misure di funzioni di struttura ad lhc

Misure di Funzioni di Struttura ad LHC

by

Alessandro Tricoli

Rutherford-Appleton Laboratory andUniversity of Oxford

Workshop sui Monte Carlo, la Fisica e le Simulazioni ad LHCFrascati, 23 Maggio 2006

Alessandro Tricoli, RAL & Oxford University 2MCWS Frascati, 23 Maggio 2006

Overview Introduction:

What are Parton Distribution Functions (PDFs)? (PDFs)? How they determined How the PDF Uncertainties are estimated

Why the accurate knowledge of PDFs is vital for the LHC

Impact of PDF Uncertainty on the discovery of New Physics signals: Higgs, Extra Dimensions etc.

Impact of PDF Uncertainty on SM measurements sensitive to New Physics: Inclusive Jet cross-section, Drell-Yan cross-section

How to constrain PDF at LHC, some examples: Inclusive jet cross section W and Z rapidity distributions

Conclusions


What are PDF distributions?PDFs are parameterizations of the partonic content of the proton:

i = uv, dv, g and seax = pparton / Ebeam parton momentum fraction Q2 momentum transfer

How are PDFs determined from global Fits? QCD predicts the scale dependence of fi(x,Q2) through the DGLAP evolution equations, BUT does not accurately predict the x-dependence which has non-perturbative origin. x-dependence is parameterised at a fixed scale Q0

2 ~ 1-7 GeV2 :

Valence Quarks: f ~ x (1-x)P(x)

Sea/Gluon: f ~ x- (1-x)P(x)

Different people use different parameterisations with different no. of free parameters

fi(x,Q2) is evolved from Q02 to any other Q2 by numerically solving the

conventional DGLAP equations to various orders (LO,NLO, NNLO) The free parameters are determined by fit to data from exp. observables:

DIS processes (fixed target and HERA), DY lepton pair production High Et jets (CDF, D0), W rapidity asymmetry (CDF)N dimuon (CCFR, NuTeV)

etc.

fi(x,Q2)


PDF uncertainties

The theoretical uncertainties are estimated varying the theoretical assumptions,But only recently the correlated syst. on data points are properly considered: PDF sets after year 2000 provide UNCERTAINTIES: fi(x,Q2) ± δ fi(x,Q2):

use a modified to consider non-gaussian syst. errors and their correlations. T= tolerance

Theoretical Uncertainties

Theoretical Formalism: perturbative calculations, i.e DGLAP approx., higher order truncation, etc. Model Assumptions: non-perturbative parameterisations (x-depedence) i.e. assumptions to limit the no. of free parameters

Experimental Uncertainties

Statistical and Systematic Uncertainties on experimental data inputs Correlated Systematic Uncertainties on data points:

~

Offset Method: the correlated syst. errors affect only the determination of the PDF uncertainty, NOT the best fit (centre value) e.g. ZEUS-S T2~49 Hessian method: the collective effect of the correlated syst. errors can also modify the values of the best fit e.g. CTEQ6 T2=100, MRST01: T2=50


At Hadron Colliders every Cross-Section calculation is a convolution of the cross-section at parton level and PDFs:

PDFs are vital for reliable predictions for new physics signal (Higgs,

Super- Symmetry, Extra Dimensions etc.) and background cross-section at LHC.

Why PDFs are vital at LHC ?

pA

pB

fa

fb

x1

x2

X


A lesson from Tevatron on the importance of PDFs

Today they are considered within Proton Structure Uncertainty band

PDF UncertaintiesPDF Uncertainties must be properly taken into account or SM physics features could be misinterpreted as new physics signal

(Da

ta-T

he

ory

)/T

he

ory

CDF Run I

Tevatron Jet datawere originally takenas evidence of New PhysicsSince Proton Structure UncertaintySince Proton Structure Uncertaintywas not properly consideredwas not properly considered


LHC Kinematic regime

ys

Mx exp2,1 MQ

Kinematic regime for LHC much broader than currently explored

z

z

pE

pEy ln

2

1

Test of QCD: Test DGLAP evolution at small x:

Is NLO DGLAP evolution sufficient at so small x ?

Are higher orders important?

Improve information of high x gluon distribution

xmns log~

At the EW scale cross section predictions for LHC are dominated by low-x gluon uncertainty (i.e. W and Z masses) => see later slides

At TeV scale New Physics cross section predictions are dominated by high-x gluon uncertainty(not sufficiently well constrained by PDF fits) => see later slides


Impact of PDF uncertainty on New Physics: Higgs g

g

H

q

q

W/Z

W/Z

W/Z

H

Djouadi & Ferrag, Phys. Lett. B 586 345:352 (2004)

PDF uncertainties(CTEQ6M, MRST01E, Alekhin02)on Higgs cross-sections:Up to 10% (15%)

g

g

H

t

t_

q

q

W/Z

H_


Impact of PDF uncertainty on New Physics:

Extra Dimensions

Mc= 8 TeV

Pt(GeV)

2XD

4XD

6XD

SM

Mc= 2 TeV

Pt(GeV)

(mb)

An E.D. Model: di-jets cross section in the E.D. regime is a continuity of the Standard Model one with new s running: XD

SJJJJ

XD

dM

d

dM

d

PDF uncertainties decrease discovery reach for E.D. from MC 5 (10) TeV to < 2 (3)TeV

High-x gluon is responsible of the big PDF uncertainties

E.D. are masked by PDF uncertainties:

Standard Model prediction zone:where every measured cross section can be explained by a PDF fit, and every power of discovering new physics is killed and absorbed by the PDF fit

Central value1 limits3 limits

SM predictionCTEQ6M PDFs

Pt(GeV)

Ferrag, hep-ph/0407303 (2004)


10 fb-1

~600 GeV

Impact of PDF uncertainty on SM:

Drell-Yan cross section Sensitive to New Physics:

ppXgq LQxxPDFN ),,( 221,

2?" physics new" ~ Z

High mass dileptons → Uncertainties at high-x important (up to 10%)

Mll [GeV]

40 CTEQ6PDFs

PDF Relative Uncertainty

MC@NLO



Inclusive Jet cross-section A SM measurement sensitive to New Physics: compositeness, Black Holes etc.

Experimental and theoretical errors can distort the measurements and predictions creating false signals of new physics:

PDF Uncertainty (gluon), Renormalisation and Factorisation scale uncertainty, Experimental Jet Energy scale uncertainty.

(NLOJET,CTEQ6) Factorisation & Renormalisation scales=pt/2

D. Clements, C. Butter, A. Moraes



Inclusive Jet cross-section Current PDF uncertainty: 10% at 1 TeV, 25% at 2 TeV, up to 60% at 5 TeV

Can we constrain PDF with jets at LHC as done by Tevatron?

D. Clements, C. Butter, C. Gwenlan, T. Carli, A. Cooper-Sarkar, M Sutton

UncorrelatedExp. Systematics

LHC jet data are useful to constrain the gluon PDF,Uncertainty on the extracted gluon PDF is dominated by Systematics,Statistical uncertainty negligible even at 1fb-1

ATLAS estimate:

The large PDF uncertainty indicates that we might be able to constrain the high-x gluon with high ET jets up to 1 TeV even with 1 fb-1 luminosity.


How to constrain PDFs at low-x at LHC?

At the EW scale cross sections are dominated by sea and/or gluon interactions at low-x. Furthermore, at Q2~M2

W/Z the sea is driven by the gluon (via gluon splitting) which is far less precisely determined for all x values.

Wud

WduW production:(main contributions)

Zdd

Zuu

Z production:(main contributions)

We can improve our knowledge of PDF’s at LHC measuring the vector boson production: W’s, Z’s (and photons?)


How to constrain low-x PDFs at LHC

single Z and W± Productions

4% MRST02 error

W,Z tot. cross sections

MRST PDF

NNLO corrections small ~ few%NNLO residual scale dependence < 1%

-6 -4 -2 0 2 4 60

1

2

3

4

5

x1 = 0.0003

x2 = 0.12

x1 = 0.12

x2 = 0.0003

x1 = 0.006

x2 = 0.006

yW

MRST2002-NLO LHC

dW

/dy W

. B

l

(nb

)

W±

Symmetric

W+- diff. cross section(rapidity)

PDF Set

ZEUS-S

CTEQ6.1

MRST01

lWWB lWW

B llZZ B

41.007.12

(nb) (nb) (nb)

30.076.8 06.089.1

56.066.11 43.058.8 08.092.1

23.072.11 16.072.8 03.096.1

Theoretical uncert. dominated by PDFs

LHC exp. uncertainty is sufficiently small to distinguish between different PDF sets(LHC dominated by systematic uncertainty)

W, Z very clean signals (bkg on W->e ~1%)


W -> e rapidity distributions (1)Experimentally we detect e+- from W decays: W+- -> e+-

HERWIG MC Simulations with NLO Corrections

At y=0 the total PDF uncertainty is ~ ±5.2% from ZEUS-S ~ ±3.6% from MRST01E ~ ±8.7% from CTEQ6.1MZEUS-S to MRST01E central value difference ~5% ZEUS-S to CTEQ6.1 central value difference ~3.5%

CTEQ61 MRST02 ZEUS-S


e- rapidity e+ rapidity

Generator Level

ATLASDetector Levelwith sel. cuts

Error boxesare the Full PDF Uncertainties

GOAL: syst.syst. exp. error ~4%

A. Tricoli hep-ex/0511020,

A. Tricoli, A. Cooper-Sarkar, C. Gwenlan,

CERN-2005-014, hep-ex/0509002


Effect of including the ATLAS W Rapidity “pseudo-data” in global PDF Fits: how much can we reduce the PDF errors when LHC is up and running?

Simulate real experimental conditions:

Generate 1M “data” sample with CTEQ6.1 PDF through ATLFAST detector simulation and then include this pseudo-data (with imposed 4% error) in the global ZEUS PDF fit (with Det.->Gen. level correction).Central value of ZEUS-PDF prediction shifts and uncertainty is reduced:

ZEUS-PDF BEFORE including W data

e+ CTEQ6.1 pseudo-data

low-x gluon shape parameter λ, xg(x) ~ x –λ

BEFORE λ = -0.199 ± 0.046AFTER λ = -0.181 ± 0.030

41% error reduction

NB: in ZEUS-PDF fit the e± Normalisation is left free => no assumption on Luminosity measurement

ZEUS-PDF AFTER including W data

e+ CTEQ6.1 pseudo-data

W -> e rapidity distributions (2)

In few day stat. of LHC at low Luminosity


W Charge Asymmetry measurement (1)

HERWIG MC Simulations with NLO Corrections

In the Asymmetry experimental uncertainties and the gluon/sea PDF Uncertainty mostly cancel out: ~5% PDF error within each PDF set But MRST02 predicts Asym. ~15% lower than the other PDF sets, WHY?


)(/)(/

)(/)(/)(

edydedyd

edydedydyA

e+ - e- asymmetry:

Generator Level

ATLASDetector Levelwith selection cuts

Error boxesare the Full PDF Uncertainties

Experimentally we measure e+- charge asymmetry from W decays: W+- -> e+-


W Charge Asymmetry measurement (2)A. Cooper-Sarkar

At LO the Asymmetry is dominated by uv –dv parameter :

uv –dv parameter is not well constrained by data at very low-x current PDFs simply have prejudices as to the low-x valence distributions coming from the input parameterisations.

The small PDF uncertainties at low x do NOT actually reflect the real uncertainty.

uddu

udduyA

)(qdu

At small-x qdu

duyA

VV

VV

2)(

CTEQ6.1

MRST02

uV – dV

Q2=Mw2

x- range affecting W asymmetry in the measurable rapidity range

x

Q2=7 GeV2

at Q2=MW2 and x~0.006 (corresponging to y~0 at LHC):

MRST uV –dV is 25% lower than other PDF setswhich reflects on A(y) measurement.

For the first time with the LHCwe will have valence PDF discrimination measuring valence distributions at x~0.005 on proton targets


W -> e rapidity distributionsto detect new low-x physics scenarios

Comparison between a conventional PDF set, CTEQ61, which INCLUDEs very low-x data (down to x=6 10-5 )and a “toy” PDF set MRST03 which EXCLUDES HERA low-x data (x > 5 10 -3 )

e+ - e- asymmetry

CTEQ6.1MRST2003

CTEQ6.1MRST2003

e- rapidity

e+ rapidity

Shows what would be our predictions w/o low-x HERA data warning against premature extrapolations of our knowledge to new kinematic regions

Shows the impact of low-x data on current LHC predictions: Since the validity of the DGLAP formalism is not certain at such low-x, the LHC should be able to detect new low-x scenarios right in the central rapidity region


The computation of PDF uncertainties on MCs is time consuming To estimate the full PDF uncertainty for MRST01, ZEUS-S, CTEQ61 we have to generate 92 event samples, since

30 sub-sets (15 eigenvectors) provide the full MRST02 PDF uncertainty 22 sub-sets (11 eigenvectors) provide the full ZEUS-S PDF uncertainty 40 sub-sets (20 eigenvectors) provide the full CTEQ61 PDF uncertainty

TOO LONG generation time

The PDF re-weighting technique is useful tool to quickly evaluate the full PDF uncertainties for many PDF sets, saving generation time

only 1 event sample is generated with one PDF set each event is re-weighted off-line with a second PDF set, applying an Event Weight calculated (for the moment) from the hard scatter parameters x1, x2, Q2 only

Can we compute the PDF Uncertainty with MC in a fast way:

PDF Re-weighting

),,(

),,(

),,(

),,(

221.

222.

111.

112.

Qscaleflavxf

Qscaleflavxf

Qscaleflavxf

QscaleflavxftEventWeigh

PDFn

PDFn

PDFn

PDFn


Can we use PDF re-weighting to simulate other PDFs?- OK for RAPIDITY distributions

Events generated with HERWIG & MRST02and re-weighted with CTEQ61are compared toEvents generated with HERWIG & CTEQ61

Accuracy of ~0.5% in rapidity and no evidence of a y-dependent bias. For the PT distribution it’s more complex:

it needs re-weighting of the Parton Shower (Sudakov Form factors)

Relative differencebetween Re-weightedand Generateddistributions

W- W+

CTEQ61 Generated

CTEQ61 Re-weighted from MRST02

CTEQ61 Generated

CTEQ61 Re-weighted from MRST02

W- W+

Weighted meanon whole y-range


Conclusions

Precision Parton Distribution Functions are crucial for new physics discoveries at LHC: PDF uncertainties can compromise the potential for discovery

At LHC we are not limited by statistic but by systematic uncertainties To discriminate between conventional PDF sets we need to reach high experimental accuracy ( ~ few%)

LHC experiments are currently working hard to understand better and improve the detector performances to determine and reduce systematic errors.

The SM processes like Z, W productions, Jet productions (and hopefully Direct Photon) are good candidates to constrain PDF’s at the LHC

LHC can significantly constrain PDF’s, especially the gluon distribution with unprecedented precision The W charge asymmetry can constrain for the first time valence distributions at very low-x New low-x physics scenarios can be easily accessible by the LHC with early data

From now to the LHC start up, 2007, our PDF knowledge might improve HERA-II: substantial increase in luminosity, possibilities for new measurements

Projection: significant improvement to high-x PDF uncertainties (high-scale physics at the LHC) impact on New Physics searches


EXTRAS


How to constrain PDFs at mid-low-x at LHC?

At the EW scale cross sections are dominated by sea and/or gluon interactions at low-x. Furthermore, at Q2~M2

W/Z the sea is driven by the gluon (via gluon splitting) which is far less precisely determined for all x values.

Wud

WduW production:(main contributions) Zdd

Zuu

Z production:(main contributions)

Direct production:(LO contributions)

Compton:(~90%)

Annihilation:(~10%)

We can improve our knowledge of PDF’s at LHC measuring the vector boson production: W’s, Z’s (and photons?)


How to constrain gluon-PDFs at LHCZ + b-jet (1)

Sensitive to b content of the proton:

(J.Campbell et al. Phys.Rev.D69:074021,2004)

Also background to Higgs searches:

(J.Campbell et al. Phys.Rev.D67:095002,2003)

Why do we measure the b-PDF? bb->Z @ LHC is ~5% of entire Z production

Knowing σZ to about 1% requires

a b-PDF precision of the order of 20%

Now we have only HERA measurements, far from this precision


How to constrain gluon-PDFs at LHC

Z + b-jet (PDF Uncertainty) HERWIG with

MRST03CNNLO, CTEQ5M1, Alehkin1000

Nu

mbe

r of

eve

nts

PDF Differences in total Z+b cross-section are of the order of 5% to 10 %

S. Diglio, A. Tonazzo and M. Verducci (2005)

Z+b selected events (10 fb-1)

Signal+Background

Background

Jet PT (GeV)

Event selection: only Z→

Two isolated muons with high PT

inclusive b-tagging of jet

ATLAS


How to constrain gluon-PDFs at LHCdirect production

Typical Jet + eventJet and photon are back to back

Good candidate to constrain PDF’s on a wide pT range:smaller energy scale uncertainty than jets, no jet-finder bias sensitivity to high-x comes with high-pt and high- photons

Problems: Large background (especially at low PT) Can the Theoretical-Experimental Discrepancy in PT distribution be well understood?

ATLAS

I. Hollins (2005)

Kumar et al. Physics Review D 67

In NLO cross-section calculations: discrepancy

between different PDF set predictions up to ~20%


Differences between PDF sets

different data sets in fit different sub-selection of data different treatment of exp. sys. errors

different choices of

tolerance to define fi (CTEQ: Δχ2=100, MRST: Δχ2=50 Alekhin: Δχ2=1)

parametric form Axa(1-x)b[..] etc theoretical assumptions about sea flavour symmetryfactorisation/renormalisation scheme/scale

Q02

αS

treatment of heavy flavours


PDF Re-weighting Implementation I generate a MC event with one specific PDF set, say pdf set n.1

This event happens to have: One hard process scale (Q=MW)

Two primary partons with two specific flavours(flav1,flav2) Momentum fractions x1, x2 of the two primary partons (calculated at the

Hard Process, before the Parton Shower in the backward evolution is applied in the MC) according to the probability (i.e. xf) estimated by the PDF they are generated with (say pdf set n.1)

Offline (with LHAPDFv3) I evaluate the probability, i.e. xf, of picking up the same flavoured partons with the same momentum fractions x1,x2, according to a second PDF set, i.e. PDF set n.2, at the same energy scale, i.e. Q.

Then I perform the Ratio:

),,(

),,(

),,(

),,(

221.

222.

111.

112.

Qscaleflavxf

Qscaleflavxf

Qscaleflavxf

QscaleflavxftEventWeigh

PDFn

PDFn

PDFn

PDFn


PDF scenario at LHC start up (2007)might be different

In most of the relevant x regions accessible at LHC HERA data are most important source of information in PDF determinations (low-x sea and gluon PDFs)

HERA now in second stage of operation (HERA-II)

substantial increase in luminosity

possibilities for new measurements

HERA-II projection shows significant improvement to high-x PDF uncertainties relevant for high-scale physics at the LHC

where we expect new physics !!

- significant improvement to valence-valence-quarkquark uncertainties over all-x all-x

- significant improvement to sea and gluonsea and gluon uncertainties at mid-to-high-xmid-to-high-x

- little visible improvement to sea and gluon uncertainties at low-x

Gluon fractional error

x

C. Gwenlan, A. Cooper-Sarkar,C. Targett-Adams, hep-ph/0509220 (2005)


Impact of PDF uncertainty on New Physics:

Extra Dimensions (Theory) Hierarchy problem:

•EW symmetry breaking scale ~ 102 GeV•GUT scale ~ 1016 GeV•Planck scale ~ 1019 GeV

Alternative: 1 fondamental scale: ~ few tens TeV and 1+3+ time-space structure

Phenomenological aspects: • Possibility to produce Gravitons at LHC: low Planck scale• Kaluza Klein (KK)excitations: compactified extra dimensions

• Violation of the expected (MS)SM evolution behavior of em,w,s

(E. Dudas, R. Dienes, T. Ghergetta, hep/ph9803466 and hep/ph9807522)

Exerimentally: Evolution of s by measuring di-jets cross section on a large energy range

Parameters: number of extra-dimensions compactification scale Mc

MGUT ~30 TeV(4+2)D, R=1/10 Tev-1

MSSM+XD


How to constrain gluon-PDFs at LHC

Z + b-jet (Measurement) Signal: Background:

Event selection: only Z→

Two isolated muons (Pt > 20 GeV/c, opposite charge, invariant mass close to Mz) inclusive b-tagging of jet (total Z+ b selection efficiency ~15%, purity ~53% )

Z+b Z+jet

Di-muons Invariant Mass Di-muons Invariant Mass

GeV

Z+b selected events (10 fb-1)

Signal+Background

Background

Jet PT (GeV)ATLAS



Inclusive Jet cross-section

PDF error: 10% at 1 TeV, 25% at 2 TeV, up to 60% at 5 TeV Can we constrain PDF with jets at LHC as done by Tevatron?

The large PDF uncertainty indicates that we might be able to constrain the high-x gluon with high ET jets up to 1 TeV even with 1 fb-1 luminosity.

PDF error is dominant at high pT , but low stat. PDF error negligible at low pT w.r.t. other syst. uncertainty sources :

Fact.&Ren. Scale uncertainty ~14% at 1 TeV 1% (10%) exp. energy scale uncertainty => 6% (70%) incl. jet x-sec. error

Proportional Error

PDF error dominated byEigenv.29,30: high x gluon dominated

PDF set 30

PDF set 29

C. Gwenlan, A. Cooper-Sarkar, C. Targett-Adams, hep-ph/0509220 (2005)

D. Clements, C. Butter, A. Moraes


Higgs production and decays at LHC Higgs production mechanisms

Higgs decays


Parton Luminosity uncertainty

Note: high x gluon should become better determined from Run 2 Tevatron data

PDF uncertainties encoded in parton-parton luminosity functions:

LHC (Alekhin 2002)

Tevatron (Alekhin 2002)

J. Stirling


High ET jet cross section at LHC

(James Stirling)

MRST2001E pdf error band

T



Inclusive Jet cross-section (Syst.)

cms energy=14TeV, CTEQ6, NLOJET

Factorisation and Renormalisation scale uncertaintydominant theoretical uncertainty at low pT being overtaken by pdf uncertainties at a leading jet pT of ~1TeV

Jet Energy scale uncertaintythis systematic error is stat. significant, particularly for low pT jets



Inclusive Jet cross-section (NLO/LO) The ratio of the inclusive jet cross-section as calculated for pdfs CTEQ6L1(LO) to CTEQ6m (NLO) using PYTHIA

Proportional Error

CTEQ6MEigenv.29,30: high x gluon dominated

ckin(3): PT min of hard scatter



D.-Y. production.

CTEQ6.1E

x

% uncertainty

x

-5

+5

x

% uncertainty

x

-5

),( 0Qxux

+5

High mass dileptons → Uncertainties at high x important

),( 0Qxxu

Q2 = 104


Direct production

Pythia v6.221

Photon PT spectrum I. Hollins (2005)


W± Production at LHC

pp -> W± + …W

p p

Wud

Wdu Valence-Sea and Sea-Sea : largest contribution

CabibboSuppressed

Wcs

Wsc Sea-Sea: next largest contribution (Cabibbo dominating), whereas ~5% at Tevatron

(17%)

(23%)

Cabibbo Suppressed Contribution 1-3% at LHC

LHC


W -> e rapidity distributions

Signal:W -> eCTEQ6.1

W ->

Z -> e-e+

Z ->

e- No Cuts e+ No Cuts

e- After Sel. Cuts e+ After Sel. Cuts

Signal vs Background

Small Background contamination: ~1%=> Very clean measurement


•Data on the low-x valence distributions comes only from the CCFR/NuTeV data on Fe targets. The data extend down to x~0.01, but are subject to significant uncertainties from heavy target corrections in the low-x region.

•HERA neutral current data at high-Q2, involving Z exchange, make valence measurements on protons- but data are not yet very accurate and also only extend down to x~0.01

•Current PDFs simply have prejudices as to the low-x valence distributions - coming from the input parametrisations. The PDF uncertainties at low x do not actually reflect the real uncertainty (horse’s mouth- Thorne)

•LHC W asymmetry can provide new information and constraints in the x region 0.0005 < x <0.05

A. Cooper-Sarkar


Z + b-jet

Background and Systematic uncertainties

Efficiency of b-tagging we can expect Δεb/εb = 5%

Background from mistag Check mis-tagging on a sample where no b-quark jets should be

present: we use W + jets. Precision will be dominated by other sources of systematics:

Luminosity measurement Jet reconstruction and energy resolution

It is likely that the overall precision will be some-%, comparable to uncertainty on theoretical prediction


_d – u Asymmetry measurement

at LHC ? (I)

_

It has been known that dbar ≠ ubar in the sea, since the violation of the Gottfried sum-rule in 1992. More recently, E866 Drell-Yan data have measured the shape of dbar-ubar.

This difference is usually fitted as a ‘valence-like’ quantity: dbar-ubar→0 as x → 0 e.g. dbar-ubar = 0.24 x0.5 (1-x)9 at Q2

0 ~ 7 GeV2

James Stirling


d – u Asymmetry measurement at LHC ? (II)

__

The measured difference between dbar and ubar is actually very small, and is negligible at the Q2 of interest at the LHC. But the question has been raised: what if dbar-ubar ≠ 0 as x → 0 ?

Could this be significant for W production at LHC?x (dbar-ubar) dbar ubarE866


d – u Asymmetry measurement at LHC ? (III)

__

Try the parametrisation 0.005x-0.16(1-x)13 (1+100x) at Q20 ~ 7 GeV2 inspired by the

shape of the gluonx (dbar-ubar) dbar ubar

dbar and ubar difference still negligible at the Q2 of interest at the LHC : dbar-ubar DOES NOT EVOLVE in Q2 the way that the singlet quantities gluon and sea do, it doesn’t even evolve in the more modest way that a non-singlet valence quantity does- it is the difference between two quantities which evolve in the same way.

To get it to matter at LHC Q2 it would have to be ‘fine-tuned’ at the starting scale

misure di funzioni di struttura ad lhc

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