:

The calculation of the complete set of P(2) splitting functions by Moch, Vermaseren and Vogt (hep-ph/0403192,0404111) completes the calculational tools for a consistent NNLO pQCD treatment of Tevatron & LHC hard-scattering cross sections!

beyond lowest order in pQCD

see above see book see next slide!

SSI 2006 31

7 pages later…

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

• and for the structure functions…

… where up to and including the O(αS3) coefficient

functions are known

• terminology:– LO: P(0)

– NLO: P(0,1) and C(1)

– NNLO: P(0,1,2) and C(1,2)

• the more pQCD orders are included, the weaker the dependence on the (unphysical) factorisation scale, μF

2

– and also the (unphysical) renormalisation scale, μR2 ; note above has μR

2 = Q2

SSI 2006 33

Scattering processes at high energy hadron colliders can be classified as either HARD or SOFT

Quantum Chromodynamics (QCD) is the underlying theory for all such processes, but the approach (and the level of understanding) is very different for the two cases

For HARD processes, e.g. W or high-ET jet production, the rates and event properties can be predicted with some precision using perturbation theory

For SOFT processes, e.g. the total cross section or diffractive processes, the rates and properties are dominated by non-perturbative QCD effects, which are much less well understood

What can we calculate?

for inclusive production, the basic calculational framework is provided by the QCD FACTORISATION THEOREM:

higher-order pQCD corrections; accompanying radiation, jets

parton distribution functions

underlying event

X = W, Z, top, jets,SUSY, H, …

p

p

hard scattering in hadron-hadron collisions

kinematics

• collision energy:

• parton momenta:

• invariant mass:

• rapidity:

x1P

proton

x2P

proton

M

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100100

101

102

103

104

105

106

107

108

109

fixedtargetHERA

x1,2 = (M/1.96 TeV) exp(±y)Q = M

Tevatron parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

422 04y =

Q2

(GeV

2 )

x10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

100

101

102

103

104

105

106

107

108

109

fixedtargetHERA

x1,2 = (M/14 TeV) exp(±y)Q = M

LHC parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

M = 10 TeV

66y = 40 224Q

2 (G

eV2 )

x

x1P

proton

x2P

proton

M

DGLAP evolution

SSI 2006 37

early history: the Drell-Yan process

μ+

μ-

γ*quark

antiquark

τ = Mμμ2/s

“The full range of processes of the type A + B →μ+μ- + X with incident p,π, K, γ etc affords the interesting possibility of comparing their parton and antiparton structures” (Drell and Yan, 1970)

(nowadays) … and to study the scattering of quarks and gluons, and how such scattering creates new particles

SSI 2006 38

jets! (1981)

jet

jet

antiprotonproton

e.g. two gluons scattering at wide angle

SSI 2006 39

factorisation• the factorisation of ‘hard scattering’ cross sections into products of parton

distributions was experimentally confirmed and theoretically plausible• however, it was not at all obvious in QCD (i.e. with quark–gluon

interactions included)

μ+

μ-

γ*

• in QCD, for any hard, inclusive process, the soft, nonperturbative structure of the proton can be factored out & confined to universal measurable parton distribution functions fa(x,μF

2) Collins, Soper, Sterman (1982-5)

and evolution of fa(x,μF2) in factorisation scale calculable using the DGLAP

equations, as we have seen earlier

Log singularities from soft and collinear gluon emissions

Drell-Yan in more detailμ+

μ-

γ*quark

antiquark

scaling!

also

beyond leading order …

++++ + …+

Note:• collinear divergences, with same coefficients of logs as in DIS: P(x)• finite correction: fq(x)• introduce a factorisation scale, as before:

• then fold the parton-level cross section with q0(x1) and q0(x2), and with the same ‘renormalised’ distributions as before*, we obtain

• the standard scale choice is μ=M

finiteAltarelli et alKubar et al1978-80*

Note:• the full calculation at O(αS) also includes

• which gives rise to αS q * g terms in the cross section (see QCD book)

• the (finite) correction is sometimes called the ‘K-factor’, it is generally large and positive

• … and is factorisation scheme/scale dependent (to compensate the scheme dependence of the pdfs)

+

using high-precision Drell-Yan data to constrain the sea-quark pdfs

Note: MRST

SSI 2006 43

Anastasiou, Dixon, Melnikov, Petriello (hep-ph/0306192)

the asymmetric sea

10-2 10-1 1000.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

MRST2001

Q2 = 10 GeV2

ant

idow

n / a

ntiu

p

x

• the sea presumably arises when ‘primordial‘valence quarks emit gluons which in turn split into quark-antiquark pairs, with suppressed splitting into heavier quark pairs

• so we naively expect

• why such a big d-u asymmetry? meson cloud, Pauli exclusion, …?

• and is ?

The ratio of Drell-Yan cross sections for pp,pn → μ+μ- + X provides a measure of the difference between the u and d sea quark distributions

W, Z cross sections: Tevatron and LHC

NNLO QCD

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

CDF(e, μ) D0(e, μ)

NNLONLO

LO

Tevatron (Run 2)

Z(x10)W

CDF(e, μ) D0(e, μ)

σ . B

l (n

b)

partons: MRST2004

14

15

16

17

18

19

20

21

22

23

24

partons: MRST2004

W

NLONNLO

LO

LHC Z(x10)

σ . B

l (n

b)

parton level cross sections (narrow width approximation)

+ pQCD corrections to NNLO, EW to NLO

SSI 2006 46

Anastasiou, Dixon,Melnikov, Petriello

Z rapidity distributionat the Tevatron

SSI 2006 47

Drell-Yan as a probe of new physicsLarge Extra Dimension models have new resonances which could contribute to Drell-Yan

μ+

μ-

G

⇒ need to understand the SM contribution to high precision!

SSI 2006 48

where X=W, Z, H, high-ET jets, SUSY sparticles, black hole, …, and Q is the ‘hard scale’ (e.g. = MX), usually μF = μR = Q, and σ is known …

• to some fixed order in pQCD, e.g. high-ET jets

• or in some leading logarithm approximation (LL, NLL, …) to all orders via resummation

Summary: the QCD factorization theorem for hard-scattering (short-distance) inclusive processes

^

σ̂

• where ab→cd represents all quark & gluon 2→2 scattering processes

• NLO pQCD corrections also known

High-ET jet production

jet

jet

see QCD book

CDF

SSI 2006 50

jets at NNLOThe NNLO coefficient C is not yet known, the curves show guesses C=0 (solid), C=±B2/A(dashed) → the scale dependence and hence δ σthis significantly reduced

Other advantages of NNLO:

• better matching of partons ⇔hadrons• reduced power corrections• better description of final state kinematics (e.g. transverse momentum)

Glover

Tevatron jet inclusive cross section at ET = 100 GeV

SSI 2006 51

jets at NNLO contd.• 2 loop, 2 parton final state

• | 1 loop |2, 2 parton final state

• 1 loop, 3 parton final states or 2 +1 final state

• tree, 4 parton final states or 3 + 1 parton final states or 2 + 2 parton final state

⇒ rapid progress in recent years [many authors]

• many 2→2 scattering processes with up to one off-shell leg now calculated at two loops• … to be combined with the tree-level 2→4, the one-loop 2→3 and the self-interference of the one-loop 2→2 to yield physical NNLO cross sections• complete results expected ‘soon’

soft, collinear

SSI 2006 52

Higgs production

• the HO pQCD corrections to σ(gg→H) are large (more diagrams, more colour)

Ht

g

g

Djouadi & Ferrag

SSI 2006 53

top quark production

NLO known, but awaits full NNLO pQCD calculation; NNLO & NnLL“soft+virtual” approximations exist

SSI 2006 54

parton luminosity functions• a quick and easy way to assess the mass and collider energy dependence of production cross sections

s Ma

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 (see later)

SSI 2006 55

Tevatron

LHC

LHC / Tevatron

see CHS for more

SSI 2006 56

future hadron colliders: energy vs luminosity?

102 103 10410-1

100

101

102

103

104

105

106

107

108

14 TeV

40 TeV

parton luminosity: gg → X

gluo

n-gl

uon

lum

inos

ity

[pb]

MX [GeV]for MX > O(1 TeV), energy × 3 is better than luminosity × 10 (everything else assumed equal!)

recall parton-parton luminosity:

so that

with τ = MX2/s

SSI 2006 57

what limits the precision of the predictions?

• the order of the perturbative expansion

• the uncertainty in the input parton distribution functions

• example: σ(Z) @ LHCδσpdf ≈ ±3%, δσpt ≈ ± 2%→ δσtheory ≈ ± 4%

whereas for gg→H :δσpdf << δσpt

14

15

16

17

18

19

20

21

22

23

24

partons: MRST2002NNLO evolution: van Neerven, Vogt approximation to Vermaseren et al. momentsNNLO W,Z corrections: van Neerven et al. with Harlander, Kilgore corrections

NLONNLO

LO

LHC Z(x10)

W

σ . B

l (n

b)

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

NNLONLO

LO

Tevatron (Run 2)

CDF D0(e) D0(μ)

Z(x10)

W

CDF D0(e) D0(μ)

σ . B

l (

nb)

±4% total error(MRST 2002)

±2% total error(MRST 2002)

SSI 2006 58

pdf uncertainties• MRST, CTEQ, Alekhin, … also produce ‘pdfs

with errors’• typically, 30-40 ‘error’ sets based on a ‘best fit’

set to reflect ±1σ 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. δF2 ≈ ±3% → δu ≈ ±3%)

• however, there are also systematic pdf uncertainties reflecting theoretical assumptions/prejudices in the way the global fit is set up and performed

SSI 2006 59

uncertainty in gluon distribution (CTEQ)

CTEQ6.1E: 1 + 40 error setsMRST2001E: 1 + 30 error sets

SSI 2006 60

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

SSI 2006 61

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 ± δ fi

(MRST: Δχ2=50, CTEQ: Δχ2=100, Alekhin: Δχ2=1)– factorisation/renormalisation scheme/scale – Q0

2

– 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)

similar partons different Δχ2

different partons

SSI 2006 62

Djouadi & Ferrag, hep-ph/0310209

SSI 2006 63

Note: CTEQ gluon ‘more or less’ consistent with MRST gluon

SSI 2006 64

• MRST: Q02 = 1 GeV2, Qcut

2 = 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

SSI 2006 65

0.01 0.1 1-4-3-2-1012345678

f(x)

x0.01 0.1 1

-4-3-2-1012345678

f(x)

x0.01 0.1 1

-4-3-2-1012345678

f(x)

x

extrapolation errors

theoretical insight/guess: f ~ A x as x → 0

theoretical insight/guess: f ~ ± A x–0.5 as x → 0

SSI 2006 66

χ2

θ0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Experiment B

Experiment A

systematic error

systematic error

θ

measurement #

• 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. μH and νN data) – when jet and Drell-Yan data are combined with DIS data

tensions within the global fit

SSI 2006 67

CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100

beyond perturbation theorynon-perturbative effects arise in many different ways• emission of gluons with kT < Q0 off ‘active’ partons • soft exchanges between partons of the same or different beam

particlesmanifestations include…• hard scattering occurs at net non-zero transverse momentum• ‘underlying event’ additional hadronic energy

precision phenomenology requires a quantitative understanding of these effects!

‘intrinsic’ transverse momentumsimple parton model assumes partons have zero transverse momentum

… but data shows that the DY lepton pair is produced with non-zero <pT>

+

the perturbative tail is even more apparent in W, Z production at the Tevatron, and can be well accounted for by the 2→2 scattering processes:

… with known NLO pQCD corrections. Note that the pT distribution diverges as pT→0 due to soft gluon emission:

the O(αS) virtual gluon correction contributes at pT=0, in such a way as to make the integrated distribution finite

intrinsic kT can also be included, by convoluting with the pQCD contribution

SSI 2006 71

• when pT << M , the pQCD series contains large logarithms ln(M2/pT2)

at each order:

resummation

which spoils the convergence of the series when

• fortunately, these logarithms can be resummed to all orders in pQCD, to generate a Sudakov form factor:

… which regulates the LO singularity at pT = 0

• the effect of the form factor is (just about) visible in the (Tevatron) data

SSI 2006 72

resummation contd.

• theoretical refinements include the addition of sub-leading logarithms (e.g. NNLL) and nonperturbativecontributions, and merging the resummed contributions with the fixed order (e.g. NLO) contributions appropriate for large pT

• the resummation formalism is also valid for Higgs production at LHC via gg→H

qT (GeV)

KuleszaStermanVogelsang

Z

SSI 2006 73

• comparison of resummed / fixed-order calculations for Higgs (MH= 125 GeV) pT distribution at LHC

Balazs et al, hep-ph/0403052

• differences due mainly to different NnLO and NnLL contributions included

• Tevatron dσ(Z)/dpTprovides good test of calculations

SSI 2006 74

full event simulation at hadron colliders• it is important (designing detectors,

interpreting events, etc.) to have a good understanding of all features of the collisions – not just the ‘hard scattering’ part

• this is very difficult because our understanding of the non-perturbative part of QCD is still quite primitive

• at present, therefore, we have to resort to models (PYTHIA, HERWIG, …) …

SSI 2006 75

Monte Carlo Event Generators• programs that simulates particle physics events with the

same probability as they occur in nature• widely used for signal and background estimates• the main programs in current use are PYTHIA and HERWIG• the simulation comprises different phases:

– start by simulating a hard scattering process – the fundamental interaction (usually a 2→2 process but could be more complicated for particular signal/background processes)

– this is followed by the simulation of (soft and collinear) QCD radiation using a parton shower algorithm

– non-perturbative models are then used to simulate the hadronizationof the quarks and gluons into the observed hadrons and the underlying event

a Monte Carlo event

t

t̄

q

q̄

Initial and Final State parton showers resum the large QCD logs.

Hard Perturbative scattering:

Usually calculated at leading order in QCD, electroweak theory or some BSM model.

Perturbative Decays calculated in QCD, EW or some BSM theory.

Multiple perturbative scattering.

Non-perturbative modelling of the hadronization process.

Modelling of the soft underlying event

Finally the unstable hadrons are decayed.

t

t̄

p, p̄

p, p̄

t

t̄ b̄

W−

b

W+

ν� �+

p, p̄

p, p̄

t

t̄ b̄

W−

b

W+

ν� �+

Hadrons

Hadr

ons

Hadron

s

Hadr

ons

Hadr

ons

Hadrons

Hadr

ons

p, p̄

p, p̄

t

t̄ b̄

W−

b

W+

ν� �+

Hadrons

Hadr

ons

Hadron

s

Hadr

ons

Hadr

ons

Hadrons

Hadr

ons

Hadr

ons

p, p̄

p, p̄

t

t̄ b̄

W−

b

W+

ν� �+

p, p̄

p, p̄

from Peter Richardson (HERWIG)

(had

ron

colli

der)

pro

cess

es in

HE

RW

IG

from

Pet

er R

icha

rdso

n

SS

I 200

678

how

ever

…•

the

tuni

ng o

f the

non

pertu

rbat

ive

parts

of t

he m

odel

s is

pe

rform

ed a

sin

gle

colli

der e

nerg

y (o

r lim

ited

rang

e of

en

ergi

es) –

can

we

trust

the

extra

pola

tion

to L

HC

?!

•in

gen

eral

the

even

t gen

erat

ors

only

use

lead

ing

orde

r m

atrix

ele

men

ts a

nd th

eref

ore

the

norm

alis

atio

n is

un

certa

in•

this

can

be

over

com

e by

reno

rmal

isin

gto

kno

wn

NLO

et

c re

sults

or b

y in

corp

orat

ing

next

-to-le

adin

g or

der

mat

rix e

lem

ents

(rea

l + v

irtua

l em

issi

ons)

–se

e be

low

•on

ly s

oft a

nd c

ollin

ear e

mis

sion

is a

ccou

nted

for i

n th

e pa

rton

show

er, t

here

fore

the

emis

sion

of a

dditi

onal

har

d,

high

ET

jets

is g

ener

ally

sig

nific

antly

und

eres

timat

ed•

for t

his

reas

on, i

t is

poss

ible

that

man

y of

the

prev

ious

LH

C s

tudi

es o

f new

phy

sics

sig

nals

hav

e si

gnifi

cant

ly

unde

rest

imat

ed th

e S

tand

ard

Mod

el b

ackg

roun

ds

tt̄

p,p̄

p,p̄

+

inte

rfaci

ng N

n LO

and

parto

n sh

ower

s

Ben

efits

of b

oth:

Nn L

Oco

rrect

ove

rall

rate

, har

d sc

atte

ring

kine

mat

ics,

redu

ced

scal

e de

p.PS

com

plet

e ev

ent p

ictu

re, c

orre

ct tr

eatm

ent o

f col

linea

r log

s to

all

orde

rs

Exam

ple:

MC

@N

LO

Frix

ione

, Web

ber,

Nas

on,

ww

w.h

ep.p

hy.c

am.a

c.uk

/theo

ry/w

ebbe

r/MC

atN

LO/

proc

esse

s in

clud

ed s

o fa

r …pp

→W

W,W

Z,ZZ

,bb,

tt,H

0 ,W,Z

/γ

p Tdi

strib

utio

n of

ttat

Tev

atro

n

SS

I 200

681

and

final

ly …

SS

I 200

682

cent

ral e

xclu

sive

diff

ract

ive

phys

ics

•p +

p →

H +

X–

the

rate

(σpa

rton,

pdfs

, αS)

–th

e ki

nem

atic

dist

ribtn

s. (d

σ/dy

dpT)

–th

e en

viro

nmen

t (je

ts, u

nder

lyin

g ev

ent,

back

grou

nds,

…)

μ μ

μ μ

•p +

p →

p +

H +

p–

a re

al c

halle

nge

for t

heor

y (p

QC

D+

npQ

CD

) and

exp

erim

ent

(tagg

ing

forw

ard

prot

ons,

tri

gger

ing,

…)

com

pare

…

with

…

b

b

SS

I 200

683

EM

E

IC

D/M

G E

FH

E

CH

E

hard

dou

ble

pom

eron

hard

col

or

sing

let e

xcha

nge

‘rapi

dity

gap

’col

lisio

n ev

ents

DDty

pica

l jet

eve

nt

hard

sin

gle

diffr

actio

n

forw

ard

prot

on ta

ggin

g at

LH

C: t

he p

hysi

cs c

ase

•al

l obj

ects

pro

duce

d th

is w

ay m

ust b

e in

a 0

++st

ate →

spin

-par

ity

filte

r/ana

lyse

r•

with

a m

ass

reso

lutio

n of

~O

(1 G

eV) f

rom

the

prot

on ta

ggin

g, th

e S

tand

ard

Mod

elH

→bb

deca

y m

ode

open

s up

, with

S/B

> 1

•H

→W

W( *)

also

look

s ve

ry p

rom

isin

g

•in

cer

tain

regi

ons

of M

SS

Mpa

ram

eter

sp

ace,

S/B

> 2

0, a

nd d

oubl

e pr

oton

tagg

ing

is T

HE

disc

over

y ch

anne

l

•in

oth

er re

gion

s of

MS

SM

par

amet

er s

pace

, exp

licit

CP

vio

latio

n in

th

e H

iggs

sec

tor s

how

s up

as

an a

zim

utha

lasy

mm

etry

in th

e ta

gged

pr

oton

s →

dire

ct p

robe

of C

P s

truct

ure

of H

iggs

sec

tor a

t LH

C•

any

exot

ic 0

++st

ate,

whi

ch c

oupl

es s

trong

ly to

glu

e, is

a re

al

poss

ibili

ty: r

adio

ns, g

luin

obal

ls, …

p +

p →

p ⊕

X ⊕

p

e.g.

mA

= 13

0 G

eV,

tan

β=

50ΔM

= 1

GeV

, L =

30

fb-1 S

B

mh

= 12

4.4

GeV

71

3

m

H=

135.

5 G

eV

124

2m

A=

130

G

eV

1

2

e.g.

SM

Hig

gs →

bbΔM

= 1

GeV

, L =

30

fb-1 S

B

mh

= 12

0 G

eV

11

4

Kho

ze M

artin

Rys

kin

SS

I 200

685

the

chal

leng

es …

gap survivalne

ed to

cal

cula

tepr

oduc

tion

ampl

itude

and

gap

Sur

viva

l Fac

tor:

mix

of p

QC

Dan

d np

QC

D⇒

sign

ifica

nt u

ncer

tain

ties

Khoz

eM

artin

Rys

kin

Kaid

alov

WJS

de R

oeck

Cox

Fors

haw

Mon

kPi

lkin

gton

Hel

sink

i gr

oup

Sacl

aygr

oup

…

theo

ry

expe

rimen

t

X

man

y! (f

orw

ard

prot

on/a

ntip

roto

n ta

ggin

g,

pile

-up,

low

eve

nt ra

te, t

rigge

ring,

…)

impo

rtant

che

cks

from

Tev

atro

n fo

r X=

dije

ts, γ

γ, q

uark

onia

, …

SS

I 200

686

sum

mar

y•

than

ks to

> 3

0 ye

ars

theo

retic

al s

tudi

es, s

uppo

rted

by

expe

rimen

tal m

easu

rem

ents

, we

now

kno

w h

ow to

cal

cula

te

(an

impo

rtant

cla

ss o

f) pr

oton

-pro

ton

collid

er e

vent

rate

s re

liabl

y an

d w

ith a

hig

h pr

ecis

ion

•th

e ke

y in

gred

ient

s ar

e th

e fa

ctor

isat

ion

theo

rem

and

the

univ

ersa

l par

ton

dist

ribut

ion

func

tions

•su

ch c

alcu

latio

ns u

nder

pin

sear

ches

(at t

he T

evat

ron

and

the

LHC

) for

Hig

gs, S

US

Y, e

tc

•…

but m

uch

wor

k st

ill n

eeds

to b

e do

ne, i

n pa

rticu

lar

–ca

lcul

atin

g m

ore

and

mor

e N

NLO

pQ

CD

corr

ectio

ns (a

nd s

ome

mis

sing

NLO

one

s to

o) –

see

Lanc

e D

ixon

’s le

ctur

es–

furth

er re

finin

g th

e pd

fs, a

nd u

nder

stan

ding

thei

r unc

erta

intie

s–

unde

rsta

ndin

g th

e de

taile

d ev

ent s

truct

ure,

whi

ch is

out

side

the

dom

ain

of p

QC

Dan

d is

cur

rent

ly s

impl

y m

odel

led

–ex

tend

ing

the

calc

ulat

ions

to n

ew ty

pes

of N

ew P

hysi

cs

prod

uctio

n pr

oces

ses,

e.g

. exc

lusi

ve/d

iffra

ctiv

e pr

oduc

tion