Erratum Stronger C-odd color charge correlations in the proton at higher energy Adrian Dumitru Department of Natural Sciences Baruch College

2025-04-29 0 0 1.54MB 9 页 10玖币

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Erratum: Stronger C-odd color charge correlations in the proton at higher energy

Adrian Dumitru

Department of Natural Sciences, Baruch College,

CUNY 17 Lexington Avenue, New York, NY 10010, USA and

The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY 10016, USA

Heikki M¨antysaari∗

Department of Physics, University of Jyv¨askyl¨a, P.O. Box 35, 40014 University of Jyv¨askyl¨a, Finland and

Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland

Risto Paatelainen

Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland

In the calculation of the ρa(⃗q1)ρb(⃗q2)ρc(⃗q3)C=−1cor-

relator in Ref. [1] the symmetry factors for the diagrams

of the “Fig. 7 type” included an incorrect factor 2, see

Erratum of Ref. [1].

In this work we have evaluated the expressions in

Ref. [1] numerically in order to calculate the C-odd odd-

eron amplitude in coordinate space. Once the ﬁxed sym-

metry factors are taken into account, the numerical re-

sults presented in this letter change. Furthermore, we

also realized that an overall factor (−1) was missing from

all our results.

When the ﬁxed symmetry factors are taken into ac-

count, the original conclusions change to some extent.

We originally reported ﬁnding a stronger Odderon am-

plitude with decreasing Bjorken-x. This remains true for

small dipoles, compared to the impact parameter. How-

ever, at larger dipole size rthe C-odd amplitude may

either increase or decrease, depending on the impact pa-

rameter.

We now present an updated numerical analysis of the

odderon coordinate space amplitude. First, the angular

dependence of the Odderon (deﬁned in Eq. (3) of the

original manusript) is shown in Fig. 1. The Odderon is

parametrized as

O(⃗r,⃗

b) = a1(r, b) cos θ+a3(r, b) cos 3θ(1)

and the dominant coeﬃcient a1is shown in the following

Figures. Depending on the dipole size and on the im-

pact parameter, the NLO correction can be quite large

already at x= 0.1, and it in general exhibits a relatively

moderate xdependence.

The impact parameter dependence of the coeﬃcient

a1quantifying the magnitude of the Odderon is shown

in Fig. 2. As already mentioned above, the NLO correc-

tion now reduces the amplitude at small b≪r, while a

stronger Odderon is obtained with decreasing xat larger

impact parameters.

Similarly the dependence on the dipole size ris shown

in Fig. 3, now at small and large b. Again a decreasing

∗Electronic address: heikki.mantysaari@jyu.ﬁ

(in magnitude) Odderon with decreasing xis obtained

at small impact parameter, consistent with expectations

based on perturbative small-xevolution of the (hard)

odderon [2]. On the other hand, at larger bthe behavior

is opposite.

In the original publication we reported that a1levels

oﬀ at large r≃0.7 fm. Such behavior is still visible in

Fig. 3(left) for small b(although we now restrict to r≤

0.6 fm where the numerical evaluation is most reliable).

At greater impact parameter b, however, see Fig. 3(right),

no levelling oﬀ of the Odderon amplitude is seen up to the

largest dipoles considered here. The behavior of a1(r) at

diﬀerent impact parameters is also visible from Fig. 4.

We also provide updated two-dimensional grids for the

coeﬃcients a1and a3at diﬀerent r. The grids for a1are

illustrated in Fig. 4and numerical values can be found

in the supplementary material.

arXiv:2210.05390v2 [hep-ph] 24 Feb 2025

(a) Large dipole, small impact parameter (b) Small dipole, large impact parameter

FIG. 1: Angular dependence of O(⃗r,⃗

b) at various x. The error bars show the estimated uncertainty of the numerical

Monte Carlo integration.

(a) Small dipole (b) Large dipole

FIG. 2: Dependence on the impact parameter.

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Erratum:StrongerC-oddcolorchargecorrelationsintheprotonathigherenergyAdrianDumitruDepartmentofNaturalSciences,BaruchCollege,CUNY17LexingtonAvenue,NewYork,NY10010,USAandTheGraduateSchoolandUniversityCenter,TheCityUniversityofNewYork,365FifthAvenue,NewYork,NY10016,USAHeikkiM¨antysaari∗DepartmentofPhys...

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Erratum Stronger C-odd color charge correlations in the proton at higher energy Adrian Dumitru Department of Natural Sciences Baruch College

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