Probes of small-x QCD from HERA to the LHC

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Probes of small-x QCD!from HERA to the LHC

Juan Rojo!Rudolf Peierls Center for Theoretical Physics!

University of Oxford!!

Institute for Subatomic Physics!University of Utrecht, 27/09/2016

1Juan Rojo Institute for Subatomic Physics, Utrecht, 27/09/2016

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Probes of small-x QCD!from HERA to the LHC

Juan Rojo!VU Amsterdam & Theory group, Nikhef!

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Institute for Subatomic Physics!University of Utrecht, 27/09/2016

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from next Monday!

Juan Rojo Institute for Subatomic Physics, Utrecht, 27/09/2016

Anatomy of Hadron Collisions!In high-energy hadron colliders, such as the LHC, the collisions involve composite particles (protons) with internal structure (quarks and gluons)


!In high-energy hadron colliders, such as the LHC, the collisions involve composite particles (protons) with internal structure (quarks and gluons)

!Calculations of cross-sections in hadron collisions require the combination of perturbative, quark/gluon-initiated processes, and non-perturbative, parton distributions, information

Parton Distributions!Non-perturbative From global analysis

Quark/gluon collisions!Perturbative!From SM Lagrangian

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Anatomy of Hadron Collisions


Parton Distributions

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The distribution of energy that quarks and gluons carry inside the proton is quantified by the Parton Distribution Functions (PDFs)

g(x,Q): Probability of finding a gluon inside a proton, carrying a fraction x of the proton momentum, when probed with energy Q

x: Fraction of the proton’s momentum

Q: Energy of the quark/gluon collision!Inverse of the resolution length



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PDFs are determined by non-perturbative QCD dynamics: cannot be computed from first principles, and need to be extracted from experimental data with a global analysis!




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PDFs are determined by non-perturbative QCD dynamics: cannot be computed from first principles, and need to be extracted from experimental data with a global analysis!

Energy conservation!

Dependence with quark/gluon collision energy Q determined in perturbation theory!



The Factorization Theorem

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The QCD Factorization Theorem guarantees PDF universality: extract them from a subset of process and use them to provide pure predictions for new processes

Determine PDFs in lepton-proton collisions ….

And use them to compute cross-sections in proton-proton collisions at the LHC


The global PDF analysis

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Hadronic scale: Global PDF fit results

LHC scale

Perturbative Evolution

Combine state-of-the-art theory calculations, the constraints from PDF-sensitive measurements from different processes and colliders, and a statistically robust fitting methodology!

Extract Parton Distributions at hadronic scales of a few GeV, where non-perturbative QCD sets in!

Use perturbative evolution to compute PDFs at high scales as input to LHC predictions

High scales: input to LHC


The global PDF analysis

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Hadronic scale: Global PDF fit results

LHC scale

Perturbative Evolution

Combine state-of-the-art theory calculations, the constraints from PDF-sensitive measurements from different processes and colliders, and a statistically robust fitting methodology!

Extract Parton Distributions at hadronic scales of a few GeV, where non-perturbative QCD sets in!

Use perturbative evolution to compute PDFs at high scales as input to LHC predictions

High scales: input to LHC


Dramatic rise of !small-x gluon

Probes of small-x QCD !in electron-proton collisions


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Beyond fixed-order DGLAP


Perturbative fixed-order QCD calculations have been extremely successful in describing a wealth of data from proton-proton and electron-proton collisions!

However, there are theoretical indications that eventually we need to go beyond fixed-order DGLAP!

At very small-x, logarithmically enhanced terms in 1/x become dominant and need to be resummed: small-x/high-energy/BFKL resummation formalism …..!

The steep rise in the small-x gluon will eventually trigger non-linear recombinations: gluon saturation, BK/JIMWLK equations …..

Even in framework of fixed-order QCD, low-x studies plagued by huge uncertainties in gluon PDF

HERA data ends here

HERA data ends here

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Beyond fixed-order DGLAP in HERA data


Remove ``dangerous’’ points at small-x and Q2 by means of a saturation-inspired cut!

Backwards evolution to predict the data excluded from the fit!

Compare with non-linear calculations, in this case BK with running coupling!

Some hints for deviations from NNLO QCD, but so far inconclusive Caola, Forte, Rojo 09,10!Albacete, Milhano, Quiroga, Rojo 12

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Beyond fixed-order DGLAP in HERA data


Related exercise: fit the final HERA combination on inclusive structure functions for different values of the cut in small Q data (where ``non-DGLAP’’ effects could be important)!

The χ2 degrades for the lower cuts, but interplay with other effects (heavy quarks, higher twists) make interpretation of these finding challenging (similar studies from HERAPDF, CT, MMHT)

NNPDF 15

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Global PDFs with BFKL resumation


Ultimately, the need for (or lack of) BKFL resummation can only be assessed by performing a global PDF analysis with NLO+NLLx matched theory!

Fit ongoing, based on the NNPDF3.0 framework - stay tuned for the results!

small-x resumed gluon-gluon splitting functionBonvini, Marzani, Peraro 16

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Global PDFs with BFKL resummation


x 7<10 6<10 5<10 4<10 3<10 2<10 1<10

) [re

f] 2

) / g

( x,

Q2

g ( x

, Q

0.8

0.9

1

1.1

1.2

1.3

1.4

2 GeV4=102Q

NLO baseline

NLO+NLLx

2 GeV4=102Q

Impact of BFKL logs

Preliminary

NNPDF, in preparation

Ultimately, the need for (or lack of) BKFL resummation can only be assessed by performing a global PDF analysis with NLO+NLLx matched theory!

Fit ongoing, based on the NNPDF3.0 framework - stay tuned for the results!

Probes of small-x QCD !at the LHC


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Small-x QCD at the LHC


At small-x, the gluon is the dominant PDFs, seeding the DGLAP evolution of the quarks!

Moreover, the quark singlet is well constrained from HERA inclusive structure functions!

What do we need to access the low-x gluon?!

To begin with, we require processes which are gluon-initiated already a leading order!

Consider kinematics for 2 -> 1 production: what are the values of the PDF Bjorken-x probed?

Therefore, to access the low-x region one requires processes that!

Involve production of final states with low invariant mass M!

The more forward in rapidity, the better!

The larger the center-of-mass energy of the collider, the better

Final state invariant mass

Hadronic CoM energy

Rapidity

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Direct photon production


D’Enterria, Rojo 12

Direct sensitivity to the gluon PDF via the QCD Compton scattering! High rates at the LHC, wide range of production kinematics accessible

Pros

Cons

Only NLO available, NNLO still far in the future! Dependence on the poorly-understood fragmentation component! Central production (ATLAS, CMS) only probes the region of intermediate x

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Direct photon production


Being able to measure low pT photons in the forward region would open a unique window to low-x QCD dynamics and PDFs at the LHC!

Both in proton-proton, proton-lead and lead-lead collisions

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Top quark production


Enhanced sensitivity to the gluon PDF via gg luminosity!

High rates and wide kinematical coverage!

NNLO for differential distributions!

Significant impact on the large-x gluon demonstrated

Pros

Cons! Central production (ATLAS, CMS) probes only the large-x region!

Limited statistics by LHCb in the forward region!

NNLO only for stable tops, realistic final states in progress

Preliminary

M. Czakon, N. Hartland, A. Mitov, E. R. Nocera, JR, in preparation

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Charm production in forward region


x 6−10 5−10 4−10 3−10 2−10 1−10

)

2 =

4 G

eV

2g (

x, Q

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=0.118sαNNPDF3.0 NLO

data+-

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x 6−10 5−10 4−10 3−10 2−10 1−10

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data+-

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=0.118sα), NNPDF3.0 NLO, 2g(x,Q

Figure 11: Left plot: The NNPDF3.0 small-x gluon, evaluated at Q = 2 GeV, comparing the baselineglobal fit result with with the new gluon obtained after the inclusion in the fit of the LHCb charmproduction data. In the latter case, we show both the reweighted results (rwg) and those after theunweighting procedure. Right plot: comparison of the percentage PDF uncertainties for the NNPDF3.0gluon at small-x both with and without the LHCb data.

at 13 TeV. A tabulation of our results is provided in Appendix A, and predictions for di↵erentbinnings and other meson species are available from the authors.

4.1 Forward heavy quark production atps = 13 TeV

First of all, we provide the theory predictions needed to compare with the upcoming LHCb dataon charm and bottom production at the LHC Run II with

ps = 13 TeV. We will assume the

same binning as for the 7 TeV measurements [32,33], and provide the complete set of theoreticaluncertainties from scales, PDFs, and charm/bottom mass variations. The predictions for anyother binning are also available upon request from the authors. Predictions will be given usingthe improved NNPDF3.0+LHCb PDF as input.

First of all, in Fig. 12 we show the predictions for the double di↵erential distributions,d

2

�(D)/dyDdpDT , for the production of D

0 mesons at LHCb for a center-of-mass energy ofps = 13 TeV, both in a central and in a forward rapidity bin. We compare the results of the two

exclusive calculations, POWHEG and aMC@NLO matched to Pythia8. Theory uncertaintiesare computed adding in quadrature scale, PDF and charm mass uncertainties. This comparisonshows that there is good agreement between the two calculations, both in terms of central valuesand in terms of the total uncertainty band. This agreement also holds for other D mesons andrapidity regions, not shown here. Thanks to using the improved NNPDF3.0 PDFs with

ps = 7

TeV LHCb data, PDF uncertainties turn out to be subdominant even atps = 13 TeV, with

scale variations being the dominant source of theoretical uncertainties.The corresponding comparison for B

0 mesons is shown in Fig. 13. As in the case of thecharm, there is a good agreement between the POWHEG and aMC@NLO calculations, fromlow pT ' 0 to the highest values of pT available. The agreement between the theory uncertaintybands in the two independent calculations provides confidence on the robustness of our results.

The tabulation of the results shown in Figs. 12 and 13 is provided in Appendix A, in particularin Tables 3 (for D0 mesons) and 4 (for B0 mesons).

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Forward data from LHCb probe the very low-x region!High rates, small statistical

uncertainties! NNLO within reach! Data available at different CoM

energies, including 13 TeV

Pros

Cons!

Large corrections to the perturbative expansion (large TH uncertainties from missing higher orders)!Dependence on charm fragmentation and hadronization

c

c

Gauld, Rojo, Rottoli, Talbert 15

Significant reduction on small-x gluon PDF uncertainties

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Soft and semi-hard QCD in MC generators


Soft and semi-hard QCD particle production (UE, MPI etc) ubiquitous at the LHC!Depends directly on the very low-x gluon

PDFs! Central ingredient of the tuning of LO and

NLO event generators at the LHCSkands, Carrazza, Rojo, 14

Small-x QCD from the LHC !to Neutrino Telescopes

24 x

6−10 5−10 4−10 3−10 2−10 1−10

)

2 =

4 G

eV

2g (

x, Q

0

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data+-

,D0

no LHCb D

data (wgt)+-

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with LHCb D


x 6−10 5−10 4−10 3−10 2−10 1−10

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enta

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rtain

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ps = 7





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Gauld, Rojo, Rottoli, Sarkar, Talbert 15

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From the LHC to Neutrino Telescopes Observation of Ultra-High Energy (UHE) neutrino events at IceCube heralds start of Neutrino Astronomy!

New window to the Universe, but interpretation of IceCube data requires control over backgrounds


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At large energies, the prompt flux from D meson decays dominates!But affected by large theory errors! How can we tame them?!Main problem: huge PDF uncertainties of small-x gluon….!More problems: prompt charm flux has not been observed yet …


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From the LHC to Neutrino Telescopes Use collider data to provide state-of-the-art predictions for backgrounds at Neutrino Telescopes

Include LHCb forward charm production data in the global fit!

Validate perturbative QCD calculations on collider data, and constrain the small-x gluon!

Compute optimised predictions for prompt neutrino fluxes at high energies!

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The LHCb forward charm production data cover the same kinematical region as prompt neutrino production in high-energy cosmic rays



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x 6−10 5−10 4−10 3−10 2−10 1−10

)

2 =

4 G

eV

2g

( x

, Q

0

2

4

6

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12

14

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data+-

,D0

no LHCb D

data (wgt)+-

,D0

with LHCb D

data (unw)+-

,D0

with LHCb D


x 6−10 5−10 4−10 3−10 2−10 1−10

Pe

rce

nta

ge

PD

F u

nce

rta

inty

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ps = 7





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x 6−10 5−10 4−10 3−10 2−10 1−10

)

2 =

4 G

eV

2g

( x

, Q

0

2

4

6

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10

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14

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data+-

,D0

no LHCb D

data (wgt)+-

,D0

with LHCb D

data (unw)+-

,D0

with LHCb D


x 6−10 5−10 4−10 3−10 2−10 1−10

Pe

rce

nta

ge

PD

F u

nce

rta

inty

0

20

40

60

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200=0.118sα), NNPDF3.0 NLO, 2g(x,Q

data+-

,D0

no LHCb D

data+-

,D0

with LHCb D









2




ps = 7





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Gauld, Rojo, Rottoli, Talbert 15 Gauld, Rojo, Rottoli, Sarkar, Talbert 15

We predict that detection of the prompt neutrino flux should be within IceCube reach Juan Rojo Institute for Subatomic Physics, Utrecht, 27/09/2016

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!


x 6−10 5−10 4−10 3−10 2−10 1−10

)

2 =

4 G

eV

2g

( x

, Q

0

2

4

6

8

10

12

14

16


data+-

,D0

no LHCb D

data (wgt)+-

,D0

with LHCb D

data (unw)+-

,D0

with LHCb D


x 6−10 5−10 4−10 3−10 2−10 1−10

Pe

rce

nta

ge

PD

F u

nce

rta

inty

0

20

40

60

80

100

120

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200=0.118sα), NNPDF3.0 NLO, 2g(x,Q

data+-

,D0

no LHCb D

data+-

,D0

with LHCb D









2




ps = 7





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Gauld, Rojo, Rottoli, Talbert 15 KM3NET Letter of Intent 2016

Calculation being already used by IceCube and KM3NETJuan Rojo Institute for Subatomic Physics, Utrecht, 27/09/2016

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Small-x nuclear PDFs: Terra Incognita


For nuclear PDFs (the PDFs of nucleons within bound nuclei) non-DGLAP effects are generically expected to be larger. However, available fits poorly constrained at medium and small-xDr Juan Rojo FOM-Projectruimte 2016

Hard Probes in proton-lead collision atp

sNN = 5.02 TeV at the LHCExperiment Process Observables Ref Motivation Kin. coverage

ALICE D-meson production [22] x Q

ALICE Charged jets [23] x Q

ALICE Charged hadron production [24] x Q

ALICE Heavy hadron production [25] x Q

ALICE Dijet correlations [26] x Q

ALICE D meson production [27] x Q

ALICE inclusive W production [28] x Q ' 80 GeV

ATLAS Inclusive charged particles [29] x Q

ATLAS inclusive W production yW!l [30] x Q

ATLAS Inclusive Z production yZ and pZT [31] quark flavor separation 0.001 x 0.1

low-x quarks Q = 91.2 GeV

CMS Inclusive Z production yZ and pZT [32] quark flavor separation 0.001 x 0.1

low-x quarks Q = 91.2 GeV

CMS bottom-quark jets pb�jetT [33] small-x gluon 0.0001 x 0.01

in-medium fragmentation 2 GeV Q 20 GeV

CMS B meson production pBT [34] small-x gluon 0.0001 x 0.01

in-medium fragmentation 2 GeV Q 20 GeV

CMS inclusive W production yW!l [35] x Q

CMS Dijet production hdijet and EdijetT [36] x

Q

CMS Charm quark jets pc�jetT [37] x

Q

LHCb D meson production [38] x Q

Table 2: Summary of LHC measurements in p+Pb collisions that provide PDF-sensitive information. For eachmeasurement, we indicate the name of the experiment, the center-of-mass energy per nucleon-nucleon collisionp

sNN = 5.02 TeV, the specific process and the corresponding distributions that have been reported and the publi-cation reference. In addition, we also indicate the motivation to include each into a nuclear PDF fit, and the kinematiccoverage in x and Q for each measurement.

different flavours and of the gluon, in a wide range of x and Q, will be achieved. To illustrate this point,in Fig. 3 we show the kinematic coverage in the (x,Q = MX) plane of the data on deep-inelastic nuclearstructure functions, compared to the extended coverage in the nucleon structure that will be achieved in thisproject thanks to the exploitation of the LHC proton-lead collisions.

10.4 Extreme QCD with direct photons in the forward regions in ALICE

The production of direct photons in hadronic collisions represent unique probe of the strong interactions. Asthe applicant demonstrated, prompt photon production at the LHC provides stringent constraints on the gluonPDF in the region x ' 0.02. At the LHC so far measurements of photons have been restricted to the centralregion, while the forward region, which allows to probe QCD in the extreme low x region, has so far remainedelusive. This very low x region is of fundamental importance for our understanding of hadron structure. Toillustrate this point, in Ref. the applicant demonstrated how very stringent constraints on the small-x gluonPDF can be obtained from charm production data in the forward region. This has important consequencesfor improved predictions for backgrounds as neutrino telescopes, the so-called prompt neutrino flux.

Recently, a new extension of the ALICE detector, the so called FoCal (FOrward Calorimeter) has beenproposed. Following it commissioning in around 2022, FOCAL would allow measurements of inclusivephotons at hadron production in the forward region and down to very small pT . This would provide an un-

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Producing a truly global nuclear PDF fit with the constraints from the LHC data should be a high-priority for the small-x QCD / heavy ion community

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A 100 TeV collider: the ultimate small-x machine At a future 100 TeV hadron collider, under consideration know, knowledge of PDFs and QCD in the small-x regime would be of paramount importance

Even relatively high mass particles, like W, become sensitive to small-x QCD effects there


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Probes of small-x QCD from HERA to the LHC