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PDFs, αs and quark masses

S.Alekhin (Univ. of Hamburg & IHEP Protvino)

UPHC19, Saclay, 26 Nov 2019

sa, Blümlein, Moch, Plačakytė PRD 96, 014011 (2017)sa, Blümlein, Moch EPJC 78, 477 (2018) sa, Blümlein, Moch hep-ph/1909.03533sa, Blümlein, Moch hep-ph/1910.11165

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QCD evolution

massless NNLO, massive NLO OMEs (OPENQCDRAD)

DIS inclusive

NNLO(OPENQCDRAD)

Power corr.(TMC+high-twist)

t-quark

(Hathor, fasttop)

Drell-Yan (W,Z,γ)

NNLO(FEWZ-grids)

DIS heavy quark

NNLO(approx.)(OPENQCDRAD)

5-flavour PDFs3-flavour PDFs

ABM PDF fit framework

mc,b

mc,b

mt

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Heavy-quark electro-production with FFN

Only 3 light flavors appear in the initial state

The dominant mechanism is photon-gluon fusion The complete coefficient functions up to the NLO

Involved high-order calculations:

– NNLO terms due to threshold resummation

– NNLO Mellin moments

Witten NPB 104, 445 (1976)

Laenen, Riemersma, Smith, van Neerven NPB 392, 162 (1993)

Lo Presti, Kawamura, Lo Presti, Moch, Vogt NPB 864, 399 (2012)Laenen, Moch PRD 59, 034027 (1999)

Ablinger at al. NPB 844, 26 (2011)

Bierenbaum, Blümlein, Klein NPB 829, 417 (2009)

Ablinger et al. NPB 890, 48 (2014)

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Modeling NNLO massive coefficients

Combination of the threshold corrections (small s), high-energy limit (small x), and the NNLO massive OMEs (large Q2) Kawamura, Lo Presti, Moch, Vogt NPB 864, 399 (2012)

small ssmall x

large Q2

ξ=Q2/m2

η=s/4m2-1

Catani-Hautmann

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Recent progress in FFN scheme Wilson coefficients

Update with the pure singlet massive OMEs → improved theoretical uncertaintiessa, Moch, Blümlein PRD 96, 014011 (2017)

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Running mass in DIS

The quantum corrections due to the self-energy loop Integrals receive contribution down to scale of O(Λ

QCD)

→ sensitivity to the high order corrections, particularly at the production threshold

The pole mass is defined for the free (unobserved) quarks as a the QCD Lagrangian parameter and is commonly used in the QCD calculations

sa, Moch PLB 699, 345 (2011)

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m

c(m

c)=1.250±0.019(exp.) GeV

ABMP16upd m

c(m

c)=1.252±0.018(exp.) GeV

ABMP16

HERA charm data and mc

Kiyo, Mishima, Sumino PLB 752, 122 (2016)

Kühn, LoopsLegs2018

H1, ZEUS EPJC 78, 473 (2018)

Good consistency with the earlier resultsand other determinations → further confirmation of the FFN scheme relevance for the HERA kinematics

Theory: FFN scheme, running massdefinition

mc(m

c)=1.246±0.023 (h.o.) GeV

mc(m

c)=1.279±0.008 GeV

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m

b(m

b)=3.96±0.10(exp.) GeV

ABMP16upd

mb(m

b)=3.84±0.13(exp.) GeV

ABMP16 m

b(m

b)=4.18+0.04-0.03 GeV

HERA beauty data and mb

PDG 2018

H1, ZEUS EPJC 78, 473 (2018)

Improved agreement with other determinations, evidently due to data purification

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Buza, Matiounine, Smith, van Neerven EPJC 1, 301 (1998)

The VFN scheme works well at μ ≫ mh (W,Z,t-quark production,….)

Problematic for DIS ⇒ additional modeling of power-like terms required at small scales (ACOT, BMSN, FONLL, RT….)

FFN and VFN schemes

⇒ ⊗

Collins, Tung NPB 278, 934 (1986)

LO:

NLO:

Asymptotic 3-flavor coefficient function

Massive operator matrix elements (OMEs)

Matching condition for the heavy-quark PDFs

NNLO: log-terms; constant terms up to the gluonic one Blümlein, et al., work in progress

2-mass contributions in NLO and NNLOBlümlein et al. PLB 782, 362 (2018)

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Glück, Reya, Stratmann NPB 422, 37 (1994)

BMSN prescription of GMVFN scheme

Smooth matching with the FFNS at Q → mh

without additional damping or re-scaling factors

FOPT heavy-quark PDFs → large logs missing?

In the O(αs

2) the FFNS and GMVFNS are comparable at

large scales since the big logs appear in the high order corrections to the massive coefficient functions

Buza, Matiounine, Smith, van Neerven EPJC 1, 301 (1998)

sa, Blümlein, Klein, Moch PRD 81, 014032 (2010)

FONLL: Cacciari, Greco, Nason JHEP 9805, 007 (1998)

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Comparison of the FOPT and evolved c-quark PDFs

LO: The FOPT and evolved PFGs nicely match at mh; at large scales they diverge due to

large logs are resummed by evolution

NLO (NLO OMES and NLO evolution): The difference between FOPT and evolved PDFs at large scales dramatically reduces due to large log are partially included into NLO OMEs and therefore are taken into account In the FOPT as well.

NNLO (NLO OMES and NNLO evolution): A kink w.r.t. FOPT appears at small x

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BMSN scheme with the evolved PDFs Comparison with the model FFN fit: – NLO massive Wison coeffs., – m

c(pole)=1.4 GeV

The difference with FOPT appears rather due to inconsistent evolution than due to big-logs → theoretical uncertainty in the VFN schemes

Two variants of 4-flavor PDF evolution: NNLO (commonly used in the VFN fits) – consistent with light PDF evolution inconsistent with NLO matching NLO – inconsistent with light PDF evolution consistent with NLO matching Substantial difference between NLO and NNLO versions

The evolved predictions demonstrate strong x-dependence and weak Q2-dependence

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Impact ov the scheme variation on the PDFs

Only heavy-quark data are used (inclusive DIS dropped) → illuminating impact of the Scheme choice

Gluon distribution goes down by ~25% at x~10-4 for the NNLO evolved VFN scheme → should be considered as the scheme uncertainty

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GMVFN modeling (Thorne’s scheme)

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Big spread in mc(pole) preferred by the PDF fits with various schemes;

value of mc(pole) used in the PDF fits are systematically lower than the PDG value

c-quark mass in the GMVFN schemes

Wide spread of the mc obtained in different version of the GMVFN schemes →

quantitative illustration of the GMVFNS uncertainties

H1/ZEUS PLB 718, 550 (2012)

mc(m

c)=1.19+0.08-0.15 GeV ACOT....

Gao, Guzzi, Nadolsky EPJC 73, 2541 (2013)

mc(m

c)=1.34+0.04-0.01 GeV FONLL

Bertone et. al JHEP 1608, 050 (2016)

mc(pole) ~ 1.3 GeV in VFN PDF fits

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Running mass for the t-quark data

HATHOR (NNLO terms are checked with TOP++)

Langenfeld, Moch, Uwer PRD 80, 054009 (2009)

Czakon, Fiedler, Mitov PRL 110, 252004 (2013)

Pole MSbar

Running mass definition provides nice perturbative stability

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Impact of t-quark data

Running t-quark mass is determined simultaneously with PDFs

mt(m

t)= 160.9±1.1 GeV

mt(pole)=170.4±1.2 GeV

mt(MC)~172.5 GeV from LHC

mt(MC)~174 GeV from Tevatron

mt(pole)=170.5±0.8 GeV

mt(pole)=171.1±1.1 GeV

Ongoing efforts to quantify the difference between m

t(MC) and

other determinations

ABMP16updated

ATLAS hep-ex/1905.02302

CMS hep-ex/1904.05237

Hoang et al.

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sa, Moch, Thier PLB 763, 341 (2016)

t-quark: single production (mass determination)

mt(m

t)= 161.1± 3.8 GeV (single-top only)

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Vacuum stability is quite sensitive to the t-quark mass; stability is provided up to Plank-mass scale using α

s and m

t in a consistent way.

Electroweak vacuum stability

mr: Kniehl, Pikelner, Veretin CPC 206, 84 (2016)

Buttazzo et al., JHEP 12, 089 (2013)

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Combination of the DY data (disentangle PDFs) and the DIS ones (constrain αs )

Run-II HERA data pull αs up by 0.001

the value of αs is still lower than the PDG one: pulled up by the SLAC and NMC

data; pulled down by the BCDMS and HERA ones

αsfrom DIS

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Higher twists in DIS: generalities

Virchaux, Milsztajn PLB 274, 221 (1992)

High twists appear in the DIS dataat large x(equiv. W) and/or small Q2

Operator product expansion:

F2,T

=F2,T

(leading twist) + H2,T

(x)/Q2 + ... – additive

F2,T

=F2,T

(leading twist) (1 + h2,T

(x)/Q2 +…) –

multiplicative

The only one in accordance with QCD

For multiplicative form the LT anomalous dimensions strongly affect the HT terms at small x

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The value of αS and twist-4 terms are strongly

correlated both at large and at small x

With HT=0 the errors are reduced → no uncertainty due to HTs

With account of the HT terms the value of αS is

stable with respect to the cuts

MRST: αS(M

Z)=0.1153(20) (NNLO)

(W2>15 GeV2, Q2> 10 GeV2)

A stringent cut on Q is necessary for the fit with HT=0

Correlation of αS

with twist-4 terms

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Summary

The values of quark masses and αS provide excellent benchmarking tool when

fitted with simultaneously with the PDFs

– the FFN scheme provides nice agreement with existing HERA data on charm production; running c- and b-quark masses

mc(m

c)=1.250±0.019(exp.) GeV

mb(m

b)=3.96±0.10(exp.) GeV

from the updated version of the ABMP16 fit

– consistent values of

αS(M

Z)=0.1147(8) with proper treatemnt of the higher-twist terms

αS(M

Z)=0.1153(8) with proper higher-twist terms set to 0 and

the cuts W2>12.5 GeV2, Q2> 10 GeV2 on DIS data – consistent values of

mt(m

t)== 160.8±1.1 GeV (ttbar + single top)

mt(m

t)= 161.1± 3.8 GeV (single-top only)

with the use of running mass definition

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EXTRAS

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High twists at small x

HT(x) continues a trend observed at larger x

H2(x) is comparable to 0 at small x

hT=0.05±0.07 → slow vanishing at x → 0

Alternative explanations are considered: resummation, saturation, data defects, etc.

F2,T

=F2,T

(leading twist) + H2,T

(x)/Q2 H(x)=xhP(x)

Controlled bySLAC data

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No mass singularities for massive partons ⇒ collinear QCD evolution does not work

The mass singularities ~ln(μ/mh) appear at μ≫m

h and the evolution restores. New

charm(bottom) quark distribution may be introduced, however, extrapolation to smaller scales is still problematic

Intrinsic charm is often introduced within the VFN framework ⇒ interplay with the “standard” VFN modeling of power-like terms

Original formulation of the intrinsic charm implies its power-like behavior;

Strong constraint on such terms was obtained from analysis of the DIS inclusive and semi-inclusive data

Intrinsic charm: pitfalls

Jimenez-Delgado, Hobbs, Londergan, Melnitchouk PRL 114, 082002 (2015)

Brodsky, Peterson, Sakai PRD 23, 2745 (1981)

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ABMP16 CJ15 CT10 CT14 epWZ16 MMHT14

NPDF

28 21 26 26 14 31

μ0

2 (GeV2) 9 1.69 1.69 1.69 1.9 1

χ2 4065 4108 4148 4153 4336 4048

PDF shape xα(1-x)β

exp[P(x,ln(x))]xα(1-x)βP(x,√x) xα(1-x)β

exp[P(x,√x)]xα(1-x)β

exp[P(x,√x)]xα(1-x)βP(x,√x) xα(1-x)βP(x,√x)

Constraints ū=đ (x→0) αuv

=αdv

αū=α

đ=α

s

ū=đ (x→0)

αuv

=αdv

βuv

=βdv

αū=α

đ=α

s

αū=α

đ=α

s

ū=đ (x→0)

αs(M

Z) 0.1153 0.1147 0.1150 0.1160 0.1162 0.1158

Checking styles of PDF shape

Various PDF-shape modifications provide comparable description with NPDF

~30

Some deterioration, which happens in cases is apparently due to constraints on large(small)-x exponents

Conservative estimate of uncertainty in αs(M

Z): 0.0007, more optimistic: 0.0003