The odderon discovery by the D0 and TOTEM collaborations
Christophe Royon
On behalf of D0 and TOTEM Collaborations
University of Kansas, Lawrence, USALomonosov 2021, Moscow, Russia

August 19-25 2021
Introduction to the Odderon
D0 and TOTEM data
Extrapolation of TOTEM data to Tevatron energies
Comparison between D0 data and TOTEM extrapolated data

What do we want to study?

We want to study elastic interactions: pp → pp or p p̄ → p p̄These are very clean events, where nothing is produced outside the two protons
How to detect/measure these events? We need to detect the intact protons afterinteraction!
Interactions explained by the exchange of a colorless object (≥ 2 gluons, photon, etc...)between the two protons
The odderon discovery by the D0 and TOTEM collaborations

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The odderon in a nutshell
Pomeron and Odderon correspond topositive and negative C parity: Pomeronis made of two gluons which leads to a+1 parity whereas the odderon is madeof 3 gluons corresponding to a −1 parity
Scattering amplitudes can be written as:
Let us assume that elastic
scattering can be due to exchangeof colorless objects: Pomeron andOdderon
Charge parity C : Charge
conjugation changes the sign of allquantum charges
The odderon discovery by the D0 and TOTEM collaborations

App = Even + Odd
App̄ = Even − Odd
From the equations above, it is clearthat observing a difference between pp
and p p̄ interactions would be a clear
way to observe the odderon
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What is the odderon? The QCD picture

Multi-gluon exchanges in hadron-hadroninteractions in elastic pp interactions(Bartels-Kwiecinski-Praszalowicz)
From B. Nicolescu: The Odderon is definedas a singularity in the complex plane,
located at J = 1 when t = 0 and which
contributes to the odd crossing amplitude
The odderon discovery by the D0 and TOTEM collaborations

Leads to contributions on 3,... gluon
exchanges in terms of QCD for theperturbative odderon
Colorless C -odd 3-gluon state(odderon) predicts differences inelastic dσ/dt for pp and p p̄interactions since it corresponds todifferent amplitudes/ interferences
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Measurement of elastic scattering at Tevatron and LHC
Study of elastic pp → pp reaction:exchange of momentum between thetwo protons which remain intact
Measure intact protons scatteredclose to the beam using Roman Pots
installed both by D0 and TOTEMcollaborations
From counting the number of events
as a function of |t| (4-momentum
transferred square at the protonvertex measured by tracking theprotons), we get dσ/dt
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Why has the odderon not been observed yet? Why is it so elusive?
The situation is not that simple: elastic
scattering at low energies can be due toexchanges of additional particles topomeron/odderon: ρ, ω, φ, reggeons...
How to distinguish between all theseexchanges? Not easy...
At ISR energies, there was already someindication of a possible difference between
pp and p p̄ interactions, differences ofabout 3σ between pp and p p̄ interactions
but this was not considered to be a clean
proof of the odderon because of these
additional reggeon, meson exchanges at√low sThe odderon discovery by the D0 and TOTEM collaborations

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What is the expected situation at the LHC?
Expected elastic dσ/dt before LHC
measurements
Many different predictions including
many possible contributions at high|t|, such as pomeron, reggeon,mesons (ω, φ) whereas otherpredictions mentioned that, at highenergies, we should be more
asymptotical and pomeron
dominated
Almost nobody thought about theodderon (except a few theorists such
as Martynov, Nicolescu...)The odderon discovery by the D0 and TOTEM collaborations

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Are we in the asymptotic regime at the LHC?
Contrary to what some models
expected before LHC, the elastic
cross section is smooth: we do notsee reggeons, mesons...!
Effects of reggeon, meson exchanges
are negligible at LHC energies: wecan concentrate on
pomeron/odderon studies!
We can directly look for theexistence of the odderon bycomparing pp and p p̄ elastic crosssections at very high energies: 1.96
TeV (Tevatron), 2.76, 7, 8, 13(LHC)The odderon discovery by the D0 and TOTEM collaborations

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D0 elastic p p̄ dσ/dt cross section measurements

D0 collected elastic p p̄ data with
intact p and p̄ detected in the Forward
Proton Detector with 31 nb−1 Phys.
Rev. D 86 (2012) 012009
Measurement of elastic p p̄ dσ/dt at
1.96 TeV for 0.26 < |t| < 1.2 GeV2
The odderon discovery by the D0 and TOTEM collaborations

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TOTEM cross section measurements

The odderon discovery by the D0 and TOTEM collaborations

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TOTEM elastic pp dσ/dt cross section measurements
Elastic pp dσ/dt measurements: tag both intact protons in TOTEM Roman Pots 2.76,
7, 8 and 13 TeV
Very precise measurements at 2.76, 7, 8 and 13 TeV: Eur. Phys. J. C 80 (2020) no.2, 91;
EPL 95 (2011) no. 41004; Nucl. Phys. B 899 (2015) 527; Eur. Phys. J. C79 (2019) no.10, 861

The odderon discovery by the D0 and TOTEM collaborations

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dσ/dt (mb/GeV2 )Strategy to compare pp and p p̄ data sets100√
s = 13 TeV√
s = 8 TeV√
s = 7 TeV√
s = 2.76 TeV√
s = 1.96 TeV (extrap.)

TOTEM

10−1

10−2

0.4

0.5

0.6

0.7

The odderon discovery by the D0 and TOTEM collaborations

0.80.91|t| (GeV2 )In order to identify differences
between pp and p p̄ elastic
dσ/dt data, we need to compare
TOTEM measurements at 2.76,7, 8, 13 TeV and D0
measurements at 1.96 TeV
All TOTEM dσ/dt
measurements show the samefeatures, namely the presence ofa dip and a bump in data,
whereas D0 data do not show
this feature

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dσ/dtReference points of elastic dσ/dt

TOTEM-D0

bump+10bump+510A
5A
bumpbump2
A

mid1

mid2

dip

dip2

A/2
A/2

|t|

Define 8 characteristic points of elastic pp
dσ/dt cross sections (dip, bump...) thatare feature of elastic pp interactions

The odderon discovery by the D0 and TOTEM collaborations

Determine how the values of |t| anddσ/dt of characteristic points vary as√
a function of s in order to predict
their values at 1.96 TeV
We use data points closest to thosecharacteristic points (avoidingmodel-dependent fits)
Data bins are merged in case there are
two adjacent dip or bump points ofabout equal value
This gives a distribution of t and√dσ/dt values as a function of s for
all characteristic points
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RBump over dip ratio

TOTEM - D010Bump over dip ratio measured for pp
interactions at ISR and LHC energies

pp TOTEM
pp ISRTOTEM extrapolated
Fit of pp (exp+const)
pp ISR
pp UA4
pp D0

Bump over dip ratio in pp elastic
collisions: decreasing as a function of√s up to ∼ 100 GeV and flat above

R = R 0 + a0 ⋅ exp(b ⋅ s)
0R0 = 1.77 ± 0.01
a0 = 40 ± 24
b0 = (-6.7 ± 1.6) ⋅ 10-2 GeV-1

1102

103

The odderon discovery by the D0 and TOTEM collaborations

104s (GeV)

D0 p p̄ shows a ratio of 1.00±0.21
given the fact that no bump/dip isobserved in p p̄ data within
uncertainties: more than 3σdifference between pp and p p̄elastic data (assuming flat behavior√
above s = 100GeV )13 / 24

Fits of t and dσ/dt values for reference points
Fit of all reference points using the following formulae:√|t| = a log( s[TeV]) + b√(dσ/dt) = c s [TeV] + d
The same form is used for the 8 reference points (this is an assumption and works todescribe all characteristic points): this simple form is chosen since we fit at most 4 points,√corresponding to s = 2.76, 7, 8 and 13 TeV
We also tried alternate parametrizations such as |t| = e(s)f leading to compatible results
well within 1σLeads to very good χ2 per dof, better than 1 for most of the fits
Extrapolating the fits leads to predictions for |t| and dσ/dt at 1.96 TeV for eachcharacteristic point
The odderon discovery by the D0 and TOTEM collaborations

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(a)TOTEM-D0

0.9

dip2

0.8

mid2

0.7

bump0.6

mid1

0.4
246810√1214s (TeV)√|t| = a log( s[TeV]) + b
The odderon discovery by the D0 and TOTEM collaborations(b)

TOTEM-D0
10−1

bump+10bump+5bump (×2)
mid1
dip2 (×0.5)

10−2

dipbump2
bump+5bump+100.5(mb/GeV2 )1dσ/dt|t| (GeV2 )Variation of t and dσ/dt values for reference points2)
bump2 (×0.
mid2 (×0.1)
dip (×0.1)

10−3246810√

1214s (TeV)√(dσ/dt) = c s [TeV] + d15 / 24

Fits of TOTEM extrapolated characteristic points at 1.96 TeVThe last step is to predict the pp elastic cross sections at the same t values as measured
by D0 in order to make a direct comparison
Fit the reference points extrapolated to 1.96 TeV from TOTEM measurements using a23
2
double exponential fit (χ2 = 0.63 per dof): h(t) = a1 e −b1 |t| −c1 |t| + d1 e −f1 |t| −g1 |t| −h1 |t|This function is chosen for fitting purposes only
Low-t diffractive cone (1st function) and asymmetric structure of bump/dip (2nd function)
The two exponential terms cross around the dip, one rapidly falling and becoming negligible
in the high t-range where the other term rises above the dip

Systematic uncertainties evaluated from an ensemble of MC experiments in which thecross section values of the eight characteristic points are varied within their Gaussian
uncertainties. Fits without a dip and bump position matching the extrapolated values
within their uncertainties are rejected, and slope and intercept constraints are used todiscard unphysical fits
Such formula leads also to a good description of TOTEM data in the dip/bump region at2.76, 7, 8 and 13 TeV
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σtot(mb)Relative normalization between D0 measurement and extrapolated
TOTEM data: total pp cross section at 1.96 TeV
Differences in normalization taken into
account by adjusting TOTEM and D0 data
sets to have the same cross sections at theoptical point dσ/dt(t = 0) (NB: OP crosssections expected to be equal if there are
only C-even exchanges)

115
TOTEM-D0110
105
1009590

TOTEM measurements
fit±1 σ fit uncertainty bandextrapolation

858075246810√1214s (TeV)

Predict the pp total cross section fromextrapolated fit to TOTEM data (χ2 =0.27)√σtot = a2 log2 s[TeV] + b2
Other parametrizations lead to same results

Leads to estimate of pp σtot =82.7 ± 3.1 mb at 1.96 TeV
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Relative normalization between D0 measurement and extrapolated
TOTEM data: Rescaling TOTEM dataAdjust 1.96 TeV dσ/dt(t = 0) from extrapolated TOTEM data to D0 measurement
From TOTEM pp σtot , obtain dσ/dt(t = 0) :
 16π(~c)2 dσ2σtot =1 + ρ2dt t=0Assuming ρ = 0.145, the ratio of the imaginary and the real part of the elastic amplitude,
as taken from COMPETE extrapolation
This leads to a TOTEM dσ/dt(t = 0) at the OP of 357.1 ± 26.4 mb/GeV2
D0 measured the optical point of dσ/dt at small t: 341±48 mb/GeV2
TOTEM data rescaled by 0.954 ± 0.071
NB: We do not claim that we performed a measurement of dσ/dt at the OP at t = 0 (itwould require additional measurements closer to t = 0), but we use the two extrapolations
simply in order to obtain a common and somewhat arbitrary normalization point
The odderon discovery by the D0 and TOTEM collaborations

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Predictions at√s = 1.96 TeV

dσ/dt (mb/GeV2 )Reference points at 1.96 TeV (extrapolating TOTEM data) and 1σ uncertainty band
Comparison with D0 data
10−1√

TOTEM-D0
s = 1.96 TeVpp̄ measurement by D0
pp extrapolation by TOTEM:
band center at D0 bins
band width (±1 σ)10−20.5

The odderon discovery by the D0 and TOTEM collaborations

0.60.70.80.91|t| (GeV2 )19 / 24Comparison between D0 measurement and extrapolated TOTEM data
χ2 test to examine the probability for the D0 and TOTEM dσ/dt to agree
χ2 = Σi,j [(Ti − Di )Cij−1 (Tj − Dj )] +(A − A0 )2 (B − B0 )2+σA2σB2where Tj and Dj are the j th dσ/dt values for TOTEM and D0, Cij the covariance matrix,A (B) the nuisance parameters for scale (slope) with A0 (B0 ) their nominal values
Slopes constrained to their measured values (pp to p p̄ integrated elastic cross section√ratio (dominated by the exp part) becomes 1 in the limit s → ∞ which means similarslopes at small |t| as observed in data)
Test using the difference of the integrated cross section in the examined |t|-range with its
fully correlated uncertainty, and the experimental and extrapolated points with theircovariance matrices
Given the constraints on the OP normalization and logarithmic slopes of the elastic crosssections, the χ2 test with six degrees of freedom yields the p-value of 0.00061,
corresponding to a significance of 3.4σ
The odderon discovery by the D0 and TOTEM collaborations

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Combination with additional TOTEM measurement: ρ measurement

Measure elastic scattering at very low t: Coulomb-Nuclear interference regiondσ∼ |AC + AN (1 − αG (t))|2dt
The differential cross section is sensitive to the phase of the nuclear amplitude
In the CNI region, both the modulus and the phase of the nuclear amplitude can be usedN (0))
to determine ρ = Re(Awhere the modulus is constrained by the measurement in theIm(AN (0))
hadronic region and the phase by the t dependence
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A previous measurement by TOTEM: ρ and σtot measurements as anindication for odderon

ρ is the ratio of the real to imaginary part of the elastic amplitude at t = 0
Using low |t| data in the Coulomb-nuclear interference region, measurement of ρ at 13
TeV: ρ = 0.09 ± 0.01 (EPJC 79 (2019) 785)
Combination of the measured ρ and σtot values not compatible with any set of models
without odderon exchange (COMPETE predictions above as an example)
This result can be explained by the exchange of the Odderon in addition to the Pomeron
The odderon discovery by the D0 and TOTEM collaborations

22 / 24Comparison between D0 measurement and extrapolated TOTEM data

Combination with the independent evidence of the odderon found by the TOTEM
Collaboration using ρ and total cross section measurements at low t in a completely
different kinematical domain
For the models included in COMPETE, the TOTEM ρ measurement at 13 TeV provideda 3.4 to 4.6σ significance, to be combined with the D0/TOTEM result
The combined significance ranges from 5.3 to 5.7σ depending on the model
Models without colorless C -odd gluonic compound are excluded including the Durham
model and different sets of COMPETE models (blue, magenta and green bands on theprevious slide)The odderon discovery by the D0 and TOTEM collaborations

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Conclusion
Detailed comparison between p p̄ (1.96 TeV from D0) and pp (2.76, 7, 8, 13 TeV fromTOTEM) elastic dσ/dt data - FERMILAB-PUB-20-568-E; CERN-EP-2020-236
R ratio of bump/dip shows a difference of more than 3σ between D0 (R=1.0±0.21),√and TOTEM (assuming flat behavior above s = 100 GeV)
Fits of 8 “characteristic” points of elastic pp dσ/dt data such as dip, bump, etc as a√function of s in order to predict pp data at 1.96 TeV
pp and p p̄ cross sections differ with a significance of 3.4σ in a model-independent
way and thus provides evidence that the Colorless C -odd gluonic compound i.e.
the odderon is needed to explain elastic scattering at high energies
When combined with the ρ and total cross section result at 13 TeV, thesignificance is in the range 5.3 to 5.7σ and thus constitutes the first experimental
observation of the odderon: Major discovery at CERN/Tevatron

The odderon discovery by the D0 and TOTEM collaborations

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