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

Abstract

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...

New feature in the differential cross sections at 13 TeV measured at the LHC

“…There are many different semi-phenomenological models which give a qualitatively description of the behavior of the differential cross sections of the elastic proton-proton scattering at √ s = 13 TeV (for example [16,17,18]. Some examples can be found in the review [19]; hence, we do not give a deep analysis of those models.…”

The interplay of hadronic amplitudes and Coulomb phase in LHC measurements at 13 TeV

“…As in the previous paper for 7 and 8 TeV [2], we identify in the 13 TeV data the real and imaginary amplitudes, and extract from the data the information on the parameters. The results for the real part are compared with predictions for ρ and for amplitude derivative D R from dispersion relations [3].…”

“…13 TeV in the −t range from 0.0008 to 0.1996 GeV 2 . The Coulomb interference phase is calculated according to KF [2] subtracting constant values 2 and 3 radians. Attention must be given to the apparently small changes in σ, since they are direct cause of the changes in ρ.…”

“…In the present study of forward data, each part of the amplitude is written with an exponential factor with a slope, multiplying a linear term in t, thus with three parameters. We consider that this is (almost) a model free construction, as these analytical forms are necessary and sufficient to describe the properties of the nuclear parts and yet are able to describe forward data with accuracy [2,3]. The six parameters are studied using fits to data with appropriate statistical control.…”

“…The parameters µ I and µ R , with their roles of pointing towards zeros in the amplitudes, are very important for the accurate description of the forward elastic data [2,3].…”