Interference between Coulomb and hadronic scattering in elastic high-energy nucleon collisions

Kundrát, V.; Lokajíček, M.

doi:10.1016/j.physletb.2005.02.025

Cited by 18 publications

(18 citation statements)

References 32 publications

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“…The results for a point-like proton [22,23] have been generalized [7] allowing for different slopes for the real and imaginary nuclear amplitudes. A second approach is the form-factor phase, which considers an eikonal treatment for the superposition of amplitudes and a geometrical size with a form factor for the proton structure [20,21,24,25].…”

Section: Discussionmentioning

confidence: 99%

“…The importance of the different slopes in the analysis of pp elastic scattering has been investigated in the framework of the so-called dispersion relations for slopes [17]. It is important to note that also the CoulombNuclear phase φ(t) depends essentially on the form of the nuclear amplitudes [20,21]. In Appendix A, generalizing previous work [7,[22][23][24], we derive the expression for the phase to be used with the assumed amplitudes written above.…”

Section: Amplitudes and Observables In Forward Scatteringmentioning

confidence: 96%

“…The phase φ of the quantum interference between Coulomb and nuclear interactions was studied by several authors [7,[20][21][22][23][24][25][26]. A first approach for the so-called Coulomb phase is the point-like (pure Coulomb) phase, derived by West Yennie [22,23] calculated in the context of quantum field theory, considering the nuclear imaginary and real amplitudes with the same t…”

Section: Appendix A: Coulomb Phasementioning

confidence: 99%

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Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV

et al. 2017

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Recent measurements of the differential cross sections in the forward region of pp elastic scattering at 7 and 8 TeV show the precise form of the t dependence. We present a detailed analysis of these measurements including the structures of the real and imaginary parts of the scattering amplitude. A good description is achieved, confirming in all experiments the existence of a zero in the real part in the forward region close to the origin, in agreement with the prediction of a theorem by Martin, with an important role in the observed form of dσ/dt. A universal value for the position of this zero and regularity in other features of the amplitudes are found, leading to quantitative predictions for the forward elastic scattering at 13 TeV. LHC experiments in elastic pp scatteringWith an enormous gap in the center-of-mass energy with respect to previous data in pp and pp scattering, the Totem and Atlas experimental groups at LHC have recently measured dσ/dt in the forward t ranges at √ s = 7 and 8 TeV [1][2][3][4][5]. These measurements offer a unique opportunity to investigate the behavior of p-p collisions at the highest energies reached in laboratory. A detailed and precise analysis of these data can establish a precious milestone for the understanding of the high energy behavior of p-p interactions. The datasets and their t ranges are listed in Table 1, where we use the obvious notation T7, T8, A7, A8 to specify Totem (T) and Atlas (A) Collaborations and center-of-mass energies 7 and 8 TeV.In order to build a bridge towards theoretical models aiming at the understanding of the dynamics, it is important that the analysis of these LHC data be made with identification of the structures of the individual parts of the complex scattering amplitude. The disentanglement of the two terms in the a e-mail: kendi@if.ufrj.br observed modulus dσ/dt is the crucial task. At each energy, parameterizations must search to exhibit clearly the properties of magnitudes, signs, slopes and zeros of the real and imaginary parts. External support, as dispersion relations and connections with analyses at other energies, gives important clues. The intervention of the electromagnetic interactions must be treated coherently with a proposed analytical form for the nuclear part, and account must be taken of phase of the Coulomb-Nuclear Interference (CNI), which is calculated in Appendix A.In the present work we perform a detailed examination of the data trying to satisfy these requirements. Each part of the amplitude is written with an exponential factor with a slope, multiplying a linear term in t, thus with three parameters. These analytical forms are sufficient to describe the properties of the nuclear parts. The six parameters for each dataset are studied using fits to data with appropriate statistical control. Correlations are studied, and resulting values are proposed for each dataset. Good description of the measurements is obtained, with details in the shape of the forward diffractive peak, exhibiting the zero of the real par...

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Section: Discussionmentioning

confidence: 99%

Section: Amplitudes and Observables In Forward Scatteringmentioning

confidence: 96%

Section: Appendix A: Coulomb Phasementioning

confidence: 99%

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Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV

et al. 2017

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“…[5]- [9]). Then the complete scattering amplitude has been written in the simplified form [5] (for details see Ref.…”

Section: The West and Yennie Formulamentioning

confidence: 99%

Phenomenological models of elastic nucleon scattering and predictions for LHC

et al. 2011

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“…(6.3)The integrals that appear in the evaluation of Eq. (6.1) are reduced to the form[18] 1 − e B(t −t)/2 , (6.4) that is solved in terms of exponential integrals[19] asI(B) = E 1 [ B 2 4p 2 + t ] − E i [ − Bt 2 ] + ln [ B 2 4p 2 + t ] + ln [ − Bt 2 ] + 2γ . (6.5)The real and imaginary parts of the phase are then writtenΦ R (s, t) = (−/+) ln − t s + 1 c 2 + 1 c 2 I(B R ) + I(B I ) ,(6.6) and Φ I (s, t) = (−/+) c c 2 + 1 I(B I ) − I(B R ) .…”

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confidence: 99%

Amplitudes and observables in pp elastic scattering at $\sqrt{s}=7\ \mbox{TeV}$

2013

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A precise analysis of the pp elastic scattering data at 7 TeV in terms of its amplitudes is performed as an extension of previous studies for lower energies. Slopes B R and B I of the real and imaginary amplitudes are independent quantities, and a proper expression for the Coulomb phase is used. The real and imaginary amplitudes are fully disentangled, consistently with forward dispersion relations for amplitudes and for slopes. We present analytic expressions for the amplitudes that cover all t range completely, while values of total cross section σ, ratio ρ, B I and B R enter consistently to describe forward scattering.It is stressed that the identification of the amplitudes is an essential step for the description of elastic scattering, and pointed out the importance of the experimental investigation of the transition range from non-perturbative to perturbative dynamics, that may confirm the three gluon exchange mechanism observed at lower energies.

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Interference between Coulomb and hadronic scattering in elastic high-energy nucleon collisions

Cited by 18 publications

References 32 publications

Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV

Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV

Phenomenological models of elastic nucleon scattering and predictions for LHC

Amplitudes and observables in pp elastic scattering at $\sqrt{s}=7\ \mbox{TeV}$

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