PDF Issues in Faserν and SND - Robert Thorne January 15th 2021 University College London - CERN Indico
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PDF Issues in Faserν and SND
Robert Thorne
January 15th 2021
University College London
CERN – January 2021
I will discuss what opportunities we envision for learning about PDFs from potential data at the FASERν and SND in the context of what has happened at previous DIS experiments. Essentially all related to heavy quarks, i.e. charm, in one manner or another. Possible future interest in broader area, e.g. nuclear PDFs, but not concentrated on here - though many issues common to nucleon and nuclear PDFs in practice. CERN – January 2021 1
Comparison of neutrino flux/interactions - FASERν 1908.02310. FASERν flux dominated by νµ(ν̄µ) coming from pion and kaon decay, i.e. not charm mesons in the initial state. CERN – January 2021 2
At low energies νµ(ν̄µ) dominates flux at SND (2002.08722), but at energies up to Eν ∼ 104GeV σν ∝ Eν . At high Energies SND flux dominated by νe(ν̄e), and with larger contribution from ντ (ν̄τ ). These are coming from charm meson decay. CERN – January 2021 3
Consequence of distance from beam axis of respective detectors, with shorter decay time for heavy measons facilitating more contribution away from beam axis. CERN – January 2021 4
Can see this also in numerical comparison of CC interaction expected,
and mean energies.
FASERν – 1908.02310
SND – 2002.08722
CERN – January 2021 5
Hence, more scope for FASERν in terms of physics where the (largely muon) neutrino is the probe of the nucleons in the FASERν target. Fig. from 1908.02310. Spectrum extends to a slightly higher energy than previous fixed-target neutrino DIS experiments, e.g NuTeV. CERN – January 2021 6
Neutrino Cross section. Very firmly in the regime of Deep-Inelastic Scattering, and determined essentially entirely by PDFs. At LO in QCD Where q = (u + d)/2 + s + b and q̄ = (d¯ + ū)/2 + c Where for ν → ν̄ then q → q̄. y is inelasticity. CERN – January 2021 7
Q0 is a cut-off for the “non-perturbative regime”, plot by P. Plesniak. At most a few % contribution from nonperturbative regime, mainly near E = 100GeV. CERN – January 2021 8
PDFs regime of 0.001 < x < 0.03 and 1GeV2 < Q2 < 50GeV2. Dominant contributions from u, d which are known to couple of percent level. Cross section and uncertainty (at LO for now) using MMHT2014 PDFs of order 2% and similar for MSHT2020 (plot by T Cridge). CERN – January 2021 9
Nuclear PDF corrections add additional (essentially uncorrelated) uncertainty of ∼ 3 − 4%. Plot from 2001.03073. CERN – January 2021 10
Total uncertainty in normalization of order ∼ 5%. Better than knowledge of flux, and of FASERν sensitivity. Plot from 1908.02310. CERN – January 2021 11
Charged Current Charm production However, if heavy flavour detected in the final state more interesting for PDFs Long existing measurements of dimuon production in neutrino DIS on heavy targets CCFR, NuTeV, (Phys.Rev.D 74 (2006) 012008). Dominated by strange (anti)quark initial state - traditionally main constraint on strangeness. CERN – January 2021 12
Measurements using both νµ and ν̄µ beams at different energies. Possibility of reaching up to ∼ 5 times greater energy at FASERν, i.e. ∼ 5 times lower in x. Also no dependence on D → µ branching ratio, which gives O(10%) uncertainty CERN – January 2021 13
Extremely high precision data on W, Z from ATLAS
Difficulties in fitting both W and
Z distributions fixed by increase
in strange quark fraction
s+s̄
RS = ū+d¯
in ATLAS study (PRL 109
(2012) 012001).
CERN – January 2021 14MSHT2020 PDFs compared to MMHT2014 at NNLO.
s+s̄
Look at Rs = ū+d¯
.
Currently an increase in the strange quark below x = 0.1 due to W, Z
data (mainly ATLAS 7, 8 TeV).
Still significant uncertainty, and some tension, at higher x. Important
constraint from FASERν possible.
CERN – January 2021 15Prediction (at LO for now) for charm fraction in final state from MMHT2014 PDFs and MSHT2020 PDFs (plot by T Cridge). Need measurement of precision better than ∼ 10% for constraint, but currently tension between LHC and DIS measurements. CERN – January 2021 16
Charm meson production probed by neutrino production. Charm mesons dominant source of neutrino flux, or more specifically interactions at SND. Charm produced in LHC collisions at pseudo-rapidity ∼ 7 − 9. Corresponds to x1 ∼ 0.04 − 0.8 and x2 ∼ 10−7 − 5 × 10−5. On the edge of LHCb lower limit. CERN – January 2021 17
Theoretical Issues in cross section calculation. One parton at potentially very high x and another at very small x leads to many complications/opportunities. At high x there is the question of intrinsic charm. What is the status of intrinsic charm? Plot from 1908.02310. CERN – January 2021 18
Intrinsic charm
Formally of higher twist, i.e. O(Λ2/m2c ).
Proposed that it could be enhanced at high x by Brodsky et al in 1983.
ĉ(x) = Ax2[6x(1 + x) ln x + (1 − x)(1 + 10x + x2)]
Possible enhancement at high-x, similar to the large higher twist
expected at low W 2.
Therefore no expected constraint from HERA data.
Potentially of relevance for LHC neutrino data.
CERN – January 2021 19Investigations in PDF fits CT add this type of intrinsic charm model, and sea quark type intrinsic charm, and see the effect on global fits. Some limited evidence for preference, e.g JHEP 02 (2018) 059. CERN – January 2021 20
NNPDF recently started including “fitted charm” (not identical to “intrinsic charm”) as their default, e.g. EPJC 76 (2016) 11, 647. Very different to perturbative only charm, with much bigger uncertainty. Larger than perturbative charm at highest x but smaller for x ∼ 0.01. CERN – January 2021 21
Also very different to CT instrinsic charm models. Tends to be lower that perturbative charm at lowish x. Possibility of large terms in g → c in transition matrix. Really higher order theory correction? CERN – January 2021 22
Small-x issues. However, independent of the issues associatted with intrinsic charm at high-x, there are numerous uncertainties associatted with convergence of perturbation theory, particularly related to small-x. To begin with there is simply very large scale uncertainty (approximate indication of theory uncertainty) from the NLO calculation (Bai et al. 2002.03012 ). CERN – January 2021 23
PDF uncertainty.
As well as (perturbative theory uncertainties) there is a huge intrinsic
PDF uncertainty at this very low x value.
xg(x,Q), comparison
10
MSHT2020NNLO
8 NNPDF3.1
6 CT18ANNLO
Q = 2.00e+00 GeV
Generated with APFEL 2.7.1 Web
4
2
0
−2
−4
−6
−8
−10
10−7 10−6 10−5 10−4 10−3 10−2 10−1 1
x
There is literally no constraining data in this regime in PDF fits, so any
genuine uncertainty estimate explodes here.
CERN – January 2021 24Large scale uncertainty a feature of low physical scale ∼ mc and
relatively slowly convergent series.
However, also the problem of small-x logarithms
∞
αS2 X αSn lnn(1/x)
σ∝ σn
x n=0 n!
i.e. in terms of the fractional momentum x of the one of partons there
is an extra power of ln(1/x) for each power of αS
In this case αS ≈ 0.35 while ln(1/x) can be as low as ln(1/x) ∼ 15 (the
cross section involves a convolution so this is the maximum value).
Scale variation at fixed order gives no information at all about missing
higher power terms of ln(1/x).
CERN – January 2021 25Fits to LHCb data including ratios (both from different energies and different rapidities) can reduce effect of scale uncertainties (Gauld et al 1610.09373). Not guaranteed to be so stable under genuine higher-order corrections. CERN – January 2021 26
Long-known and hugely studied problem mainly in the context of structure functions. Basic resummation of leading and next-to-leading logarthims known - BFKL resummation. Far more required for realistic and accurate resummation including running coupling effects, momentum conservation ....... Known moderately well (we think) for structure functions. CERN – January 2021 27
For example, the fit to final HERA inclusive cross sections is not optimal
at NNLO at low x and high y, where
σ ∝ F2(x, Q2) − y 2FL(x, Q2)
Improved by small-x resummation, as shown by e.g. the xFitter
collaboration 1802.00064 and NNPDF 1710.05935.
CERN – January 2021 28Improvement due to increase in FL(x, Q2) for the same fitted F2(x, Q2) which dominates the cross section in most regions. i.e. small-x resummation leads to different changes for different physical quantities. Could alter charm cross section at the LHC for a given fit gluon, but this is not calculated at all precisely yet. CERN – January 2021 29
Note the same sort of small-x conclusions were already made in 2007 (hep-ph/0611204) with less precise earlier HERA data and more basic, but qualitatively very similar resummation calculations. CERN – January 2021 30
Fits with resummation in PDFs and LHCb data performed (Gauld et al 1808.02034). However, resummation not performed in cross section. CERN – January 2021 31
Beyond Leading Twist Perturbation Theory. In this regime can also get potential non-universal corrections at higher twist O(Λ2QCD /Q2) corrections at small x. Expected (with some uncertainty/disagreement) due to saturation of cross section and PDF growth - this can start to occur roughly when xg(x, Q2) > Q2R2, where R2 ∼ (0.2GeV)2. For example, improvement in fit to high-y, low-x, Q2 HERA data can be explained phenomenologically by O(Λ2QCD /Q2) corrections to FL(x, Q2) (1601.03413, 1704.03187 – plots from latter). CERN – January 2021 32
Conclusions FASERν is particularly well suited to use the dominantly muon neutrino flux from light mesons to measure charm production in the final state. This could provide a good constraint on the (relatively uncertain) strange quark in a x-range extending a little beyond previous DIS experiments. Also in a region where less direct LHC - ATLAS constraints are in tension to some degree with DIS constraints. Dominant flux produced by charm mesons from SND can be a useful constraint on charm production from high-x and very low-x PDFs. FASERν elecron and tau contributions sensitive at even more extreme values. Impact on study of intrinsic charm at high-x probably limited. PDF, particularly gluon uncertainty so large for x < 10−6 even though there are a wide range of large theoretical uncertainties – fixed order (scale), small-x resummation, higher-twist, saturation – a measurement will give very useful constraints. Uncertainties likely minimised by ratios in which systematic uncertainties (theory and experiment) cancel. CERN – January 2021 33
Back-up CERN – January 2021 34
High-x Strange Quark.
There is also the possibility
of looking at the less νe
well know strange quark e
via charm quark jets
at the EIC.
Requires dealing with
fragmentation (but so
W
do some current methods
at some level).
jet
p
Plot from https://arxiv.org/abs/2006.12520 Arratia et al..
CERN – January 2021 35From a CT study one
can see the likely x 1
reco Q2JB [GeV2]
and Q2 range likely to 0.9
be covered. 0.8
0.7
Higher x than the 103 0.6
main constraints from 0.5
the LHC, and from the 0.4
most precise dimuon 0.3
measurements. 2
0.2
10
0.1
0
−2 −1
10 10 1
reco xJB
Plot from https://arxiv.org/abs/2006.12520.
CERN – January 2021 36Inclusion of new NNLO corrections. NNLO corrections to dimuon production (Phys. Rev. Lett. 116 (2016), Berger et al., J. Gao, arXiv:1710.04258). NNLO correction negative, but larger in size at lower x Impacts on tension between dimuon data and LHC W, Z data. CERN – January 2021 37
In some NNPDF fits try fitting old EMC data (NPB 213 (1983) 31-64). Clearly prefers supression at smaller x, and also some enhancement as x → 1. Consistent with suggestions from LHC data sensitive to flavours (W, Z). Note however, EMC data relied on large corrections using LO theory generators and extremely basic PDFs. Significant question mark. CERN – January 2021 38
MSTW tried fitting EMC data. Overshoot lower x data even at NLO with dynamical charm. High-x intrinsic charm with modified coefficient functions, m2c → m2c + Λ2, at threshold works ok. At low Q2 and W 2 we likely need to worry about nonperturbative or higher twist effects beyond just that of intrinsic charm. Similar with hadronization issues in Monte Carlos for higher energy production. CERN – January 2021 39
Choices for Heavy Flavours in DIS.
Near threshold Q2 ∼ m2H massive quarks not partons. Created in final
state.
Described using Fixed Flavour Number Scheme FFNS.
Variable Flavour - at high scales Q2 m2H heavy quarks behave like
massless partons. Sum ln(Q2/m2H ) terms via evolution.
Partons in different number regions related to each other perturbatively.
n +1 n
fj f (Q2) = Ajk (Q2/m2H ) ⊗ fk f (Q2),
Perturbative matrix elements Ajk (Q2/m2H ) (Buza et al.) containing
n n +1
ln(Q2/m2H ) terms relate fi f (Q2) and fi f (Q2) → correct evolution for
both.
CERN – January 2021 40Affects distinction between “intrinsic charm” and “fitted charm”. CERN – January 2021 41
Higher orders At O(αS3 ) similar form seemingly, but AHg not yet fully known. Calculation of matrix elements part of an enormous project by Blümlein et al. e.g (Nucl.Phys.B 890 (2014) 48-151). Goes into PDFs or into NNLO FFNS cross sections. CERN – January 2021 42
Level of uncertainty in AHg (top) and Agg,H (bottom) (McGowan). CERN – January 2021 43
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