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M. Pavon Valderrama

Publications and source records attributed to M. Pavon Valderrama.

35 records · Page 2Linked to original sources
arXiv2008

Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space

The renormalization of the chiral np interaction in the 1S0 channel to N3LO in Weinberg counting for the long distance potential with one single momentum and energy independent counterterm is carried out. This renormalization scheme yields finite and unique results and is free of short distance off-shell ambiguities. We observe good convergence in the entire elastic range below pion production threshold and find that there are some small physical effects missing in the purely pionic chiral NN potential with or without inclusion of explicit Delta degrees of freedom. We also study the renormalizability of the standard Weinberg counting at NLO and N2LO when a momentum dependent polynomial counterterm is included. Our numerical results suggest that the inclusion of this counterterm does not yield a convergent amplitude (at NLO and N2LO).

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arXiv2007

Deuteron form factors in chiral effective theory: regulator-independent results and the role of two-pion exchange

We evaluate the deuteron charge, quadrupole, and magnetic form factors using wave functions obtained from chiral effective theory ($χ$ET) when the potential includes one-pion exchange, chiral two-pion exchange, and genuine contact interactions. We study the manner in which the results for form factors behave as the regulator is removed from the $χ$ET calculation, and compare co-ordinate- and momentum-space approaches. We show that, for both the LO and NNLO chiral potential, results obtained by imposing boundary conditions in co-ordinate space at $r=0$ are equivalent to the $Λ\to \infty$ limit of momentum-space calculations. The regulator-independent predictions for deuteron form factors that result from taking the $Λ\to \infty$ limit using the LO $χ$ET potential are in reasonable agreement with data up to momentum transfers of order 600 MeV, provided that phenomenological information for nucleon structure is employed. In this range the use of the NNLO $χ$ET potential results in only small changes to the LO predictions, and it improves the description of the zero of the charge form factor.

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arXiv2007

Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.

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arXiv2007

Renormalization Group Analysis of Boundary Conditions in Potential Scattering

We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting equation can be interpreted as a variable phase equation of a complementary boundary value problem. We discuss the corresponding infrared fixed points and the perturbative expansion around them generating a short distance modified effective range theory. We also discuss ultraviolet fixed points, limit cycles and attractors with a given fractality which take place for singular attractive potentials at the origin. The scaling behaviour of scattering observables can analytically be determined and is studied with some emphasis on the low energy nucleon-nucleon interaction via singular pion exchange potentials. The generalization to coupled channels is also studied.

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arXiv2006

Renormalization of Singular Potentials and Power Counting

We analyze the renormalization of the nucleon--nucleon interaction at low energies in coordinate space for both one and two pion exchange chiral potentials. The singularity structure of the long range potential and the requirement of orthogonality respectively determines, once renormalizability is imposed, the minimum and maximum number of counterterms allowed in the effective description of the nucleon--nucleon interaction in a non-perturbative context.

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arXiv2006

Deuteron radial moments for renormalized chiral potentials

We calculate deuteron positive and negative radial moments involving any bilinear function of the deuteron S and D wave functions for renormalized OPE and TPE chiral potentials. The role played by the strong singularities of the potentials at the origin and the short distance insensitivity of the results when the potentials are fully iterated is emphasized as compared to realistic potentials.

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arXiv2006

Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Non-Central Phases

We extend the renormalization of the NN interaction with Chiral Two Pion Exchange Potential to the calculation of non-central partial wave phase shifts with total angular momentum j<=5 . The short distance singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines exactly the number of undetermined parameters after renormalization.

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arXiv2006

Chiral Expansion, Renormalization and the Nuclear Force

The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.

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arXiv2006

Pion Deuteron Scattering and Chiral Expansions

We discuss convergence issues as well as short distance constraints on the deuteron wave functions based on chiral perturbation theory relevant to pion deuteron scattering. Non-analytical terms arise in the multiple scattering series for the pion-deuteron scattering length limiting the accuracy of the calculations. This result resembles similar findings in the structure of the NN interaction. The effects are found not to be numerically large. The iso-scalar $πN $ scattering length from the iso-vector one and the $πd$ scattering length yields values compatible with the experimental number and with much smaller errors.

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arXiv2006

Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Central Phases and the Deuteron

We analyze the renormalization of the NN interaction at low energies and the deuteron bound state through the Chiral Two Pion Exchange Potential assumed to be valid from zero to infinity. The short distance Van der Waals singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines that, after renormalization, in the 1S0 singlet channel and in the 3S1-3D1 triplet channel one can use the deuteron binding energy, the asymptotic D/S ratio and the S-wave scattering lengths as well as the chiral potential parameters as independent variables. We use then the asymptotic wave function normalization As of the deuteron and the singlet and triplet effective ranges to determine the chiral constants yielding c1, c3 and c4. The role of finite cut-off corrections, the loss of predictive power due to uncertainties in the input data and the connection to OPE distorted waves perturbative approaches is also discussed.

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arXiv2005

Renormalization of the Deuteron with One Pion Exchange

We analyze the deuteron bound state through the One Pion Exchange Potential. We pay attention to the short distance peculiar singularity structure of the bound state wave functions in coordinate space and the elimination of short distance ambiguities by selecting the regular solution at the origin. We determine the so far elusive amplitude of the converging exponential solutions at the origin. All bound state deuteron properties can then be uniquely deduced from the deuteron binding energy, the pion-nucleon coupling constant and pion mass. This generates correlations among deuteron properties. Scattering phase shifts and low energy parameters in the 3S1-3D1 channel are constructed by requiring orthogonality of the positive energy states to the deuteron bound state, yielding an energy independent combination of boundary conditions. We also analyze from the viewpoint of short distance boundary conditions the weak binding regime on the light of long distance perturbation theory and discuss the approach to the chiral limit.

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arXiv2004

Singlet NN Regularization using a Boundary Condition for OPE and TPE potentials

Boundary conditions provide a simple and physically compelling Wilsonian renormalization method in coordinate space in the framework of effective field theory as applied to nucleon-nucleon interaction in the non perturbative regime, enabling to remove unphysical regularization cut-offs while keeping physical low energy threshold parameters such as the scattering length and effective range invariant. We illustrate how the method successfully works in the $^1S_0$ channel for the One Pion Exchange (OPE) and Two Pion Exchange (TPE) potentials

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arXiv2004

Determination of low energy parameters for NN-scattering at $N^4 LO$ in all partial waves with $j\le 5$

The Variable S-matrix approach offers a unique way to extract low energy threshold parameters for a given NN potential. We extract those parameters for the np system from the NijmII and Reid93 potentials, to all partial waves with total angular momentum $j \le m5 $, using the generalized effective range expansion % $$ ({\bf f}^{sj})_{l,l'} k^l k^{l'} = -({{\bf a}^{sj}}^{-1})_{l,l'} + \frac12 ({\bf r}^{sj})_{l,l'} k^2 + ({\bf v_2}^{sj})_{l,l'} k^4 + + ({\bf v_3}^{sj})_{l,l'} k^6 + + ({\bf v_4}^{sj})_{l,l'} k^8 + ... - {\rm i} k^{l+l'+1} $$ % where $ {\bf f}^{sj} = ({\bf S}^{sj} - {\bf 1}) / (2 {\rm i} k) $ is the scattering amplitude and ${\bf S}^{sj}$ is the unitary S-matrix in coupled channel space with total spin $s$ and total angular momentum $j$. Our calculation includes all the relevant contributions of the full amplitude to order ${\cal O} (k^8) $ in the CM momentum. We also discuss the validity of the generalized effective range expansion in the region of analyticity $ k \le m_π/2$.

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arXiv2004

Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions

A non perturbative renormalization scheme for Nucleon-Nucleon interaction based on boundary conditions at short distances is presented and applied to the One Pion Exchange Potential. It is free of off-shell ambiguities and ultraviolet divergences, provides finite results at any step of the calculation and allows to remove the short distance cut-off in a suitable way. Low energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are eliminated. This allows to compute scattering phase shifts which are, by construction consistent with the effective range expansion to a given order in the C.M. momentum $p$. In the singlet $^1S_0$ and triplet $^3S_1- ^3D_1$ channels ultraviolet fixed points and limit cycles are obtained respectively for the threshold parameters. Data are described satisfactorily up to CM momenta of about $p \sim m_π$.

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arXiv2003

Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions

We present a simple and physically compelling boundary condition regularization scheme in the framework of effective field theory as applied to nucleon-nucleon interaction. It is free of off-shell ambiguities and ultraviolet divergences and provides finite results at any step of the calculation. Low energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are removed. This allows to compute scattering phase shifts which are, by construction consistent with effective range expansion to a given order in the CM momentum and are free from finite cut-off artifacts. We illustrate how the method works in the $^1S_0$ channel for the One Pion Exchange potential.

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arXiv2001

The Inverse Amplitude Method in $ππ$ Scattering in Chiral Perturbation Theory to Two Loops

The inverse amplitude method is used to unitarize the two loop $ππ$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.

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