Proton PDFs at the LHeC and FCC-ehLAL Orsay 2018

Gavin Pownall 1,2 Claire Gwenlan 1 Max Klein 3

1University of Oxford (GB)

2Deutsches Elektronen-Synchrotron (DE)

3University of Liverpool

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 1 / 28

1 Description of data

2 PDFs

3 αs studies

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 2 / 28

Description of data

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 3 / 28

LHeC Data

Data simulated by Max Klein, full description available:http://hep.ph.liv.ac.uk/∼mklein/lhecdata/

Ee/GeV Ep/TeV e Charge e Polarisation Luminosity/fb−1

60 1 -1 0 10060 7 +1 0 10060 7 -1 0.8 30060 7 -1 -0.8 1000

All datasets include neutral current (NC) and charged current(CC) interactions.Also testing data with 1/10 luminosity→ constraints on PDFsafter just one year of running. This data does not include lowenergy set.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 4 / 28

FCC Data

Data simulated by Max Klein, full description available:http://hep.ph.liv.ac.uk/∼mklein/fccdata/

Ee/GeV Ep/TeV e Charge e Polarisation Luminosity/fb−1

20 7 -1 0 10060 50 +1 0 10060 50 -1 0.8 30060 50 -1 -0.8 1000

All datasets include neutral current (NC) and charged current(CC) interactions.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 5 / 28

Kinematic plane

LHeC data to x = 10−6

FCC data to x = 10−7

LHeC higher concentration at high-x.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 6 / 28

LHeC data

Data provided to LO inpQCD - what we’re reallyinterested in is error.Provided data shifted toHERA PDF theory line(error retained as apercentage).Data then perturbedrandomly (gaussian dist.).

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 7 / 28

Framework

Version 2.0.0 “Frozen Frog”

HERAPDF parameterisationansatz used:

xqi(x) = AixBi (1 − x)Ci P(n)

i (x)

Primed gluon terms removedfrom fit.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 8 / 28

PDFs

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 9 / 28

LHeC Global Comparison

PDF results compared to status today.

x0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rat

io t

o C

T14

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 = 1.9 GeV2up valence distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

x0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rat

io t

o C

T14

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 = 1.9 GeV2down valence distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

Valence quark ratios at full and 10% luminosity.Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 10 / 28

LHeC Global Comparison

PDF results compared to status today.

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rat

io t

o C

T14

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 = 1.9 GeV2sea quark distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

Sea ratios at full and 10% luminosity.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 11 / 28

LHeC Global Comparison

PDF results compared to status today.

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

)2 =

1.9

GeV

2xg

(x, Q

-410

-310

-210

-110

1

10

2 = 1.9 GeV2gluon distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rat

io t

o C

T14

-2

-1

0

1

2

3

4

5

2 = 1.9 GeV2gluon distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

Gluon linear distributions.Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 12 / 28

LHeC Global Comparison

PDF results compared to status today.

x-710 -610 -510 -410 -310 -210 -110

)2 =

1.9

GeV

2xg

(x, Q

-2

-1

0

1

2

3

4

5

6

7

2 = 1.9 GeV2gluon distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

x-710 -610 -510 -410 -310 -210 -110

Rat

io t

o C

T14

-2

-1

0

1

2

3

4

5

6

7

2 = 1.9 GeV2gluon distribution at Q

NNLO PDF (68% C.L.)

CT14

NNPDF3.0

MMHT2014

HERAPDF2.0_EIG

LHeC (1/10)

LHeC

Gluon log-x distributions.Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 13 / 28

Direct comparison

Valence distributions at low x.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 14 / 28

Direct comparison

Valence distributions at high x.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 15 / 28

Direct comparison

u and d distributions at low x.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 16 / 28

Direct comparison

Gluon and strange distributions at low x.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 17 / 28

Does HERA make a difference any more?

LHeC with and without HERA DIS data.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 18 / 28

Does HERA make a difference any more?

FCC with and without HERA DIS data.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 19 / 28

Initial fit summary/discussion

Sea and gluon: LHeC performs better at high-x, FCC atlow-x.

Both data sets have the same luminosity.When FCC probes lower x (higher COM), it is balanced bya loss at high-x.

Valence: LHeC performs better at all x.Same argument as above.Valence quarks dominated by high-x.

HERA DIS data makes minimal difference.Most LHeC constraining power comes from first 10% ofdata.

Study dominated by systematics.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 20 / 28

Relaxing constraints

xuv = Auv xBuv (1 − x)Cuv

xdv = Adv xBdv (1 − x)Cdv

xu = Au x Bu (1 − x)Cu (1 + Dux)

xd = Ad xBd (1 − x)Cd

xg = Ag xBg (1 − x)Cg

xs = Asx Bs (1 − x)Cs

With constraints:Au = Ad

Bs = Bd = Bu

which ensure u = d as x → 0.Ag (momentum sum rule)

Auv , Adv (number sum rule)fs = (s + s)/(u + d) = 0.4

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 21 / 28

Relaxing sea constraints

Free parameters Au,Bu,Bd ,Bs , fs .

d and u; strange quark.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 22 / 28

Comparison to full HL-LHC PDF fit

Preliminary results.HL-LHC plots: Lucian Harland-Lang, HL-LHC workshop,

CERN, June 2018

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 23 / 28

Comparison to full HL-LHC PDF fit

Preliminary results.HL-LHC plots: Lucian Harland-Lang, HL-LHC workshop,

CERN, June 2018

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 24 / 28

Low-x resummation

Still a work in progress...

Credit: Francesco Giuli (University of Oxford)

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 25 / 28

αs studies

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 26 / 28

αs scan

LHeC precision: 0.2%FCC precision: 0.5%

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 27 / 28

What if HERA is added?

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 28 / 28

What if HERA is added?

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 29 / 28

Backups

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 30 / 28

LHeC data

Data provided to LO inpQCD - what we’re reallyinterested in is error.

Provided data shifted toHERA PDF theory line(error retained as apercentage).Data then perturbedrandomly (gaussian dist.).

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 31 / 28

LHeC data

Data provided to LO inpQCD - what we’re reallyinterested in is error.Provided data shifted toHERA PDF theory line(error retained as apercentage).

Data then perturbedrandomly (gaussian dist.).

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 32 / 28

LHeC data

Data provided to LO inpQCD - what we’re reallyinterested in is error.Provided data shifted toHERA PDF theory line(error retained as apercentage).Data then perturbedrandomly (gaussian dist.).

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 33 / 28

Difference made by perturbing data points...

Very little.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 34 / 28

Gluon constraints

xg(x) = AgxBg (1 − x)Cg − A ′gxB′g (1 − x)C′g

Add extra parameter Dg...

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 35 / 28

Relaxing sea quarks

Free parameters Au,Bu,Bd ,Bs , fs .

u better constrained by LHeC even with relaxed parameters.d similar constraining power as previous HERA fit.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 36 / 28

Relaxing sea quarks

Free parameters Au,Bu,Bd ,Bs , fs .

Freeing all at once may be too brutal - more work to be done.

Gavin Pownall - gavin.pownall@cern.ch Proton PDFs at the LHeC and FCC-eh 37 / 28